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Surface Chemkin User Manual - CVD Group

1. 10 11 12 13 SITE PLANE SDEN 1 04E 9 PLANAR SITE ASH V FIRST SPECIES ON PLANE SITE ASH2 V ASH3 V H S CH3 V AS V AS2 V 2 V EMPTY PLANAR SITE END AN END STATEMENT IS OPTIONAL SITE LEDGE SDEN 1 66E 10 LEDGE SITE GACH L FIRST SPECIES ON LEDGE DMG L 2 THIS SPECIES OCCUPIES 2 SITES E EMPTY LEDGE SITE SITESDEN 1 0E 10 GA S SITE WITH ONLY ONE SPECIES SITE NAME NOT INCLUDED Figure 7 Sample Site Data Table 1 Summary of the Rules for Site D ata Site data must start with a line containing the word SITE followed by an optional slash delimited name i e SITE name The standard state site density is required as a slash delimited number in moles cm following the word SITE and or the site name and preceded by the word SDEN The site density is followed by one or more site species name declarations Declaring a site with no site species is an error Site and species names are composed of up to sixteen upper or lower case character symbols The names cannot begin with the characters or a number an ionic species name may end with one or more or signs an embedded plus sign must be enclosed in parentheses Names cannot include a slash All species names should be unique duplicate species names will be ignored and a warning issued A spec
2. 62 ISKWRK ISKWRK IiIYLD N 1 N 1 NIIYLD reaction indices 63 ISKWRK ISKWRK IiYION N 1 N 1 NIIYLD ion indices 64 ISKWRK ISKWRK IiKYLD N 1 MAXSPR L 1 yield flags L 1 MAXSPR N 1 NIIYLD 65 RSKWRK ISKWRK IrPYLD N 1 NYPAR L 1 yield parameters L 1 NYPAR N 1 NIIYLD 66 RSKWRY ISKWRY IrYNCF N 1 NPHASE L 1 phase balance L 1 NPHASE N 1 NIIYLD 170
3. KKKKKK SUBROUTINE SKIENR IR ISKWRK SKWRK IENRFL IEION PEDEP Returns an integer flag to indicate if reaction IR is ion energy dependent and if so formulation specific parameters INPUT IR Integer scalar reaction index ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT IENRFL Integer scalar 0 reaction IR does not have an ion energy dependenc 1 reaction IR does have an ion energy dependenc IEION Integer scalar species index of the ion on which reaction is dependent PEDEP Real array supplemental parameters for an ion energy dependent reaction rate formulation dimension at least NEDPAR the number of supplemental rate parameters required 111 SKINDX SKINDX SKINDX SKINDX SKINDX SKINDX SKINDX KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKAKKKKKKKK KKKKKK T SUBROUTINE SKINDX ISKWRK NELM KKGAS KKSUR KKBULK KKTOT NNPHAS NNSURF NFSURF NLSURF NNBULK NFBULK NLBULK IISUR Returns a group of indices defining the size of the surface reaction mechanism INPUT ISKWRK Integer workspace array dimension at least LENISK OUTPU NELM Integer scalar total element count KKGAS Integer scalar total gas phase species count KKSUR Integer scalar total surf
4. s W k 1 Ke 69 where n is the unit inward pointing normal vector to the surface and the gas phase diffusion velocities are related to the species and temperature gradients by K T 1 g D VT E r E bei ky 70 XW a PY T Here the X are the gas phase mole fractions the Y are the gas phase mass fractions W is the mean molecular weight Dj is the ordinary multicomponent diffusion coefficient matrix and the Dj are the thermal diffusion coefficients Both types of diffusion coefficients can be evaluated by calls to the TRANSPORT Package In nonreacting fluid mechanics the fluid velocity normal to a solid wall is zero However if there are chemical reactions at the wall then the velocity can be nonzero This so called Stefan flow velocity occurs when there is a net mass flux between the surface and the gas The induced Stefan velocity is given by 1 K Y s Wi 71 P k sl n The expression for the Stefan velocity is easily obtained from the interfacial mass balance Eq 69 by summing over all K species and noting that the mass fractions must sum to one i e 3 gt Il Pa and that the sum of the diffusion fluxes must be zero i e 44 Y V 0 73 Exothermicity or endothermicity of surface reactions contributes to the energy balance at an interface Diffusive and convective fluxes in the gas phase are balanced by thermal radiative and chemical heat release at the surface T
5. FEAS SEA Led 5620E08 0967E08 0000E05 5620E08 0000E15 0000E15 1685 000 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 6006564E 13 3077030E 04 QA 0 00 DOM O ww OQ OO OO O OOO oo SS YN P4S0YNP QYNA A AS QYQNPAS YN YN AS QQ NP YN F 9 5 Output from SURFACE CHEMKIN Interpreter CHEMKIN SURFACE MECHANISM INTERPRETER H DOUBLE PRECISION Vers 7 20 2000 06 18 C T opyright 1995 Sandia Corporation he U S Government retains a limited license in this software CKLIB CHEMKIN GAS PHASE CHEMICAL KINETICS LIBRARY DOUBLE PRECISION Vers 5 28 2000 08 05 Copyright 1995 Sandia Corporation The U S Government retains a limited license in this software SPECIES MOLECULAR ELEMENT COUNT CONSIDERED WEIGHT Density Nsites H N SIF Gas phase species Ta H2 2 01594 2 0 0 0 2 H 1 00797 1 000 0 3 N2 28 01340 0 2 0 0 4 N 14 00670 Qsrbi O 0 5 NH 15 01467 1 1 0 0 6 NH2 16 02264 2 1 0 0 7 NNH 29 02137 L 2 O O 8 N2H2 30 02934 Dis 2 00 0 9 N2H3 31 03731 3 2 0 0 10 N2H4 32 04528 4 2 0 0 11 HF 20 00637 Lee Or 0 lt i 12 F 18 99840 05 20 O all 13 SIF4 104 07960 O 0 1 4 14 SIF3 85 08120 O Qd 15 SIHES 86 0891
6. Column Any 1 to 30 1 to 18 19 to 24 25 to 44 45 46 to 55 56 to 65 66 to 73 74 to 78 80 81 to 100 1 to 75 80 1 to 75 80 1 to 60 80 Any Alternative lines for more than 2 temperature intervals in place of Lines 4 6 above TEMP followed by space delimited minimum fit temperature common temperatures in increasing order and maximum fit temperature Coefficients a a5 for a temperature interval Coefficients ag a7 for a temperature interval A4 Free 5 E15 8 2 E15 8 a Use only when all the thermodynamic data are to be taken from Interpreter input b Include line 2 only with THERMO ALL it is already in the Thermodynamic Database 58 1 to 80 1 to 75 1 to 30 5 5 Surface Reaction Mechanism Description The surface reaction mechanism may consist of any number of chemical reactions involving the solid species named in the site and bulk data as well as the gas phase species declared in the gas phase CHEMKIN Interpreter A reaction may be reversible or irreversible Reaction data must start with the word REACTIONS or REAC On the same line the user may specify units of the Arrhenius rate coefficients to follow by including the words CAL MOLE KCAL MOLE JOULES MOLE KJOULES MOLE EVOLTS or KELVINS to indicate the units for all rate parameters that have energy units e g the activation energy E of Eq 35 an ion energy such as Ejon or Ejon0 Of Eq 51 or Eyicia of Eq 62 The s
7. E 15 ONO UU o FH 0000 e b s OO GOO 9 7 Sample FORTRAN Application Program PROGRAM SDRIV AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA AAA This is Surface by th the driver routine for SKSAMPLE th xample code for Chemkin The file is used to make sksample exe The parameters and unit numbers that may be changed user are described below unit LIN LOUT LINC LINS dime LIWO LRWO LCWO ATOL RTOL 2000000000 0004001000400000900000UM0 numbers user Keyword input formatted solution and diagnostic printing output K gas phase Chemkin Linking File K Surface Chemkin Linking File nsions ti RK maximum integer workspace available for SKSAMPLI RK maximum real workspace available for SKSAMPLE ti RK maximum character workspace available for SKSAMPLI numerical tolerances for solution convergence the absolute tolerance for solution values the relative tolerance for solution values OR RR RR RR RR RR RN RR RR RR RR SR ATTA AAA TATA AAT ATTA TATA TATA TTT TT IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N E PARAMETER LIN 5 LOUT 6 LINCK 25 LINSK 26 RTOL 1 0E 6 1 ATOL 1 0E 15 LIWORK 4000 LRWORK 4500 LCWORK 200 2 ZERO 0 0 e DIMENSION IWORK LIWORK RWORK LRWORK CHARACTER 16
8. INPUT P Real scalar pressure cgs units dynes cm 2 TEE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ACT Real array activities of the species dimension at least KKTOT the total species count The first KKGAS activities are mole fractions the next KKSURF activities are site fractions species density normalized by the site density surface concentration in moles cm 2 is ACT K SITE_DENSITY sites per species and the next KKBULK activities for bulk phase species should be from 0 to 1 and should sum to 1 for each phase SDEN Real array site densities for the site types dimension at least NPHASE the total phase count but the subroutine only uses site phas ntries NFSURF lt N lt NLSURF cgs units moles cm 2 ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK T OUTPUT CZ Real array gas phase and surface species concentrations and bulk species activities dimension at least KKTOT the total species count The first KKGAS gas phase concentrations are moles cm 3 the next KKSURF site concentrations are moles cm 2 and the final KKBULK entries are bulk species activities 95 SKATHM SKATHM SKATHM SKATHM SKATHM SKATHM SKATHM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
9. In a later section we discuss mass action kinetics where the rate of progress of reactions depends on molar concentrations either in the gas phase or on surface sites and activities in the bulk phases However for the purposes of formulating and solving the conservation equations that describe physical situations it is often more natural to use gas phase mass fractions and surface site fractions as dependent variables Therefore it is important to establish the rules for converting between the different ways to describe the composition of the gas and the surface 29 For the gas phase species the molar concentrations X in moles cm3 are written as X Y p W k xf KL 7 e I Y p We 2 Ey 7 where the Y are the mass fractions p is the gas phase mass density and the W are the molecular weights On the surface sites we can describe the composition in terms of an array of surface species site fractions Z This array is of length K It is composed of N subunits of the site fractions of each of the species on a given site phase n The site fractions on each site are normalized Kin gt Zum 1 ho Nos N 8 k K n The sum in Eq 8 runs from the first species in phase n to the last species in phase n The surface molar concentration of a species is then X Z 0 0 m 9 where T is the density of sites of phase n in moles cm2 and o n is the number of sites that each species k occupies For the s
10. Integer scalar number of elements Integer scalar number of gas phase species Integer scalar number of surface site species Integer scalar number of bulk species Integer scalar total number of species Integer scalar total number of phases Integer scalar number of surface phases Integer scalar number of bulk phases Number of surface reactions Number of reactions for which sites are not conserved Integer scalar flag if gt 0 indicates another material follows this one in the linking file Integer scalar flag if gt 0 indicates an error occurred during reading of the linking file SKMXTP SKMXTP SKMXTP SKMXTP SKMXTP SKMXTP KKEKKKK KKK KKK KKK KK KKK KKK KKK KKK KKK KKK KKK KKK KKEKEKK KKKKKKKKKKKKKKKKKKKKK KKKKKK SKMXTP ISKWRK MXTP KKKKK he maximum number of temperatures used in e thermodynamic properties of t Integer workspace array dime Integer scalar maximum numbe fitting the thermodynamic pro 119 he species nsion at least LENISK r of temperatures used in perties of the species SKNCF SKNCF SKNCF SKNCF SKNCF SKNCF SKNCF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKNCF NELDIM ISKWRK NEL Returns the elemental composition of the species INPUT NELDIM Integer scalar first dimension of the matrix NEL must be at least NELEM
11. OUTPUT IBMFL Integer scalar flag for Bohm reactions 0 reaction IR does not use BOHM sticking coefficients 1 reaction IR does use BOHM sticking coefficients 110 SKICOV SKICOV SKICOV SKICOV SKICOV SKICOV SKICOV KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKICOV IR NDIM ISKWRK RSKWRK NCOVI KCOVI CPARI Returns the coverage species index numbers and their coverage parameters for reaction IR INPUT IR Integer scalar surface reaction index NDIM Integer scalar first dimension of array CPAR the coverage parameters NDIM must be at least NSCOV the total number of coverage parameters ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT NCOVI Integer scalar total number of species that modify the rate of reaction IR through coverage dependence KCOVI Integer array species indices for the NCOVI species that modify the rate of a coverage dependence reaction dimension at least KKTOT the total species count CPARI Real matrix coverage parameters for the coverage species of reaction IR dimension at least NSCOV for the first the number of coverage parameters required and at least KKTOT for the second the total species count SKIENR SKIENR SKIENR SKIENR SKIENR SKIENR SKIENR ee ee eee ee ee RAR KKKKKKKKKKKKKKKKKKKKKKKKKK
12. dimension at least NPHASE the total phase count but subroutine calculates entries only for site phases cgs units moles cm 2 sec SKRDEX SKRDEX SKRDEX SKRDEX SKRDEX SKRDEX SKRDEX KKKKKKKK RA RR RR RA kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkkkkkkxk KKKKKK SUBROUTINE SKRDEX IR ISKWRK RSKWRK RD Returns the perturbation factor of the IRth reaction or changes its value depending on the sign of IR INPUT IR Integer scalar reaction index IR gt 0 gets RD I from RSKWRK IR lt 0 puts RD I into RSKWRK ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK If IR lt 0 RD Real scalar perturbation factor for reaction IR OUTPUT If IR gt 0 RD Real scalar perturbation factor for reaction IR 126 SKRHI Gl X SKRHEX SKRHEX SKRHEX SKRHEX SKRHEX SKRH ARKRARKAR RA RR RA RARA RARA RARA RARA RARA RR KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTIN Returns a coefficie depending INPUT K ISKWRK RSKWRK TE Ko lt 0 A6 OUTPUT If K gt O Ao T SKRHEX K ISKWRK RSKWRK A6 n array of the sixth thermodynamic polynomial nts for a species or changes their value on the sign of K Integer scalar species index K gt 0 gets A6 from RSKWRK K lt 0 puts A6 into RSKWRK I R nteger workspace array dimension at least LENISK eal workspace ar
13. n of elemen nteger vec hin aca THANDHHDMDHN bi IRAY NN his subroutine can do everything that the subroutine SKCOMP can do has the capabilities of separa nto categories and then search IRAY by ele tegories that each element of IRAY will be charac ments of each ca ts in eac tor ISET tegory ISTR h category wit KKKKKK S ETS NSETS ISET Ea me er string vec hin I To search SKPCMP IND SKPCMP NT ng the elements of nt and category assigned to are tor SETS of vector length tegory in IRAY must be grouped congrously RAY is specified by for the existence of an may additionally be composed of two substrings ISTR ELEM ENT_NAM E CAT EGORY NA ER is one of the categori return the first posit the category CATEGORY_ times ELEMENT_NAME If ELEMENT NAME is not NT are returned with within ISTR from subroutine SKCOMP Consider t IRAY NN SE NSETS ISET RED 6 H COLORS 2 4 S T Gl 2 STONE s specified in SETS ion in NAME occurred withi found within th a value of zero IND and NT return wi I N he following example BLUE r EL Cur RAY where T will re EM n ENT_NAME sp If JADE RUBY TOPAZ Suse where CATEGO In this case occurre
14. n provide a subroutine of the form Y ML MU PD NROWPD RPAR IPAR PD RPAR ROWPD NEQ which supplies df dy by loading PD as follows For a ful the partial d For a ban df 1 dy j PD from the t In either each point at 1 Jacobian MF 21 erivative of f 1i w ML and MU arguments in this case ded Jacobian MF i e load the diago op down load PD i j with d 1 dy 3 ith respect to y j Ignore the 24 load PD i 3 MU 1 3 with nal lines of df dy into the rows of case only nonzero lements need be loaded D Write a main program which calls subroutine DVODE once for which answers ar desired This should also provide for possible use of logical unit 6 for output of error messages 160 OOOO OrO O70 Oy OA GQ Av Qs QO O A201 OX QOL O O 2 OO Arco OQ 2A QO Q O WOOO OA OY AcE A QQ by DVODI E N Y T TOUT ITOL RTOL ATOL E 10 ITASK ISTATI IOPT RWORK LRW IWORK LIW JAC MF Gl E The E On the first call to DVODE supply arguments as follows Name of subroutine for right hand side vector f This name must be declared external in calling program Number of first order ODE s Array of initial values of length NEQ The initial value of the independent variable First point where output is desired ne T 1 or 2 according as ATOL below is a scalar or array Relative tolerance
15. 3 420E 10 NH2 NNH 1 422E 11 N2H2 3 396E 10 N2H3 N2H4 5 744E 13 HF 2 829E 01 F SIF4 6 035E 02 SIF3 8 522E 11 SIHF3 SIF3NH2 1 277E 10 NH3 6 568E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 4 850E 02 SIF3NH2 S 1 534E 04 SIF2NH S NH2SIFNH S 2 084E 04 NHSIFNHSIFNH 4 171E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 4 700E 08 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 2 659E 08 TIME 1 000000000000000E 002 GAS PHASE STATE Pos 3 1752E 03 T 1 7130E 03 DENSITY 4 5844E 07 GAS PHASE MOLE FRACTIONS H2 5 055E 06 H 2 264E 08 N2 N 2 490E 13 NH 1 807E 09 NH2 NNH 7 943E 11 N2H2 1 742E 09 N2H3 N2H4 2 231E 12 HF 4 074E 01 F SIF4 2 667E 02 SIF3 5 378E 11 SIHF3 SIF3NH2 2 443E 10 NH3 5 659E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 2 927E 02 SIF3NH2 S 7 350E 05 SIF2NH S NH2SIFNH S 1 896E 04 NHSIFNHSIFNH 3 797E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 7 497E 08 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 3 963E 08 155 O O 15 000E 00 000E 00 000E 00 000E 00 000E 00 084E 02 9 159E 01 Bo GO OT 863E 10 428E 06 230E 11 559E 11 630E 11 1 291E 02 9 378E 01 ss OT dy 256E 09 011E 05 209E 11 104E 10 881
16. CONTINUE ENDIF IF NNBULK GT 0 THEN KFIRST IWORK NIPKF NFBULK 1 KLAST IWORK NIPKL NLBULK 1 DO 150 K KFIRST KLAST RWORK NACT K 1 RWORK NX K 1 CONTINUE ENDIF IF NNSURF GT 0 THEN DO 175 N NESURF NLSURF RWORK NSDEN N 1 Z KKTOT 1 N NFSURF 1 CONTINUE ENDIF CALL SKRAT P T RWORK NACT RWORK NSDEN IWORK NISK il RWORK NRSK RWORK NSDOT RWORK NSITDT Form mass density equation SUM 0 0 DO 200 K 1 KKGAS SUM SUM AVRAT RWORK NSDOT K 1 RWORK NWT K 1 CONTINUE ZP KKTOT 1 SUM Form the gas phase mass conservation equation DO 300 K WDOT WT SDOT ZP K 1 KKGAS RWORK NWDOT K RWORK NWT K RWORK NSDOT K 1 Z K ZP KKTOT 1 AVRAT SDOT WT 1 1 1 CONTINU Ra IF NNSURF GT 0 THEN Form the surface mass equations DO 410 N NFSURF NLSURF SITDOT RWORK NSITDT N SDENO RWORK NSDEN N KFIRST IWORK NIPKF N KLAST IWORK NIPKL N DO 400 KFIRST KLAST SDOT RWORK NSDOT K RCOV RWORK NRCOV K ZP K SDOT RCOV Z K CONTINU CONTINUE ENDIF 1 1 1 1 1 Gl IF NNBULK GT Form the KFIRST KLAST DO 500 0 THEN bulk mass equations IWORK NIPKF NFBULK IWORK NIPKL NLBULK KFIRST KLAST K 152 WDOT WT Z KKTOT 1 1 SITDOT SDE E 1 1 C 500 575 ZP CONTI ENDI
17. GT 0 TH Initial surface si KFIRST KLAST DO 110 RWOR CONTINU ENDIF NNBULK GT Initial bulk deposi JE KFIRST KLAST DO 120 K FINN IWORK NIP IWORK NIP KFIRST NZ K 1 0 TH IWORK NIP EN te fractions KF NFSURF KL NLSURF KLAST RWORK NX E A amounts KF NEBULK 1 1 IWORK NIP KFIRST KL NLBULK KLAST 149 ana ana ana RWORK NZ K 1 0 0 120 CONTINUE ENDIF Initial gas phase mass density CALL CKRHOY P T RWORK NZ IWORK RWORK RWORK NZ KKTOT IF NNSURF GT 0 THEN Initial surface site densities DO 130 N NFSURF NLSURF IZ NZ KKTOT 1 N NESURF RWORK IZ RWORK NSDEN N 1 Z KKTOT 1 N NFSURF 1 RWORK NSDEN N 1 130 CONTINUE ENDIF Gl Integration control parameters for LSOD TT2 TT1 MF 22 ISTATE 1 Integration loop 250 CONTINU Gl Print the solution CALL CKPY RWORK NZ KKTOT T RWORK NZ IWORK RWORK P WRITE LOUT WRITE LOUT TIME TT2 WRITE LOUT 7100 P T RWORK NZ KKTOT WRITE LOUT GAS PHASE MOLE FRACTIONS CALL CKYTX RWORK NZ IWORK RWORK RWORK NX CALL PRT1 KKGAS CWORK IKSYM LOUT RWORK NX IF NNSURF GT 0 THEN DO 190 N NFSURF NLSURF WRITE LOUT I SURFACE SITE FRACTIONS ON PHASE SITE N KKPHAS IWORK NIPKK N 1 KFIRST IWORK NIPK
18. IF LIWORK LT ITOT OR LRWORK LT NTOT OR LCWORK LT LCTOT THEN IF LIWORK LT ITOT WRITE LOUT dk ERROR IWORK must be at least ITOT IF LRWORK LT NTOT WRITE LOUT al ERROR RWORK must be at least NTOT IF LCWORK LT LCTOT WRITE LOUT 1 ERROR CWORK must be at least LCTOT RETURN ENDIF CALL SKPKK IWORK NISK IWORK NIPKK IWORK NIPKF IWORK NIPKL CALL SKSDEN IWORK NISK RWORK NRSK RWORK NSDEN CALL SKCOV IWORK NISK IWORK NICOV DO 30 K 1 KKTOT RWORK NRCOV K 1 IWORK NICOV K 1 RWORK NX K 1 0 0 CONTINUE CALL SKSYMS IWORK NISK CWORK LOUT CWORK IKSYM IERR KERR KERR OR IERR CALL SKSYMP IWORK NISK CWORK LOUT CWORK IPSYM IERR KERR KERR OR IERR CALL SKWT IWORK NISK RWORK NRSK RWORK NWT CALL SKRP IWORK NISK RWORK NRSK RU RUC PATM IF KERR THEN WRITE LOUT STOP ERROR INITIALIZING CONSTANTS RETURN ENDIF Pressure and temperature WRITE LOUT A 1 INPUT INITIAL PRESSURE ATM AND TEMPERATURE K READ LIN PA T WRITE LOUT 7105 PA T P PA PATM Initial non zero moles CONTINUE LINE WRITE LOUT A INPUT INITIAL ACTIVITY OF NEXT SPECIES READ LIN A END 45 LINE WRITE LOUT 1X A LINE ILEN INDEX LINE IF ILEN EQ 1 GO TO 40 ILEN ILEN 1 IF ILEN LE 0 ILEN LEN LINE IF INDEX LINE 1 ILEN END EQ 0 THEN IF LINE 1 ILEN NE THEN CALL SKSNUM
19. KKTOT SDOT SITDOT Returns the partial derivative of the production rates of the species with respect to the activity for each species It also returns the matching production rates SUBROUTINE SKRAT P T ACT SDEN ISKWRK RSKWRK SDOT SITDOT Returns production rates for the species and sites SUBROUTINE SKRATI IR ROP ISKWRK RSKWRK SDOTI SITDTI Returns rates of production of the species by surface reaction IR 88 7 12 Equilibrium Constants and Rate of Progress Variables SUBROUTINE SKEQ P T ACT SDEN ISKWRK RSKWRK EQKC Returns the equilibrium constants for the surface reactions given pressure temperature species activities and the site densities SUBROUTINE SKROP P T ACT SDEN ISKWRK RSKWRK ROP Returns rates of progress for the surface reactions 7 13 Utilities SUBROUTINE SKCOMP ISTR IRAY NN IND NT Search for the occurrence of character string ISTR in the NN character strings of array IRAY IND is the first location in IRAY of ISTR if found or 0 if not found and NT is the total number of times it occurs Consider the following example IRAY BOOK BLUE BEAR BOOK NN 4 If ISTR BLUE then IND 2 and NT 1 if ISTR RED then IND 0 and NT 0 and if ISTR BOOK then IND 1 and NT 2 89 SUBROUTINE SKPCMP ISTR IRAY NN SETS NSETS ISET IND NT This subroutine can do everything that the subroutine SKCOMP can do and additionally has the capabilities of separat
20. OUTPUT KNUM NT NVAL RVAL SKSOR SUBROUTIN Returns a INPUT T ISKWRK RSKWRK OUTPUT SOR SKSYM Gl SUBROUTIN T Returns a INPUT CSKWRK LOUT UTPUT NAM Ho KERR Integer scalar species index if the species name appears in LINE Integer scalar number of times the species name occurs in the linkfile Integer scalar number of value character strings found in LINE Real array real values for their character strings in LINE dimension at least NEXP the number of values expected Logical syntax or dimensioning error flag SKSOR SKSOR SKSOR SKSOR SKSOR SKSOR KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKSOR T ISKWRK RSKWRK SOR array of the nondimensional entropies Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K Integer workspace array dimension at leas Real workspace array dimension at leas LENISK LENRSK cr ct Real array nondimensional entropies for the species dimension at least KKTOT the total species count SKSYME SKSYME SKSYME SKSYME SKSYME SKSYM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK Gl SKSYME ISKWRK CSKWRK LOUT ENAM KERR character strin
21. Real array rates of progress for the surface reactions dimension at least IISUR the total surface reaction count cgs units moles cm 2 sec ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT CIK Real array contributions of the surface reactions to the production rate of species KSPEC dimension at least IISUR the total surface reaction count cgs units mole cm 2 sec SKCOV SKCOV SKCOV SKCOV SKCOV SKCOV SKCOV KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KARA SUBROUTINE SKCOV ISKWRK KOCC Returns an array of site occupancy numbers for the species INPUT ISKWRK Integer workspace array dimension at least LENISK OUTPUT KOCC Integer array site occupancy numbers for the species dimension at least KKTOT the total species count 98 SKCPML SKCPML SKCPML SKCPML SKCPML SKCPML SKCPML KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKCPML T ISKWRK RSKWRK CPML Returns an array of the specific heats at constant pressure in molar units INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension a
22. SICL4 SI S BOHM ENRGDEP 1 0 5 1 0 UNITS EVOLT E CL SICL3 S SI B SICL S amp gt SICL2 S SICL2 SICL S BOHM YIELD 0 0712 1 21 0 5 1 0 UNITS EVOLT A Eth ev ab for A Ei a Eth a b END ATERIAL WALL SITE METAL SDEN 2 25E 9 AL S ALCL S END REACTIONS MWOFF CL E gt CL 0 6 0 0 BOHM CL AL S gt ALCL S 1 0 0 0 STICK END Figure 15 Interpreter Input File using Multiple M aterials 78 Q oo non qo Q PROGRAM RDLINK IMPLICIT DOUBLE PRECISION A H O Z INTEGER I N PARAMETER LINKCK 25 LINKSK 26 LOUT 6 MAXMAT 10 LENIWK 10000 LENRWK 10000 LENCWK 500 I R and C are integer real and character workspace arrays respectively DIMENSION I LENIWK R LENRWK CHARACTER 16 C LENCWK Dimension arrays specific to each material DIMENSION NPHASE MAXMAT IISUR MAXMAT KKSU MAXMAT KKBULK MAXMAT MAXMAT NNSU MAXMAT NFSURF MAXMAT NLSURF MAXMAT NNBULK MAXMAT NFBULK MAXMAT IMISK MAXMAT IMRSK MAXMAT IMCSK MAXMAT RE RE OPEN LINKCK FORM FORMATTED STATUS UNKNOWN FILE chem asc OPEN LINKSK FORM FORMATTED STATUS UNKNOWN FILE surf asc Q HEMKIN gas phase workspace required CALL CKLEN LINKCK LOUT LENICK LENRCK LENCCK IFLAG IF IFLAG GT 0 THEN STOP ENDIF ITOT LENICK NTOT LENRCK ICTOT LENCCK Set up counter and loop over multiple materials in SURFACE CHEMK
23. plasma systems which includes for example modeling the reactions of highly energetic ionic species with a surface Optional rate expressions allow reaction rates to depend upon ion energy rather than a single thermodynamic temperature In addition subroutines treat temperature as an array allowing an Application to define a different temperature for each species SURFACE CHEMKIN allows use of real non integer stoichiometric coefficients and an arbitrary reaction order with respect to species concentrations can also be specified independent of the reaction s stoichiometric coefficients Several different reaction mechanisms can be specified in the Interpreter input file through the construct of multiple materials CONTENTS LIST OF FIGURES NOMENCLATURE Pre exponential factor in sticking coefficient expression Activity of aii bulk phase species Coefficients to fits of thermodynamic data pt Standard state specific Helmholtz free energy for the k species Area Standard state Helmholtz free energy for the kth species Pre exponential factor in the rate constant of the i reaction Temperature exponent in sticking coefficient expression Activation energy in sticking coefficient expression Specific heat at constant pressure of the k species Standard state specific heat at constant pressure of the k species Ordinary multicomponent diffusion coefficients Thermal diffusion coefficient Activation energy in the rate c
24. reactions NYPAR 4 MAXORD Maximum number of change orders allowed in a reaction MAXTP Maximum number of temperatures allowed in fits of thermodynamic properties for any species MAXTP 3 NCP Number of polynomial coefficients to fits of CP R for a species NCP 5 NCP1 NCP 1 NCP2 NCP 2 NCP2T Total number of thermodynamic fit coefficients for species NCP2T MAXTP 1 NCP2 14 ISKWRK POINTERS TO INTEGER VARIABLES TiLENI ISKWRK IiLENI is the total length of ISKWRK required IiLENR ISKWRK IiLENR is the total length of RSKWRK required TiLENC ISKWRK IiLENC is the total length of CSKWRK required TiKSUR ISKWRK IiKSUR is the total surface species count TiKBLK ISKWRK IiKTOT is the total species count gas surface bulk IiNPHA ISKWRK IiNPHA is the total phase count TiFSUR ISKWRK IiFSUR is the phase index of the first site TiLSUR ISKWRK IiLSUR is the phase index of the last site IiNSUR ISKWRK IiNSUR is the total surface phage count IiFBLK ISKWRK IiFBLK is the phase index of the first bulk IiLBLK ISKWRK IiLBLK is the phase index of the last bulk TiNBLK ISKWRK IiNBLK is the total bulk phase count IiNIIS ISKWRK IiNIIS is the total surface reaction count TiNCOV ISKWRK IiNCOV is the total coverage reaction count TiNREV ISKWRK IiNREV is the total count of surface reactions which use explicit reverse parameters IiNSTK ISKWRK IiNSTK is the total count of sticking surface reactions IiNCON ISKWRK IiNCON is t
25. 02 0 3H 12187E 03 0 88747E 02 0 1 0 00 12187E 03 0 88747E 02 0 1 0 00 12187E 03 0 88747E 02 0 1 0 gt gt gt gt gt gt 18 84 52486288E 03 0 3S 20939481E 06 0 84 52486288E 03 0 28 20939481E 06 0 84 52486288E 03 0 18 20939481E 06 0 84 52486288E 03 0 3S 20939481E 06 0 84 52486288E 03 0 3S 20939481E 06 0 84 52486288E 03 0 000 20939481E 06 0 1F 1S 20939481E 06 0 97538E 00 0 OF os 97538E 00 0 1F 3S 97538E 00 0 1F 2S 97538E 00 0 1F 1s 97538E 00 0 2F 2S 97538E 00 0 000 OS 84197538E 00 0 52486288E 03 0 000 20939481E 06 0 000 OS 84197538E 00 0 52486288E 03 0 NHNH2 S SIF3NH2 S SIF2NH S NH2SIFNH S NHSIFNHSIFNH S 3NHSIF S SI D N D N D 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 1685 000 300 000 42757187E 1 0 83710416E 02 0 45272678E 0 HF HF HF HF HF HF 143
26. 04 0 44780081E 01 0 34298433E 01 0 25250392E 03 0 80470663E 06 0 33336490E 09 0 43425671E 13 0 37097800E 04 0 26751302E 01 0 37695923E 01 0 59256858E 03 0 21359336E 06 0 13644331E 08 0 63575666E 12 0 35908836E 04 0 78130486E 00 END Figure 9 Examples of Thermodynamic D ata Input 57 CASE 3 ALL THERMODYNAMIC DATA FROM INPUT o PRBRWNHERBWNHE NA Line Number last Table 3 Summary of the Rules for Thermodynamic D ata Contents THERMO or THERMO ALL Temperature ranges for 2 sets of coefficients lowest T common T and highest T Species name must start in Column 1 Date not used Atomic symbols and formula Phase of species S L or G for solid liquid or gas respectively Low temperature High temperature Common temperature if needed else blank Atomic symbols and formula if needed else blank The integer 1 Atomic symbols and formula if needed else blank Coefficients aq a5 in Eqs 19 21 for upper temperature interval The integer 2 Coefficients ag a7 for upper temperature interval and az a2 and a3 for lower The integer 3 Coefficients a4 a5 a6 a7 for lower temperature interval The integer 4 Repeat lines 3 6 for each species END Optional end of thermodynamic data Format Free 3F10 0 18A1 6A1 4 2A1 13 Al E10 0 E10 0 E8 0 2A1 13 n 4 2A1 13 5 E15 8 n 5 E15 8 n 4 E15 8 n Free
27. 1 2 RO mmary UTINE DVODE ISTAT RPAR EXTER NAL F JAC DOUBI E PRECISION F NEQ IOPT IPAR Y RWORK T TOUT LRW TE IW Y T INTEG ER NEQ ITOL 1 DIMEN 1 MF IPAR SION Y R RPAR ITASK TOL IPAR TOUT ISTATE ATOL RTOL ATOL IOPT RWORK eure ORK RTOL ATOL ITASK LIW JAC MF RWORK RPAR LRW IWORK LIW LRW IWORK LIW DVODE with This DVO sys DE dy dt dy i DVODE on he OD dt f t y f 1 EPACK user i or is a package based on the nterface standard Variable coefficient Ordinary Differe fixed leading coefficient implementatio version is in double precision solves the initial value problem for s tems of first order ODEs in component form f i t y 1 y 2 Y NI ntial n Equation solver tiff or nonstiff EO i 1 NEQ EPISODE and and EPISODEB packages with minor modifications Revision 890615 890922 910228 920227 920721 920722 920831 History YYM Date Writte Added inter Minor revis Modificatio 1 Applied 2 Changed 3 Added Names of ro DD n ns by D D u rupt restart ability ions in line format m P Pang subgennam to get generic intrinsic intrinsic names to
28. 1 714E 04 NHSIFNHSIFNH 3 433E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999992 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 030E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 066E 08 TIME 3 500000000000000E 002 GAS PHASE STATE Ps 3 3220E 03 T 1 7130E 03 DENSITY 4 3374E 07 GAS PHASE MOLE FRACTIONS H2 1 643E 05 H 2 429E 08 N2 N 1 300E 11 NH 2 974E 08 NH2 NNH 1 203E 09 N2H2 2 465E 08 N2H3 N2H4 2 412E 11 HF 5 121E 01 F SIF4 4 849E 04 SIF3 1 476E 12 SIHF3 SIF3NH2 3 723E 10 NH3 4 874E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 8 564E 04 SIF3NH2 S 1 450E 06 SIF2NH S NH2SIFNH S 1 709E 04 NHSIFNHSIFNH 3 422E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 038E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 093E 08 TIME 4 000000000000000E 002 GAS PHASE STATE P 3 3236E 03 T 1 7130E 03 DENSITY 4 3349E 07 GAS PHASE MOLE FRACTIONS H2 1 884E 05 H 2 486E 08 N2 N 1 831E 11 NH 3 881E 08 NH2 NNH 1 596E 09 N2H2 3 262E 08 N2H3 N2H4 3 121E 11 HF 5 132E 01 F SIF4 2 177E 04 SIF3 6 732E 13 SIHF3 SIF3NH2 3 743E 10 NH3 4 865E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 3 895E 04 SIF3NH2 S 6 515E 07 SIF2NH S NH2SIFNH S 1 707E 04 NHSIFNHSIFNH 3 418E 04 NHNH2 S SUM OF SURFACE SITE FRACTIO
29. CWORK LCWORK EXTERNAL CKTIME TSTART CKTIME ZERO Cc OPEN LINCK FORM FORMATTED STATUS UNKNOWN FILE chem asc OPEN LINSK FORM FORMATTED STATUS UNKNOWN FILE surf asc e CALL SKSAMP LIN LOUT LINCK LINSK ATOL RTOL LIWORK IWORK 1 LRWORK RWORK LCWORK CWORK Cc TEND CKTIME TSTART IF TEND GT 60 THEN WRITE LOUT A 1PE15 2 Total CPUtime min TEND 60 ELSE WRITE LOUT A 1PE15 2 Total CPUtime sec TEND ENDIF e CLOSE LINCK CLOSE LINSK STOP END 146 SUBROUTINE SKSAMP LIN LOUT LINCK LINSK ATOL RTOL LIWORK 1 IWORK LRWORK RWORK LCWORK CWORK IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N PARAMETER NLMAX 50 ITOL 1 IOPT 0 ITASK 1 DIMENSION IWORK LIWORK RWORK LRWORK COMMON RPAR T AVRAT RU COMMON IPAR KKGAS KKSURF KKBULK KKTOT NFSURF NLSURF NFBULK NLBULK NISK NIPKK NIPKF NIPKL NRSK NSDEN NRCOV NX NWDOT NWT NACT NSDOT NSITDT NNSURF N R WN CHARACTER CWORK LCWORK 16 LINE 80 LOGICAL KERR IERR EXTERNAL FUN DATA KERR FALS E s7 E Find lengths necessary for arrays CALL CKLEN LINCK LOUT LENI LENR LENC IFLAG1 CALL SKLEN LINSK LOUT LENIS LENRS LENCS IFLAG2 IF IFLAG1 GT 0 OR IFLAG2 GT 0 RETURN Q LITOT LENI LENIS LRTOT LENR LENRS LCTOT MAX LENC LENCS IF L
30. END BULK GA_RICH HASE 4 NPHASE 4 GA2AS 1 3 00 GA3AS 1 3 00 E DENSITY OF THE S OPTIONAL BULK GA POOR GAAS2 2 3 15 GAAS3 2 3 15 GAAS4 2 3 15 END IPHASE 5 NPHASE 5 BULK GA_STOICH PHASE 6 NPHASE 6 GAAS 3 5 24 BULK PHASE CAN HAV SPECIES BULK GA B 2 5581 PHASE 7 NPHASE 7 BULK AS B 2 7489 PHASE 8 NPHASE 8 REACTIONS ASH3 AS P lt gt ASH3 P AS B 4 0E11 0 GAME3 GA L lt gt GA CH3 3 L GA B 1 0E11 0 GA CH3 3 L GA2AS 1 lt gt AS GA CH3 L AME 1 0E13 0 EV 1 0E11 0 GA CH3 3 L GA3AS 1 lt gt AS GA L 3GAME 1 0E13 0 DUPLICATE GA CH3 3 L GA3AS 1 lt gt AS GA L 3GAME 1 0512 0 DUPLICATE GA2AS 1 lt gt GA B GAAS 3 TOETS O GAAS2 2 lt gt AS B GAAS 3 1 0E13 O GAAS3 2 lt gt AS2 GAAS 3 1 0E13 O GAAS4 2 lt gt AS B AS2 GAAS 3 1 0E13 0 END CH3 H2 2 CH3 CH3 903 600 2000 O000hH 220 550 540 2211 0E 1001 9201 3471 8711 GA CH3 CH4 H C2H6 C2H5 C2H4 H2 E 17 1 E 17 1 E 05 E 00 E 03 E 14 14 0 0 E 19 T BR 05 E 16 0 E 08 0 Figure 13 Sample Surface Reaction M echanism 72 OW BW ouoo OO 010 8750 8300 5210 2066 0 0 0 59500 JACKO AND PRIC 35410 CLARK amp DOV CLARK amp DOV MICHAEL GLAN amp TRO 1 IS THE ati ai CJ Gl
31. ES IS g 3 1 JUST ONE EA 30000 40000 40000 40000 40000 7 The data structure is illustrated in Fig 14 where each column represents a phase The gas phase is always the first phase the surface site phases are stored next followed by the bulk phases The species are stored sequentially beginning with the first gas phase species and ending with the last bulk species The gas phase species are listed in the same order as they were presented to the CHEMKIN Interpreter The species in the surface and bulk phases are in the same order as they appear in the Surface Interpreter input Gas Phase Surface Species Bulk Solids ASH3 15 ASH3 P 18 GA CH3 3 L 22 GAZAS 1 24 GAAS2 2 27 GAAS 3 28 GA B 29 AS B AS 16 ASH P 19 GA CH3 2 L 23 GA3AS 1 25 GAAS3 2 GAMES 17 AS P 20 GA CH3 L 26 GAAS4 2 GAME2 21 GA L GAME GA CH3 CH4 H 10 C2H6 11 C2H5 12 C2H4 13 H2 14 AS OPNPAPYN H Figure 14 Schematic Diagram of the Phase and Species D ata Structure There are several indices and arrays of indices that are quite useful in referencing particular species and phases They are returned from two subroutines SKINDX and SKPKK described in the following T SUBROUTINE SKINDX ISKWRK NELEM KKGAS KKSUR KKBULK KKTOT NNPHAS NNSURF NFSURE NLSURF NNBULK NFBULK NLBULK IISUR SUBROUTINE SKPKK ISKWRK KKPHAS KFIRST KL
32. INPUT EES Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT HMS Real array enthalpies for the species dimension at least KKTOT the total species count cgs units ergs gm 109 SKHORT SKHORT SKHORT SKHORT SKHORT SKHORT SKHORT ee ee ee ee ee A KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKHORT T ISKWRK RSKWRK HORT Returns an array of the nondimensional enthalpies INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT HORT Real array nondimensional enthalpies for the species dimension at least KKTOT the total species count SKIBHM SKIBHM SKIBHM SKIBHM SKIBHM SKIBHM SKIBHM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKIBHM IR ISKWRK IBMFL Returns an integer flag to indicate whether reaction IR uses BOHM sticking coefficients INPUT IR Integer scalar surface reaction index ISKWRK Integer workspace array dimension at least LENISK
33. It is up to the user s application program to ensure that the current site concentrations are correct Subroutines that return an array of species production rates also return an array of surface phase production rates which would all be zero if sites are conserved in every elementary reaction 3 3 Species Temperature Array In many modeling applications at each point in space there is a single scalar thermodynamic temperature However in models for multi fluid plasma systems for example one might solve a separate energy equation for each gas phase species or for groups of species Subroutines in the CHEMKIN and SURFACE CHEMKIN Libraries consider temperature to be an array The number of entries in the temperature array can be any number between 1 and the total number of gas phase species The example below illustrates how the temperature array may be defined and used in an Application DIMENSION T 3 HML KKTOT KTFL KKGAS KION KKGAS amp ISKWRK RSKWRK C C MAKE THE DEFAULT T T PERATURE FOR ALL C GAS PHASE SPECIES TEMPERATURE NUMBER 1 DO 100 K 1 KKGAS KTFL K 1 100 CONTINUE C C GET THE SPECIES NUMBER OF THE ELECTRON C THE NUMBER OF POSITIVE IONS IN THE MECHANISM C AND THEIR SPECIES NUMBERS CAL
34. K I IS of reac K I N ce react K 1 Is he speci K I N h species i K I Is coefficients Is of Is of Is stoic Is KW t KW t KW KW R R R R K I N he Lth species i K I Is he stoichiome species in the surface reactions is the sum of gas phas K I N hiometri K I Is KW ta K IiN n io KW es n KW for 1 AXS n IiN tric KWRK 1 c coeffi KW h SE RK IiCOV REA starts an array of the total ly for the surface reactions he reactant count for the Nth UNK e p starts a matrix of indices surface reactions R L 1 is the species index for h surface reaction U starts a matrix of stoichiometric species in the surface reactions PR L 1 is the stoichiometric the Nth surface reaction SUM starts an array containing sums coefficients of the gas phase only species the Nth surface reaction an array of reaction cients for starts indices for those with coverage parameters Is wi Is indices for th KW th KW R R K I N K I 1 is the reactio coverage parameters ISKWRK IiKCOV n index of the Nth reaction starts an array of species cover age dependendent species in the surface reactions with coverage parameters Is Nt Is KW KW R R K I N K I IS indices for t IS wi IS KW th KW
35. KKKKKK SUBROUTINE SKGMS T ISKWRK RSKWRK GMS Returns an array of the standard state Gibbs free energies in mass units INPUT EEE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT GMS Real array standard state Gibbs free energies for the species dimension at least KKTOT the total species count cgs units ergs gm 108 SKHML SKHML SKHML SKHML SKHML SKHML SKHML ee ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKHML T ISKWRK RSKWRK HML Returns an array of the enthalpies in molar units INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT HML Real array enthalpies for the species dimension at least KKTOT the total species count cgs units ergs mole SKHMS SKHMS SKHMS SKHMS SKHMS SKHMS SKHMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKHMS T ISKWRK RSKWRK HMS Returns an array of the enthalpies in mass units
36. LINE 1 ILEN 1 LOUT CWORK IKSYM KKTOT CWORK IPSYM NPHASE IWORK NIPKK KNUM NKF NVAL VAL IERR IF IERR THEN WRITE LOUT Error reading moles KERR TRUE ELSE RWORK NX KNUM 1 VAL ENDIF ENDIF ana AQ ana ana 45 50 55 60 110 GO TO 40 ENDIF CONTINUE IF KERR THEN WRITE LOUT STOP ERROR INITIALIZING USER INPUT RETURN ENDIF Surface area to volume ratio WRITE LOUT A INPUT SURFACE AREA TO VOLUME RATIO READ LIN AVRAT WRITE LOUT 7105 AVRAT Final time and print interval WRITE LOUT A INPUT FINAL TIME AND DT READ LIN Xi TZ DT WRITE LOUT 7105 T2 DT Normalize the mole fractions for each phase DO 60 N 1 NPHASE XTOT 0 0 KFIRST IWORK NIPKF N 1 KLAST IWORK NIPKL N 1 DO 50 K KFIRST KLAST XTOT XTOT RWORK NX K 1 CONTINUE IF XTOT NE 0 0 THEN DO 55 K KFIRST KLAST RWORK NX K 1 RWORK NX K 1 XTOT CONTINUE ELSE WRITE LOUT ERROR NO SPECIES WERE INPUT FOR PHASE CWORK IPSYM N 1 KERR TRUE ENDIF CONTINUE IF KERR THEN WRITE LOUT STOP ERROR INITIALIZING SOLUTION RETURN ENDIF Initial conditions TT1 0 0 Initial gas phase mass fractions IWORK RWORK RWORK NZ CALL CKXTY RWORK NX IF NNSURE
37. N but the substring before the slash is not a member of the subset associated with SETS N 122 NT SKPKK S UBROUTIN INPUT O K ISKWRK UTPUT KPHAS KFIRST KLAST SKPNT SUBROUTIN Reads fro ay ay IND 0 whether or not the substring is in IRAY Integer scalar total occurrence of ISTR in IRAY or total number of times ISTR occurs in a subset of IRAY SKPKK SKPKK SKPKK SKPKK SKPKK SKPKK ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKPKK ISKWRK KKPHAS KFIRST KLAST Returns arrays of species pointers for the phases Integer workspace array dimension at least LENISK OtHOMHORM H nteger array the total species counts for phases imension at least NPHASE the total phase count nteger array species indices for the first species of he phases imension at least NPHASE the total phase count nteger array species indices for the last species of he phases imension at least NPHASE the total phase count SKPNT SKPNT SKPNT SKPNT SKPNT SKPNT AR RARKARKRARR RARA RARA RARA RARA RARA RARA RARA RAR KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKPNT LSAVE LOUT VERS PREC LENI LENR LENC IERR ma file information about a SURFACE CHEMKIN linkfile pointers for the SURFACE CHEMKIN Library and returns lengths of work arrays INPUT L LOU
38. a gas phase mechanism from the file chem asc and create a Linking File surf asc of pertinent information about the surface mechanism and the species it involves The information in the SURFACE CHEMKIN Linking File is subsequently accessed by various subroutines in the SURFACE CHEMKIN Library to provide information on thermodynamic properties and chemical production rates Output from the interpreter is written to FORTRAN s standard output unit The Surface Interpreter input includes information on surface sites phases surface species bulk phases bulk species thermodynamic data and the reaction mechanism Interpreter input information is given in 80 column format An optional material name is read first followed by site data then by bulk data optional thermodynamic data may follow and optional reaction data are specified last Such sets of information can be repeated for any number of different materials The thermodynamic data for the species may come from the interpreter input file and or from a Thermodynamic Database therm dat The syntax for the four types of input is described below With the exception of the thermodynamic data all input is format free For the thermodynamic data we have chosen to use the same format as in the NASA Chemical Equilibrium code of Gordon and McBride and Gas phase CHEMKIN 5 1 Material Declaration Entirely different surface reaction mechanisms i e with different surface and bulk phases and sp
39. at least LENISK RSKWRK Real workspace array dimension at least LENRSK CSKWRK Character string workspace array dimension at least LENCSK IFLAG Integer scalar to indicate successful reading of linkfile IFLAG gt O is an error type 112 SKINU SKINU SKINU SKINU SKINU SKINU SKINU ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKINU IS NDIM ISKWRK RSKWRK NSPEC KI NU Returns the number of species in a surface reaction and the species indices and stoichiometric coefficients INPUT IR Integer scalar index number of a surface reaction IR must be greater than 0 and less than or equal to IISUR the total surface reaction count NDIM Integer scalar dimension of the arrays KI and NU NDIM must be at least MAXSPR the total number of species allowed in a surface reaction ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT NSPEC Integer scalar the number of species reactants products in surface reaction IR REA Integer array species indices for the species in surface reaction IR dimension at least MAXSPR the total number of species allowed in a surface reaction NU Integer array stoichiometric coefficients of the species in surface reaction IR dimension at least MAXSPR the total number of species allowed in a surface reaction NU is negative if the Nth species i
40. cm 2 is ntries dimension at least LENISK dimension at least LENRSK gas phase and surface species concen trations trations are moles cm 3 te concentrations are moles cm 2 k species activi and ties CY ACT K SITE_D the next KKBULK ac should be from 0 to 1 phase 100 INSITY sites per species and tivities for bulk phase species and should sum to 1 for each SKDEN SKDEN KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK SKDEN SKDEN SKDEN SKDEN SKDEN KKKKKKKKKKKKKKKKKKKKKKKKKK KARA SUBROUTIN Returns a INPUT P T ACT SDEN ISKWRK RSKWRK OUTPUT DEN T SKDEN P T ACT SDEN ISKWRK RSKWRK DI Real scalar cgs units Real array pressure species temperatures cgs units K Real array dimension The first at least dynes cm 2 temperature s real array of species densities Em Z So dimension is determined by the application program to be the total number of nominally 1 activities of the species KKTOT the total species count KKGAS activities are mole fractions the next KKSURF activities are site fractions species density normalized by the site density surface concentration in moles cm 2 is ACT K SITE DENSITY NFSURF lt N lt cgs units Integer workspace array Real workspa
41. concentration units the equilibrium constants are more easily determined from the thermodynamic properties in pressure units K they are related by Kg no Y Dri N Uki K n Pim 2 sh okela E sta 37 r e E BT oc i RT E He k Pi SKEQ where Pim denotes a pressure of 1 atm and I is the standard state surface site density of site type n The sum in the first exponent runs only over the gas phase species and the sum in the second exponent runs only over surface species in surface phase n The equilibrium constant K is obtained from the standard state Gibbs free energy of reaction AS AH K Et 38 yoo Sat E The A refers to the change that occurs in passing completely from reactants to products in the th reaction More specifically AS Es Se R 2 ki R o K o os 40 RE RE 3 6 Non Integer Stoichiometric Coefficients Previous versions of CHEMKIN and SURFACE CHEMKIN allowed only integer stoichiometric coefficients This was based upon the reasonable assumption that kinetic mechanisms would deal with elementary chemical reactions for which it makes little sense to talk about a fraction of a molecule participating as a product or reactant However in many real world applications the elementary reactions are not known Instead the kinetics may only be summarized in terms of global expressions In response to user requests CHEMKIN and SURFACE CHEMKIN allow use of non integer stoichiometric coefficients Exa
42. d 15 The UNITS auxiliary keyword can be used to override the current default units for parameters with energy units or the pre exponential for a given reaction The usage is UNITS string where string is one of the following EVOLTS KELVINS CAL MOLE KCAL MOLE JOULES MOLE or KJOULES MOLE for parameters with energy units or MOLES or MOLECULES for pre exponential 16 The string MWOFF can be used to turn off the Motz Wise correction of Eq 57 or the string MWON can be used to turn on this correction for a sticking coefficient reaction Using the MWOFF or MWON auxiliary keyword overrides the default option set up on the REACTION line or the default supplied by SURFACE CHEMKIN which is MWON 5 5 3 PROBLEMS HAVING NO REACTIONS In some problems only information about the surface and bulk species is needed e g chemical equilibrium computations For these cases it is not necessary to include reaction data The Interpreter will create the linking file surf asc but it will not contain any reaction information Therefore no subroutines in the SURFACE CHEMKIN Subroutine Library that deal with chemical reactions e g chemical production rates will be used although doing so would not generate an error the production rates of all species would be returned as zero 5 5 4 UNIT CONVERSION FOR PRE EXPONENTIAL FACTOR The SURFACE CHEMKIN Interpreter provides the option of specifying units of the Arrhenius parameters The paramet
43. dimer The surface mechanism in the example has two surface sites called PLANE and LEDGE There are five bulk mixtures phases although three of them are not actually mixtures but pure compounds The first three bulk mixtures have been assigned the names GA RICH GA POOR and GA STOICH whereas the remaining two have not been given any specific names The mechanisms have been contrived to illustrate a variety of points about the data structures and should not be taken as a source of data for Gallium Arsenide deposition processes 71 ELEMENTS GA SPECIES ASH3 AS2 AS H Cl GAME3 GAME2 GAME AS ND EACTIONS CH3 M lt gt C L TROE H2 2 6041 2H6 M 6927 CH3 H M lt gt LOW 8 0E26 H2 2 CH4 H lt gt CH3 C2H6 CH3 lt gt C C2H6 H lt gt C2H CH4 M 3 0 0 H2 2H5 CH4 5 H2 OW 3 18E41 7 03 2762 1322 H C2H4 M lt gt C2H5 M LOW 3 47E 1 2 2 76 2120 H2 2 C2H5 H lt gt CH3 H H M lt gt H2 M H H H2 lt gt H2 GAME 3 lt gt GAME GAME 2 lt gt GAME END Figure 12 Sample Gas Phase Reaction M echanism NPHASE 1 KKGAS SITE PLANE SDEN 1 0E 09 H 2 NPHASE 2 ASH3 P ASH P AS P SITE LEDGE SDEN 1 0E 13 HASE 3 NPHASE 3 GA CH3 3 L GA CH3 2 L GA CH3 L GA L
44. form and the usual rate expression We allow the sticking coefficient form only for the simple case of a surface reaction in which there is exactly one gas phase reactant species although there can be any number of surface species specified as reactants The sticking coefficients functional form is taken to be Y minll arar 52 1 l In this case a and b are unitless and c has units compatible with R SURFACE CHEMKIN also allows for surface coverage modification of a sticking coefficient analogous to Eq 48 We give three successively complex examples of using sticking coefficients First to specify that SiH2 g reacts with probability y upon each collision with the surface one could write the reaction SiH2 g gt Si b Ho 53 In this example we have not explicitly included the surface in writing Eq 53 A somewhat more detailed way of using the sticking coefficient specification would be to say that SiH2 g reacts with probability y upon each collision with a bare surface silicon atom Si s SiH2 g Si s gt Si s Si b H2 54 CAUTION Because is defined as a probability it must lie between 0 and 1 to make physical sense Therefore SURFACE CHEMKIN checks the value of y and an unphysical sticking coefficient greater than 1 is changed to the value 1 Some earlier versions of SURFACE CHEMKIN did not truncate the values at 1 38 If the surface site fraction of Si s were unity then a frac
45. fractions appear in Eq 48 rather than molar concentrations X moles cm for surface species The term associated with 44 now makes it possible for the rate of progress of a reaction to be proportional to any arbitrary power of a surface species concentration Also using this modified expression for k y the net pre exponential factor may be a function of coverage 36 kil logio A logy 4 mi Z n 49 k K N and the activation energy is a function of the coverage ki lv E E Ex Z m1 50 k K Inf For reactions with optional coverage dependence the rate or progress is calculated employing Eq 32 with the forward rate coefficient from Eq 48 The reverse rate constant is calculated via Eq 36 If the form of Eq 48 is not flexible enough to describe a certain coverage behavior one can repeat the same reaction several times with different values for the coverage parameters such that the sum of the rate constants approximates the desired form 3 9 lon Energy Dependent Rate Expression In many examples of materials processing ions interact with surfaces to alter the morphology sputter material or enhance heterogeneous chemical reactions Ions are often accelerated through a plasma sheath near grounded or electrically biased materials In this way the directed energy of ions encountering a surface may be significantly greater than the ion temperature in the plasma gas SURFACE CHEMKIN therefore ma
46. gas phase It may also be used in conjunction with the TRANSPORT Property package which provides information about molecular diffusion Thus these three packages provide a foundation on which a user can build application software to analyze gas phase and heterogeneous chemistry in flowing systems In addition the CHEMKIN Collection includes several Applications that incorporate the SURFACE CHEMKIN capabilities for modeling common reactor geometries The SURFACE CHEMKIN software package includes an Interpreter pre processor and a subroutine library These software tools help a user to work efficiently with large systems of chemical reactions and develop software representations of systems of equations that define a particular problem A general discussion of this structured approach for simulating chemically reacting flow can be found in Kee and Miller 2 1 1 Structure and Use of SURFACE CHEMKIN Using the SURFACE CHEMKIN package is analogous to using the CHEMKIN package y the SURFACE CHEMKIN package can only be used after the CHEMKIN Interpreter has been executed necessary to be familiar with CHEMKIN before the SURFACE CHEMKIN package can be used effectively Therefore it is The CHEMKIN interpreter introduces the chemical elements that are used in either the gas phase reaction mechanism or the surface reaction mechanism Gas phase species which can appear in surface reactions are also introduced with the CHEMKIN Interpreter Thus if a
47. ideas into a form that was amenable to efficient computation In the spirit of CHEMKIN Chapter 3 is a compendium of some important equations in heterogeneous chemical kinetics Many of the equations are simply definitions but in any case derivations are either sketchy or not given Although some readers will find the equations quite familiar we find it useful to have them stated concisely in one document For most equations the package contains a subroutine that when given the variables on the right hand side returns the variable on the left Below some of the equation numbers is stated in brackets the name of the subroutine that provides information about that equation Using CHEMKIN and SURFACE CHEMKIN and possibly the TRANSPORT Package requires the manipulation of many programs and files Chapter 4 explains the mechanics of using these software packages and describes the job control logic for running a typical problem Chapter 5 explains the SURFACE CHEMKIN Interpreter and how to set up the required symbolic input to define a reaction mechanism We have allowed the possibility of including multiple site types multiple 18 mixtures of bulk species and multiple materials Each site type and bulk mixture may contain several species Therefore the data structures needed to refer to the phases and the species can be complex Chapter 6 provides detailed information on the computational data structures that we use to refer to pha
48. l O The stoichiometric coefficients for elementary reactions v are integers and y is the chemical symbol for the kth species Usually an elementary reaction involves only three or four species hence the Uy matrix is quite sparse for a large set of reactions The net production rate 5 in moles cm2 sec for each of the K species regardless of phase is the sum of the rate of production for all reactions involving the kth species I Y via k 1 K 30 k 2 ki di SKRAT where Vri Vki Yi 31 SKNU The rate of progress variable q for the ith reaction is given by the difference of the forward rates and the reverse rates K K ke x Tx 32 qi mul e IIl a SKROP It is not a requirement that the number of sites of type n balance in a given reaction The production rate Ip in moles cm2 sec for each surface phase is Global reactions are sometimes stated with non integer stoichiometric coefficients SURFACE CHEMKIN can accommodate non integer stoichiometric coefficients 32 f I Y Ac n 1 g ho M n 83 i l where K n Ao n i X 0 0 n 34 k K n The term Ao n i is the net change in number of surface sites of type n for surface reaction i As discussed above the form of the concentrations X depends upon whether species k is in the gas phase on the surface or in the bulk Furthermore the units of the rate constants will depend on the reactants
49. names However because six letters can be used only four are available in the subroutine names because SK occupies two the mnemonics can be more explicit 7 2 Initialization SUBROUTINE SKINDX ISKWRK NELM KKGAS KKSUR KKBULK KKTOT NNPHAS NNSURF NFSURF NLSURF NNBULK NFBULK NLBULK IISUR Returns a group of indices defining the size of the surface reaction mechanism In the following list subroutines whose arguments lists have changed from previous versions of SURFACE CHEMKIN are underlined 81 SUBROUTINE SKINIT LENISK LENRSK LENCSK LINSK LOUT ISKWRK RSKWRK CSKWRK IFLAG Reads the surface linkfile and creates internal work arrays ISKWRK RSKWRK and CSKWRK SKINIT must be called before any other SURFACE CHEMKIN subroutine can be used as the work arrays must be available as their input SUBROUTINE SKLEN LINSK LOUT LENI LENR LENC IFLAG Reads the first record of the linkfile to return the lengths required for the integer real and character work arrays SUBROUTINE SKLEN2 LINSK LOUT LENI LENR LENC NELEM NKKGAS NKKSUR NKKBLK NKKTOT NPHASE NNSUR NNBLK NIISUR NIICON MORE IFLAG Reads the first record of the linkfile to return the lengths required for the integer real and character work arrays as well as other size information needed for memory allocation The routine also advances to the end of the first material 7 3 Information about Elements SUBROUTINE SKSYME IS
50. parameter scalar Absolute tolerance parameter scalar or array The estimated local error in Y i will be controlled so as to be roughly less in magnitude than EWT i RTOL abs Y i ATOL if ITOL 1 or EWT i RTOL abs Y 1 ATOL i if ITOL 2 Thus the local error test passes if in each component either the absolute error is less than ATOL or ATOL i or the relative error is less than RTOL Use RTOL 0 0 for pure absolute error control and use ATOL 0 0 or ATOL i 0 0 for pure relative error control Caution Actual global errors may exceed these local tolerances so choose them conservatively 1 for normal computation of output values of Y at t TOUT Integer flag input and output Set ISTATE 1 0 to indicate no optional input used Real work array of length at least 20 16 NEQ for MF 10 22 9 NEQ 2 NEQ 2 for MF 21 or 22 22 11 NEQ 3 ML 2 MU NEQ for MF 24 or 25 Declared length of RWORK in user s DIMENSION statement Integer work array of length at least 30 for MF 10 30 NEQ for MF 21 22 24 or 25 If MF 24 or 25 input in IWORK 1 IWORK 2 the lower and upper half bandwidths ML MU Declared length of IWORK in user s DIMENSION Name of subroutine for Jacobian matrix MF 21 or 24 If used this name must be declared external in calling program If not used pass a dummy name Meth
51. power equal to the reaction order for that species for all site species that are reactants Here O is the number of sites that the surface species occupies and v is the reaction j order for that species The product term will be equal to one when there are unity site occupancies for all of the surface species in the reaction Implicit in the sticking coefficient description just presented is an assumption that the sticking coefficient is relatively small i e much less than one In this case the molecular motion in the vicinity of the solid surface is random and the collision frequency of gas phase species with the surface is not affected by the surface itself However when the sticking coefficient is large i e close to one then the velocity distribution becomes skewed Species whose random motion carries them close to the surface have a high probability of staying there which causes a non Maxwellian velocity distribution that in turn alters the Early versions of SURFACE CHEMKIN always applied Eq 57 Later versions allow optional use of Eq 56 to relate the sticking coefficient to rate constants through use of the keyword MWOFF on the REACTION line described later 39 net species flux near the surface Motz and Wise analyzed this situation and provided a correction factor that modified Eq 56 as Dv o i Yi 1 i RT kp a 57 i y 12 To 127 Goodwin and Gavillet have incorporated this effec
52. reactions the default Including MWOFF or MWON as an auxiliary keyword for an individual reaction discussed later will override the setting given on the REACTION line The reaction description can begin anywhere on this line All blank spaces except those separating the Arrhenius coefficients are ignored Each reaction description must have lt gt or gt between the last reactant and the first product Each species in a reaction is described with a unique sequence of characters name as they appear in the species data and the thermodynamic data However if a species name is not unique because it is duplicated in another phase the name must be modified by appending its slash delimited phase name i e as name phase Stoichiometric coefficients are represented by an integer or real number preceding a species name The default is to assume a stoichiometric coefficient of 1 The symbol preceding the stoichiometric coefficient denotes a coefficient which is additionally multiplied by a yield multiplier A reaction description may be contained on more than one line If a line contains the symbol amp all information following the amp symbol will be ignored and the next line will be considered a continuation of the first Three Arrhenius coefficients must appear in order A f and E on each Reaction line separated from each other and from the reaction description by at least one blank space no blanks are
53. set to TRUE on return from the subroutine Example input LINE GA S BULK1 1 2 NEXP 1 the number of values expected LOUT 6 a logical unit number on which to write diagnostic messages KNAM Array of character species names KKTOT Total number of species PNAM Array of character phase names NNPHAS Total number of phases KKPHAS Index array of the number of species in the phases Output KNUM The index number of the species which has the name GA S and resides in phase BULK1 NT 1 if there is only one species GA S in phase BULK1 NVAL 1 the number of values found in LINE following the species nam RVAL 1 1 200E 00 the substring converted to a real number KERR FALSE INPUT LINE Character string length depends on calling routine NEXP Integer scalar number of values to be found in LINE If NEXP lt 0 then IABS NEXP values ar xpected but it is not an error condition if less values are found LOUT Integer scalar formatted output file unit number KNAM Character string array species names dimension at least KKTOT the total species count KKTOT Integer scalar the total species count PNAM Character string array phase names dimension at least NNPHAS the total phase count NNPHAS Integer scalar the total phase count KKPHAS Integer array total species counts for the phases dimensio j n at least NNPHAS the total phase count 132
54. species for bulk phase species should sum to 1 for each for the site types the total phase count NLSURF moles cm 2 Integer workspace array workspace array for the reactions dimension at least IISUR the total surface reaction count cgs units depends on reaction 106 s sit dimension at leas dimension at leas phas moles ntries LENISK LENRSK cv ot equilibrium constants in concentration units cm SKFLGS SKFLGS SKFLGS SKFLGS SKFLGS SKFLGS SKFLGS ee eee ee ee ee ee eee oes KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKFLGS IR ISKWRK NRPP IREV ISTFL ICOV IMOTZ IEDP IBHM IORD IYLD T Returns several integer flags describing surface reaction IR INPUT IR Integer scalar surface reaction index ISKWRK Integer workspace array dimension at least LENISK OUTPUT NRPP Integer scalar number of species reactants products for surface reaction IR combined with reversibility flag NRPP gt 0 NRPP species reversible surface reaction lt 0 ABS NRPP species irreversible reaction IREV Integer scalar flag for explicit reverse Arrhenius parameters 1 reaction has explicit reverse Arrhenius parameters 0 no may or may not be reversible s NRPP ISTFL Integer scalar flag for sticking coefficients 1 reaction does not use sticking coefficients 0 no IMOTZ Integer scalar flag for Motz Wise correction of s
55. species densities in grams of species k per cm The array elements corresponding to the surface species have no physical meaning and are set to the species molar densities in moles cm2 The final elements of the DEN array contain the mass densities of the bulk species in grams of species k per cm3 If the user does not specify a mass density as input to the Surface Interpreter then these are given a value of 1 All the species can be identified by a character string name and the user can also optionally specify character string names for the phases and each material The species names are those that were given as input to the Interpreters and the application program can retrieve the names by calling the following subroutine SUBROUTINE SKSYMS ISKWRK CSKWRK LOUT KNAME KERR The input is the integer and character working space ISKWRK and CSKWRK and LOUT a file number on which to write diagnostic messages The output is an array of character names KNAME and a logical error flag KERR In the example we are considering here the species names are shown in Fig 14 As concrete illustrations KNAME 1 ASH3 KNAME KLAST NLSURP GA L or KNAME KFIRST 7 GA B The phase names are optional and can be specified in the SURFACE CHEMKIN Interpreter input The names can be retrieved from an application program by the following subroutine call SUBROUTINE SKSYMP ISKWRK CSKWRK LOUT
56. t species t cgs units Real array dimension The first KKGAS the next KKSURF species de surface co K mperatures activi at least nsi nce nominally KKTOT the t ac activities are ntration in mo ACT K SITE D T INSITY sit the next KKBUL should be from phase Real array si but the subrou NFSURF lt N lt cgs units Real Real array K ac te dimension at least tine only us NLSURF moles cm 2 Integer workspace array workspace array partials deriva of the species with respect tivities to 1 and shou densities NPHASE t of surface reaction IR n index dimension is determined by he total number of Ty ties of the species otal species count tivities are mole fractions site fractions ty normalized by the site density les cm 2 is s per species and for bulk phase species ld sum to 1 for each for the site types the total phase count di di mens mens tive s sit to the phas ntries at least LENISK at least LENRSK ion ion of rates ntial production pre expone constant for surface reaction IR dimension at least KKTOT moles cm 2 sec cgs units the t 102 otal species count units of A SKDRDC SKDRDC SKDRDC SKDRDC SKDRDC SKDRDC SKDRDC KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKK
57. the next line i e do not break species names into two lines 10 There may be more than one set of BULK data 11 All characters on a line following an exclamation mark are considered comments and are ignored 12 BULK data are not required 53 BULK GA RICH GA2AS 1 3 0 GA3AS 1 3 0 E ND lan END statement is optional BULK GA_RICH GA2AS 1 3 0 GA3AS 1 3 0 GA2AS 1 2 0 THIS NAME IS A DUPLICATE AND WILL BE IGNORED BULK AS B BULK PHASE WITH NO NAME SUPPLIED ONLY ONE BULK SPECIES AND NO DENSITY SUPPLIED END Figure 8 Sample Bulk Data 54 5 4 Thermodynamic Data Any chemical species that appears in a problem must have thermodynamic data associated with it This data is used in evaluation of thermodynamic properties entropy enthalpy heat capacity and reverse reaction rate constants through the equilibrium constant Often thermodynamic data for a species for instance a surface species is unknown Such data can sometimes be calculated via theoretical techniques However the user can work around the need for actual thermodynamic data for all species with the following trick If every reaction in the mechanism is either irreversible or if Arrhenius rate parameters are given explicitly for the reverse reaction then the thermodynamic data for species are not actually used for anything related to the kinetics In this case the user can supply d
58. the reaction line may optionally be used to specify the coefficients a b and c of Eq 52 for a sticking coefficient In order for the second field to apply to sticking coefficient parameters the next line of input must contain the auxiliary information word STICK Examples of some reaction data are shown in Fig 10 Table 4 summarizes the reaction data rules REACTIONS KCAL MOLE NONCON ASH3 AS P lt gt ASH3 P AS D 4 0E11 0 25 Ref 21 ASH3 AS P lt gt ASH3 P AS D 4 0E11 Oo 0 same as previous ASH lt gt AS D H S 1 0 0 0 STICK L 2 GAME amp continued on next line GA CH3 3 L GA2AS A lt gt AS GA CH3 1 0E13 O 4000 Figure 10 Examples of Reaction Data 61 10 11 12 13 Table 4 Summary of the Rules for Surface Reaction Data The first reaction line must start with the word REACTIONS or REAC and may be followed by units definition s the word MWOFF or the word NONCON Valid unit declarations are EVOLTS KELVINS CAL MOLE KCAL MOLE JOULES MOLE KJOULES MOLE MOLES and MOLECULES The word NONCON is required on the first reaction line if any of the reactions do not conserve the number of surface sites of a given type The word MWOFF can be used to turn off the Motz Wise correction of Eq 57 for all sticking coefficient reactions or the word MWON can be used to specify that the Motz Wise correction is to be used for all sticking coefficient
59. the total element count ISKWRK Integer workspace array dimension at least LENISK OUTPUT NEL Integer matrix elemental compositions of the species dimension at least NELEM for the first the total element count and at least KKTOT for the second the total species count NEL M K is the quantity of element M in species K SKNCON SKNCON SKNCON SKNCON SKNCON SKNCON SKNCON KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKNCON ISKWRK RSKWRK NCON Returns the total number of surface reactions which do not conserve sites of the phases INPUT ISKWRK Integer workspace array dimension at least LENISK OUTPUT NCON Integer array count of surface reactions which do not conserve sites in the phases dimension at least NPHASE the total phase count 120 SKNU SKNU SKNU SKNU SKNU SKNU SKNU ee ee ee ee ee ee eee ores KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKNU IDIM ISKWRK RSKWRK KSTOIC NSTOIC Returns the stoichiometric coefficients of the species and the net change in phases for all of the surface reactions in a mechanism INPUT IDIM Integer scalar first dimension of the array NSTOIC must be at least IISUR the total surface reaction count ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT KSTOIC Integer matrix st
60. this mechanism the SI S could have been just as well left out of the mechanism entirely However if other gas phase species had been present say phosphine carrying phosphorus as a dopant these species could compete for the available silicon sites on the surface Thus by writing the reactions as we have we have left open the possibility for other species to occupy surface sites and thus inhibit the deposition of silicon As an example of the full use of SURFACE CHEMKIN assume that an application program needs to evaluate a boundary condition concerning the energy balance at a surface of an isothermal particle The energy balance would take the following form with the surface normal n pointing into the particle Kg e Kh ni T AVT gt pY Vy T ig cel T S Wihy 1 k l k K wi The dependent variables in this expression are the temperature T gas phase mass fractions Y and convective velocity u The surface site fractions and the bulk species activities are also dependent variables but do not appear explicitly in the expression The first term in this equation describes thermal conduction to the surface from the gas phase The thermal conductivity 2 would be evaluated by a call to the TRANSPORT Library and the temperature gradient could be evaluated by finite differences The second term concerns the diffusive and convective flux of energy by gas phase species at the surface The mass density p and the gas phase enthalpie
61. we list some of the relevant indices and counters for this input file For material 1 Material name MATNAM 1 WAFER NELEM 1 4 KKGAS 1 6 KKSUR 1 4 KKBULK 1 1 KKTOT 1 11 NNPHAS 1 3 NNSURF 1 1 NFSURF 1 2 NLSURF 1 2 NNBULK 1 1 NFBULK 1 3 NLBULK 1 3 TISUR 1 4 KKPHAS 1 6 4 1 KFIRST 1 1 7 11 KLAST 1 6 10 11 KNAME 1 E CL2 CL SICL4 SICL2 CL SI S SICL S SICL2 S SICL3 S SI B PNAM 1 GAS POLY BULK1 For material 2 Material name MATNAM 2 WALL NELEM 2 4 KKGAS 2 6 KKSUR 2 2 KKBULK 2 KKTOT 2 8 NNPHAS 2 2 NNSURF 2 1 NFSURF 2 2 NLSURF 2 2 NNBULK 2 NFBULK 2 0 NLBULK 2 0 IISUR 2 2 KKPHAS 2 6 2 KFIRST 2 1 7 KLAST 2 6 8 KNAME 2 E CL2 CL SICL4 SICL2 CL AL S ALCL S PNAM 2 GAS METAL 4 0 0 4 A number of changes must be made in an application program to accommodate multiple materials For example instead of storing a simple integer KKSURF for the number of surface species the program must store an integer array KKSURF NMAT dimensioned at least the number of materials specified in the input file An array like KFIRST N becomes a two dimensional array KFIRST N NMAT with the first The mechanism has been contrived to illustrate a variety of points about the data structures and should not be taken as a source of data for silicon or aluminum processes 76 dimension large enough to hold the maximum number of phases in a gi
62. 1 rev parameters L 1 NSPAR N 1 NIIREV Sticking reaction data if NIISTK gt 0 43 NIISTK 44 ISKWRK ISKWRK IilSTK N 1 N 1 NIISTK reaction indices 45 ISKWRK ISKWRK IiKSTK N 1 N 1 NIISTK species indices 46 ISKWRK ISKWRK IiMSTK N 1 N 1 NIISTK Motz wise flag Bohm reaction data if NIIBHM gt 0 47 NIIBHM 48 ISKWRK ISKWRK IiBHM N 1 N 1 NIIBHM reaction indices 49 ISKWRK ISKWRK IiKBHM N 1 N 1 NIIBHM Real stoichiometry data if NIIRNU gt 0 50 NIIRNU 51 ISKWRK ISKWRK IiRNU N 1 N 1 NIIRNU reaction indices 52 RSKWRK ISKWRK IrRNU N 1 MAXSPR L 1 real coeff nts L 1 MAXSPR N 1 NIIRNU Change order data if NIIORD gt 0 53 NIIORD MAXORD 54 ISKWRK ISKWRK IilORD N 1 N 1 NIIORD reaction indices 55 ISKWRK ISKWRK IiKORD N 1 MAXORD L 1 species indices L 1 MAXORD N 1 NIIORD 169 56 RSKWRK ISKWRK IrKORD N 1 MAXORD L 1 order values L 1 AXORD N 1 NIIORD Temperature dependent reaction data if NIIEDP gt 0 57 NIIEDP NEDPAR 58 ISKWRK ISKWRK IiIEDP N 1 N 1 NIIEDP reaction indices 59 ISKWRK ISKWRK IiKEDP N 1 N 1 NIIEDP species indices 60 RSKWRK ISKWRK IrPEDP L 1 NEDPAR L 1 parameters L 1 NEDPAR I 1 NIIEDP Yield modify data if NIIYLD gt 0 61 NIIYLD NYPAR
63. 100E 14 500E 12 140E 17 60E 12 50E 16 00E 13 00E 20 30E 13 90E 12 00E 16 00E 12 27E 11 00E 12 00E 13 00E 11 00E 11 00E 11 ELEMENTS H N SI E END SPECIES H2 H N2 N NH NH2 NNH N2H2 N2H3 N2H4 HF F SIF4 SIF3 SIHF3 SIF3NH2 NH3 END REACTIONS H H M H2 M H2 0 0 H H H2 H2 H2 NH N N2 H NH H N H2 NH2 H NH H2 NH3 H NH2 H2 NNH N2 H NNH H N2 H2 NNH NH2 N2 NH3 NNH NH N2 NH2 NH2 NH N2H2 H NH NH N2 H H NH2 N N2 H H N2H2 M NNH H M N2 2 H2 2 N2H2 H NNH H2 N2H2 NH NNH NH2 N2H2 NH2 NH3 NNH NH2 NH2 N2H2 H2 NH3 M NH2 H M N2H3 H NH2 NH2 N2H3 M N2H2 H M N2H3 NH NH2 N2H2 NH2 NH2 M N2H4 M H N2H4 H2 N2H3 NH2 N2H4 NH3 N2H3 NH H M NH2 M NH2 NH2 NH3 NH F NH3 NH2 HF SIF4 SIF3 F H SIF4 HF SIF3 NH2 SIF4 SIF3NH2 F NH3 SIF3 SIF3NH2 H NH3 SIF3 SIHF3 NH2 END 140 f 0 SO 06000600 NWN 0 OG 0 00 0 0 0 O O GO GOD OS GG SO Ce e SOS GONG OV O0 0 0 0 0 0 cen OSSOS SOGRO SS ES DO DO OO 2500 1500 0 10000 800 147170 50000 40950 5000 10000 ee OOO O OO OC O 0 000 000 000 C o O 200000000 OS OOOO Os ooo amp SE eu es a 00 GO GO GO GS SO 0 00 00 O NH3 CST ICHAEL AM AM AM AM H3CST 3 CST 2022Y4G9qec I H3 CST CST CST CST CST C2222 I WW WW NNNNANNANAN MSG KONDRATIEV PHO amp MEC PHO amp MEC GUESS GUESS PHO amp MEC A 9 3 Output from CHEM
64. 3 NLBULK NMAT IISUR NMAT KKTOT KKTOT KKSURF NMAT KKBULK NMAT MORE I ITOT The last integer entry for a material will be non zero if there are more materials IF MORE EQ 1 THEN NMAT NMAT 1 IMISK NMAT ITOT 1 IMRSK NMAT NTOT 1 IMCSK NMAT ICTOT 1 GO TO 10 ENDIF END Figure 16 Sample Program to Handle M ultiple M aterials 80 7 QUICK REFERENCE TO THE SURFACE SUBROUTINE LIBRARY This chapter is arranged by topical area to provide a quick reference to each of the Surface Library Subroutines In addition to the subroutine call list itself the purpose of the subroutine is briefly described 7 1 Mnemonics There are some rules of thumb for explaining the subroutine naming conventions All subroutine names begin with the letters SK so that SURFACE CHEMKIN Subroutines are easily recognized and so that they are likely different from any user subroutine names The four remaining letters generally identify the purpose of the subroutine Thermodynamic properties are referred to by CP specific heat H enthalpy S entropy U internal energy G Gibbs free energy and A Helmholtz free energy The thermodynamic property subroutines may be called to return properties in mass units denoted by MS or S as the last letter s or in molar units denoted by ML or L as the last letter s The mnemonics for the variable names in the subroutine call lists are roughly the same as for the subroutine
65. 4E 08 TIME 2 500000000000000E 002 GAS PHASE STATE P 3 3106E 03 T 1 7130E 03 DENSITY 4 3558E 07 GAS PHASE MOLE FRACTIONS H2 1 178E 05 H 2 339E 08 N2 N 5 001E 12 NH 1 472E 08 NH2 NNH 5 909E 10 N2H2 1 220E 08 N2H3 N2H4 1 267E 11 HF 5 038E 01 F SIF4 2 405E 03 SIF3 6 877E 12 SIHF3 SIF3NH2 3 599E 10 NH3 4 937E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 3 963E 03 SIF3NH2 S 7 140E 06 SIF2NH S NH2SIFNH S 1 725E 04 NHSIFNHSIFNH 3 455E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 012E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 006E 08 156 HH Ho 864E 09 453E 05 147E 10 958E 10 054E 11 3 499E 03 Oy A O dy 799E 01 265E 08 888E 05 994E 10 798E 10 631E 11 1 670E 03 9 896E 01 SW WU DN BS 629E 08 322E 05 066E 10 595E 10 908E 11 7 736E 04 947E 01 TIME 3 000000000000000E 002 GAS PHASE STATE pos 3 3184E 03 T 1 7130E 03 DENSITY 4 3431E 07 GAS PHASE MOLE FRACTIONS H2 1 408E 05 H 2 380E 08 N2 N 8 522E 12 NH 2 167E 08 NH2 NNH 8 688E 10 N2H2 1 786E 08 N2H3 N2H4 1 794E 11 HF 5 095E 01 F SIF4 1 080E 03 SIF3 3 211E 12 SIHF3 SIF3NH2 3 683E 10 NH3 4 894E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 1 861E 03 SIF3NH2 S 3 222E 06 SIF2NH S NH2SIFNH S
66. 7 Te 200 cd 8 16 SIF3NH2 101 10384 2 Ho 3 17 NH3 17 03061 3 LT 00 SITE SI3N4 0 417E 08 moles cm 2 18 NHSIF S 62 09907 2 Tod do A 19 SIF3NH2 S 101 10384 2 Ls fio 8 20 SIF2NH S 81 09747 2 E ra 21 NH2SIFNH S 78 12171 2 Bop To dl 22 NHSIFNHSIFNH S 139 21281 4 Bi 338 2 TA 23 NHNH2 S 3103731 2 A O BULK BULK1 24 SI D 28 08600 0 207E 01 g cm 3 O26 20 6 A 220 BULK BULK2 25 N D 14 00670 0 137E 01 g cm 3 OL 0 0 144 uN URFACE REACTIONS CONSIDER H3 NHSIF S gt NHN 2 S SI IF3NH2 S gt SIF2NH S HF GB WU NH H2SIFNH S SIF2NH S gt NHSIFNHSIFNH S HF HSIFNHSIFNH S SIF2NH S gt 3NHSIF S N D HF ZllZ2ZZnneg NOTE A units mole cm sec K NO ERRORS FOUND ON INPUT D IF 4 NHNH2 S gt SIF3NH2 S N E units cal mole ED HE D HF H3 SIF2NH S gt NH2SIFNH S HF RIP0O0OJ ASCII Version 1 1 surface linkfile surf asc written WORKING SPACE REQUIREMENTS ARE INTEGER 481 REAL 642 CHARACTER 34 Total CPUtime sec 0 03125 9 6 Sample Problem Input 2 63e 3 1713 SIF4 0 14286 NH3 0 85714 NHSIF S 6 251E 2 NHNH2 S 0 91587 SIF3NH2 S 2 354E 4 SIF2NH S 2 0837E 2 NH2SIFNH S 1 806E 4 NHSIFNHSIFNH S 3 6127E 4 N D 1 0 SI D 1 0 END 6 0 5 0E 2 5 0E 3 145 56 10 00 56 00 00 E 08 E 08 E 05 E 08 EFIS
67. 7E 05 SIF3 1 412E 13 SIHF3 SIF3NH2 3 756E 10 NH3 4 859E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 7 928E 05 SIF3NH2 S 1 314E 07 SIF2NH S NH2SIFNH S 1 705E 04 NHSIFNHSIFNH 3 415E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999992 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 044E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 113E 08 TIME 5 000000000000000E 002 GAS PHASE STATE P 3 3246E 03 T 1 7130E 03 DENSITY 4 3332E 07 GAS PHASE MOLE FRACTIONS H2 2 386E 05 H 2 628E 08 N2 N 3 071E 11 NH 5 957E 08 NH2 NNH 2 558E 09 N2H2 5 211E 08 N2H3 N2H4 4 810E 11 HF 5 140E 01 F SIF4 4 387E 05 SIF3 1 412E 13 SIHF3 SIF3NH2 3 756E 10 NH3 4 859E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 7 928E 05 SIF3NH2 S 1 314E 07 SIF2NH S NH2SIFNH S 1 705E 04 NHSIFNHSIFNH 3 415E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999992 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 044E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 113E 08 STOP TIME LIMIT REACHED Total CPUtime sec 6 25E 02 158 Ano EN 953E 07 060E 05 658E 10 511E 10 135E 11 3 228E 05 Y JP 993E 01 107E 07 494E 05 188E 09 215E 10 140E 11 1 450E 05 9 994E 01 JJ JP ds 107E 07 494E 05 188E 09 215E 10 140E 11 1 450E 05 9 994E 01 9 9 VODE Su SUB
68. AST T The input to SKINDX and SKPKK is the integer work space ISKWRK On output all the indices will have values that pertain to the particular reaction mechanisms For the example we are considering here the indices have the following values NELEM Number of elements Here NELEM 4 As presented on the first line of input to the CHEMKIN interpreter the four elements are GA AS H C KKGAS Number of gas phase species Here KKGAS 14 KKSUR Number of surface species There are seven surface species in this problem and they exist on two sites Thus KKSUR 7 73 KKBULK Total number of bulk species There are eight bulk species that are arranged in five bulk phases Thus KKBULK 8 KKTOT Total number of species KKTOT KKGAS KKSUR KKBULK so in this example KKTOT 29 NNPHAS Number of phases gas sites bulk Here there are eight phases NNPHAS 8 The first is the gas phase the second two are surface phases and the final five are bulk phases NN SURF Number of surface phases Here there are two surface phases NNSURF 2 NFSURF Pointer to the first surface phase The first surface phase is the second phase overall i e NFSURF 2 Since the gas phase is always the first phase the first surface phase will always be the second phase overall However there can be problems in which there are no surface phases only bulk phases In that case NFSURF 0 NLSURF Pointer to the last surface phase Here the last surface p
69. D Input to SURFACE CHEMKIN Interpreter SI3N4 SIF S 2 F3NH2 S 2 F2NH S 2 2SIFNH S 2 NH2 S 2 SI D 2 066 N D 1 374 THERMO ALL 300 NHSIF 0 24 0 81 0 97 NHNH2 0 24 0 81 0 97 SIF3N 0 24 0 81 0 97 SIF2N 0 24 0 8 0 97 NH2S 0 24 0 8 0 97 NHSIF 0 24 0 8 0 97 SI D 0 24 0 81 0 97 N D 0 24 0 8T END REACT H3 IF4 IF3 H3 H2S HSI D A A d A Uy U A A 600 S 753989E 01 0 255620E 03 0 27279380E 11 0 J 3 67N 593603E 08 0 S 753989E 01 0 255620E 03 0 27279380E 593603E 08 0 H2 S 753989E 01 0 255620E 03 0 27279380E 593603E 08 0 H S 753989E 01 0 255620E 03 0 27279380E J 3 67N 593603E 08 0 FNH S 753989E 01 0 255620E 03 0 27279380E 11 0 J 3 67N 593603E 08 0 NHSIFNH S 753989E 01 0 255620E 03 0 27279380E J 3 67SI 593603E 08 0 753989E 01 0 255620E 03 0 27279380E J 3 67N 593603E 08 0 753989E 01 0 255620E 03 0 0 97593603E 08 0 IONS NH2 S IFNH S FNHSIFNH S SIFNHSIFNH S 4 J 3 67N 88 12 88 12 SDEN 4 1683e 9 1685 1H 12187E 03 0 88747E 02 0 2H 12187E 03 0 88747E 02 0 1 0 J 3 67N H 88 12 12187E 03 0 88747E 02 0 1 0 J 3 67N H 88 12 88 12 88 12 88 12 88 12 27279380E NHSIF S NHNH2 S SIF2NH S SIF2NH S SIF2NH S 12187E 03 0 88747E 02 0 1 0 2H 12187E 03 0 88747E
70. E 11 6 970E 03 631E 01 TIME 1 500000000000000E 002 GAS PHASE STATE pos 3 2558E 03 T 1 7130E 03 DENSITY 4 4466E 07 GAS PHASE MOLE FRACTIONS H2 7 295E 06 H 2 281E 08 N2 N 9 816E 13 NH 4 684E 09 NH2 NNH 1 978E 10 N2H2 4 189E 09 N2H3 N2H4 4 816E 12 HF 4 647E 01 F SIF4 1 193E 02 SIF3 2 873E 11 SIHF3 SIF3NH2 3 091E 10 NH3 5 233E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 1 601E 02 SIF3NH2 S 3 431E 05 SIF2NH S NH2SIFNH S 1 798E 04 NHSIFNHSIFNH 3 600E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 8 990E 08 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 4 585E 08 TIME 2 000000000000000E 002 GAS PHASE STATE RPS 3 2934E 03 T 1 7130E 03 DENSITY 4 3840E 07 GAS PHASE MOLE FRACTIONS H2 9 524E 06 H 2 306E 08 N2 N 2 505E 12 NH 9 016E 09 NH2 NNH 3 679E 10 N2H2 7 662E 09 N2H3 N2H4 8 295E 12 HF 4 914E 01 F SIF4 5 356E 03 SIF3 1 435E 11 SIHF3 SIF3NH2 3 429E 10 NH3 5 032E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 8 165E 03 SIF3NH2 S 1 573E 05 SIF2NH S NH2SIFNH S 1 749E 04 NHSIFNHSIFNH 3 502E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999993 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 9 750E 08 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 4 87
71. Examples of auxiliary information are shown in Fig 11 The above rules are summarized in Table 5 REACTIONS KCAL MOL Gl THE FOLLOWING ARE CONTRIVED EXAMPL SICL S lt gt CL SI S CL SICL S lt gt DUPLICATE RORD SI S CL SICL S lt gt DUPLICATE CL gt CL STICK CL SICL3 S BOHM ENRGDEP 1 0 5 tr tr gt SICL2 S BOHM YIELD 0 0712 1 21 0 5 1 0 CL2 SICL3 S SI B gt SICL4 SICL S tr CL2 SI S STICK 0 CL2 SI S COV SICL S MWOFF aLe O40 3247 SI B gt SICL4 SI S UNITS EVOLT 1 0 CL SICL3 S SI B SICL2 FORD CL2 2 43 SICL S amp SICL S UNITS EVOLT Figure 11 Examples of Auxiliary Information Definitions 65 ES OF AUXILIARY KEYWORD USAG 1 0E 3 REV 1 0E13 0 1 1 4E11 FORD CL 1 0 1 0 0 50 Gl 0 0 2 0 0 Vel dll 20 0 0 15 0 0 0 0 0 0 0 0 0 0 10 11 12 13 14 Table 5 Summary of the Rules for Auxiliary Information D ata Auxiliary information lines may follow a reversible reaction to specify the reverse rate parameters explicitly auxiliary information must follow any reactions that are duplicated Auxiliary keyword declarations may appear anywhere on the line in any order Any number of auxiliary keywords may appear on a line and more than one line may be used but a keyw
72. F IF NNSU Form DOS ZP CONTI NDIF E RETURN END K RWORK NSDOT K 1 RWORK NWT K 1 AVRAT NUE RF GT 0 THEN the surface site number density equations 5 N NFSURF NLSURF KKTOT 1 N NFSURF 1 RWORK NSITDT N 1 NUE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C E 10 6010 SUBROUTI IMPLICIT DIMENSIO CHARACTE DO 10 K WRITI CONTINU FORMAT Gl E RETURN END NE PRT1 KK KSYM LOUT X DOUBLE PRECISION A H O Z INTEGER I N N X KK R KSYM KK 1 KK 3 LOUT 6010 KSYM L X L L K MIN K 2 KK 3X 3 A12 1PE10 3 4X 153 9 8 Output from Sample Application Program LIB CHEMKIN GAS PHASE CHEMICAL KINETICS LIBRARY OUBLE PRECISION Vers 5 28 2000 08 05 opyright 1995 Sandia Corporation Cc D The U S Government retains a limited license in this software LIB CHEMKIN SURFACE KINETICS LIBRARY OUBLE PRECISION Vers 7 17 2000 07 02 opyright 1995 Sandia Corporation he U S Government retains a limited license in this software No DU qu NPUT INITIAL PRESSURE ATM AND TEMPERATURE K 0 263E 02 0 171E 04 NPUT INITIAL ACTIVITY OF NEXT SPECIES SIF4 0 14286 NPUT INITIAL ACTIVITY OF NEXT SPECIES NH3 0 85714 NPUT INITIAL ACTIVITY OF NEXT SPECIES NHSIF S 6 251E 2 NPUT INITIAL ACT
73. F N 1 CALL PRT1 KKPHAS CWORK IKSYM KFIRST 1 LOUT E 1 RWORK NZ KFIRST 1 SUM 0 0 KFIRST IWORK NIPKF N 1 KLAST IWORK NIPKL N 1 DO 185 K KFIRST KLAST SUM SUM RWORK NZ K 1 1 8 5 CONTINUE WRITE LOUT SUM OF SURFACE SITE FRACTIONS SUM IZ NZ KKTOT 1 N NFSURF WRITE LOUT SURFACE SITE DENSITY RWORK IZ 190 CONTINUE ENDIF IF NNBULK GT 0 THEN DO 195 N NFBULK NLBULK WRITE LOUT BULK DEPOSITION GM CM 2 IN PHAS KKPHAS IWORK NIPKK N 1 KFIRST IWORK NIPKF N 1 CALL PRT1 KKPHAS CWORK IKSYM KFIRST 1 LOUT 1 RWORK NZ KFIRST 1 195 CONTINUE ENDIF Gl 150 ana C E e 350 NH 7003 7100 1 7105 7110 7115 IF TT2 GE T2 THEN WRITE LOUT STOP TIME LIMIT REACHED RETURN ENDIF TT2 MIN TT2 DT T2 Call the differential equation solver CONTINUE CALL DVODE FUN NEO RWORK NZ TT1 TT2 ITOL RTOL ATOL ITASK ISTATE IOPT RWORK NRODE LRW IWORK NIODE LIW JAC MF RWORK IWORK IF ISTATE LE 1 THEN IF ISTATE EQ 1 THEN ISTATE 2 GO TO 350 ELSE WRITE LOUT ERROR ISTATE ISTATE RETURN ENDIF ENDIF GO TO 250 FORMAT 1H1 FORMAT 1H GA
74. H NNH NH2 7 N2H2 NH2 NH3 NNH 8 NH2 NH2 N2H2 H2 9 NH3 M NH2 H M 20 N2H3 H NH2 NH2 21 N2H3 M N2H2 H M 22 N2H3 NH NH2 N2H2 23 NH2 NH2 M N2H4 M 24 H N2H4 H2 N2H3 25 NH2 N2H4 NH3 N2H3 26 NH H M NH2 M 27 NH2 NH2 NH3 NH 28 F NH3 NH2 HF 29 SIF4 SIF3 F 30 H SIF4 HF SIF3 31 NH2 SIF4 SIF3NH2 F 32 NH3 SIF3 SIF3NH2 H 33 NH3 SIF3 SIHF3 NH2 NOTE A units mole cm sec K E units cal mole NO ERRORS FOUND ON INPUT ASCII Vers 1 1 CHEMKIN linkfile chem asc written WORKING SPACE REQUIREMENTS ARE INTEGER 1086 REAL 723 CHARACTER 21 Total CPUtime sec 0 15625 142 0d JN a a GE H O ADF Wo Fee CR I U E IN gt E 00E 20E 00E 00E 92E 36E 0 00E 0 00E 00E 00E 00E 54E 20E 00E 00E 00E 00E 00E 40E 60E 50E 00E 00E 2 30E 90E 00E 00E 27E 00E 00E 00E 00E 00E Ck A A T b exp E RT Was Ww 5 4 DwWwWWW Ww po ORE REG OR ES By IS Gd Gy IND 0 gt a ta H pa AS DA CO O O Do E o E a OO OO O OO 0 0 PP OD 0 0 0 0 01 b OD Oo oo 60 000 AS SUS Gt ASA O gt DD GS EAD O DO o E 3650 10171 5000 1000 1000 1000 90600 46000 0 0 2500 1500 0 10000 800 147170 50000 40950 5000 10000 ooo O 10 DO DD Y Da oO 10 OO OS ES Oo 2 OOD Oc 00 0 00 Oo OO amp O O a 9 4 SITE NH SI SI NH NH NH END BUL BUL EN
75. HERMODYNAMIC DATA FROM DATABASE INPUT 1 Assign the database as file therm dat 2 Include the following lines in the Interpreter input THERMO Data in Table 3 format lines 3 6 repeated for species not in the database or to override species in database END optional 56 5 4 3 1 Do not need to supply the database 2 Include the following lines in the Interpreter input THERMO ALL Line 2 of Table3 format Data in Table 3 format lines 3 6 repeated for at least all species named in the species data END optional THERMO OH 1212860 1H 1 G 0300 00 5000 00 1000 00 0 02882730E 02 0 10139743E 02 0 02276877E 05 0 02174683E 09 0 05126305E 14 0 03886888E 05 0 05595712E 02 0 03637266E 02 0 01850910E 02 0 16761646E 05 0 02387202E 07 0 08431442E 11 0 03606781E 05 0 13588605E 01 OH 1212860 1H 1E 1 0300 00 5000 00 0 02719058E 02 0 15085714E 02 0 05029369E 0 08261951E 09 0 04947452E 13 0 15763414E 06 0 06234536E 02 0 03326978 0 13457859E 02 0 03777167E 04 0 04687749E 07 0 01780982E 10 0 15740294E4 0 02744042E 02 OH 1212860 1H 1E 1 0300 00 5000 00 0 02846204E 02 0 10418347E 02 0 02416850E 05 0 02483215E 09 0 07775605E 14 0 01807280E 06 0 04422712E 02 0 03390037E 02 0 07922381E 02 0 01943429E 04 0 02001769E 07 0 05702087E 11 0 01830493E 06 0 12498923E 01 MyOH 00 1H 1 0 0G 300 000 5000 000 TEMP 300 000 1000 000 2500 000 5000 000 0 30563941E 01 0 89059362E 03 0 20849917E 06 0 24115927E 10 0 10516720E 14 0 37260112E
76. I Integer scalar dimension required for integer work array ISKWRK LENR Integer scalar dimension required for real work array RSKWRK LENC Integer scalar dimension required for character work array CSKWRK 118 SKLEN2 SKLEN2 SKLEN2 SKLEN2 SKLEN2 SKLEN2 SKLEN2 KKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKEKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKLEN2 LINSK LOUT LENI LENR LENC NELEM NKKGAS NKKSUR NKKBLK NKKTOT NPHASE NNSUR NNBLK NIISUR NIICON MORE IFLAG Reads the first record of the linkfile to return the lengths required for the integer real and character work arrays as well as other size information needed for memory allocation T INPUT LINSK LOUT O L PUT I a T N E NR E ENC LEM KGAS KSUR KBLK KTOT HASE NSUR NBLK IISUR IICON ORE VANA NE SA IFLAG SKMXTP SUBROUTIN Returns t fitting t Gl n INPUT ISKWRK OUTPUT MXTP he routine also advances to the end of the first material Integer scalar input unit number assigned to linkfile Integer scalar formatted output unit file number Integer scalar dimension required for integer work array ISKWRK Integer scalar dimension required for real work array RSKWRK Integer scalar dimension required for character work array CSKWRK
77. IN link file NMAT 1 10 CONTINUE SURFACE CHEMKIN workspace required for this material CALL SKLEN LINKSK LOUT LENISK LENRSK LENCSK IFLAG IF IFLAG GT 0 THEN WRITE LOUT ERROR INITIALIZING SURFACE DATA FOR MATERIAL NMAT STOP ENDIF Total workspace required so far ITOT ITOT LENISK NTOT NTOT LENRSK ICTOT ICTOT LENCSK IF ITOT GT LENIWK OR NTOT GT LENRWK OR CTOT GT LENCWK THEN WRITE LOUT NOT ENOUGH WORK SPACE FOR MATERIAL NMAT STOP ENDIF 79 NLBULK MAXMAT WRITE LOUT ERROR INTIALIZING GAS PHASE LINK FILE Q oo non qo IF NMAT EQ 1 THEN Store CHEMKIN gas phase data common to all materials starting at I 1 R 1 and C 1 CALL CKINIT LENICK LENRCK LENCCK LINKCK LOUT 1 I R C IFLAG IF IFLAG GT 0 THEN WRITE LOUT ERROR INITIALIZING GAS PHASE DATA STOP ENDIF CALL CKINDX I R MM KKGAS II NFIT KKTOT KKGAS IMISK NMAT LENICK 1 IMRSK NMAT LENRCK 1 IMCSK NMAT LENCCK 1 ENDIF Store SURFACE CHEMKIN data for this material starting at I IMISK NMAT R IMRSK NMAT and C IMCSK NMAT INI IMISK NMAT INR IMRSK NMAT INC IMCSK NMAT CALL SKINIT LENISK LENRSK LENCSK LINKSK LOUT 1 I INI R INR C INC IFLAG CALL SKINDX I INI MM KKGAS KKSURF NMAT KKBULK NMAT 1 KK NMAT NPHASE NMAT NNSURF NMAT NFSURF NMAT 2 NLSURF NMAT NNBULK NMAT NFBULK NMAT
78. IND 0 and NT 0 and if ISTR JADE then IND 3 and NT 2 If ISTR BLUE COLORS then IND 2 and NT 1 if ISTR BLUE STONES then IND 0 and NT 0 if ISTR JADE GEMS then IND 0 and NT 0 and if ISTR JADE STONES then IND 6 and NT 1 90 SUBROUTINE SKPNT LSAVE LOUT VERS PREC LENI LENR LENC IERR Reads from a file information about a SURFACE CHEMKIN linkfile pointers for the SURFACE CHEMKIN Library and returns lengths of work arrays SUBROUTINE SKSNUM LINE NEXP LOUT KNAM KKTOT PNAM NNPHAS KKPHAS KNUM NT NVAL RVAL KERR This subroutine is used to read a format free input line of combined alphanumeric data It can be used to parse an input character string LINE which may be composed of several blank delimited substrings This subroutine assumes that the first substring in LINE is the name of a species in the SURFACE CHEMKIN mechanism If the species name is not unique within the Surface CHEMKIN mechanism the phase of the species should be input immediately after the species name delimited by slashes Upon return from the subroutine KNUM returns the index position of the species within the SURFACE CHEMKIN linkfile If the species name is not unique KNUM returns the first position and NT returns the number of the times the species occurs within the linkfile If the species name is not found or there is a syntax error on return KNUM 0 NT 0 and KERR TRUE The substrings in LINE following the first a
79. IVITY OF NEXT SPECIES NHNH2 S 0 91587 NPUT INITIAL ACTIVITY OF NEXT SPECIES SIF3NH2 S 2 354E 4 NPUT INITIAL ACTIVITY OF NEXT SPECIES SIF2NH S 2 0837E 2 NPUT INITIAL ACTIVITY OF NEXT SPECIES NH2SIFNH S 806E 4 NPUT INITIAL ACTIVITY OF NEXT SPECIES NHSIFNHSIFNH S 3 6127E 4 NPUT INITIAL ACTIVITY OF NEXT SPECIES N D 0 NPUT INITIAL ACTIVITY OF NEXT SPECIES SI D 0 NPUT INITIAL ACTIVITY OF NEXT SPECIES END NPUT SURFACE AREA TO VOLUME RATIO 0 600E 01 NPUT FINAL TIME AND DT 0 500E 01 0 500E 02 154 TIME 0 000000000000000E 000 GAS PHASE STATE pos 2 6648E 03 T 1 7130E 03 DENSITY 5 5132E 07 GAS PHASE MOLE FRACTIONS H2 0 000E 00 H 0 000E 00 N2 N 0 000E 00 NH 0 000E 00 NH2 NNH 0 000E 00 N2H2 0 000E 00 N2H3 N2H4 0 000E 00 HF 0 000E 00 F SIF4 1 429E 01 SIF3 0 000E 00 SIHF3 SIF3NH2 0 000E 00 NH3 8 571E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 6 251E 02 SIF3NH2 S 2 354E 04 SIF2NH S NH2SIFNH S 1 806E 04 NHSIFNHSIFNH 3 613E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 1 00000000000000 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 0 000E 00 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 0 000E 00 TIME 5 000000000000000E 003 GAS PHASE STATE RPS 3 0065E 03 T 1 7130E 03 DENSITY 4 8817E 07 GAS PHASE MOLE FRACTIONS H2 2 704E 06 H 2 254E 08 N2 N 2 284E 14 NH
80. IWORK GE LITOT AND LRWORK GE LRTOT AND LCWORK GE LCTOT 1THEN CALL CKINIT LENI LENR LENC LINCK LOUT IWORK RWORK dl CWORK IFLAG1 NISK LENI 1 NRSK LENR 1 CALL SKINIT LENIS LENRS LENCS LINSK LOUT IWORK NISK 1 RWORK NRSK CWORK IFLAG2 IF IFLAG1 GT 0 OR IFLAG2 GT 0 RETURN CALL CKINDX IWORK RWORK MM KKGAS II NFIT CALL SKINDX IWORK NISK NELEM KKGAS KKSUR KKBULK 1 KKTOT NPHASE NNSURF NFSURF NLSURF 2 NNBULK NFBULK NLBULK IISUR IKSYM LCTOT 1 IPSYM IKSYM KKTOT LCTOT IPSYM NPHASE 1 ENDIF NIPKK NISK LENIS NIPKF NIPKK NPHASE NIPKL NIPKF NPHASE NICOV NIPKL NPHASE NEQ KKTOT 1 NNSURF NIODE NICOV KKTOT LIW 30 NEO ITOT NIODE LIW 1 NSDEN NRSK LENRS NRCOV NSDEN NPHASE NX NRCOV KKTOT NZ NX KKTOT NWDOT NZ KKTOT 1 NNSURF NWT NWDOT KKGAS NACT NWT KKTOT NSDOT NACT KKTOT NSITDT NSDOT KKTOT NRODE NSITDT NPHASE LRW 22 9 NEQ 2 NEQ 2 NTOT NRODE LRW 1 147 30 148
81. K T SUBROUTINE SKDRDC KSPEC P T ACT SDEN ISKWRK RSKWRK DKDC Returns the partial derivative of the production rates of the species with respect to the concentration of species KSPEC INPUT KSPEC Integer scalar species index P Real scalar pressure cgs units dynes cm 2 EA Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ACT Real array activities of the species dimension at least KKTOT the total species count The first KKGAS activities are mole fractions the next KKSURF activities are site fractions species density normalized by the site density surface concentration in moles cm 2 is ACT K SITE_DENSITY sites per species and the next KKBULK activities for bulk phase species should be from 0 to 1 and should sum to 1 for each phase SDEN Real array site densities for the site types dimension at least NPHASE the total phase count but the subroutine only uses site phas ntries NFSURF lt N lt NLSURF cgs units moles cm 2 ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK T OUTPUT DKDC Real array partial derivative of the production rates of the species with respect to the concentration of species KSPEC dimension at least KKTOT the
82. KIN Interpreter CHEMKIN GAS PHASE MECHANISM INTERPRETER DOUBLE PRECISION Vers 6 24 2000 06 18 Copyright 1995 Sandia Corporation The U S Government retains a limited license in this software ELEMENTS ATOMIC CONSIDERED WEIGHT Lo A 1 00797 2 N 14 0067 3 ST 28 0860 4 F 18 9984 G P H H A A R SPECIES S G MOLECULAR TEMPERATURE ELEMENT COUNT CONSIDERED E E WEIGHT LOW HIGH H N SIF 1 H2 G 0 2 01594 300 5000 2 0 0 0 27 G 0 1 00797 300 5000 1 0 0 0 3 N2 G 0 28 01340 300 5000 0 2 000 O 4 N G 0 14 00670 300 5000 0 1 0 0 5 NH G 0 15 01467 300 5000 1 1 0 0 6 NH2 G 0 16 02264 300 5000 2 1 0 0 7 NNH G 0 29 02137 250 4000 E 2 00 8 N2H2 G 0 30 02934 300 5000 2 Bo Do 0 9 N2H3 G 0 31 03731 300 5000 35 52 20 00 0 N2H4 G 0 32 04528 300 5000 4 2 0 0 1 HF G 0 20 00637 300 5000 1 0 0 1 2e E G 0 18 99840 300 4000 0 0 0 1 3 SIF4 G 0 104 07960 300 2000 0 0 1 4 4 SIF3 G 0 85 08120 300 3000 E O 3 5 SIHF3 G 0 86 08917 300 3000 do Or SE 3 6 SIF3NH2 G 0 101 10384 300 3000 2 E do 8 7 NH3 G 0 17 03061 300 5000 3 1 0 0 141 REACTIONS CONSIDERED 1 H H M H2 M H2 Enhanced by 0 000E 00 2 H H H2 H2 H2 3 NH N N2 H 4 NH H N H2 5 NH2 H NH H2 6 NH3 H NH2 H2 7 NNH N2 H 8 NNH H N2 H2 9 NNH NH2 N2 NH3 0 NNH NH N2 NH2 1 NH2 NH N2H2 H 2 NH NH N2 H H 3 NH2 N N2 H H 4 N2H2 M NNH H M N2 Enhanced by 2 000E 00 H2 Enhanced by 2 000E 00 5 N2H2 H NNH H2 6 N2H2 N
83. KKKKKK XP LOUT KNAM KKTOT PNAM NNPHAS KNUM NT NVAL RVAL KERR read a format free input line of a It can be used to parse an input ch may be composed of several blank subroutine assumes that the first is the name of a species in the SURFACE CHEMKIN species name is not unique within the SURFACE the phase of the species should be input SUBROUTINE SKSNUM LINE NE KKPHAS This subroutine is used to combined alphanumerical dat character string LINE whi delimited substrings This substring in LINE mechanism If th CHEMKIN mechanism immediately after the speci Upon return from the subroutine KNUM returns the index position s name delimited by slashes of the species within the SURFACE CHEMKIN linkfile If the not unique NT returns the number of th species name is linkfile If th syntax error on return KNUM returns the first position and times the species occurs within the species n KNUM 0 NT 0 and KERR TRUE The substrings in LINE following the first are expected to ame is not found or there is a represent numbers They are converted into floating point values and stored in the output vector RVAL Upon input NEXP is equal to the number of values expected to be found If NEXP numbers are not found KERR will be
84. KKKKKKAKKKKK KKKKKKKKKKKKKKKKKKAKKKKKKKK KKKKKK T SUBROUTINE SKATHM MDIM NDIM1 NDIM2 ISKWRK RSKWRK NT TMP A Returns the polynomial coefficients of the fits for thermodynamic properties of all of the species INPUT MDIM Integer scalar first dimension of an array of temperatures used in thermodynamic fits for species MDIM must be at least MAXTP the maximum number of temperatures used to fit the thermodynamics NDIM1 Integer scalar first dimension of A the three dimensional array of thermodynamic fit coefficients NDIM1 must be at least NPCP2 the total number of coefficients for one temperature rang NDIM2 Integer scalar second dimension of A NDIM2 must be at least MAXTP 1 the total number of temperature ranges ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT Where NT K is the number of temperatures used in fitting the thermodynamic properties of species K TMP N is the Nth temperature NT K 1 is the number of temperature ranges for which the polynomial coefficients are valid then A L N K is the Lth polynomial coefficient for the Nth temperature range and the Kth species i e lt N 1 gt lt N 2 gt lt lt N NT 1 gt P E O X L p Y R N E O Ss M S 1 I A O L N gt gt e TMP 1 TMP 2 TMP 3 e 7 TMP NT 1 TMP N
85. KKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKSML T ISKWRK RSKWRK SML Returns an array of the standard state entropies in molar units INPUT EEE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT SML Real array standard state entropies for the species dimension at least KKTOT the total species count cgs units ergs mole K 130 SKSMS SKSMS SKSMS SKSMS SKSMS SKSMS SKSMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKAKKKKKKKK KKKKKK SUBROUTINE SKSMS T ISKWRK RSKWRK SMS Returns an array of the standard state entropies in mass units INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT SMS Real array standard state entropies for the species dimension at least KKTOT the total species count cgs units ergs gm K 131 SKSNUM SKSNUM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK SKSNUM KKKKKKK SKSNUM SKSNUM SKSNUM SKSNUM KKKKKKKKKKKKKKKKKKK
86. KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKSDEN ISKWRK RSKWRK SDENO Returns a real array of standard state phase densities as given on input to the interpreter INPUT RSKWRK Real workspace array dimension at least LENRSK OUTPUT SDENO Real array standard state densities for the site types AS READ BY THE INTERPRETER dimension at least NPHASE the total phase count but the subroutine only uses site phas ntries NFSURF lt N lt NLSURF cgs units moles cm 2 129 SKSMH SKSMH SKSMH SKSMH SKSMH SKSMH SKSMH KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKSMH T ISKWRK RSKWRK SMH Returns the array of dimensionless entropies minus enthalpies for the species It is normally not called directly by the user INPUT TE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT SMH Real array dimensionless entropies minus enthalpies for the species dimension at least KKTOT the total species count SMH K S K R H K RT SKSML SKSML SKSML SKSML SKSML SKSML SKSML KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
87. KRPAR SKRPAR ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKRPAR ISKWRK RSKWRK ENRGI Allows the user to input auxiliary reaction rate parameters for special types of reactions The first parameter is the species ion directed energy for ion energy dependent reactions INPUT ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK ENRGI Real array species ion energies used in the NIIEDP reactions dimension at least KKGAS the total gas phase species count Default value stored in RSKWRK is set to 0 0 in SKINIT T SKSAVE SKSAVE SKSAVE SKSAVE SKSAVE SKSAVE SKSAV ee ee ee ee ee RAR KKKKKKKKKKKKKKKKKKKKKKKKKK Gl KKKKKK SUBROUTINE SKSAVE LOUT LSAVE ISKWRK RSKWRK CSKWRK Writes to a binary file information about a SURFACE CHEMKIN linkfile pointers for the SURFACE CHEMKIN Library and SURFACE CHEMKIN work arrays INPUT LOUT Integer scalar formatted output file unit number LSAVE Integer scalar unformatted output file unit number ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK CSKWRK Character string workspace array dimension at least LENCSK SKSDEN SKSDEN SKSDEN SKSDEN SKSDEN SKSDEN SKSDEN KKKKKKK
88. KW R K I 1 s ISKWRK IiKCHG charges for the species Is for example IS IS eleme IS fo IS IS fi IS fo IS of an TS IS co ES su IS fo IS Lt IS KW KW KW KW E KW KW ts KW E KW d KW KW un KW rf KW KW KW R R R R R R R R T R DADO DD R KG gt K 1 K I K I K Te Ke K I K 1 Ke K I TSKWR number of temperatures dividing the ranges of of the species 1 a value of TSKWR composition for K 1 N nt M in species TSKWR he species K K 1 K 1 hermodynamic fits ISKWRK TiNR participant species ndidates the reversibility of the reactio is the c 2 IiKCMP EL K T NSCV pecies K is a liquid starts an array of electronic harge of species K indicates two excess electrons starts a matrix of elemental the species EM M 1 is the quantity of starts an array of site coverage th KNT is TA s is the n for PP for i s coverage of species K tarts an array of the total thermodynamic umber of dividing te species K starts an array of the surface reactio mperatures the total ns ns K I 4 Is 1 tN Y a N i N species action IS has N participant reactants products nd reaction IS is reversible participant species in an rreversible reaction
89. KWRK CSKWRK LOUT ENAM KERR Returns a character string array of element names 7 4 Information about Species SUBROUTINE SKATCZ P T ACT SDEN ISKWRK RSKWRK CZ Returns the concentrations of the species given the pressure temperature and activities SUBROUTINE SKCHRG ISKWRK RSKWRK KCHARG Returns an array containing electronic charges of the species SUBROUTINE SKCOV ISKWRK KOCC Returns an array of site occupancy numbers for the species SUBROUTINE SKCZTA T CZ SDEN ISKWRK RSKWRK ACT Returns the activities of the species given the pressure temperature and concentrations 82 SUBROUTINE SKDEN P T ACT SDEN ISKWRK RSKWRK DEN Returns a real array of species densities SUBROUTINE SKKTEL ISKWRK KTFL Allows the user to assign a location in the temperature array to use for the gas phase species SUBROUTINE SKNCF NELDIM ISKWRK NEL Returns the elemental composition of the species SUBROUTINE SKSYMS ISKWRK CSKWRK LOUT KNAM KERR Returns a character array of species names SUBROUTINE SKWT ISKWRK RSKWRK WT Returns the molecular weights of the species 7 5 Information about Phases and Materials SUBROUTINE SKPKK ISKWRK KKPHAS KFIRST KLAST Returns arrays of species pointers for the phases SUBROUTINE SKSDEN ISKWRK RSKWRK SDENO Returns a real array of standard state phase densities as given on input to the interpreter SUBROUTINE SKSYMM ISKWRK CSKWRK
90. L SKKION ISKWRK KELECT KKION KION Cc C MAKE THE ELECTRON S TEMPERATURE NUMBER 2 IF KELECT NE 0 KTFL KELECT 2 C C MAKE THE TEMPERATURE FOR ALL IONS NUMBER 3 DO 200 K 1 KKION KTFL KION K 3 200 CONTINUE C PUT THESE TEMPERATURE POINTERS INTO THE SURFACE CHEMKIN WORK SPACI CALL SKKTFL ISKWRK KTFL Gl C GET ARRAY OF SPECIES ENTHALPIES CALL SKHML T ISKWRK RSKWRK HML 27 The array KTFL tells SURFACE CHEMKIN which entry in the temperature array to use for each gas phase each species the Library always uses temperature number 1 for surface or bulk phase species In this example the default for neutral gas phase species is to use temperature number 1 in the temperature array A separate energy equation may have been solved for the electron and so for that species the example specifies that temperature number 2 in the temperature array is to be used The energies of all of the ions may have been solved as a group by some other equation and the example forces SURFACE CHEMKIN to use the third temperature in the temperature array for each ionic species The fcall to SKKTFL tells the Library how to associate each species with the appropriate entry in the temperature array via the array KTFL The default in SURFACE CHEMKIN is a single thermodynamic temperature If this is the case an application program does not have to do anything with the KTFL array and its entr
91. LOUT MATNAM KERR Returns the character string name of a material SUBROUTINE SKSYMP ISKWRK CSKWRK LOUT PNAM KERR Returns a character string array of phase names 7 6 Information about Surface Reactions SUBROUTINE SKABE ISKWRK RSKWRK RA RB RE ISTFL Returns the Arrhenius coefficients or the sticking coefficients of the surface reactions and integer flags to indicate the type of the coefficients SUBROUTINE SKFLGS IR ISKWRK NRPP IREV ISTFL ICOV IMOTZ 83 IEDP IBHM IORD IYLD Returns several integer flags describing surface reaction IR SUBROUTINE SKIBHM IR ISKWRK IBMFL Returns an integer flag to indicate whether reaction IR uses BOHM sticking coefficients SUBROUTINE SKICOV IR NDIM ISKWRK RSKWRK NCOVI KCOVI CPARI Returns the coverage species index numbers and their coverage parameters for reaction IR SUBROUTINE SKIENR IR ISKWRK SKWRK IENRFL IEION PEDEP Returns an integer flag to indicate if reaction IR is ion energy dependent and if so formulation specific parameters SUBROUTINE SKINU IS NDIM ISKWRK RSKWRK NSPEC KI NU Returns the number of species in a surface reaction and the species indices and stoichiometric coefficients SUBROUTINE SKIORD IDIM KDIM ISKWRK RSKWRK NFORD IFORD FORD NRORD IRORD RORD Returns the number and indices of surface reactions with modified species orders and the order values for the species in the surface mechanism
92. NS 0 999999999999992 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 041E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 105E 08 157 PB ANO 252E 08 756E 05 368E 10 354E 10 037 E 11 3 526E 04 sonw 973E 01 342E 07 191E 05 901E 10 086E 10 096E 11 1 594E 04 9 985E 01 JU JUN 041E 07 625E 05 664E 10 803E 10 123E 11 7 180E 05 990E 01 TIME 4 500000000000000E 002 GAS PHASE STATE P 3 3243E 03 T 1 7130E 03 DENSITY 4 3337E 07 GAS PHASE MOLE FRACTIONS H2 2 131E 05 H 2 553E 08 N2 N 2 427E 11 NH 4 878E 08 NH2 NNH 2 047E 09 N2H2 4 177E 08 N2H3 N2H4 3 920E 11 HF 5 138E 01 F SIF4 9 773E 05 SIF3 3 069E 13 SIHF3 SIF3NH2 3 752E 10 NH3 4 861E 01 SURFACE SITE FRACTIONS ON PHASE SITE 2 NHSIF S 1 760E 04 SIF3NH2 S 2 926E 07 SIF2NH S NH2SIFNH S 1 706E 04 NHSIFNHSIFNH 3 416E 04 NHNH2 S SUM OF SURFACE SITE FRACTIONS 0 999999999999992 SURFACE SITE DENSITY 4 168300000000000E 009 BULK DEPOSITION GM CM 2 IN PHASE 3 SI D 1 043E 07 BULK DEPOSITION GM CM 2 IN PHASE 4 N D 5 111E 08 TIME 5 000000000000000E 002 GAS PHASE STATE P 3 3246E 03 T 1 7130E 03 DENSITY 4 3332E 07 GAS PHASE MOLE FRACTIONS H2 2 386E 05 H 2 628E 08 N2 N 3 071E 11 NH 5 957E 08 NH2 NNH 2 558E 09 N2H2 5 211E 08 N2H3 N2H4 4 810E 11 HF 5 140E 01 F SIF4 4 38
93. OV NEDPAR NYPAR AXORD 7 NELEM NKKGAS NKKSUR NKKBLK NKKTOT NPHASE NFSUR NLSUR NNSUR NFBLK NLBLK NNBLK NIISUR NIICOV NIIREV NIISTK NIICON NIIBHM NIIRNU NIIORD NIIEDP NIIYLD NKKION KEL MORE 8 SKMIN Surface data 9 CSKWRK ISKWRK TICMNAM material name Element data 10 CSKWRK ISKWRK ICENAM M 1 M 1 NELEM names 11 RSKWRK ISKWRK IrAwT M 1 M 1 NELEM weight Species data 168 12 CSKWRK ISKWRK IcKNAM K 1 K 1 NKKTOT names 13 RSKWRK ISKWRK IrKWT K 1 K 1 NKKTOT weight 14 ISKWRK ISKWRK IiKCMP K 1 NELEM P M 1 NELEM K 1 NKKTOT composition 15 ISKWRK ISKWRK IiKCHG K 1 K 1 NKKTOT charge 16 ISKWRK ISKWRK IiKNT K 1 K 1 NKKTOT fit temp s 17 ISKWRK ISKWRK IiKPHS K 1 K 1 NKKTOT phase 18 ISKWRK ISKWRK IiNSCV K 1 K 1 NKKTOT coverage 19 RSKWRK ISKWRK IrKDEN K 1 K 1 NKKTOT density 20 RSKWRK ISKWRK IrKTMP K 1 MAXTP L 1 fit temperatures L 1 MAXTP K 1 NKKTOT 21 RSKWRK ISKWRK IrKTHM L 1 NCP2 K 1 NCP2T N 1 N 1 NCP2 L 1 NTR K 1 NKKTOT thermo coeff nts Ion data if NKKION gt 0 22 NKKION 23 ISKWRK ISKWRK IiIONS K 1 K 1 NKKION spec
94. PNAM KERR Here the output consists of character string names for the phases The first phase is always the gas and its name is PNAM 1 GAS In the present example PNAME 2 PLANE PNAME NFBULK GA 75 RICH and so on If the user does not specify phase names default names are supplied Thus in this example PNAME 8 BULK5 6 1 Mechanisms with Multiple Materials In some reacting flow simulations there may be different types of solid surfaces at which very distinct heterogeneous chemistry takes place For example in a plasma etching reactor there might be a wafer composed of silicon and reactor side walls composed of aluminum Although the main purpose of the simulation might be to understand the etching chemistry at the wafer reactions at the walls also serve to create and destroy species Because chemical reaction mechanisms occurring at the surfaces can be quite different SURFACE CHEMKIN allows the use of multiple materials in Interpreter input files This essentially allows the user to specify several different and complete surface reaction mechanisms one after another separated by a MATERIAL line An example of such an Interpreter input file is shown in Fig 15 It should be pointed out that the numbering of surface and bulk species phases etc proceeds independently for each material This is best illustrated using the example mechanism in Fig 15 In the spirit of the previous section
95. R R K I N explicit K I Is indices for t IS KW R K I N 1 is KWRK IiI hose wit 1 is reverse KWRK IiI hose wit 1 is coefficient reaction IS indices of the gas phas KW R K I IS KWRK IiK cn coverage dependent species for the h reaction with coverage parameters R h EV starts an array of reaction explicit reverse Arrhenius parameters he reaction index of the Nth reaction parameters STK starts an array of reaction h sticking coefficients the reaction index of the Nth sticking STK starts an array of species species with order 1 in the surface reactions with sticking coefficients IS KW R K I N 1 is th species index of the gas phase species with order 1 in the Nth sticking coefficient 165 reaction TiMSTK ISKWRK I ISKWRK IiMSTK starts an array of 0 1 flags for Motz Wise rate correction for the surface reactions with sticking coefficients ISKWRK I N 1 1 use Motz Wise rate correction for the Nth sticking reaction IiIBHM ISKWRK I ISKWRK IilBHM starts an array of reaction indices for the Bohm surface reactions ISKWRK I N 1 is the reaction index of the Nth Bohm reaction TiKBHM ISKWRK I ISKWRK IiKBHM starts an array of species ndices used in the Bohm formulation KWRK I N 1 is the index of the species used for the h Bohm reaction KWRK I ISKWRK IiI dices fo
96. S PHASE STATE o P 1PE12 4 T 1PE12 4 DENSITY 1PE12 4 FORMAT 12E11 3 FORMAT 26X 5 1X A10 FORMAT 22X 10E11 3 END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C G C 0000000000000 WN SUBROUTINE FUN NEO TIME Z ZP RWORK IWORK IMPLICIT DOUBLE PRECISION A H 0 Z INTEGER I N DIMENSION Z NEQ ZP NEO RWORK IWORK COMMON RPAR T AVRAT RU COMMON IPAR KKGAS KKSURF KKBULK KKTOT NFSURF NLSURF NFBULK NLBULK NISK NIPKK NIPKF NIPKL NRSK NSDEN NRCOV NX NWDOT NWT NACT NSDOT NSITDT NNSURF NNBULK Variables in Z are Z K Y K K 1 KKGAS Z K SURFACE SITE FRACTIONS K KFIRST NFSURF KLAST NLSURF Z K BULK SPECIES MASS K KFIRST NFBULK KLAST NLBULK Z K GAS PHASE MASS DENSITY K KKTOT 1 Z K SURFACE SITE MOLAR DENSITIES K KKTOT 2 KKTOT 1 NNSURF Call CHEMKIN and SURFACE CHEMKIN subroutines CALL CKPY Z KKTOT 1 T Z 1 IWORK RWORK P CALL CKWYP P T Z 1 IWORK RWORK RWORK NWDOT CALL CKYTX Z IWORK RWORK RWORK NACT 151 J ana ana E C 100 50 175 200 300 400 410 IF NNSURF GT 0 THEN KFIRST IWORK NIPKF NESURF 1 KLAST IWORK NIPKL NLSURF 1 DO 100 K KFIRST KLAST RWORK NACT K 1 Z K
97. SUBROUTINE SKIREV IR ISKWRK RSKWRK IREV RAR RBR RER Returns an integer flag to indicate whether reaction IR has an explicitly assigned reverse rate constant It also returns the reverse Arrhenius expression values for surface reaction IR if it was explicitly assigned in the SURFACE CHEMKIN interpreter If reverse Arrhenius values were not explicitly assigned RAR RBR and RER will be zero SUBROUTINE SKIRNU IDIM NDIM ISKWRK RSKWRK NIRNU IRNU NSPEC KI RNU Returns the number and indices of surface reactions with real stoichiometric coefficients number of species in the reactions and the species indices and coefficients 84 SUBROUTINE SKISTK IR ISKWRK ISTFL Returns an integer flag to indicate whether reaction IR uses sticking coefficients SUBROUTINE SKIYLD IR ISKWRK RSKWRK IYLD IYION KYLD PYLD Returns an integer flag to indicate whether reaction IR has yield modified species the species index of its ion yield modify flags for its reactants and products and parameters for the yield expression SUBROUTINE SKKION ISKWRK KELECT KKION KION Returns the species number of the electron the number of positive ions in the gas phase and an array of species number for each positive ion SUBROUTINE SKNCON ISKWRK RSKWRK NCON Returns the total number of surface reactions which do not conserve sites of the phases SUBROUTINE SKNU IDIM ISKWRK RSKWRK KSTOIC NSTOIC Returns the stoichio
98. SUR 036 1 CHEMKIN Collection Release 3 6 September 2000 SURFACE CHEMKIN A SOFTWARE PACKAGE FOR THE ANALYSIS OF HETEROGENEOUS CHEMICAL KINETICS AT A SOLID SURFACE GAS PHASE INTERFACE Reaction Design Licensing For licensing information please contact Reaction Design 858 550 1920 USA or CHEMKIN ReactionDesign com Technical Support Reaction Design provides an allotment of technical support to its Licensees free of charge To request technical support please include your license number along with input or output files and any error messages pertaining to your question or problem Requests may be directed in the following manner E Mail Support ReactionDesign com Fax 858 550 1925 Phone 858 550 1920 Technical Support may also be purchased Please contact Reaction Design for the technical support hourly rates at Support ReactionDesign com or 858 550 1920 USA Copyright Copyright 2000 Reaction Design All rights reserved No part of this book may be reproduced in any form or by any means without express written permission from Reaction Design Trademark AURORA CHEMKIN The CHEMKIN Collection CONP CRESLAF EQUIL Equilib OPPDIF PLUG PREMIX Reaction Design SENKIN SHOCK SPIN SURFACE CHEMKIN SURFTHERM TRANSPORT TWOPNT are all trademarks of Reaction Design or Sandia National Laboratories Limitation of Warranty The software is provided as is by Reaction Design without warranty of a
99. T lt 0 SEREM SAVE UTPUT ERS Integer scalar input unit for binary data file Integer scalar formatted output file unit number Real scalar version number of the SURFACE CHEMKIN linkfile Character string machine precision of the linkfile Integer scalar length required for integer work array Integer scalar length required for real work array Integer scalar length required for character work array Logical error flag 123 SKRA Gl X SKRAEX SKRAEX SKRAEX SKRAEX SKRAEX AR RARKARRRA RARA RARA RARA RARA RARA RARA RARA RAR KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKRAEX IR ISKWRK RSKWRK RA Returns the Pre exponential rate constant T SKRAEX or sticking coefficient of the IRth reaction or changes its value depending on the sign of IR INPUT IR Integer scalar reaction index IR gt 0 gets RA I from RSKWRK IR lt 0 puts RA I into RSKWRK ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK If IR lt O RA Real scalar pre exponential or sticking coefficient for reaction IR cgs units mole cm sec K for pre exponential none for sticking coefficients OUTPUT If IR gt 0 RA Real scalar pre exponential or sticking coefficient for reaction IR cgs units mole cm sec K for pre exponential none for sticking co
100. T NT Integer array total number of temperatures used in fitting coefficients of thermodynamic properties for the species dimension at least KKTOT the total species count TMP Real matrix temperatures for dividing the thermodynamic fits for species dimension at least MAXTP for the first and at least KKTOT for the second the total species count cgs units K A Real thr dimensioned array of fit coefficients to the thermodynamic data for species dimension exactly NPCP2 for the first exactly MAXTP 1 for the second and at least KKTOT for the third the total species count The indicies in A N L K mean N 1 NN represent polynomial coefficients in CP R CP R K A 1 L K A 2 L K T A 3 L K T 2 N NN 1 is for the formation enthalpies i e HO R A NN 1 L K N NN 2 is for the formation entropies i e SO R A NN 2 L K 96 L 1 is for temperature lt TMP 2 K L 2 is for TMP 2 K lt temperature lt TMP 3 L NTMP 1 is for TMP NTMP 1 lt temperature K is th species index SKCHRG SKCHRG SKCHRG SKCHRG SKCHRG SKCHRG SKCHRG KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKCHRG ISKWRK RSKWRK KCHARG Returns an array containing electronic charges of the species INPUT ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at leas
101. WRK RSKWRK WT Returns the molecular weights of the species INPUT RSKWRK Real workspace array dimension at least LENRSK OUTPUT WT Real array molecular masses for the species dimension at least KKTOT the total species count cgs units gm mole 136 9 SAMPLE PROBLEM The problem that we have chosen for an example involves the time dependent deposition of a solid film on the surfaces of a fixed volume fixed temperature container that was initially filled with a gas mixture As with any new application for the SURFACE CHEMKIN package one of the first tasks is to derive a system of equations that describes the process to be simulated Here the first equation involves the conservation of mass in the container Tu VO Wg ASWgs k 1L Kg 79 where is time mz is the mass of gas phase species y in the container V is the container volume is the molar production destruction rate of gas phase species by gas phase chemical reactions W are the species molecular weights A is the container wall surface area and s is the molar production rate of gas phase species by surface reactions After introducing the gas phase mass density p m V where mis the total gas phase mass and the gas phase species mass fractions Y m m some manipulation leads to the following equation Me O OMe TA yo eh Ky 80 dt p dt p pV The total mass in the gas phase depends on the production destruction of gas phase species
102. ace species count KKBULK Integer scalar total bulk species count KKTOT Integer scalar total species count KKGAS KKSUR KKBULK NNPHAS Integer scalar total phase count gas sites bulks NNSURF Integer scalar total surface phase count NE SURF Integer scalar phase index of the first surface phase NLSURF Integer scalar phase index of the last surface phase NNBULK Integer scalar total bulk phase count NFBULK Integer scalar phase index of the first bulk phase NLBULK Integer scalar phase index of the last bulk phase IISUR Integer scalar total surface reaction count SKINIT SKINIT SKINIT SKINIT SKINIT SKINIT SKINIT KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKINIT LENISK LENRSK LENCSK LINSK LOUT ISKWRK RSKWRK CSKWRK IFLAG Reads the surface linkfile and creates internal work arrays ISKWRK RSKWRK and CSKWRK SKINIT must be called before any other Surface CHEMKIN subroutine can be used as the work arrays must be available as their input INPUT LENISK Integer scalar length of the integer array ISKWRK LENRSK Integer scalar length of the real array RSKWRK LENCSK Integer scalar length of the character string array CSKWRK LINSK Integer scalar linkfile input file unit number LOUT Integer scalar formatted output file unit number OUTPUT ISKWRK Integer workspace array dimension
103. acter string array phase names dimension at least NNPHAS the total phase count Logical character length error flag SKSYMR SKSYMR SKSYMR SKSYMR SKSYMR SKSYMR KKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKEKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK E SKSYMR IR LOUT ISKWRK RSKWRK CSKWRK LT RNAM KERR he character string representation of reaction IR Integer scalar reaction index Integer scalar formatted output file unit number Integer workspace array dimension at least LENISK Real workspace array dimension at least LENRSK Character string workspace array dimension at least LENCSK Integer scalar nunber of non blank characters in the reaction string Character string representation of reaction Logical character length error flag 134 SKSYMS SUBROUTINE Returns a T INPUT CSKWRK LOUT OUTPUT KNAM KERR SKUML SUBROUTINE Returns an INPUT T ISKWRK RSKWRK OUTPUT UML SKUMS SUBROUTINE Returns an INPUT ECE ISKWRK RSKWRK OUTPUT UMS SKSYMS SKSYMS SKSYMS SKSYMS SKSYMS SKSYMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKSYMS ISKWRK CSKWRK LOUT KNAM KE character array of species names E ps po Character string workspace array dimension at least LENCSK Integer scalar formatted output file unit number Char
104. acter string array species names dimension at least KKTOT the total species count Logical character length error flag SKUML SKUML SKUML SKUML SKUML SKUML KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKUML T ISKWRK RSKWRK UML array of the internal energies in molar units Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K Integer workspace array dimension at least LENISK Real workspace array dimension at least LENRSK Real array internal energies of the species dimension at least KKTOT the total species count cgs units ergs mole SKUMS SKUMS SKUMS SKUMS SKUMS SKUMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SKUMS T ISKWRK RSKWRK UMS array of the internal energies in mass units Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K Integer workspace array dimension at least LENISK Real workspace array dimension at least LENRSK Real array internal energies of the species dimension at least KKTOT the total species count cgs units ergs gm 135 SKWT SKWT SKWT SKWT SKWT SKWT SKWT ee RR KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKWT ISK
105. action IR cgs units mole cm sec K Real scalar explicit temperature dependence xponents for reaction IR Real scalar explicit activation energy for reaction IR cgs units Kelvins 115 SKIRNU SUBROUTIN Returns t s toichiometric coefficients SKIRNU SKIRNU SKIRNU SKIRNU SKIRNU SKIRNU KEKE KKK KKK KKK KKK KKK KKK KKK KKK KK KKK KKK KA KA AAA AAA KEKE KK KKK KKK KKK KKK KKK KKKKK KKKKKK E SKIRNU IDIM NDIM ISKWRK RSKWRK NIRNU IRNU NSPEC KI RNU he number and indices of surface reactions with real number of species in the reactions and the species indices and coefficients INPUT IDIM Integer scalar dimension of the arrays IRNU and NSPEC and the second dimension of matrices KI and RNU IDIM must be at least NIRNU the number of surface reactions with real stoichiometric coefficients NDIM Integer scalar first dimension of matrices KI and RNU NDIM must be at least MAXSPR the maximum number of species allowed in a surface reaction ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT NIRNU Integer scalar total number of surface reactions with real stoichiometric coefficients IRNU Integer array indices of surface reactions with real stoichiometric coefficients dimension at least NIRNU NSPEC Integer array total number of spe
106. ake of parallelism we adopt the nomenclature for bulk species X a xK K 10 It is almost never a good approximation that bulk species form an ideal solution Therefore the concept of an activity and the standard state to which it refers must be introduced at the outset In the limiting case of an ideal solution the activity of a species is equal to its mole fraction SURFACE CHEMKIN takes the approach that the activity a of bulk species k is used in all chemical rate expressions Moreover SURFACE CHEMKIN does not explicitly evaluate the relationship between bulk mole fraction and the bulk activities Instead it is up to the Application program to specify the relationship between the two 26 3 2 Surface Site Non conservation It is possible that a given surface reaction or reactions will not conserve the number of surface sites In that case the density of sites I is not necessarily a constant Therefore one must take care in using an equality such as Eq 9 when relating a site fraction and a surface molar concentration that is to ensure that the current correct value of T t is used It may be necessary to add equations to calculate the current value of the total site concentration of each surface phase Because surface site non conservation is an issue that can alter the basic governing equations of the system we require that one acknowledge its use by adding a keyword on the REACTION line discussed later
107. allowed within a number There cannot be more than six reactants or six products in a reaction To specify a sticking coefficient rather than a rate constant the three numbers after the reaction description have the meaning a b and c see Eq 52 and the auxiliary information word STICK must appear on the next line of input To use this option the reaction must have only one gas phase species as a reactant and its stoichiometric coefficient must be 1 All characters on a line following an exclamation mark are comments 62 5 5 2 SURFACE REACTION AUXILIARY INFORMATION DATA Auxiliary information data appears on one or more separate lines after the reaction data line is read and serves to modify or give additional parameters needed to evaluate that reaction s rate expression The format in an auxiliary information line is a character string keyword followed by a slash delimited field containing an appropriate number of parameters either integer floating point E format or character For a reversible reaction auxiliary information data may follow the reaction to specify Arrhenius parameters for the reverse rate expression Here the three Arrhenius parameters A and E for the reverse rate must follow the auxiliary keyword REV Using this option overrides the reverse rates that would normally be computed through the equilibrium constant Eq 36 It sometimes happens that two or more reactions can involve the same se
108. ame of a gas phase species or a bulk species and must be unique among the site species An optional slash delimited site occupancy number may follow a species name i e the number of individual sites that this species occupies For example a large chemical species might cover two or more sites The default site occupancy for a surface species is 1 The sets of SITE data input can continue for as many site types as are needed Any set of up to sixteen upper or lower case characters can be used as a site name or species symbol In addition each species must be composed of elements that have been identified in the CHEMKIN Interpreter and thus contained in the CHEMKIN Linking File unit number LINKCK One of the primary purposes of the site data is to define the order in which FORTRAN arrays of site species information are referenced in the Surface Subroutine Library Any line starting with or any portion of a line following an exclamation mark is considered a comment and will be ignored Blank lines are also ignored Figure 7 shows sample site data The rules for site data are summarized in Table 1 Species symbols may not begin with a number a plus sign a pound sign or an equality sign have imbedded blanks or include a slash An ionic species may end with any number of plus or minus signs an imbedded plus sign must be enclosed in parentheses 51
109. an flow velocity Specific internal energy of the k species Exponential constant in reaction yield expression Internal energy of the k species Standard state internal energy of the k species Volume Diffusion velocity of the k species Molecular weight of the positive ionic species in a Bohm type reaction Molecular weight of k species Mean molecular weight of a mixture Height Array of species mole fractions Array of surface species site fractions Mole fraction of the k species Molar concentration of the k species Mass fraction of the k species Site fraction of the k species on site n 10 none moles cm sec ergs g K ergs mole K sec K K K none cm sec ergs g none ergs mole ergs mole cm cm sec g mole g mole g mole cm none none none moles cm none none GREEK ki Mk 10 Mk Hki Xk Parameter in mechanism Temperature exponent in the rate constant of the i reaction Standard state density for surface phase n Site density for surface phase n Production rate for surface phase n Site density summed over all surface phases Sticking coefficient for the i surface reaction Thermal conductivity Mass density Mass density of the k bulk species Stoichiometric coefficient of species Kin reaction i Vg Oj Vki Stoichiometric coefficient of the k reactant species in the i reaction Stoichiometric coefficient of the k product species in the i rea
110. and products in a particular reaction The forward rate constants k for the J reactions are by default assumed to have the following Arrhenius temperature dependence Cc ky AT hi exp oF 35 RT SKABE SKRAEX where the pre exponential factor A the temperature exponent and the activation energy E are specified These three parameters are required input to the SURFACE CHEMKIN package for each reaction There are a number of ways in which the rate expression for a reaction can be altered which are summarized as separate sections in this chapter For reversible reactions the reverse rate constants k are related to the forward rate constants through the equilibrium constants as The user can over ride the use of Eq 36 by explicitly declaring Arrhenius coefficients for the reverse reaction in the Interpreter input via the auxiliary keyword REV explained in Chapter 5 An Application program can call Library routine SKIREV to find out if reverse coefficients were input for a given reaction and their values Two gas constants R and R are used throughout this manual and the SURFACE CHEMKIN software Rc is used only in conjunction with the activation energy E and has compatible units The reason for the duality is that many users would rather use different units say calories mole for the activation energies even though other units say cgs or SI are used elsewhere 33 Although K is given in
111. array of the non dimensional specific heats at constant pressure SUBROUTINE SKHORT T ISKWRK RSKWRK HORT Returns an array of the non dimensional enthalpies SUBROUTINE SKMXTP ISKWRK MXTP Returns the maximum number of temperatures used in fitting the thermodynamic properties of the species SUBROUTINE SKRHEX K ISKWRK RSKWRK A6 Returns an array of the sixth thermodynamic polynomial coefficients for a species or changes their value depending on the sign of K SUBROUTINE SKSOR T ISKWRK RSKWRK SOR Returns an array of the non dimensional entropies 7 9 Thermodynamic Properties Mass Units 86 SUBROUTINE SKAMS T ISKWRK RSKWRK AMS Returns an array of the standard state Helmholtz free energies in mass units SUBROUTINE SKCPMS T ISKWRK RSKWRK CPMS Returns an array of the specific heats at constant pressure in mass units SUBROUTINE SKGMS T ISKWRK RSKWRK GMS Returns an array of the standard state Gibbs free energies in mass units SUBROUTINE SKHMS T ISKWRK RSKWRK HMS Returns an array of the enthalpies in mass units SUBROUTINE SKSMS T ISKWRK RSKWRK SMS Returns an array of the standard state entropies in mass units SUBROUTINE SKUMS T ISKWRK RSKWRK UMS Returns an array of the internal energies in mass units 7 10 Thermodynamic Properties Molar Units SUBROUTINE SKAML T ISKWRK RSKWRK AML Returns an array of the standard state Helmholtz free energies
112. ase and an array of species number for each positive ion INPUT ISKWRK Integer workspace array dimension at least LENISK OUTPUT KELECT Integer scalar species index of the electron species KKION Integer scalar total gas phase positive ion count KION Integer array species indices for the gas phase positive ions dimension at least NKKGAS the gas phase species count 117 SKKTFL SKKTFL SKKTFL SKKTFL SKKTFL SKKTFL SKKTFL ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKKTFL ISKWRK KTFL Allows the user to assign a location in the temperature array to use for the gas phase species INPUT ISKWRK Integer workspace array dimension at least LENISK KTFL Integer array indices into the temperature s for gas phase species dimension at least KKGAS the total gas phase species count Default value stored in ISKWRK is set to 1 in SKINIT SKLEN SKLEN SKLEN SKLEN SKLEN SKLEN SKLEN KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKLEN LINSK LOUT LENI LENR LENC IFLAG Reads the first record of the linkfile to return the lengths required for the integer real and character work arrays INPUT LINSK Integer scalar input unit number assigned to linkfile LOUT Integer scalar formatted output unit file number OUTPUT LEN
113. atabase manual An alternative input data format allows specification of more than two temperature ranges Use of this format is not backwards compatible with the old NASA format but does provide more flexibility in describing the thermodynamic data for complex functions of temperature This alternative approach is summarized at the end of Table 3 The alternative lines 7 9 can be used in place of lines 4 6 Lines 7 specifies all of the temperature values that define the temperature intervals Lines 8 9 are then repeated for each specified temperature interval in descending order of temperature ranges When thermodynamic data input is required it must immediately follow species data SITE and BULK data The first thermodynamic data line must start with the word THERMO or THER If all the 55 thermodynamic data are input directly to the Interpreter then the first line of this section must read THERMO ALL and the program will not expect a Thermodynamic Database from unit number LTHRM for this option the next line must be line 2 of Table 3 For either option the subsequent thermodynamic data lines must be in the format of lines 3 6 of Table 3 For the THERMO option the default midpoint temperature is taken from the second line of information already in the Thermodynamic Database The THERMO input can include as many species as are needed Thermodynamic data for any species that were not declared in the SITE and BULK sections will be ignore
114. by surface reaction as stated by 5 As W 81 We rewrite this equation slightly to make p a dependent variable and use the area to volume A V as a parameter Kg RS We 82 On the surface the number of moles of species k is given by Ng Zk mi AJO n 83 137 where Zy n is the site fraction of species k on surface site n fraction of sites occupied by species k in phase n T is the density of sites in phase n in moles cm2 and oy n is the number of sites that species k occupies The molar production destruction rate of surface species k by surface reaction is stated as Es SAs SRL 84 In terms of site fractions Z n the equation governing the surface species is given as dZ n _ SkOk N Zn dl y 85 dt T r dt where the last term can be dropped if the number of surface sites if fixed When surface reactions create or destroy sites then a conservation equation is included for the site densities of each phase n di 86 Ti 86 However our sample mechanism conserves sites so the time derivative in Eq 86 is trivially zero The governing system of ordinary differential equations and accompanying initial conditions form an initial value problem The equations will be solved using the software VODE We find this software to be highly reliable for the solution of a wide range of stiff initial value problems The FORTRAN code for solution of the sample problem is given i
115. ce array NLSURF Real array dimension at least KKTOT cgm units the next KKBULK activities should be from 0 to 1 and phase Real array site densities dimension at least NPHASE but the subroutine only us sites per species for bulk phase species should sum to 1 for each and for the site types the total phase count s sit moles cm 2 phas ntries dimension at least LENISK dimension at least LENRSK the gm cm 3 for gas densities for the species total species count phase species bm cm 2 for surface species gm cm 3 for bul mass densities are not required to be input to NOT E k species the Interpreter for bulk phase species If they are input they are returned by this subroutine If not DEN 1 0 for the bulk species 101 SKDRDA SUBROUTIN SKDRDA SKDRDA SKDRDA SKD RDA SKDRDA SKDRDA KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK Py T Returns t with respect INPUT IR P T ACT SD ISKWRK RSKWRK OUTPUT DKDAI SK DRDA IR P T KKKKKK ACT SDEN ISKWRK RSKWRK DKDAT he partial derivative of the rates of production of the species H nteger scalar Real scalar cgs units Real array the application to the pre exponential constan surface reactio pressure dynes cm 2 temperature s program to be
116. cies in a surface reaction dimension at least NIRNU RIA Integer matrix species indices for species in a surface reaction dimension at least MAXSPR for the first and at least NIRNU for the second KI M N is the species index of the Mth species in the Nth real coefficient surface reaction RNU Real matrix stoichiometric coefficients for species in the NIRNU reactions dimension at least MAXSPR for the first and at least NIRNU for the second RNU M N is the stoichiometric coefficient of the Mth species in the Nth real coefficient surface reaction and RNU M lt O if the Mth species is a reactant RNU M gt 0 if the Mth species is a product SKISTK SKISTK SKISTK SKISTK SKISTK SKISTK SKISTK kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkkxkxkxkkxkkxkkkxkxkkkxkxkkxkxkxkkxkkkxxkx k KKEKKKKKKKK KKK KKK A KKKKKK SUBROUTINE SKISTK IR ISKWRK ISTFL Returns a sS INPUT IR ISKWRK OUTPUT ISTFL n integer flag to indicate whether reaction IR uses ticking coefficients Integer scalar index of a surface reaction Integer workspace array dimension at least LI ENISK Integer scalar 0 reaction IR does not use sticking coefficients 1 reaction IR does use sticking coefficients 116 SKIYLD SKIYLD SKIYLD SKIYLD SKIYLD SKIYLD SKIYLD ee ee ee ee ee ee KKKKKKKKKKKKKKKKKKAKKKKKKKK KKKKKK SUBROUTINE SKIYLD IR ISKWRK RSKWRK IYLD IYION KYLD PYLD Returns an integer flag to indicate whethe
117. ction Production rate of the k species from gas phase reactions Stefan Boltzmann constant Number of sites occupied by the ee species Emissivity Coverage parameter Coverage parameter Chemical potential of the k species Chemical potential of the k species Coverage parameter Dependent variable in an Application program Yield enhancement factor ion energy yield reaction Chemical symbol of the k species 11 none moles cm moles cm2 moles cm sec moles cm none erg cm K sec g cm g cm mole cm3sec erg cm2sec K none cal mole K none none none none none 1 INTRODUCTION Heterogeneous reaction at the interface between a solid surface and adjacent gas is central to many chemical processes The development of the software package SURFACE CHEMKIN was motivated by the need to understand the complex surface chemistry in chemical vapor deposition systems However the approach and implementation are general to allow use in such diverse applications as chemical vapor deposition chemical etching combustion of solids and catalytic processes and a wide range of chemical systems The SURFACE CHEMKIN software provides a powerful capability to help model understand and optimize important industrial and research chemical processes The SURFACE CHEMKIN software is designed to work in conjunction with the CHEMKIN software which handles the chemical kinetics and thermodynamic properties in the
118. d Figure 9 shows some examples of thermodynamic property input In these examples for OH OH and OH it is seen from columns 25 34 that the elemental composition of each molecule is one O atom and one H atom In addition columns 35 39 indicate that two of the species OH and OH are ionic since they contain 1 and 1 electrons E respectively The G in column 45 indicates that all three species are gaseous This phase information is ignored by SURFACE CHEMKIN The 1000 00 in columns 66 73 for OH indicates that the common temperature between the high and low temperature fits is 1000 00 K If columns 66 73 are left blank as they are for OH and OH then the common temperature is that given in columns 21 31 of line 2 in Table 3 which in this example is in the Thermodynamic Database An alternative format is shown for OH if more than two temperature ranges are required In this case we ve given the molecule a different name MyOH but the elemental composition is the same as for OH The line after the elemental composition contains the TEMP description of minimum common and maximum temperatures and a set of coefficients for each temperature range ordered from highest to lowest The following cases summarize the possibilities for specifying thermodynamic data 54 1 CASE 1 ALL THERMODYNAMIC DATA FROM DATABASE ONLY 1 Assign the database as file therm dat 2 No THERMO data required as input 54 2 CASE 2 T
119. d within the total number n the category CATEGORY_NAME cified category no category is specified th the same values as they would RY NAME IND will of IND and JADE This assumes that the elements of IRAY were grouped into two sets consisting of 4 and 2 elements respectively and the following names COLORS RED BLUE JADE RUBY and STONES TOPAZ JADE If ISTR BLUE then IND 2 and NT 1 if ISTR PINK then IND 0 and NT 0 and if ISTR JADE then IND 3 and NT 2 If ISTR BLUE COLORS then IND 2 and NT 1 if ISTR BLUE STONES then IND 0 and NT 0 if ISTR JADE GEMS then IND 0 and NT 0 and if ISTR JADE STONES then IND 6 and NT 1 INPUT ISTR Character string which may or may not end with a slash delimited substring TRAY Character string array dimension at least NN NN Integer scalar number of entries in IRAY SETS Character string array cross reference set to relate with elements of IRAY dimension at least NSETS NSETS Integer scalar number of entries in SETS ISET Integer array total number of entries in a subset of IRAY dimension at least NSETS OUTPUT IND Integer scalar index of ISTR in IRAY If ISTR is not in IRAY IND 0 If the slash delimited substring of ISTR is not in SETS IND 0 If the slash delimited substring of ISTR is in SETS
120. declared in the list of species names in the CHEMKIN Interpreter input The keyword ENRGDEP allows the rate constant to depend on ion energy according to Eq 51 The keyword is followed by the three parameters E fi and g which are slash delimited ion 0 gt There must be exactly one positive ionic reactant species in the reaction Only irreversible reactions are allowed with this option The keyword FORD or RORD can be used to change the reaction order with respect to species concentration of the forward or reverse reaction respectively for any species in the mechanism regardless of whether the species appears as a reactant or a product in the reaction The species name and the new reaction order slash delimited follow the keyword To modify the stoichiometric coefficients in a sub reaction using the ion yield option one must precede each species in the sub reaction or its stoichiometric coefficient with the pound sign Following the reaction line declare the YIELD auxiliary keyword then the four parameters hyield Evyielao ti and u of Eq 62 between slashes There must be exactly one positive ionic reactant species in the reaction Only irreversible reactions are allowed with this option The sub reaction demarked with the symbols must satisfy mass elemental charge and site balance unless the NONCON option appeared on the REACTION line 66 Table 5 Summary of the Rules for Auxiliary Information Data Cont
121. e which handles gas phase molecular transport may or may not be needed in a particular application If it is used the TRANSPORT Property Fitting Program reads the CHEMKIN Linking File and identifies all the gas phase species that are present in the gas phase reaction mechanism Then drawing on a database of molecular parameters it computes polynomial fits to the temperature dependent pure species viscosities thermal conductivities and binary diffusion coefficients As with the other packages it provides a Linking File that is read by an initialization subroutine in the TRANSPORT Property Subroutine Library Subroutines from this library may be called by the Application program to return transport properties for individual species or for multicomponent gas mixtures 47 It is clear from the foregoing description that using these software packages requires the interaction of many programs and the manipulation of many input and output files Therefore while the modular structure of the software provides a powerful capability to formulate a wide variety of applications writing a new application also requires that users be reasonably familiar with their computers operating systems and compilers It may also be noted from the flow chart of Fig 5 that the three utility software packages do not solve any problems they simply make subroutines available to aid formulation of a problem for the CHEMKIN Application This structure provides maximum flexibi
122. e Interpreter The first two lines identify a site type called SILICON that has a site density of 1 66 x 10 moles cm2 Only one species SI S exists on this site type The bulk material is identified as SI B and it has a mass density of 2 33 g cm This is a very simple example that has only one site type occupied by only one species and only one pure bulk material In general however an input file could specify many different site types each of which could be occupied by a variety of species Furthermore there could be several bulk phase mixtures that could each be composed of several species Examples of all these possibilities are given later in the manual The reaction mechanism itself is listed next The symbol gt in each reaction expression indicates that all the reactions are irreversible The three numbers following each reaction expression are its Arrhenius rate parameters pre exponential factor temperature exponent and activation energy All of the reactions in the mechanism have the same form a gas phase species reacting on a silicon site The reaction of silane at the surface is illustrated in Fig 2 Each silicon containing gas phase species can react on an atomic surface site SI S to deposit a silicon atom as SI B and release hydrogen back into the gas phase We have included SI S as both a reactant and a product to indicate that a site must be available at which the gas phase species can react In the
123. ecies Index of the first gas phase species Index of the last gas phase species Total number of surface species Index of the first surface species in phase n Index of the last surface species in phase n Vector containing the number of species in each phase Equilibrium constant in concentration units for the i th reaction depends on reaction Equilibrium constant in pressure units for the i th reaction none Number of coefficients in polynomial fits to Cy R Mass of the k species g Index for phases Surface normal unit vector points from the gas into the bulk layer Total number of phases Avogadro s number Total number of bulk phases Index of the first bulk phase Index of the last bulk phase Number of gas phases always equals 1 Total number of surface site types phases Index of first surface phase Index of last surface phase Pressure dynes cm Pressure of one standard atmosphere dynes cm Rate of progress of the i h reaction moles cm2sec Universal gas constant ergs mole K Universal gas constant in same units as activation energy E cal mole K Wion Reverse reaction order specified for he k species in i reaction Production rate of the k species from surface reactions Standard state specific entropy of the ae species Standard state entropy of the a species Time Temperature Ambient temperature Electron temperature Exponential constant in reaction yield expression Convective velocity Stef
124. ecies and different surface reactions can be specified in the same SURFACE CHEMKIN input file through the use of multiple materials At the beginning of each separate portion of the input file corresponding to a given material the user gives an input line with the keyword MATERIAL followed by an optional slash delimited material name If no name for the material is supplied the interpreter substitutes a default name MATERIALn where n is the number of the material e g MATERIAL2 for the second material given in an input file An example of the usage of multiple materials is given at the end of Chapter 6 of this manual 50 5 2 Site Data Surface phase species exist on sites and a site and its species must be identified on one or more lines of site data The first line in a set of site data must start with the word SITE an optional name may be associated with a site if it immediately follows SITE and is delimited by slashes If no name for the site is supplied the interpreter substitutes the default name SITEn where n is the number of a site e g SITE2 for the second site type listed Following SITE and or the site name the word SDEN and a slash delimited density the standard state site density for this site in moles cm for the site is required The species that can reside on the site type are declared by a list of species symbols names on the same line or on additional lines The name of a site species must not duplicate the n
125. ed users can construct their own subroutines to calculate a T P X possibly incorporating models for non ideality of the bulk phase and can have the consequences properly incorporated into the surface kinetics mechanism Although the activities of all components of an ideal solution must sum to 1 this condition is not enforced in SURFACE CHEMKIN It is however enforced in many of the CHEMKIN Applications that employ SURFACE CHEMKIN Since SURFACE CHEMKIN allows for a number of different types of species gas species any number of types of surface sites species residing on surface sites pure bulk species bulk mixtures and species present in a bulk mixture it is necessary to be able to keep track of them We use the notion of different physical phases to group the chemical species in a problem Our nomenclature corresponds to that of Eriksson which has been extended to account for surface sites The order in which we discuss the phases is the order in which SURFACE CHEMKIN groups them Phase number 1 is the gas phase Information about species in the gas phase is passed to SURFACE CHEMKIN from the gas phase CHEMKIN interpreter The mole fractions of the gas phase species correspond to species activities mentioned below We consider every type of surface site to be a distinct phase If there are N types of sites specified then phases 2 through N 1 are these sites The user can specify the names of chemical species
126. efficients 124 SKRAT SKRAT SKRAT SKRAT SKRAT SKRAT SKRAT KKEKKKKK KKK KKK KKK KKK KKK KKK KKK KKK KKK KK KKK KKKX kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkkkkkkxk KKKKKK SUBROUTINE SKRAT P T ACT SDEN ISKWRK RSKWRK SDOT SITDOT Returns production rates for the species and sites INPUT P Real scalar pressure cgs units dynes cm 2 TEE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ACT Real array activities of the species dimension at least KKTOT the total species count The first KKGAS activities are mole fractions the next KKSURF activities are site fractions species density normalized by the site density surface concentration in moles cm 2 is ACT K SITE_DENSITY sites per species and the next KKBULK activities for bulk phase species should be from 0 to 1 and should sum to 1 for each phase SDEN Real array site densities for the site types dimension at least NPHASE the total phase count but the subroutine only uses site phas ntries NFSURF lt N lt NLSURF cgs units moles cm 2 ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT SDOT Real array production rates of the species dimension at least KKTOT the total species count cgs un
127. ension at least LENRSK OUTPUT CPOR Real array nondimensional specific heats at constant pressure for the species dimension at least KKTOT the total species count SKCZTA SKCZTA SKCZTA SKCZTA SKCZTA SKCZTA SKCZTA KKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKEKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKCZTA T CZ SDEN ISKWRK RSKWRK ACT Returns the activities of the species given the pressure temperature and concentrations INPUT T SD ISKWRK RSKWRK CZ OUTPUT ACT EE Real array temperature s the application program species temperatures no cgs units K Real array si dimension at least NPHASE minally 1 dimension is determined by to be the total number of te densities for the site types the total phase count but the subroutine only uses sit NFSURF lt N lt NLSURF cgs units moles cm 2 nteger workspace array eal workspace array eal array nd bulk species activities imension at least KKTOT the to he first KKGAS gas phase concen he next KKSURF si he final KKBULK e Ertra M W DH ntries are bul Real array activi dimension at leas The first KKGAS ac the next KKSURF ac species densi surface conce t the to KKTOT n nd T phas tal species count ies of the species tal species count tivities are mole fractions tivities are site fractions ty normalized by the site densi tration in moles
128. equivalent to OH OH The symbol is used to mark stoichiometric coefficients that are additionally multiplied by a YIELD coefficient This is explained later D elimiters A plus sign is the delimiter between all reactant species names and between all product species names An equality sign is the delimiter between the last reactant and the first product in a reversible reaction lt gt An equality sign enclosed by angle brackets can also be used as the delimiter between the last reactant and the first product in a reversible reaction gt An equality sign with an angle bracket on the right is the delimiter between the last reactant and the first product in an irreversible reaction The second field of the reaction line is used to define the Arrhenius rate coefficients A f and E in that order as given by Eq 35 At least one blank space must separate the last species name in the reaction and first number The three numbers must be separated by at least one blank space be stated in either integer floating point or E format e g 123 or 123 0 or 12 3E1 and have units associated with them although the units do not appear on the input line Unless modified by the REACTION line the default units for A are cgs cm sec K mole the exact units depending on the order of the reaction The factor i is dimensionless The default units for the activation energies are cal mole 60 The second field of
129. ers are always stored internally in the same way i e activation energies in Kelvins dimensionless temperature exponents and pre exponential factors consistent with moles cm sec K The program converts the user input activation energies in an obvious way However it is worthwhile to state explicitly the conversion for the Arrhenius pre exponential constant In converting from molecules to Mh sm moles A moles A molecules x N A y 77 where N4 is Avogadro s number and k 1 67 Note that the v are the stoichiometric coefficients for the gas phase and surface reactant species not product species or bulk phase species 5 5 5 ERROR CHECKS The Interpreter checks each input line for proper syntax and writes self explanatory diagnostic messages on the interpreter output file if errors are encountered If an error occurs the Interpreter continues to read and diagnose the input but an error flag is written to the Linking file and Surface Library subroutine SKINIT will not initialize the work arrays Therefore the input must be error free before any of the SURFACE CHEMKIN subroutines can be called in an application program Possibilities for an error condition are as follows Site and Bulk Species Data e A duplicated species symbol name is not considered a fatal error but is eliminated from consideration and a warning diagnostic message is printed e Nosite density is found for a declared site or the site de
130. es in molar units INPUT ECs Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT AML Real array standard state Helmholtz free energies for species dimension at least KKTOT the total species count cgs units ergs mole SKAMS SKAMS SKAMS SKAMS SKAMS SKAMS SKAMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKAMS T ISKWRK RSKWRK AMS Returns an array of the standard state Helmholtz free energies in mas units INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT AMS Real array standard state Helmholtz free energies for species dimension at least KKTOT the total species count cgs units ergs gm 94 SKATCZ SKATCZ SKATCZ SKATCZ SKATCZ SKATCZ SKATCZ ee ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKATCZ P T ACT SDEN ISKWRK RSKWRK CZ Returns the concentrations of the species given the pressure temperature and activities
131. es information Information about a species say a thermodynamic property is presumed to be available in ordered arrays beginning with the first gas phase species continuing through the surface species and ending with the last bulk species In the expressions and equations below we presume that there are K species and we use the index k to refer to a specific species There are K gas phase species which by convention are always the first entries in the species arrays The index of the first gas phase species is K K f 1 by our convention and the last gas phase species index is K k K el Thus the gas phase species indices are K e lt k lt K In a similar way surface species indices are in the range Ki lt k lt K E and bulk species are in the range K M lt k lt K The surface species may be arranged on any number of sites and the bulk species may exist in any number of bulk mixtures Furthermore situations can occur in which there are no surface species and or no bulk species 7 As discussed in Chapter 2 the species are grouped in phases The first is the gas phase whose index n 1 The next N phases if they are present are the surface sites whose phase indices are bounded by N f lt n lt N The final N phases are the bulk mixtures whose indices are bounded by N f lt n lt N In each phasen there are Kypaseln species and those species have indices in the range Ke nasen Sk lt Kee 3 1 Concentration Units
132. example however the surface silicon SI S is distinguished from the bulk deposit SI B by virtue of its position as the top most atom at the surface Therefore each time a SI S is consumed by a reaction the bulk layer becomes one atom thicker 15 SITE SILICON SDEN 1 66E 09 SI S BULK SI B 2 33 REACTIONS SIH4 SI S gt SI S SI B 2H2 1 05E17 0 SI2H6 2SI S gt 2SI S 2SI B 3H2 4 55E26 0 SIH2 SI S gt SI S SI B H2 3 9933E11 0 SI2H2 2SI S gt 2SI S 2SI B H2 1 7299E20 0 2SI2H3 4SI S gt 4SI S 4SI B 3H2 6 2219E37 0 H2SISIH2 2SI S gt 2SI S 2SI B 2H2 1 7007E20 0 2SI2H5 4SI S gt 4SI S 4SI B 5H2 6 1186E37 0 2SIH3 2SI S gt 2SI S 2SI B 3H2 2 3659E20 0 2SIH 2SI S gt 2SI S 2SI B H2 2 4465E20 0 SI SI S gt SI S SI B 4 1341E11 0 H3SISIH 2SI S gt 2SI S 2SI B 2H2 1 7007E20 0 SI2 2SI S gt 2SI S 2SI B 1 7607E20 0 SI3 3SI S gt 3SI S 3SI B 8 6586E28 0 END Figure 1 Sample Reaction M echanism as Read by the SURFACE CHEMKIN Interpreter O O SiH Si s gt 2H Si b Si s 49900000101 A A A A 40000 40000 IDA AO A AOS Figure 2 Illustration of Gas Phase Silane Reacting at a Surface to D eposit a Silicon Atom and Release Two Hydrogen M olecules into the Gas Phase 16 and the silicon atom that just left the gas now forms the top most surface layer i e SI S For
133. feren EB An Report UCID 30132 tial April 1977 Experimental Ordinary Differential April 1 Collection of ODE Stepleman et al eds ernative Implemen tation 318 Authors aqgagngaagqaaagnaaagaaanagaaagaaqaagnaaanaanagnagnaaagaaaananadanaagnaagnaaagnaanaana Peter N Brown and Alan C Computing and Mathematics Research Division Hin 159 dmarsh L 316 aqagaaganagnaaaaaanagaanagaaagaagaagnaaagaaagagnaaagaagaagaaagnagaaagaaanadnaeaaanadnaaadaanaangaaaaana and Lawrence Livermor Livermore CA 9455 George D Byrne Exxon Research and Clinton Township Route 22 East Annandale NJ 0880 National Laboratory 0 Engineering Co 1 Summary of us Communication situations i age between the user a s summarized here nd the DVODE package for normal This summary describes only a subset of the full set of options available See the full description for details including optional communication nonstandard options and instructions for special situations See also the example problem with program and output following this summary A First prov SUB DOU ide a subroutine of ROUTINE F NEQ T BLE PRECISION T Y DIMENSION Y NEQ YDOT hich supplie s the vector functi Next deter tiffness occ hose real pa eciprocal of se a method hoices for M atrix in som torage limit mine or guess whe ur
134. g array of element names Character string workspace array dimension at least LENCSK Integer scalar formatted output file unit number Character string array element names dimension at least NELEM the total element count Logical character length error flag 133 SKSYMM SUBROUTIN Returns t INPUT ISKWRK CSKWRK LOUT OUTPUT MATNAM KERR SKSYMP SUBROUTIN Returns a INPUT CSKWRK LOUT OUTPUT PNAM KERR SKSYMR SUBROUTIN Returns t IN IR LO Is RS ES PUT UT KWRK KWRK KWRK UTPUT RNAM ERR B SKSYMM SKSYMM SKSYMM SKSYMM SKSYMM SKSYMM KKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKEKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK E SKSYMM ISKWRK CSKWRK LOUT MATNAM KERR he character string name of a material Integer workspace array dimension at least LENISK Character string workspace array dimension at least LENCSK Integer scalar formatted output file unit number Character string material name Logical character length error flag SKSYMP SKSYMP SKSYMP SKSYMP SKSYMP SKSYMP KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK Py T Gl SKSYMP ISKWRK CSKWRK LOUT PNAM K character string array of phase names Character string workspace array dimension at least LENCSK Integer scalar formatted output file unit number Char
135. g list of all species and in other cases it may be convenient to refer only to those species in a particular phase Thus it is important to have a data structure that is flexible enough to capture the required generality yet sufficiently friendly to make it easy to use In this chapter we use specific examples to illustrate the data structures and how to use them in an application program Consider a system involving Gallium Arsenide depositar where an example gas phase reaction mechanism is shown in Fig 12 and a surface mechanism is shown in Fig 13 The gas phase mechanism includes fourteen species even though only eleven of them appear directly in the gas phase reaction mechanism Arsine ASH3 in our notation is typically a reactant gas in a Gallium Arsenide deposition process Monatomic arsenic AS and the arsenic dimer AS2 have been included because the surface reaction mechanism includes desorption reactions which introduce them into the gas Therefore because all gas phase species are handled by CHEMKIN these extra three species must be included as input to the CHEMKIN Interpreter Of course the gas phase and surface reaction mechanisms should not be considered entirely independently If the surface mechanism generates a gas phase species then it is probably reasonable to ask if there are plausible gas phase reactions that can consume it For example perhaps a gas phase recombination reaction could be included to form an arsenic
136. gas phase species appears in the surface reaction mechanism but not in the gas phase mechanism the user must identify this species in the input to the CHEMKIN Interpreter t Caution This version of SURFACE CHEMKIN will not work with the earlier CHEMKIN or CHEMKIN II4 packages P 8 13 Like CHEMKIN the SURFACE CHEMKIN package is composed of two software pieces e the Surface Interpreter e the Surface Subroutine Library To apply SURFACE CHEMKIN to a problem the user must execute a CHEMKIN Application program that describes the particular set of governing equations Alternatively the user may write their own application To aid in the application programming effort the application can call CHEMKIN and SURFACE CHEMKIN subroutines that define the terms in the equations relating to equation of state chemical production rates and thermodynamics and then combine the results to define the problem The subroutines in the Library may be called from FORTRAN or C After running the CHEMKIN Interpreter the user runs the SURFACE CHEMKIN Interpreter which first reads the user s symbolic description of the surface reaction mechanism and then extracts from a Thermodynamic Database the appropriate thermodynamic information for the species involved CHEMKIN and the SURFACE CHEMKIN can share a common database The database has essentially the same format as that used by the NASA complex chemical equilibrium code of Gordon and McBride with detail
137. generic in comme ECK lines before each routine tines and labeled Common blocks cha to be unique in combined single double precisio Minor revisions to prologue Conversion to double precision done ACH inor changes rologue etc throughout names nts nged n code so as ACH ACH Reference 1 P Nh Coeffi pp 10 G D Numeri ACM Tr A C for th Equati GS Dis Packag Equati 1976 A C Solver North K R Trans Sus Brown G D cient ODE So 38 1051 Al Byrne and A cal Solution ans Math S Hindmarsh an e Integratio ons LLNL Byrne and A e for the In ons with Ba Hindmarsh s in Scien Holland Ams Jackson and Math Softw Byrne lver SO C Hind of Ordi oftware dG D n of Sys E tegratio ODEPACK terdam R are 6 and A C SIAM J LLNL Report UCRL marsh nary Differen 1 Byrne tems of Report UCID 30112 Hindmarsh n of Sys nded Jacobians a Systema tific Computing 1983 Sacks Davis of Variable Step Size Multistep Formulas for Stiff ODEs ACM 1980 Hindm SETA AS 98 A Polya ti 1975 pp tat VODE A Variable mput 10 1989 June 1988 thm for the ns arsh Co 412 lgori al Equatio EPISODE 71 96 n Effec A tive Package Rev EPISOD tems of LLNL tized Re 49 55 64 n Alt PP NA pp 295 Ordinary Dif
138. hase is the third phase overall Thus NLSURF 3 If a problem should have no surface phases then NLSURF 0 NNBULK Number of bulk phases Here there are five bulk phase i e NNBULK 5 NFBULK Pointer to the first bulk phase Here the first bulk phase is the fourth phase overall i e NFBULK 4 In a problem that has no bulk phases NFBULK 0 NLBULK Pointer to the last bulk phase In this problem NLBULK 8 In a problem that has no bulk phases NLBULK 0 IISUR Number of surface reaction Here there are nine surface reactions so ISUR 9 KKPHAS Array of total number of species in each phase In this example KKPHAS is an array of length 8 the total number of phases The values of each element in the array indicate the number of species in the corresponding phase Here KKPHAS 1 8 14 3 4 2 3 1 1 1 which shows that the gas phase has 14 species the first surface phase has 3 the second surface phase has 4 and so on KFIRST Array of starting species numbers of the phases In this example KFIRST is an array of length 8 the total number of phases The values of each element in the array indicate the species number of the first species in the corresponding phase Here KFIRST 1 8 1 15 18 22 24 27 28 29 which shows that in a complete list of species the first gas phase species is number 1 the first species in the first surface phase is number 15 the first species in the second surface phase is number 18 and
139. he thermodynamic fits species RSKWRK I K 1 MAXTP N 1 is the Nth tempe ding the ranges of coefficients for species RSKWRK I ISKWRK IrKTHM starts a three dimens y of coefficients for the fits to thermodyna erties for the species RSKWRK I L 1 NCP2 K 1 NCP2T N 1 is polynomial coefficient A N L K for species K i dens gm spec RSKWRK 1 RSKW R R N RSKWRK I R m R temperature rang RSKWRK I ISKWRK IrKDEN starts an array of species ities RSKWRK I K 1 is the density of the species cm 3 for gas or bulk species gm cm 2 for les ISKWRK IrAWT starts an array of ato K I M 1 is the atomic weight of elemen K I Es K I eters for the surface reactions K I N 1 NSPAR 1 L 1 is if the pr xponential factor mole cm sec K L 4 for para para Arrh expl and the coef coef coef stoi due for RSKW orde RSKW Chan RSKW depe reac the temperatur xponent the activation energy K is used as a scalar in sensitivity analysis the Nth surface reaction meters for the coverage surface reactions meter for the Nth coverage reaction enius parameters for surface reactions which icitly RSKWRK I N 1 NSPAR N 1 for N 1 3 the reverse parameters for the Nth reverse parameter reaction for N 4 a scaling factor surface reaction equilibrium constants ficien
140. he total count of surface reactions which do not conserve sites IiNBHM ISKWRK IiNBHM is the total count of Bohm surface reactions TiNRNU ISKWRK IiNRNU is the total count of surface reactions with real stoichiometry coefficients TiNORD ISKWRK IiNORD is the total count of surface reactions with changed order species TiNEDP ISKWRK IiNEDP is the total count of surface reactions with ion energy dependence TiELEC ISKWRK IiELEC is the location in a species array of the electron species TiNYLD ISKWRK IiNYLD is the total count of surface reactions with yield modified species ISKWRK POINTERS TO THE START OF ISKWRK ARRAY WORKSPACE TiPKST ISKWRK I ISKWRK IiPKST starts an array of species indices for the first species of the phases ISKWRK I N 1 is the index of the first species of phase N TiPKND ISKWRK I ISKWRK IiPKND starts an array of species indices for the last species of the phases ISKWRK I N 1 is the indes of the final species of phase N TiPTOT ISKWRK I ISKWRK IiPTOT starts an array of total counts of species in the phases ISKWRK I N 1 is the total species count of phase N TiKPHS ISKWRK I ISKWRK IiKPHS starts an array of physical phases for the species ISKWRK I K 1 1 species K is a solid 0 speciies K is a gas 164 IiKCHG IiKCMP IiNSCV IiKNT IiNRPP IiNREA IiNUNK IiNU IiNSUM IiICov IiKCOV IiIREV IiISTK IiKSTK IS
141. he total number of sites is often assumed to be conserved Any species in the solid below the surface layer is defined to be a bulk species and might be denoted by b In writing elementary reactions for a surface mechanism in a kinetic model mass elemental composition and charge must all be conserved There can be more than one type of site on the surface For example one could specify that a surface consists of ledge sites and plane sites The number of sites of each type might be a characteristic of the crystal face In our formalism there can be any number of site types One may define a species that only resides on a certain type of site For example the thermodynamic properties of a hydrogen atom on a ledge site might be different from a hydrogen on a plane site and they could be specified as different species even though their elemental composition is the same The population of different species occupying a given type of site is specified by site fractions The sum of the site fractions of the species on a given site is 1 Thus an open site is considered as a distinct species In the bulk there can be different types of bulk species The simplest consists of a pure species There can be any number of pure bulk species It is also possible to specify a bulk mixture with components A and B The composition of the bulk phase may be input by the user by specifying the activities of each of the bulk phase comp
142. his balance is stated as Kg E De EM Kh vi n AV TO as gt py V 0 celr T k 5 Wiehe A YT a 74 k 1 k Kf Inf The summation on the right hand side runs over all surface and bulk species It is interesting to note that by substituting Eq 69 into the flux term on the left hand side the energy balance can be written in a more compact form as K 7 AVT elr T D5 Wel T Apu V Tae 75 k 1 Now the reaction rate summation on the left hand side runs over all species including the gas phase species The SURFACE CHEMKIN package allows the user to specify mass densities py for the bulk species A possible use for the densities would be to convert surface reaction rate of production of a bulk species in moles cm2 sec into a growth rate G in cm sec The needed relationship is Ult Kp nh SW Pp k Kf Inf k G 45 4 THE MECHANICS OF USING SURFACE CHEMKIN SURFACE CHEMKIN is one component of a large body of software designed to facilitate the computational modeling of chemical kinetics in flowing systems An application program for example a Chemical Vapor Deposition analysis model can draw on any of three major software packages e CHEMKIN which handles gas phase equation of state thermodynamic properties and chemical kinetics e TRANSPORT which handles gas phase molecular transport properties and e SURFACE CHEMKIN which handles surface thermodynamics and chemical kinetics Each
143. his correction term Whichever of these choices has been set as the default can be overridden for an individual sticking coefficient reaction by including the auxiliary keyword MWOFF or MWON following the reaction line To apply the Bohm velocity correction for a reaction involving a positive ionic species as in Eq 58 the auxiliary keyword BOHM with no parameters must follow the reaction line In this case the three coefficients given in the second field of the reaction line are interpreted as the parameters a b and c of Eq 58 A BOHM reaction can have only one gas phase reactant species this gas phase reactant must 63 be a positive ion and its stoichiometric coefficient must be 1 The electron must be declared as a gas phase species in the gas phase reaction mechanism i e in the CHEMKIN Interpreter input A reaction rate constant can be modified to include a dependence upon the energy of a positive ionic reactant species through use of the ENRGDEP auxiliary keyword which is followed by the three parameters Ejono fi and g slash delimited of Eq 51 A reaction declared with ion energy dependence must contain exactly one positive ionic reactant species The reaction order i e the dependence of the reaction s rate of progress upon the concentration of chemical species can be changed via the FORD or RORD auxiliary keywords for the forward or reverse reaction respectively Each occurrence of these keywords must be fo
144. hose for site species Figure 8 shows sample bulk data The rules for bulk data are summarized in Table II Table 2 Summary of the Rules for Bulk Data 1 Bulk data must start with a line containing the word BULK and may be followed by a slash delimited name for the bulk phase i e BULK name 2 The BULK declaration and or bulk name must be followed by one or more bulk species declarations Declaring a bulk phase with no bulk species is an error 3 Bulk and bulk species names are composed of up to sixteen upper or lower case character symbols The names cannot begin with the or a number an ionic species name may end with one or more or signs an embedded plus sign must be enclosed in parentheses Names cannot include a slash 4 All species names should be unique duplicate species names will be ignored and a warning issued A species name may not duplicate a name of a gas phase species a surface species or another bulk species 5 All phase names must be unique For example a bulk phase name may not duplicate the name of any other phase gas surface site or bulk phase 6 Each bulk species that subsequently appears in a surface reaction must have been declared in this section 7 A bulk species declaration may start anywhere on the line 8 A bulk species name may be followed by an optional slash delimited mass density in g cm3 9 A bulk species declaration that begins on one line may not continue to
145. iMSTK IiIBHM IiKBHM IiIRNU IilORD IiKORD 9 IiKION IiIONS IiKTFL IiNEDP IilEDP IiKEDP IilYLD IiYION IiKYLD ISKWRK pointers to real variables 1 IrSKMN IrPATM IrRU IrRUC ISKWRK pointers to real arrays 2 IrSDEN IrKTMP IrKTHM IrKDEN IrAWT IrKWT IrPAR IrKCOV 3 IrRPAR IrEQ IrRNU IrNCF IrKORD IrKFT IrKRT IrKT1 4 5 IrKT2 IrPT1 1r1T1 1r1T2 IrlT3 IrPEDP IrENGI IrPYLD IrYNCF ISKWRK pointers to character string arrays 6 ICENAM ICKNAM ICMNAM ICPNAM INTEGER CONSTANTS MAXSPR Maximum number of species in any surface reaction Unless changed in the interpreter MAXSPR 12 NELEM Total count elements in problem NKKGAS Total count gas phase species in problem NSPAR Number of parameters required in the rate expression 163 for reactions in the current formulation NSPAR 3 however a 4th parameter can be used for purposes of scaling NSCOV Number of parameters required in the rate expression for a coverage reaction NSCOV 3 NEDPAR Number of parameters required in the rate expression for ion energy dependence reactions NEDPAR 3 NYPAR Number of parameters required in the yield modified
146. ies are automatically set to 1 loop 100 in the above example is not strictly needed but was included for clarity It is up to the application to decide whether to treat the temperature as an array or not The call list for SKHML above for example looks just the same whether T is a scalar or an array Thus the form of the subroutine Library call lists at least as far as temperature is concerned is generally backwards compatible with previous versions of SURFACE CHEMKIN 3 4 Standard State Thermodynamic Properties SURFACE CHEMKIN presumes that the standard state thermodynamic properties for all species regardless of phase are given in terms of polynomial fits to the specific heats at constant pressure M D aa 11 For the gas phase species the superscript 0 refers to the standard state of an ideal gas at 1 atm For perfect gases that we consider however the heat capacities are independent of pressure the actual values equal the standard state values For surface species the standard state of species k refers to the case of a chemical potential for a surface of pure species k i e Zy 1 with a fixed standard state site density T Moreover a perfect solution i e non interacting is assumed for the surface phase which is independent of the system pressure Under these assumptions the chemical potential for surface species k on surface site n may be written as Ly T P Z ue T RT inl Zy Ire 12 28 The standard s
147. ies indices Phase data 24 CSKWRK ISKWRK IcPNAM N 1 N 1 NPHASE names 25 ISKWRK ISKWRK IiPKST N 1 N 1 NPHASE starting species 26 ISKWRK ISKWRK IiPKND N 1 N 1 NPHASE ending species 27 ISKWRK ISKWRK IiPTOT N 1 N 1 NPHASE species count 28 RSKWRK ISKWRK IrSDEN N 1 N 1 NPHASE density Reaction data if NIISUR gt 0 29 ISKWRK ISKWRK IiNRPP I 1 I 1 NIISUR species count 30 ISKWRK ISKWRK IiNREA I 1 I 1 NIISUR reactant count 31 ISKWRK ISKWRK IiNU I 1 MAXSPR N 1 stoichiometry ISKWRK ISKWRK IiNUNK 1 1 MAXSPR N 1 species indices N 1 MAXSPR 1 1 NIISUR 32 ISKWRK ISKWRK IiNSUM I 1 I 1 NIISUR stoich sum 33 RSKWRK ISKWRK IrPAR I 1 NSPAR 1 N 1 N 1 NSPAR I 1 NIISUR Arrh coeff nts 34 RSKWRK ISKWRK IrEQ I 1 I 1 NIISUR equil factor 35 RSKWRK ISKWRK IrNCF I 1 NPHASE N 1 phase balance N 1 NPHASE I 1 NIISUR Coverage reaction data if NIICOV gt 0 36 NIICOV NSCOV 37 ISKWRK ISKWRK IiICOV N 1 N 1 NIICOV reaction indices 38 ISKWRK ISKWRK IiKCOV N 1 N 1 NIICOV species indices 39 RSKWRK ISKWRK IrKCOV N 1 NSCOV L 1 parameters L 1 NSCOV N 1 NIICOV Reverse reaction data if NIIREV gt 0 40 NIIREV 41 ISKWRK ISKWRK IilREV N 1 N 1 NIIREV reaction indices 42 RSKWRK ISKWRK IrPAR N 1 NSPAR_1 L
148. ies name may not duplicate a name of a gas phase species another surface species or a bulk species A site name must not duplicate the name of any other phase gas surface site or bulk phase Each surface species that subsequently appears in a surface reaction must have been declared in this section A site species name may appear anywhere on the line A site species may have a slash delimited site occupancy the number of sites that this species occupies on the surface following the species name A species name declaration that begins on one line may not continue to the next line i e do not break a species name into two lines There may be more than one set of SITE data All characters on a line following an exclamation mark are considered comments SITE data are not required 52 5 3 Bulk Data A set of bulk data may consist of one or more condensed phase species The first line in a set of bulk data must start with the word BULK and may be followed by an optional slash delimited name for the bulk phase If a name is not supplied for bulk phase n then the name BULKn is supplied by the interpreter Bulk species are declared by a list of unique species symbols names on the same line or on additional lines An optional slash delimited density in g cm may follow a species name If no density is supplied the unphysical value of 1 0 is stored as a flag The rules for bulk species symbols names are essentially the same as t
149. ies orders IRORD Integer array indices of surface reactions with modified reverse species orders dimension at least NRORD RORD Real matrix the modified reverse species orders for the NRORD surface reactions dimension at least KKTOT for the first the total species count and at least NRORD for the second RORD K N is the reverse order of species K for the Nth surface change order reaction 114 SK SUBROUTIN IRI Gl V SK IREV SKIREV SKIREV SKIREV SKIREV SKIREV KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T S KIREV IR ISKWRK RSKWRK IREV RAR RBR RER Returns an i explicitly assigned reverse rate constant It also returns the nteger flag to indicate whether reaction IR has an reverse Arrh if it was explicitly assigned in the SURFACE CHEMKIN interpreter If reverse Arrhenius values were not explicitly assigned RA IN IR IS RS R PUT RBR and KWRK KWRK OUTPUT IR RA RB EV nius expression values for surface reaction IR RER will be zero Integer scalar surface reaction index Integer workspace array dimension at least LENISK Real workspace array dimension at least LENRSK Integer scalar 1 reaction IR has explicit reverse rate parameters 0 no Real scalar explicit pre exponential constants for re
150. ign Inc San Diego CA 2000 Acknowledgements This document is based on the Sandia National Laboratories Report SAND96 8217 authored by Michael E Coltrin Robert J Kee Fran M Rupley and Ellen Meeks Reaction Design cautions that some of the material in this manual may be out of date Updates will be available periodically on Reaction Design s web site In addition on line help is available on the program CD Sample problem files can also be found on the CD and on our web site at www ReactionDesign com SUR 036 1 SURFACE CHEMKIN A SOFTWARE PACKAGE FOR THE ANALYSIS OF HETEROGENEOUS CHEMICAL KINETICS AT A SOLID SURFACE GAS PHASE INTERFACE ABSTRACT SURFACE CHEMKIN is a software package that together with CHEMKIN facilitates the formation solution and interpretation of problems involving heterogeneous and gas phase chemical kinetics in the presence of a solid surface The package consists of two major software components an Interpreter and a Surface Subroutine Library The Interpreter is a program that reads a symbolic description of a user specified chemical reaction mechanism One output from the Interpreter is a data file that forms a link to the Surface Subroutine Library which is a collection of about seventy modular FORTRAN THESE subroutines may be called from a CHEMKIN Application program to return information on chemical production rates and thermodynamic properties SURFACE CHEMKIN allows treatment of multi fluid
151. imensions provided by the user for the data arrays ISKWRK RSKWRK and CSKWRK LINKSK is the logical file number of the Surface Linking File LOUT is the logical file number for printed diagnostic and error messages and IFLAG is an 17 integer error flag In the remaining calls P and T are the pressure and temperature The array ACT contains the gas phase mole fractions the surface site fractions and the bulk species activities The output variable arrays HMS and SDOT correspond to the factors in the summation i e HMS h and SDOT Sk The FORTRAN representation of the summation in the last term given by combining the results of the above subroutine calls is simply SUM 0 0 DO 100 K FIRST SURFACE SPECIES LAST BULK SPECIES SUM SUM SDOT K WT K HMS K 100 CONTINUE The species indices FIRST SURFACE SPECIES and LAST BULK SPECIES are also available from a call to the Surface Library which Chapters 7 and 8 explain in detail 1 3 Organization of this Manual Chapter 2 introduces the formalism developed to describe surface chemistry behavior Unlike the case of gas phase chemistry where much software has been written to analyze mass action kinetics and chemically reacting flow elementary heterogeneous reactions are seldom treated with the generality provided in this package For the treatment in SURFACE CHEMKIN we first had to define a systematic convention to translate heterogeneous reaction
152. in molar units SUBROUTINE SKCPML T ISKWRK RSKWRK CPML Returns an array of the specific heats at constant pressure in molar units SUBROUTINE SKGML T ISKWRK RSKWRK GML Returns an array of the standard state Gibbs free energies in molar units SUBROUTINE SKHML T ISKWRK RSKWRK HML Returns an array of the enthalpies in molar units 87 SUBROUTINE SKSML T ISKWRK RSKWRK SML Returns an array of the standard state entropies in molar units SUBROUTINE SKUML T ISKWRK RSKWRK UML Returns an array of the internal energies in molar units 7 11 Chemical Production Rates SUBROUTINE SKCONT KSPEC ROP ISKWRK RSKWRK CIK Returns the contributions of the surface reactions to the molar production rate of species KSPEC SUBROUTINE SKDRDA IR P T ACT SDEN ISKWRK RSKWRK DKDAI Returns the partial of the rates of production of the species with respect to the pre exponential constant of surface reaction IR SUBROUTINE SKDRDC KSPEC P T ACT SDEN ISKWRK RSKWRK DKDC Returns the partial derivative of the production rates of the species with respect to the concentration of species KSPEC SUBROUTINE SKDSDC P T X ACT SDEN ISKWRK RSKWRK DSDC KKTOT SDOT SITDOT Returns the partial derivative of the production rates of the species with respect to the concentration of each species It also returns the matching production rates SUBROUTINE SKDSDX P T X ACT SDEN ISKWRK RSKWRK DSDX
153. ing the elements of IRAY into categories and then search IRAY by element and category The categories that each element of IRAY will be assigned to are specified by the input character string vector SETS of vector length NSETS Elements of each category in IRAY must be grouped congruously The number of elements in each category within IRAY is specified by the input integer vector ISET To search for the existence of an element within category ISTR may additionally be composed of two substrings ISTR ELEMENT_NAME CATEGORY_NAME where CATEGORY_NAME is one of the categories specified in SETS In this case IND will return the first position in IRAY where ELEMENT NAME occurred within the category CATEGORY_NAME NT will return the total number of times ELEMENT_NAME occurred within the category CATEGORY_NAME If ELEMENT_NAME is not found within the specified category IND and NT are returned with a value of zero If no category is specified within ISTR IND and NT return with the same values as they would from subroutine SKCOMP Consider the following example TRAY RED BLUE JADE RUBY TOPAZ JADE NN 6 SETS COLORS STONES NSETS 2 ISET 4 2 This assumes that the elements of IRAY were grouped into two sets consisting of 4 and 2 elements respectively and the following names COLORS RED BLUE JADE RUBY and STONES TOPAZ JADE If ISTR BLUE then IND 2 and NT 1 if ISTR PINK then
154. its moles cm 2 sec for 1 KKGAS the production rate of gas phase species for KKGAS 1 KKGAS KKSUR the production rate of surface species for KKGAS KKSUR 1 KKTOT the production rate of bulk species SITDOT Real array production rates of the surface phases dimension at least NPHASE the total phase count but subroutine only calculates entries for site phases cgs units moles cm 2 sec 125 SKRATI SKRATI SKRATI SKRATI SKRATI SKRATI SKRATI ee ee ee ee ee ea KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKRATI IR ROP ISKWRK RSKWRK SDOTI SITDTI Returns rates of production of the species by surface reaction IR T INPUT IR Integer scalar reaction index ROP Real array rates of progress for the surface reactions dimension at least IISUR the total surface reaction count cgs units moles cm 2 sec ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT SDOTI Real array production rates of the species by reaction IR dimension at least KKTOT the total species count cgs units moles cm 2 sec for 1 KKGAS the production rate of gas phase species for KKGAS 1 KKGAS KKSUR the production rate of surface species for KKGAS KKSUR 1 KKTOT the production rate of bulk species SITDTI Real array production rates of the surface phases due to reaction IR
155. kes the provision for a reaction rate constant to depend upon the energy of a positive ionic reactant species Ejon The functional form allowed is as follows k Eion k thermal mas O ef ED 6 j 51 The reaction rate depends upon a threshold energy Eion 0 and the energy expressions can be raised to a specified power in two different ways through the use of the parameters f and g lon energy dependent reactions are declared in the Interpreter input via the auxiliary keyword ENRGDEP An Application program can find out which reactions were declared as ion energy dependent reactions and get an array of the parameters by a call to SKIENR Because the subroutines that evaluate rate constants in SURFACE CHEMKIN take temperature as an argument and not species energy subroutine SKRPAR must 37 be called to input an array of ion energies ENRGI before the rate constant routine is called Use of the ENRGDEP keyword is only allowed for irreversible reactions 3 10 Sticking Coefficients For some simple surface reaction mechanisms we have found it conyenient to specify the surface reaction rate constant in terms of a sticking coefficient probability For example one might have a measurement or intuition about the probability that a certain process takes place when a given collision occurs For consistency in expressing each surface reaction in terms of a rate constant we provide a conversion between this sticking coefficient
156. lity because the software does not need to be concerned with details of the limitless range of problems that a user may wish to pose and solve The schematic diagram in Fig 6 shows how an application program might interact with the low level chemical kinetics and transport software packages The boxes with the light borders indicate those blocks of software that are relegated to subroutine calls to one of the utility packages and the boxes with the heavy borders indicate those blocks of software that must be included in a particular application We show the problem independent mathematical software as a box with a light border to indicate that many problems can be solved with readily available high quality mathematical software Certainly this is true for problems that can be formulated as systems of nonlinear algebraic equations or ordinary differential equation initial value or boundary value problems 48 Input parameters initial conditions Thermodynamic properties Problem independent Define governing Chemical Numerical software equations kinetics Transport properties Write output and post processing files Post processing Figure 6 Schematic Representation of an Ideal Applications Program 49 5 USING THE SURFACE CHEMKIN INTERPRETER The SURFACE CHEMKIN Interpreter is used to read a symbolic description of a surface reaction mechanism from the FORTRAN S standard input and numerical information about
157. llowed by the species name and the new reaction order e g FORD SI S 0 5 This option overrides the values of vj and vg in Eq 32 pertaining to the particular species named on the line The reaction order for all other species maintain their default values of vj and o Multiple occurrences of the FORD and RORD construct may appear on the auxiliary line A FORD or RORD keyword can be specified even for species that do not appear as a reactant or product in the reaction although one might reasonably wonder how such a functional dependence could occur To modify the expression for the forward rate constant by optional coverage parameters see Eq 48 one uses the auxiliary information keyword COV followed by slash delimited surface species name and the three parameters 7 Ugi and More than one set of COV data can appear for a given reaction and these would be applied multiplicatively as in Eq 48 lon enhanced reaction yield can be applied to a reaction using the following two steps First place a pound sign in front of the name or the stoichiometric coefficient if one was given of each species that is subject to the ion energy yield enhancement The sub reaction of species and coefficients demarked with the sign must satisfy mass elemental charge and site balance unless the NONCON flag was also given on the REACTION line Second the auxiliary keyword YIELD must appear after the
158. m 0 to 1 and should sum to 1 fo phase SDEN Real array site densities for the site types but the subroutine only uses site phas ntri SKROP rmined by r of ount E y normalized by the site density and cies r each dimension at least NPHASE the total phase count NFSURF lt N lt NLSURF cgs units moles cm 2 S ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT ROP Real array rates of progress for the surface reactions dimension at least IISUR the total surface reaction count cgs units moles cm 2 sec SKRP SKRP SKRP SKRP SKRP SKRP KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKRP ISKWRK RSKWRK RU RUC PATM SKRP Returns universal gas constants and the pressure of one standard atmosphere INPUT ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT RU Real scalar universal gas constant cgs units 8 314510E7 ergs mole K RUC Real scalar universal gas constant used only in conjuction with activation energy preferred units RU 4 184 cal mole k PA Real scalar pressure of one standard atmosphere cgs units 1 01325E6 dynes cm 2 128 SKRPAR SKRPAR SKRPAR SKRPAR SKRPAR S
159. metric coefficients of the species and the net change in phases for all of the surface reactions in a mechanism SUBROUTINE SKNUF IDIM ISKWRK KSTOIF Returns the stoichiometric coefficients of the species for all reactants in all surface reactions in a mechanism note reactants only they will all be negative SUBROUTINE SKRAEX IR ISKWRK RSKWRK RA Returns the Pre exponential rate constant or sticking coefficient of the IRth reaction or changes its value depending on the sign of IR SUBROUTINE SKRDEX IR ISKWRK RSKWRK RD Returns the perturbation factor of the IRth reaction or changes its value depending on the sign of IR SUBROUTINE SKRPAR ISKWRK RSKWRK ENRGI Allows the user to input auxiliary reaction rate parameters for special types of reactions The first parameter is the species ion directed energy for ion energy dependent reactions 85 SUBROUTINE SKSYMR IR LOUT ISKWRK RSKWRK CSKWRK LT RNAM KERR Returns the character string representation of reaction IR 7 7 Gas Constants and Units SUBROUTINE SKRP ISKWRK RSKWRK RU RUC PATM Returns universal gas constants and the pressure of one standard atmosphere 7 8 Thermodynamic Properties Non dimensional SUBROUTINE SKATHM MDIM NDIM1 NDIM2 ISKWRK RSKWRK NT TMP A Returns the polynomial coefficients of the fits for thermodynamic properties of all of the species SUBROUTINE SKCPOR T ISKWRK RSKWRK CPOR Returns an
160. mples of reactions with such non integer coefficients are H s gt 0 5H gt 2 41 34 CH6 0 72C H 0 56H 0 28CH 0 28CH 42 The rate of progress of a reaction is by default still evaluated via Eq 32 with the coefficients vj and vg defined as real numbers instead of integers The CHEMKIN and SURFACE CHEMKIN Interpreters automatically allow real coefficients for reactions without requiring any special flags or keywords An Application can call subroutine SKIRNU to find out which reactions were declared to the Interpreter with real coefficients and get arrays of the coefficients 3 7 Arbitrary Reaction Order As just stated by default the rate of progress of a reaction is evaluated by Eq 32 which uses the concentration of each reactant or product species raised to the power of its stoichiometric coefficient Thus the rate of progress of a reaction that includes species A with a coefficient of 2 will be second order with respect to the concentration of A Equation 32 would always be valid when mass action kinetics are obeyed and the mechanism is written in terms of elementary reactions However often in real world applications the elementary kinetics are not known In some cases an experimental measurement finds that the rate of reaction is proportional to the concentration of a species raised to a some arbitrary power different from its stoichiometric coefficient CHEMKIN and SURFACE CHEMKIN allow the user
161. n open site must be considered as a species 22 What are the thermochemical implications of reactions such as 3 and 5 In the Atomic Site Formalism the interpretation is straightforward In reaction 3 we have converted AsH3 g and Ga s into AsHa s and Ga b Thus the change in a thermochemical property e g AH y is just the difference in the heats of formation of the products and the reactants What about in the Open Site Formalism What are the properties of O s the open site Because these two formalisms describe an identical physical event it is evident the properties of the open site must be related to those of Ga b and Ga s For example the heat of formation of this open site is just AH O s AH p Ga s AH Ga b 6 23 3 CHEMICAL RATE AND THERMODYNAMIC EXPRESSIONS This chapter lists expressions and equations that are useful in formulating chemically reacting flow problems For many expressions and equations the subroutine that evaluates it is named Species can exist in the gas phase on surface sites or in bulk mixtures In some cases it is desirable to refer to information about species without regard to the phases and in other cases it is desirable to determine information about species in one particular phase or group of phases Therefore before beginning to discuss our formalism in terms of mathematical expressions we introduce a nomenclature that facilitates manipulating speci
162. n Section 7 below After initializing the gas phase CHEMKIN Library and the SURFACE CHEMKIN Library the program reads the initial nonzero moles from input It then repeatedly calls subroutine VODE to obtain the solution at uniform print intervals The governing equation formulation is found in SUBROUTINE FUN which is called by VODE The sections below present a Unix shell script for the sample problem CHEMKIN Interpreter input and output SURFACE CHEMKIN Interpreter input and output the input to the sample problem FORTRAN code for the sample problem and output for the sample program The last section describes how to use VODE 138 9 1 Discussion of Sample Problem We illustrate the input and output of the various Interpreters and the example problem with an analysis of the deposition of Si3N4 The gas phase reaction mechanism contains a detailed description of NH3 decomposition about which there is much published information two reactions describing SiF4 decomposition and three cross reactions At the low pressures we consider the gas phase decomposition of reactants is slow The surface reaction mechanism contains six steps describing the overall conversion of 3 SiF4 and 4 NH3 molecules to 3 Si d and 4 N d and 12 HF Note that the surface reaction mechanism is from a preliminary analysis at one temperature and thus we have not supplied any activation energies Also the thermodynamic data in the mechanism is contrived and should not be
163. n is given on the required dimensioning in the calling program For all variables having units the cgs units are stated SKABE SKABE SKABE SKABE SKABE SKABE SKAB KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK Gl KKKKKK SUBROUTINE SKABE ISKWRK RSKWRK RA RB RE ISTEL Returns the Arrhenius coefficients or the sticking coefficients of the surface reactions and integer flags to indicate the type of the coefficients T INPUT ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT RA Real array pre exponential constants for reactions dimension at least IISUR the total surface reaction count cgs units mole cm sec K RB Real array temperature dependenc xponents for reactions dimension at least IISUR the total surface reaction count RE Real array activation energies for reactions dimension at least IISUR the total surface reaction count cgs units K ISTFL Integer array sticking reaction information dimension at least IISUR the total surface reaction count 1 a reaction uses sticking coefficients 0 a rection does not 93 SKAML SKAML SKAML SKAML SKAML SKAML SKAML ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKAML T ISKWRK RSKWRK AML Returns an array of the standard state Helmholtz free energi
164. n orders for the forward reaction For example such a reaction may no longer satisfy microscopic reversibility At equilibrium elementary kinetics ensure that K K K ar ky fp IT TTP TY Pe 46 k l k l ca A reaction for which one has specified a change in reaction order will not have the proper equilibrium behavior unless Fg Ry Uhi Vki k 1 K 47 The user specifying F may also wish to adjust R such that Eq 47 is satisfied SURFACE CHEMKIN does not do this automatically Another alternative would be to simply specify that the reaction is irreversible in which case the details of the reverse reaction become irrelevant 3 8 Surface Coverage Modification of Rate Expression In some cases there are experimental data that indicate the Arrhenius expression for the rate constant Eq 35 is modified by the coverage concentration of some surface species SURFACE CHEMKIN allows optional coverage parameters to be specified for species k and reaction i through use of the auxiliary keyword COV described later In this case the rate constant for the forward reaction is modified as Hal S n y 1Q7ki Zmliz a n i exf Eki Zi wl 48 kp AT Pi o St 3 T wk Wf RT where the three coverage parameters are 7j Uki and Ej for species k and reaction i The product in Eq 48 runs over only those surface species that are specified as contributing to the coverage modification Note that the surface site
165. nsity is negative e No thermodynamic data are found for a declared species e There are more species than the Interpreter is dimensioned for e A site or bulk phase name duplicates another phase name gas surface site or bulk phase name e A phase or species name contains an illegal character e Site occupancy number is negative e Bulk density for a bulk species is negative Thermodynamic Data e Thermodynamic data are format sensitive and therefore provide possibilities for error if not formatted exactly as described by Table 3 e An element in the thermodynamic data for a declared species is not included in the CHEMKIN Interpreter input element data e With the THERMO ALL option line 2 of Table 3 is not found Reaction D ata e A delimiter gt lt gt or between the reactants and the products is not found This error should not occur with the standard CHEMKIN distribution it may occur only when a Fortran 77 driver is used to build the SURFACE CHEMKIN Interpreter and in this case may be changed by a simple modification of a parameter statement in the driver program 68 e Three Arrhenius parameters are not found e Reactants and or products species names are not properly delineated by a plus sign e A species listed as a reactant or product is not declared in the species data e A reaction does not satisfy elemental balance e The number of sites in a reaction does not balance and the word NONCON was n
166. ny kind including without limitation any warranty against infringement of third party property rights fitness or merchantability or fitness for a particular purpose even if Reaction Design has been informed of such purpose Furthermore Reaction Design does not warrant guarantee or make any representations regarding the use or the results of the use of the software or documentation in terms of correctness accuracy reliability or otherwise No agent of Reaction Design is authorized to alter or exceed the warranty obligations of Reaction Design as set forth herein Any liability of Reaction Design its officers agents or employees with respect to the software or the performance thereof under any warranty contract negligence strict liability vicarious liability or other theory will be limited exclusively to product replacement or if replacement is inadequate as a remedy or A iea Design s opinion impractical to a credit of amounts paid to Reaction Design for the license of the software Literature Citation for SURFACE CHEMKIN The SURFACE CHEMKIN program and subroutine library are part of the CHEMKIN Collection R J Kee F M Rupley J A Miller M E Coltrin J F Grcar E Meeks H K Moffat A E Lutz G Dixon Lewis M D Smooke J Warnatz G H Evans R S Larson R E Mitchell L R Petzold W C Reynolds M Caracotsios W E Stewart P Glarborg C Wang and O Adigun CHEMKIN Collection Release 3 5 Reaction Des
167. od flag Standard values are 10 for nonstiff Adams method no Jacobian used 21 for stiff BDF method user supplied full Jacobian 22 for stiff method internally generated full Jacobian 24 for stiff method user supplied banded Jacobian 25 for stiff method internally generated banded Jacobian RPAR IPAR user defined real and integer arrays passed to F and JAC Note that the main program must declare arrays Y RWORK IWORK and possibly ATOL RPAR and IPAR output from the first call or any call is Y Array of computed values of y t vector T ISTATI E Corresponding value of independent variable normally TOUT 2 if DVODE was successful negative otherwis 1 means excess work done on this call Perhaps wrong MF 2 means excess accuracy requested Tolerances too small 3 means illegal input detected S printed message 4 means repeated error test failures Check all input 5 means repeated convergence failures Perhaps bad Jacobian supplied or wrong choice of MF or tolerances 6 means error weight became zero during problem Solution component i vanished and ATOL or ATOL i 0 F To continue the integration after a successful return simply reset TOUT and call DVODE again No other parameters need be reset 161 10 REFERENCES SO OOL GS ON M E Coltrin R J Kee F M Rupley and E Meeks SURFACE CHEMKIN III A Fortran Package fo
168. odeling plasma systems one sometimes encounters reactions where the energy of the incident ion determines the number of surface species etched Such surface reactions in SURFACE CHEMKIN can be modeled using a yield enhancement factor to account for the variable stoichiometry Imagine the case in which a positive ion g hits a surface and knocks off a variable number y of surface species S s For each surface species S s destroyed the example reaction produces two gas phase products P g and leaves behind some other surface species O s another gas species o s is produced by the reaction but its stoichiometric coefficient is not dependent upon the number of surface species etched I g yS s gt w2P g yO s Q g 59 The coefficient yis essentially a variable stoichiometric coefficient which depends upon the energy of the positive ionic reactant A reaction written like Equation 59 is required to satisfy mass charge and elemental balance as is every reaction in a SURFACE CHEMKIN mechanism For this always to be the case the sub reaction S s gt 2P g O s 60 consisting of all of the species in the original reaction which are multiplied by the coefficient y must also satisfy mass charge and elemental balance In addition unless the NONCON keyword was declared on the REACTION line described later the sub reaction must also conserve the number of surface sites An example of a reaction
169. oichiometric coefficients for the species in the surface reactions the first dimension must be at least IISUR the total surface reaction count and at least KKTOT for the second the total species count NSTOIC Integer matrix net change of the phases for the surface reactions the first dimension must be at least IISUR the total surface reaction count and at least NPHASE for the second the total phase count SKNUF SKNUF SKNUF SKNUF SKNUF SKNUF SKNUF DSR SS A A RR RR RR A kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkkkkkxk KKKKKK SUBROUTINE SKNUF IDIM ISKWRK KSTOIF Returns the stoichiometric coefficients of the species for all reactants in all surface reactions in a mechanism note reactants only they will all be negative INPUT IDIM Integer scalar first dimension of the array NSTOIC must be at least ISUR the total surface reaction count ISKWRK Integer workspace array dimension at least LENISK OUTPUT KSTOIF Integer matrix stoichiometric coefficients for the reactants in the surface reactions dimension at least IISUR for the first the total surface reaction count and at least KKTOT for the second the total species count 121 SKPCMP SKPCMP SKPCMP KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK SKPCMP SKPCMP KKKKKKKKKKKKKKKKKKKKKKKKKK UBROUTINE T SKPCMP ISTR nd additionally RAY i he ca pecified by the input ETS Ele he number he input element wi
170. on of Chemical Rate Sensitivity Coefficients We have found sensitivity analysis to be a powerful tool in helping interpret the results of computational simulations Sensitivity analysis is used to determine quantitatively the dependence of a solution on certain parameters that appear in a model s definition The raw first order sensitivity coefficient matrices Sj dD da report the partial derivatives of the dependent variable vector e g temperature mass fractions surface composition with respect to a parameter vector a e g reaction rate constants Since there is much mathematical literature on sensitivity analysis and various methods to compute the sensitivity coefficients from the solution we do not discuss the computation of Sy here However given the sensitivity matrix it is possible to manipulate it further to obtain the sensitivities of species production rates with respect to the dependent variables diz Ay ey olx ob da oa Tolx dd 00 1 63 where the components of amp are the mass fractions site fractions and activities for gas phase surface and bulk species respectively The term 9 X 4b converts from concentration units to the units of 42 We have included two subroutines in the Surface Library to facilitate calculation of these terms The first gives the partial derivative of the production an species k with respect to the pre exponential constant of the Arrhenius expres
171. onents The activity of a bulk species is defined in terms of the following equation for the chemical potential My T P X ug T RT Ina 7 P X 2 where uz is the standard state chemical potential of species k at temperature T and at the standard pressure 1 atm The vector X represents an array of the mole fractions of the species Two conventions are normally used to complete the specification of the activity coefficient In actuality there is no constraint that the surface must be only one atom thick However defining a surface that is several monolayers thick may be conceptually much more difficult to deal with 20 1 If the standard state is defined as a pure bulk phase of k at temperature T and 1 atm then a is further defined to approach X as X approaches 1 at 1 atm Raoult s Law 2 If the standard state is defined as the hypothetical state of species k in infinite dilution in bulk phase species j at temperature T and 1 atm then az is further defined to approach X as Xy approaches 0 at 1 atm Henry s Law Both conventions for the standard state work with SURFACE CHEMKIN as do any other definitions that conform to the formalism expressed by Eq 2 for 4 uz T is specified through the entry for species k in the thermodynamics data file The value of a T P X is required as input to all SURFACE CHEMKIN subroutines that calculate bulk phase thermodynamic quantities and reaction rates Therefore if desir
172. onstant of the i h reaction Energy of a positive ionic species Energy threshold in ion energy dependent reactions Energy threshold in reaction yield expression Exponential constant in ion energy dependent reactions Forward reaction order specified for the qe species in i th reaction Exponential constant in ion energy dependent reactions Standard state specific Gibbs free energy for the p species Bulk growth rate Standard state Gibbs free energy for the k species Specific enthalpy of the k species Multiplicative factor in reaction yield expression Enthalpy of formation Standard state enthalpy of the pi species Enthalpy of the k species Reaction index Total number of reactions By default SURFACE CHEMKIN uses activation energies in calories instead of ergs Units none none depends on m ergs g cm ergs mole depends on reaction none E cal mole ergs g K ergs mole K cm2 sec g cm sec cal mole cal mole cal mole cal mole none none none ergs mole cm sec ergs mole ergs g depends on reaction ergs mole ergs mole ergs mole Species index Forward rate constant of the i reaction depends on reaction Reverse rate constant of the i reaction depends on reaction Total number of species Total number of bulk species Index of the first bulk phase species in phase n Index of the last bulk phase species in phase n Total number of gas phase sp
173. or internal manipulations A user wishing to modify a subroutine or to write new routines will probably want to use the work arrays directly The pointers described below are starting addresses for information stored in the work arrays and are found in the labeled common block COMMON SKSTRT declared by the use of the include file skstrt h It should be noted that storage in work array ISKWRK serves several purposes for instance 1 ISKWRK N may be a constant in regards to a surface described by the mechanism and is subject to change if there are multiple surfaces 2 ISKWRK N may be a pointer where L ISKWRK N is used to locate information specific to a surface either in ISKWRK RSKWRK or CSKWRK then 3 ISKWRK L ISKWRK N may the first value of an integer array specific to a surface RSKWRK L ISKWRK N the first of a real array and CSKWRK L ISKWRK N the first of a character string array COMMON SKSTRT Integer constants 1 MAXSPR NELEM NKKGAS NSPAR NSCOV NEDPAR NYPAR MAXORD 2 MAXTP NCP NCP1 NCP2 NCP2T ISKWRK pointers to integer variables 3 IiLENI IiLENR IiLENC IiKSUR IiKBLK IiKTOT IiNPHA IiFSUR 4 IiLSUR IiNSUR IiFBLK IiLBLK IiNBLK IiNIIS IiNCOV IiNREV 5 IiNSTK IiNCON IiNBHM IiNRNU IiNORD IiNEDP IiELEC IiNYLD ISKWRK pointers to integer arrays 6 IiPKST IiPKND IiPTOT IiKPHS IiKCHG IiKCMP IiNSCV IiKNT 7 IiNRPP IiNREA IiNUNK IiNU IiNSUM IiICOV IiKCOV IiIREV 8 IilSTK IiKSTK I
174. ord and its parameter s must appear on the same line Multiple keywords appearing on the same line must be separated by at least one blank space Any blank spaces between a keyword and the first slash are ignored and any blanks between the slashes and parameter s are also ignored However no blank spaces are allowed within a keyword or parameter The keyword REV followed by three slash delimited Arrhenius coefficients may be used to specify the reverse rate parameters The keyword DUPLICATE or DUP must follow every occurrence of a duplicated reaction The keyword STICK indicates that the three coefficients on the reaction line are to be interpreted as the parameters a b and c in Eq 52 There must be exactly one gas phase reactant species its stoichiometric coefficient must be 1 The keyword COV is used to modify the forward rate constant by the expression in Eq 48 The word COV is followed by a surface species name and the three coverage parameters 77 Uki and Ezi The four entries after the word COV are slash delimited The keyword BOHM indicates that the three coefficients on the reaction line are to be interpreted as the parameters a b and c in Eq 58 the Bohm velocity correction is applied There must be exactly one gas phase reactant species and that species must be a positive ionic species its stoichiometric coefficient must be 1 Only irreversible reactions are allowed with this option The electron must be
175. ot included on the first REACTIONS line e The charge of the reaction does not balance e A reaction is a duplicate not declared by the auxiliary data keyword DUP e There are more reactions than the Interpreter is dimensioned for e There are more than six reactants or six products in a reaction Surface Reaction Auxiliary Data e An unknown or misspelled keyword occurs e Parameters for a keyword are not enclosed in slashes e There are the wrong number of parameters for a keyword e REV is declared for an irreversible reaction e Pre exponential factor for a sticking coefficient is negative e For a sticking coefficient reaction there is more than one gas phase species or the stoichiometric coefficient for the gas phase species is not 1 e More than one BOHM declaration appeared for a given reaction e BOHM keyword is given for a reversible reaction e A positive ionic species did not appear as a reactant or its stoichiometric coefficient was not 1 in a BOHM reaction e More than 1 positive ionic species was a reactant in a BOHM reaction e The electron species was not declared in the list of species in the CHEMKIN Interpreter input e Invalid string given with the UNITS auxiliary keyword e More than one ENRGDEP declaration appeared for a given reaction e A positive ionic species did not appear as a reactant or its stoichiometric coefficient was not 1 ina ENRGDEP reaction e Wrong number of ENRGDEP parameters given e In
176. package consists of a symbolic preprocessor called an Interpreter a database of either thermodynamic or transport properties and a library of subroutines that can be called from the Application program The software is highly structured and modular which provides great flexibility in applying it to a wide variety of problems However this modularity also compels the user to manipulate a number of programs and files The flow of information from the first input to the CHEMKIN Interpreter to the inclusion of a library subroutine in an application program is shown in Fig 5 We presume that all problems involving surface chemistry also involve one or more gas phase species above the surface Therefore the first step in any problem involving surface chemistry is to run the CHEMKIN Interpreter which reads the user s description of the gas phase reaction mechanism The CHEMKIN Interpreter also draws on a Thermodynamic Database containing polynomial fits to individual species specific heats enthalpies and entropies In addition to printed output the CHEMKIN Interpreter creates a Linking File containing all possible information regarding the particular gas phase reaction mechanism The Linking File is read by an initialization subroutine in the Gas Phase Subroutine Library that makes the information available to all the other subroutines in the library The next step is to execute the SURFACE CHEMKIN Interpreter which reads the user s symbolic de
177. pecial words MOLES or MOLECULES can appear on the REACTIONS line to indicate the units for Aj see Eq 35 If MOLECULES is specified then the units for Aj are cm molecules sec K If units are not specified Aj and Ej are assumed to be in cm mole sec K and cal mole respectively The lines following the REACTION line contain reaction descriptions together with their Arrhenius rate coefficients The reaction description is composed of reaction data and perhaps optional auxiliary information data The Interpreter normally considers any reaction that does not conserve the number of surface sites in each surface phase to be in error If the user wishes to include such reactions which may be perfectly valid the word NONCON must appear on the REACTION line If the user does not wish to include the Motz Wise correction in the conversion between a sticking coefficient and a rate constant i e Eq 57 the user has two choices The keyword MWOFF can be included on the REACTION line to turn off this correction for all reactions that are specified as sticking coefficient reactions or MWOFF can be used as an auxiliary keyword following an individual reaction to turn off the Motz Wise correction for that reaction only Conversely if the MWOFF parameter was given on the REACTION line the user can include the MWON auxiliary keyword following an individual reaction specifying that the Motz Wise correction is to be used for that reaction only E
178. phase count but subroutine only calculates entries for site phases cgs units moles cm 2 sec 105 SKEQ SKEQ SKEQ SKEQ SKEQ EQ SKEQ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK SUBROUTIN T SKEQ P T ACT Returns the equilibrium constants KKKKKK SDEN pressure t INPUT P s T ACT SDEN ISKWRK RSKWRK OUTPUT EQKC mperature Real scalar cgs units Real array species t pressure dynes cm 2 temperature s cgs units Real array dimension The first species de surface co mperatures K activi at least KKGAS ac the next KKSURF ac nsi KKTOT ACT K SIT the next KKBUL should be from phase Real array si but the subrou NFSURF lt N lt cgs units Real Real array E D T INSITY K activities te dimension at least tine only us O to 1 and densities NPHASE ISKWRK RSKWRK for the surface reactions given species activities and th ties of the species the total species count tivities are mole fractions tivities are site fractions ty normalized by the site density ncentration in moles cm 2 is EQKC te densities dimension is determined by the application program to be the total number of nominally 1 and sites per
179. r Analyzing Heterogeneous Chemical Kinetics at a Solid Surface Gas Phase Interface Sandia National Laboratories Report SAND96 8217 1996 R J Kee and J A Miller A Structured Approach to the Computational Modeling of Chemical Kinetics and Molecular Transport in Flowing Systems Sandia National Laboratories Report SAND86 8841 1986 R J Kee J A Miller and T H Jefferson Chemkin A General Purpose Problem Independent Transportable Fortran Chemical Kinetics Code Package Sandia National Laboratories Report SAND80 8003 1980 R J Kee F M Rupley and J A Miller Chemkin II A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics Sandia National Laboratories Report SAND89 8009 1990 S Gordon and B J McBride Computer Program for Calculation of Complex Chemical Equilibrium Compositions Rocket Performance Incident and Reflected Shocks and Chapman Jouguet Detonations NASA Report SP 273 1971 G Eriksson Acta Chem Scand 25 2651 1971 H Motz and H Wise Journal of Chemical Physics 32 1893 1960 D G Goodwin and G G Gavillet Journal of Applied Physics 68 6393 1990 P N Brown G D Byrne and A C Hindmarsh SIAM J Sci Stat Comput 10 1038 1989 162 APPENDIX A STORAGE ALLOCATION FOR THE WORK ARRAYS Work arrays ISKWRK RSKWRK and CSKWRK contain information about the elements species and reaction in the mechanism they also contain some work space needed f
180. r reaction IR has yield modified species the species index of its ion yield modify flags for its reactants and products and parameters for the yield expression INPUT IR Integer scalar surface reaction index ISKWRK Integer workspace array dimension at leas RSKWRK Real workspace array dimension at leas LENISK LENRSK CTC OUTPUT IYLD Integer scalar flag for yield modify reactions 1 reaction IR uses yield modification 0 no IYION Integer scalar species index of the ion in a yield modify reaction KYLD Integer array yield flags for the species in a yield modify reaction dimension at least MAXSPR the maximum number of species allowed in a surface reaction 1 species is yield modified 0 no PYLD Real array parameters for the yield expression in a yield modify reaction dimension at least NYPAR the number of parameters required If IYLD 1 and KYLD of the Nth species in the reaction is 1 the stoichiometric coefficient NU of the species is scaled by the results of the expression PYLD 1 Ei PYLD 3 PYLD 2 PYLD 3 PYLD 4 where Ei is the ion energy of species IYION SKKION SKKION SKKION SKKION SKKION SKKION SKKION ee RARA RARA RARA RARA RARA RARA RARA KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKKION ISKWRK KKELECT KKION KION Returns the species number of the electron the number of positive ions in the gas ph
181. r the surface reactions with yield modification RSKWRK I N 1 NYPAR L 1 is the Lth parameter for yield modification reaction N IrYNCF RSKWRK I ISKWRK IrYNCF starts a matrix of net site changes due to yield changes in the yield modified reactions RSKWRK I N 1 NNPHAS L 1 is the net change in sites for phase L due to the Nth yield modify reaction ISKWRK POINTERS TO CHARACTER WORKSPACE for one surface IcENAM CSKWRK I ISKWRK ICENAM starts an array of element names CSKWRK I M 1 is the name of element M IcKNAM CSKWRK I ISKWRK IcKNAM starts an array of species names CSKWRK I K 1 is the name of species K IcPNAM CSKWRK I ISKWRK ICPNAM starts an array of phase names CSKWRK I N 1 is the name of phase N STORING DATA INTO THE ARRAYS is usually accomplished by a CALL SKINIT which reads a linkfile generated by the surface mechanism interpreter the linkfile consists of the following records Linkfile information 1 FILVER character 16 the linkfile format version 2 PRVERS character 16 the interpreter program 3 PREC character 16 the machine precision of the linkfile data SINGLE DOUBLE 4 KERR logical to indicate whether or not an error was found by the interpreter program Parameters and constants 5 LENISK LENRSK LENCSK minimum lengths required to store linkfile data into the integer real and character workspace arrays 6 MAXSPR MAXTP NCP NSPAR NSC
182. r those wit KWRK I N 1 is oichiometry reactio KWRK I ISKWRK IiI dices for those wit TiIRNU NU starts an array of reaction real stoichiometric coefficients he reaction index of the Nth real OD To RD starts an array of reaction h changed order species KWRK I N 1 is the reaction index of the h change order reaction KWRK I ISKWRK IiKORD starts a matrix of changed ecies indices for the change order reactions KWRK I N 1 MAXORD L 1 is the index of the Lth anged order species in the Nth change order reaction KWRK I ISKWRK IilONS starts an array of species dices for the ionic species KWRK I N 1 is the species index of the Nth ionic species TiKTFL ISKWRK I ISKWRK IiKTFL starts an array of indices into a temperature array for the species ISKWRK I K 1 is the temperature index for species K IiIEDP ISKWRK I ISKWRK IilEDP starts an array of reaction indices for the surface reactions with ion energy dependenc ISKWRK I N 1 is the species index of the Nth ion nergy dependent reaction TiKEDP ISKWRK I ISKWRK IiKEDP starts an array of species indices for th nergy dependent ions in the ion energy dependence reactions ISKWRK I N 1 is the species index of the ion for the Nth nergy dependent reaction TilYLD ISKWRK I ISKWRK IilYLD starts an array of reaction indices for those with modified yield ISKWRK I N 1 is the
183. ray dimension at least LENRSK Real array the 6th thermodynamic polynomial coefficients for species K over the number of temperature ranges used in fitting thermodynamic properties dimension at least MAXTP 1 where MAXTP is the maximum number of temperatures used in fitting the thermodynamic properties of the species Real array the 6th thermodynamic polynomial coefficients for species K over the number of temperature ranges used in fitting thermodynamic properties dimension at least MAXTP 1 where MAXTP is the maximum number of temperatures used in fitting the thermodynamic properties of the species 127 SKROP SKROP SKROP SKROP SKROP SKROP KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKROP P T ACT SDEN ISKWRK RSKWRK ROP Returns rates of progress for the surface reactions INPUT P Real scalar pressure cgs units dynes cm 2 TECE Real array temperature s dimension is dete the application program to be the total numbe species temperatures nominally 1 cgs units K ACT Real array activities of the species dimension at least KKTOT the total species c The first KKGAS activities are mole fractions the next KKSURF activities are site fractions species densit surface concentration in moles cm 2 is ACT K SITE DENSITY sites per species the next KKBULK activities for bulk phase spe should be fro
184. re expected to represent numbers They are converted into floating point values and stored in the output vector RVAL Upon input NEXP is equal to the number of values expected to be found If NEXP numbers are not found KERR will be set to TRUE on return from the subroutine Example input LINE GA S BULK1 1 2 NEXP 1 the number of values expected LOUT 6 a logical unit number on which to write diagnostic messages KNAM Array of character species names KKTOT Total number of species PNAM Array of character phase names NNPHAS Total number of phases KKPHAS Index array of the number of species in the phases 91 Output KNUM The index number of the species which has the name GA S and resides in phase BULK1 NT 1 if there is only one species GA S in phase BULK1 NVAL 1 the number of values found in LINE following the species name RVAL 1 1 200E 00 the substring converted to a real number KERR FALSE SUBROUTINE SKSAVE LOUT LSAVE ISKWRK RSKWRK CSKWRK Writes to a binary file information about a SURFACE CHEMKIN linkfile pointers for the SURFACE CHEMKIN Library and SURFACE CHEMKIN work arrays 92 8 ALPHABETICAL LISTING OF THE SURFACE SUBROUTINE LIBRARY WITH DETAILED DESCRIPTIONS OF THE CALL LISTS Each subroutine in the Surface Subroutine Library is described in this chapter together with a detailed description of the variables in the call lists For all arrays informatio
185. reaction followed by the four parameters hyieig Eyieiao fi and u slash delimited of Eq 62 A reaction declared with ion enhanced reaction yield must contain one and only one positive ionic reactant species The default units for specifying the reaction rate parameters either the usual defaults set up for SURFACE CHEMKIN or the set of units requested by the user on the REACTION line can be overridden for an individual reaction through use of the UNITS auxiliary keyword Following the reaction one activates this option with UNITS string where string is one of the unit specifiers EVOLTS KELVINS CAL MOLE KCAL MOLE JOULES MOLE or KJOULES MOLE to change the units for parameters that have energy units or MOLES or MOLECULES to change the units of the pre exponential A The t Even if the default energy units are changed by giving one of these keywords the temperature appearing in the Arrhenius expression of Eq 35 i e in T raised to the 8 power and in the denominator of the activation energy term is still in Kelvins 64 UNITS auxiliary keyword allows only one string parameter but the user can repeat the UNITS string option as many times as needed for a given reaction Any number of auxiliary information lines may follow a reaction line in any order and any number of keywords may appear on an auxiliary information line however an auxiliary keyword and its parameter s must appear on the same line
186. reaction index of the Nth yield modified reaction TiYION ISKWRK I ISKWRK IiYION starts an array of species indices for the ion in a yield modified reaction ISKWRK I N 1 is the species index of the ion for the Nth yield modified reaction TiKYLD ISKWRK I ISKWRK IiKYLD starts a matrix of yield modification flags for species in yield modified reactions ISKWRK I N 1 MAXSPR L 1 1 the Lth species of the Nth yield modify reaction is to be modified 0 the species is not modified ISKWRK POINTERS TO RSKWRK REAL VARIABLES IrSKMN RSKWRK I ISKWRK IrSKMN is the minimum difference allowed for conservation of mass and site IrPATM RSKWRK I ISKWRK IrPATM is the pressure of one standard atmosphere dynes cm 2 IrRU RSKWRK I ISKWRK IrRU is the universal gas constant ergs mole k IrRUC RSKWRK I ISKWRK IrRUC is the universal gas constant IiIORD IiKORD IiIONS HH HO Hu HE HP HU HH HZ HE Nn530757009 0410530 4f050wm6 un Gl 166 cal mole K ISKWRK POINTERS TO START OF RSKWRK ARRAY WORKSPACE IrSDEN IrKTMP IrKTHM IrKDEN IrAWT IrkWT IrPAR Ircov IrRPAR IrEQ IrRNU IrNCF IrKORD IrKFT dens divi the divi arra prop ities ding temperatures in t
187. ree energy G is written as Gk Hy TSk 21 SKGML and the standard state Helmholtz free energy A is defined to be Ab Uk TS evn For a perfect gas the standard state specific heats enthalpies and internal energies are also the actual values Therefore we drop the superscript 0 on those quantities Often specific thermodynamic properties are needed in mass units per gram rather than in molar units per mole The conversion is made by dividing the property in molar units by the molecular weight The specific properties are thus given as te Cox 23 E W SKCPMS 30 hy 24 Wi SKHMS o se St 25 We SKSMS Up UK 26 W SKUMS ef GE 27 Wi SKGMS o ap LE 28 Wi SKAMS In addition to pure species properties it is sometimes desirable to know mean properties for a mixture The Gas phase CHEMKIN user s manual discusses this topic for gas phase mixtures and CHEMKIN provides subroutines to return mixture average properties At present however SURFACE CHEMKIN does not provide subroutines to return mixture averaged properties for surface or bulk phase species Thus knowing the pure species properties the user must compute any averaged properties required in an application 31 3 5 Chemical Reaction Rate Expressions The reversible or irreversible surface reactions involve K chemical species and can be represented in the general form K K Vv My O Vox i 1 1 29 k l k
188. rray si dimension at 1 but the subrou NFSURF lt N lt cgs units Integer worksp Real worksp Integer scalar Real matrix t rates of the s of species KSP dimension at 1 both the first cgs units Real array pr dimension at 1 cgs units for 1 KKGAS t for KKGAS 1 KK species for KKGAS KKSU species Real array dimension at 1 E DENSITY sites per species K activities for bulk phase speci 0 to 1 and should sum to 1 for te densities for the site types east NPHASE the total phase coun tine only uses site phas ntries NLSURF moles cm 2 ace array ace array total species count T he partial derivatives of the pro pecies with respect to the concen EC east KKTOT the total species cou and second dimensions moles cm 2 sec units of KSP oduction rates of the species east KKTOT the total species cou moles cm 2 sec ISKWRK RSKWRK DSDC SKDSDC KKTOT he production rates of the dimension is determined by of of the the total species count species density normalized by the site density ULK X are bulk species mole fractions nt ity and es each phase t r dimension at least LENISK dimension at least LENRSK duction tration he production rates of gas phas GAS KKSUR the production rates o R 1 KKTOT the production rate of east NPHASE the total phase coun species f surface bulk produc
189. s AsH3 s In our formalism we would write the adsorption reaction in Fig 3 as AsH3 g Ga s gt AsH3 s Ga b 3 In this reaction the number of sites included on the left hand side of the reaction equals the number on the right hand side the reaction conserves sites Suppose that we had wanted to describe the reverse reaction i e desorption of AsH3 from the surface We would then write the reaction as AsH3 s Ga b gt AsH3 g Ga s 4 Here Ga b is included as a reactant in order to achieve site and elemental balance We denote the formalism described in reactions 3 and 4 as the Atomic Site Formalism An alternate way of posing the above example is to look at the situation on the left side of Fig 3 not as having a surface gallium atom on a site but to say that this is really an open site at which some event may take place see Fig 4 We would write the reaction of Fig 4 as O s AsH3 g gt AsH3 s 5 where the symbol O s was used to denote an open site Since O s contains no elements it is empty this reaction conserves both sites and elements We denote the formalism described in reaction 5 as the Open Site Formalism The Atomic Site and Open Site Formalisms are equally valid ways of stating these surface reactions Either is allowed by the SURFACE CHEMKIN Interpreter Personal preference or perhaps the nature of a particular problem might dictate one over the other Note that a
190. s a reactant NU is positive if the Nth species is a product 113 SKIORD SKIORD SKIORD SKIORD SKIORD SKIORD SKIORD ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKIORD IDIM KDIM ISKWRK RSKWRK NFORD IFORD FORD NRORD IRORD RORD Returns the number and indices of surface reactions with modified species orders and the order values for the species in the T surface mechanism INPUT IDIM Integer scalar dimension of arrays IFORD and IRORD IDIM must be at least NORD the total number of surface reactions with modified species orders KDIM Integer scalar first dimension of the arrays FORD and RORD KDIM must be at least NKK the total species count ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT NFORD Integer scalar total number of surface reactions with modified forward species orders IFORD Integer array indices of surface reactions with modified forward species orders dimension at least NFORD FORD Real matrix the modified forward species orders for the NFORD surface reactions dimension at least KKTOT the total species count for the first and at least NFORD for the second FORD K N is the forward order of species K for the Nth surface change order reaction NRORD Integer scalar total number of surface reactions with modified reverse spec
191. s h would be evaluated by calls to the CHEMKIN Library The gas phase species diffusion velocities V would be evaluated in terms of diffusion coefficients that are obtained from the TRANSPORT Package and finite difference approximations to the species gradients The first term on the right hand side concerns the thermal radiation to or from the surface We now concentrate on the final term which concerns the energy generated or consumed from surface reaction The summation is over all surface and bulk species and the factors in the summation are the production rate of surface and bulk species by surface reaction s the species molecular weights Wz and the enthalpies of the surface and bulk species hy The FORTRAN representation of this term begins with Surface Library subroutine calls the output variables are underlined to help distinguish them CALL SKINIT LSIWK LSRWK LSCWK LINKSK LOUT ISKWRK RSKWRK CSKWRK IFLAG CALL SKWI ISKWRK RSKWRK WT CALL SKHMS T ISKWRK RSKWRK HMS CALL SKRAT P T ACT SDEN ISKWRK RSKWRK SDOT SITDOT The complete details for these calls are explained in later chapters of this document the object here being to illustrate the relative simplicity of a SURFACE CHEMKIN application Briefly the first call is to the initialization subroutine SKINIT which reads the Surface Linking File created by the Surface Interpreter and creates the three work arrays LSIWK LSRWK and LSCWK are the d
192. s provided in Section 5 4 The output of the SURFACE CHEMKIN Interpreter is the Surface Linking File which contains all the pertinent information on the elements species and reactions in the surface reaction mechanism Information on gas phase species comes from the CHEMKIN Linking File and thus is duplicated in the two linking files The Surface Linking File is read by an initialization routine in the Surface Subroutine Library that is called from the CHEMKIN Application The purpose of the initialization is to create three data arrays one integer one floating point and one character data type for use internally by the other subroutines in the Surface Subroutine Library The Surface Subroutine Library has approximately seventy subroutines that return information on elements species reactions thermodynamic properties and chemical production rates Generally the input to these routines will be the state of gas and the surface pressure temperature and species composition The species composition is specified in terms of gas phase mole fractions surface site fractions and bulk phase activities surface site densities are also input to complete the specification of the state of the surface 14 1 2 Example of Using the SURFACE CHEMKIN Utility We illustrate the use of SURFACE CHEMKIN by a simple example involving deposition of silicon The surface reaction mechanism is shown in Fig 1 as it appears for the input file to the Surfac
193. s when the Jacobi rt is negative and the t span of inte flag MF 10 If i F 21 22 24 25 e form In these c ations set MF to t a HOF D Ay O is See full 420030E HR3 lt 0U he Jacobian or banded MF matrix is regarded the form Y YDOT RPAR IPAR YDOT RPAR NEQ on f by loading YDOT i with f i ther or not the problem is stiff an matrix df dy has an eigenvalue large in magnitude compared to the rest If the problem is nonstiff t is stiff there are four standard and DVODE requires the Jacobian ases MF gt 0 DVODE will use a aved copy of the Jacobian matrix If this is undesirable because of he corresponding negative valu description of MF below ither as full MF 21 or 22 24 or 25 In t he banded case DVODE requires two half bandwidth parameters ML and MU These are respectively the widths of the lower and upper parts of the band excluding the main diagonal Thus the band consists of the locations 1 3 with i ML le J C If the pro directly MF compute it in If you are su SUB DOU DIM le i MU and the f blem is stiff you 21 or 24 but 1f ternally by differe pplying the Jacobia ROUTINE JAC NEQ T BLE PRECISION T Y ENSION Y NEQ PD N ull bandwidth is ML MU 1 are encouraged to supply the Jacobian this is not feasible DVODE will nce quotients MF 22 or 25
194. scription of the surface reaction mechanism Required thermodynamic data can come from the same Thermodynamic Database used by CHEMKIN or from a separate Thermodynamic Database compiled for surface species Both Interpreters provide the capability to add to or override the data in the database by user input in the reaction description The SURFACE CHEMKIN Interpreter extracts all needed information about gas phase species from the CHEMKIN Linking File Thus the CHEMKIN Interpreter must be executed before the SURFACE CHEMKIN Interpreter Like the CHEMKIN Interpreter the SURFACE CHEMKIN Interpreter also provides a printed output and a Linking File Again the Surface Linking File is 46 read by an initialization subroutine in the Surface Subroutine Library that makes the surface reaction mechanism information available to all other subroutines in the Library Gas Phase Chemistry Gas Phase Thermodynamic Chemistry Data CHEMKIN Interpreter Surface Processes Surface Reactions Transport Transport Data CHEMKIN Link File SURFACE CHEMKIN Interpreter TRANSPORT Fitting Program TRANSPORT Link File TRANSPORT Library SURFACE Link File SURFACE Library CHEMKIN Library Text Output APPLICATION Input Figure5 Relationships and Flow of Information between the CHEMKIN TRANSPORT and SURFACE CHEMKIN Packages and an Application Program A third software packag
195. ses and species in each phase Chapters 7 and 8 describe the Surface Subroutine Library Chapter 7 being composed of short descriptions for quick reference and Chapter 8 an alphabetical listing explaining the input and output in the call sequence To demonstrate SURFACE CHEMKIN explicitly Chapter 9 goes through a sample problem in detail Appendix A defines the storage allocation of the three data arrays that are created from the Linking File With this information it is possible for a user to create new subroutines for the library to suit a specialized need that was not anticipated in the current version of the Library 19 2 DEVELOPMENT OF SURFACE FORMULATION In this chapter we discuss the mathematical formalism developed to describe surface kinetics for events such as adsorption desorption surface reactions and deposition This formalism is essentially a set of rules for keeping track of surface species concentrations conservation of mass and surface sites mass action kinetics and rates such as deposition or etching rates For this discussion we define three types of species gas phase surface and bulk The first is a species in the gas phase above the surface which might be denoted in a reaction by g A surface species perhaps denoted by s is defined to be the chemical species on the top most layer of the solid i e at the solid gas interface Each surface species occupies one or more sites t
196. sion for surface reaction 1 os a Vi Gi i The production rate of species k due to reaction i is Ski VkiGi Therefore the dependence of p upon the concentration of some species is Ski _ O TK DA Mii _ Eli Ir e l T Inara a grh Ci Mi En varil T Jin mao f Ea 65 SKDRDA 67 The terms inside the curled braces will only be present if species modifies the rate of reaction i through coverage parameters as in Eq 48 The partial of the production rate of species k due to all reactions with respect to the concentration of species is then 68 SKDRDC These terms can all be combined to calculate the desired os da in the Application program Note that subroutine SKDRDA calculates the derivative with respect to the Arrhenius pre exponential if the reaction was originally stated in standard Arrhenius form or with respect to the sticking coefficient pre exponential if a sticking coefficient was used 43 3 14 Flux Matching Conditions at a Gas Surface Interface Heterogeneous reactions at a gas surface interface affect the mass and energy balance at the interface and thus have an important influence on the boundary conditions in a chemically reacting flow simulation The convective and diffusive mass fluxes of gas phase species at the surface are balanced by the production or depletion rates of gas phase species by surface reactions This relationship is nlor V
197. so on KLAST Ending species numbers for the phases In this example KLAST is an array of length 8 the total number of phases The values of each element in the array indicate the species number of the last species in the corresponding phase Here KLAST 1 8 14 17 21 23 26 27 28 29 which shows that in a complete list of species the last gas phase species number is 14 the last species in the first surface phase is number 17 the last species in the second surface phase is number 21 and so on 74 Thermodynamic properties molecular weights and reaction rates for example have values for all species regardless of the phase in which they exist In these cases the values are stored in long arrays that correspond to the data structure shown in Fig 14 Other sets of variables or parameters do not exist for all species For example we may need the mass densities for the bulk species but mass density makes no sense for surface species Nevertheless we maintain the same data structure For example the mass densities for all species can be retrieved by calling SUBROUTINE SKDEN P T ACT SDEN ISKWRK RSKWRK DEN Here the input is the gas phase pressure the temperature and the species activities mole fractions for the gas phase site fractions for the surface species and activities for the bulk species and the site densities of each site phase The first segment of output array DEN contains the gas phase
198. species east KKTOT the total species count S activities are mole fractions F activities are site fractions ACT K SIT the next KKBUL should be from Real array si dimension at 1 but the subrou NFSURF lt N lt cgs units Integer worksp Real worksp Integer scalar NLSURF ace array ace array nsity normalized by the site density ncentration in moles cm 2 is E DENSITY sites per species and K activities for bulk phase species O to 1 and should sum to 1 for each phase te densities for the site types east NPHASE the total phase count tine only uses site phas ntries moles cm 2 dimension at least LENISK dimension at least LENRSK total species count Real matrix partial derivatives of the production rates of the species with respect to the activity of species KSPEC dimension at least KKTOT both the first and second dimensions moles cm 2 sec units of KSPEC Real array production rates of the species dimension at least KKTOT moles cm 2 sec cgs units cgs units SDOT K is for 1 KKGAS t the total species count for the total species count he production rate of gas phase species for KKGAS 1 KKGAS KKSUR the production rate of surface species for KKGAS KKSU R 1 KKTOT the production rate of bulk species Real array production rates of the surface phases dimension at least NPHASE the total
199. t LENRSK OUTPUT KCHARG Integer array electronic charges of the species dimension at least KKTOT the total species count KCHARG K 2 indicates that the species K has two excess electrons SKCOMP SKCOMP SKCOMP SKCOMP SKCOMP SKCOMP SKCOMP KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKCOMP ISTR IRAY NN IND NT Search for the occurrence of character string ISTR in the NN character strings of array IRAY IND is the first location in IRAY of ISTR if found or 0 if not T found and NT is the total number of times it occurs Consider the following example IRAY BOOK BLUE BEAR BOOK NN 4 If ISTR BLUE then IND 2 and NT 1 if ISTR RED then IND 0 and NT 0 and if ISTR BOOK then IND 1 and NT 2 INPUT ISTR Character string TRAY Character string array NN Integer scalar length of IRAY OUTPUT IND Integer scalar location in IRAY of the character string ISTR or 0 if ISTR does not appear in IRAY NT Integer scalar total number of times ISTR occurs in IRAY 97 SKCONT SKCONT SKCONT SKCONT SKCONT SKCONT SKCONT ee eee ee ee eee ees KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKCONT KSPEC ROP ISKWRK RSKWRK CIK Returns the contributions of the surface reactions to the molar production rate of species KSPEC INPUT KSPEC Integer scalar species index ROP
200. t in their analysis of chemical vapor deposition of diamond films The rate of progress is calculated using Eq 32 as usual The sticking coefficient specification is only allowed for the forward reaction If the reaction is written as reversible the reverse reaction rate constant would be calculated from Eqs 57 and 36 using microscopic reversibility 3 11 Bohm Rate Expression for lonic Reactions The rate constant for a reaction involving a positive ion can be modified by applying a Bohm velocity correction as follows o bi c R T j l RT kg Bomm Ole Or 58 Ca Wion In the expression in Eq 58 the unitless pre exponential temperature exponent term and activation energy correspond to the parameters in a sticking coefficient explained above However the Bohm velocity expression the term in the square root in Eq 58 is based on the electron temperature instead of an equilibrium thermodynamic temperature The molecular weight in the last term is that of the positive ion Bohm reactions can be declared through the Interpreter input via the auxiliary keyword BOHM An Application program can find out which reactions were declared as Bohm reactions by a call to SKIBHM Use of the BOHM keyword is only allowed for irreversible reactions 3 12 lon Enhanced Reaction Yield Thus the electron must be declared as a gas phase species in the list of species names in the CHEMKIN interpreter input 40 In m
201. t least LENRSK OUTPUT CPML Real array specific heats at constant pressure for the species dimension at least KKTOT the total species count cgs units ergs mole k SKCPMS SKCPMS SKCPMS SKCPMS SKCPMS SKCPMS SKCPMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKCPMS T ISKWRK RSKWRK CPMS Returns an array of the specific heats at constant pressure in mass units INPUT EEE Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT CPMS Real array specific heats at constant pressure for the species dimension at least KKTOT the total species count cgs units ergs gm K 99 SKCPOR SKCPOR SKCPOR SKCPOR SKCPOR SKCPOR SKCPOR KKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKEKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK SUBROUTINE SKCPOR T ISKWRK RSKWRK CPOR Returns an array of the nondimensional specific heats at constant pressure INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dim
202. t of reactants and products but proceed through distinctly different reaction channels In these cases it may be appropriate to state a reaction mechanism that has two or more reactions with identical reactants and products but have different rate parameters However duplicate reactions are normally considered errors by the Interpreter if the user requires duplication e g the same reactants and products with different Arrhenius parameters an auxiliary information statement containing the keyword DUP with no parameters must follow the reaction line of each duplicate reaction including the first occurrence of the reaction that is duplicated For example to specify different rate expressions for each of three identical reactions there must be three occurrences of the keyword DUP one following each of the reactions If the three coefficients given in the second field of the reaction line are to be interpreted as the parameters a b and c of Eq 52 for a sticking coefficient then the keyword STICK with no parameters must follow the reaction line as auxiliary information There can be only one gas phase reactant species in a sticking coefficient reaction moreover its stoichiometric coefficient must be 1 By default the Motz Wise correction of Eq 57 will be applied for all reactions using sticking coefficients unless the MWOFF keyword is given on the REACTIONS line discussed earlier in which the new default will be to omit t
203. t portion of forward reaction rates for the surface RSKWRK I N 1 is the forward temperature dependent rate for the Nth surface reaction IrKRT RSKWRK I ISKWRK IrKRT starts an array of the temperatur dependent portion of reverse reaction rates for the surface reactions RSKWRK I N 1 is the reverse temperature dependent rate for the Nth surface reaction IrKTl RSKWRK I ISKWRK IrKT1 starts species scratch space IrKT2 RSKWRK I ISKWRK IrKT2 starts species scratch space IrPTl RSKWRK I ISKWRK IrPT1 starts phase scratch space TrPt2 RSKWRK I ISKWRK IrPT2 starts phase scratch space IrITl RSKWRK I ISKWRK IrIT1 starts reaction scratch space IrIT2 RSKWRK I ISKWRK IrIT2 starts reaction scratch space Tri T3 RSKWRK I ISKWRK IrIT3 starts reaction scratch space IrPEDP RSKWRK I ISKWRK IrPEDP starts a matrix of parameters for surface reactions with ion energy dependence RSKWRK I N 1 NEDPAR L 1 is the Lth parameter for the Nth ion energy dependent reaction IrENGI RSKWRK I ISKWRK IrENGI starts an array of ion energies for the gas phase species only RSKWRK I K 1 is the ion energy of species K IrPYLD RSKWRK I ISKWRK IrPYLD starts a matrix of yield parameters fo
204. tate assumed by SURFACE CHEMKIN for bulk phase species is discussed in the previous chapter Other thermodynamic properties are given in terms of integrals of the specific heats First the standard state enthalpy is given by T Hf f co dT 13 so that o M m 1 a Ey Grn OM 14 RT amp m r where the constant of integration ay4 R is the standard heat of formation at 0 K Normally however this constant is evaluated from knowledge of the standard heat of formation at 298 K since the polynomial representations are usually not valid down to 0 K The standard state entropy is written as o f Char 15 T so that o M m 1 Seg ips y O Ea 16 R m 2 m 1 where the constant of integration ay 2kR is evaluated from knowledge of the standard state entropy at 298 K The above equations are stated for an arbitrary order M th order polynomial but SURFACE CHEMKIN is designed to work with thermodynamic data in the form used in the NASA chemical equilibrium code gt In this case seven coefficients are needed for each of two temperature ranges These fits take the following form 29 Co a 7 P 2 3 4 n ak az T a3 T a4 T d5 T SKCPOR Hy ay kT 43 q Dat r g Sk rt y Tok 18 RT 2 3 4 5 T SKHORT o BE Stage A O e pos 19 R 2 3 4 SKSOR Other thermodynamic properties are easily given in terms of C3 H S The internal energy U is given as Ug H RT 20 SKUML the standard state Gibbs f
205. that exist only on a given site type The site fractions of all species that can exist on a given type of site phase sum to 1 The surface species site fractions also correspond to activities The next type of phase is a bulk mixture If a given problem has N different types of bulk mixtures then these are considered to be phases N 2 through N N 1 The user specifies the names of the species that can exist in a given bulk mixture The amounts of these species are determined indirectly by their activities which the user supplies A limiting case is a pure bulk species which is treated as a bulk mixture with only one chemical species whose activity is unity if the chemical potential does not depend on pressure 21 We now consider in more detail how to write chemical reactions involving surface and bulk species A chemical species on the top layer of the solid i e a surface species occupies a site For example an arsine molecule adsorbed on a surface could occupy a site and might be denoted AsH3 s Another example might be a bare gallium atom Ga s on top of a gallium arsenide crystal What happens if another species say a gas phase AsHz lands on top of the Ga s see Fig 3 In this case the gallium atom that was at the surface is covered up so it is no longer a surface species In our nomenclature it has become a bulk species The adsorbed AsH3 now occupies the top most layer at this site so it has become the surface specie
206. ticking coefficients 1 sticking reaction with Motz Wise correction 0 no may or may not be sticking reaction see ISTFL ICOV Integer scalar flag to indidicate that reaction has coverage dependence 1 reaction has coverage dependenc 0 no IEDP Integer scalar flag for energy dependence 1 reaction is energy dependent 0 no IBHM Integer scalar flag for Bohm correction 1 Bohm reaction 0 no IORD Integer scalar flag for species order change 1 reaction has species order change 0 no IYLD Integer scalar flag for yield modification 1 yield modification in reaction 0 no 107 SKGML SKGML SKGML SKGML SKGML SKGML SKGML ee ee ee ee ee ee KKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKK T SUBROUTINE SKGML T ISKWRK RSKWRK GML Returns an array of the standard state Gibbs free energies in molar units INPUT T Real array temperature s dimension is determined by the application program to be the total number of species temperatures nominally 1 cgs units K ISKWRK Integer workspace array dimension at least LENISK RSKWRK Real workspace array dimension at least LENRSK OUTPUT GML Real array standard state Gibbs free energies for the species dimension KKTOT the total species count cgs units ergs mole SKGMS SKGMS SKGMS SKGMS SKGMS SKGMS SKGMS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK
207. tion rates of the surface phases ty but subroutine only calculates entries for site phases cgs units moles cm 2 sec 104 SKDSDX SKDSDX SKDSDX KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKKKKKKKKKKKKKKKKKKKKKKKKK SUBROUTINE T Returns the partial derivative of t SKDSDX P T X SDOT S SKDSDX KKKKKK SKDSDX SKDSDX SKDSDX ACT SDEN ISKWRK RSKWRK DSDX KKTOT ITDOT he production rates of the species with respect to the activity for each species It also returns the matching produc INPUT P ACT F SDEN a ISKWRK RSKWRK KKTOT OUTPUT DSDXA My EJES SDOT SITDOT Real scalar p cgs units ressure dynes cm 2 tion rates Real array temperature s dimension is determined by the application program to be the total number of species temper cgs units Real array mole fraction species dimension at least KKTOT The first KKGAS X are mole fractions the next KKSURF X are site fractions species density normalized by the site density surface co atures nominally 1 K or its equivalent of the the total species count ncentration in moles cm 2 is X K SITE_ eal array ac imension at 1 he first KKGA he next KKSUR species de surface co TtTHAHCc DENSITY sites per species he next KKBULK X are bulk species mole fractions tivities of the
208. tion y of the collisions of SiH with the surface would result in a reaction However for Si s coverages less than 1 the reaction rate decreases in proportion with the coverage of Si s In a third contrived example suppose there is a probability y for a reaction to occur when SiH collides with both a Si s and a C s reaction such as SiH2 g Si s C s gt Si b SiH s CH s 55 The rate of this reaction would be proportional to both the coverage of Si s and C s To convert rate constants given as sticking coefficients y to the usual mass action kinetic rate constants there is the relation To J J oO j l RT r k Vi ie i tot pr 2mW where R is the universal gas constant W is the molecular weight of the gas phase species I is the total surface site concentration summed over all surface phases number of moles of surface sites per unit area and m is the sum of all the stoichiometric coefficients of reactants that are surface species The term involving Tot raised to the m power is needed to convert from the unitless sticking coefficient form to units appropriate for a rate constant and the term in the square root accounts for the gas surface collision frequency In the third example given above Eq 55 the value of m is 2 because there are two surface sites appearing as reactants i e Si s and C s The product term in Eq 56 is the product of the site species occupancies raised to a
209. to declare that the rate of progress of a reaction is proportional to the concentration of any species regardless of whether that species even appears as a reactant or a product in the reaction raised to any specified power To modify the reaction order for the reaction in the forward or reverse direction the user must declare the FORD or RORD auxiliary keywords respectively in the Interpreter input file These keywords are discussed in Chapter 5 An application program can call subroutine SKIORD to find out which reactions were declared to the Interpreter with modified reaction orders and get arrays of the species numbers and associated orders When the reaction order dependence of reaction i is changed via the FORD or RORD keywords the rate of progress variable q for the reaction is evaluated by K Fri K Rei qi k xa k TIX 43 k l k l where Fy is the reaction order specified through the FORD keyword and R is the reaction order specified through the RORD keyword for species k The default for species participating in reaction i is the normal mass action kinetics values Fy Dig 44 Rui Vi 45 35 if an order change parameter is not given for species k The user is advised to exercise caution when specifying a change of reaction order Such a change may produce unexpected and unphysical results in a kinetic simulation The user should also consider the kinetics of the reverse reaction when changing reactio
210. total species count cgs units moles cm 2 sec units of KSPEC 103 SKDSDC SUBROUTINE Returns t species It also INPUT ACT SDI ISKWRK RSKWRK KKTOT OUTPUT DSDC SDOT SITDOT SKDSDC SKDSDC SKDSDC SKDSDC SKDSDC KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK T KKKKKK SKDSDC P T SDOT X S he partial derivative of t with respect to the concentration of each species returns the matching produc Real scalar cgs units Real array te the applicatio P KEKE KKK KKK KKK KK KK KKK KKKKKK ACT SDEN ITDOT tion rates ressure dynes cm 2 mperature s n program to be the total number ie species temper cgs units Real array mo species dimensio The first the next K nat 1 KKGA KSUR surface co atures nominally K le fraction or its equivalent east KKTOT S X are mole frac F X are site frac tions tions ncentration in moles cm 2 is E X K S ITE D ENSITY sites per species KB ac at 1 he next K eal array imension he first KKGA he next KKSUR species de surface co NO tivi eas S ac F ac nsi ties of the species KKTOT the total species cou tivities are mole fractions tivities are site fractions ty normalized by the site dens ncentration in moles cm 2 is ACT K SIT the next KKBUL should be from Real a
211. ts for the surface reactions with real ficients ficient for the Lth species in the Nth real chiometry reaction RSKWRK I ISKWRK IrNCF starts a matrix of net to the surface reactions phase L due to the Nth surface reaction RK I ISKWRK IrKFT starts an array of th RSKWRK I ISKWRK IrSDEN starts an array of phase RSKWRK I N 1 is the density of the Nth phase RSKWRK I ISKWRK IrKTMP starts a matrix of the for rature K ional mic the Nth n the Lth K surface mic weights t M ISKWRK IrKWT starts an array of molecular K 1 is the molecular weight of species K ISKWRK IrPAR starts a matrix of Arrhenius r RSKWRK I ISKWRK IrKCOV starts a matrix of coverage RSKWRK I N 1 NSCOV L 1 is the Lth coverage RSKWRK I ISKWRK IrRPAR starts a matrix of reverse give them RSKWRK I ISKWRK IrEQ starts an array of scalars for RSKWRK I N 1 is the scalar for the Nth surface reaction RSKWRK I ISKWRK IrRNU starts a matrix of stoichiometric RSKWRK I N 1 MAXSPR L 1 is the stoichiometric site changes RSKWRK I N 1 NNPHAS L 1 is the net change in sites RK I ISKWRK IrKORD starts a matrix of species rs for the surface reactions with species change orders RK I N 1 MAXORD L 1 is the order for the Lth ge order species in the Nth change order reaction tions 167 temperatur nden
212. ummy thermodynamic data for the surface species to satisfy the Interpreter requirement Thermodynamic data may be extracted from a database therm dat and or read from the interpreter input file If all the thermodynamic data are extracted from the database then no thermodynamic data are required from the input file However if the user wishes to override information in the database or provide data on species not in the database then SURFACE CHEMKIN Interpreter thermodynamic input is needed In any case the format for the information is the same The format see Table 3 is a minor modification of that used by Gordon and McBride for the Thermodynamic Database in the NASA Chemical Equilibrium code Our modification allows for a different midpoint temperature for the fits to the properties of each chemical species We also allow a species to be composed of a maximum of five elements not four However the formatting is such that the CHEMKIN Interpreter can use the NASA database directly without any modification As Table 3 indicates the pertinent information includes the species name the elemental composition of the species and the temperature ranges over which the polynomial fits to thermodynamic data are valid The fits to Ch f R H RT and S R consist of seven coefficients for each of two temperature ranges see Eqs 17 19 Further information about the fitting procedure and data for many species are in the CHEMKIN Thermodynamic D
213. used in other contexts As such this mechanism should only be considered as illustrative and not as a source of kinetic data on the Si3N4 system The input to the sample problem gives the initial pressure as 2 63x103 atm 2 Torr and temperature 1713 K In this problem the temperature is fixed but the pressure will increase as 12 moles of HF are produced for every 7 moles of reactant destroyed The input gas phase mole fractions represent a 6 1 ratio of NH3 to SiF4 Initial site fractions of the surface species came from a steady state analysis of the system not discussed here The initial activities of the two bulk species are set to 1 The area to volume ratio is 6 a cubic box The print out from the sample problem shows the initial conditions followed by print outs of the concentrations at subsequent states of the deposition The reactants SiF4 and NH3 are seen to be depleted and the product HF forms In this fixed volume system the pressure rises discussed above There is a net decrease in the gas density as the heavy Si and N atoms are lost from the gas into the bulk 139 9 2 Input to CHEMKIN Interpreter Les SS OGO CS SC GS O O GOT ES GR G a A N a AOO O 100E 19 920E 17 300E 14 100E 15 692E 14 636E 06 100E 05 100E 15 500E 14 500E 14 500E 14 254E 14 720E 14 500E 17 500E 14 100E 14
214. using the ion enhanced yield option in the form accepted by the SURFACE CHEMKIN Interpreter is E CL SICL3 S SI B SICL S gt SICL2 S SICL2 SICL S 61 The specieal character identifies the energy dependent multiplicative factor for the stoichiometric coefficient Notice that the sub reaction consisting of every species preceded by the sign balances mass elements charge and number of surface sites The yield of this reaction per incident CL ion depends upon the energy of the ion Eq 62 below We allow the following functional form for the yield enhancement 41 V Eion hyield mas O et E eld y 62 The ion enhanced yield can depend upon a threshold energy E icid 0 and the energy expressions can be raised to a specified power in two different ways through the use of the parameters t and u Ion enhanced yield reactions can be declared through the Interpreter input via the auxiliary keyword YIELD An Application program can find out which reactions were declared as ion enhanced yield reactions and get an array of the parameters via a call to SKIYLD Because the subroutines that evaluate rate constants in SURFACE CHEMKIN take temperature as an argument and not species energy subroutine SKRPAR must be called to input an array of ion energies ENRGI before the rate constant routine is called Use of the YIELD keyword is only allowed for irreversible reactions 3 13 Manipulati
215. valid species name given for FORD or RORD keyword e A reaction order value was not found with the FORD or RORD keyword e RORD given for an irreversible reaction 69 More than MAXORD changes in reaction order declared for a given reaction Should this error occur the user can change a parameter statement in the SURFACE CHEMKIN Interpreter to increase MAXORD No species coefficients were demarked with a symbol for a YIELD reaction YIELD keyword given for a reversible reaction A positive ionic species did not appear as a reactant or its stoichiometric coefficient was not 1 ina YIELD reaction Wrong number of YIELD parameters given More than 1 positive ionic species was a reactant ina YIELD reaction 70 6 DATA STRUCTURES IN SURFACE CHEMKIN Reaction mechanisms have to consider species that may be in the gas phase on various surface sites or in various bulk phases and the number of species surface sites and bulk mixtures change from problem to problem Furthermore with the concept of multiple materials all of these quantities as a group can be specified independently for as many different materials as desired For users writing their own applications they may want to refer to a species by an integer species index such as in a FORTRAN DO loop or refer to a species by a character string such as in an input output routine Furthermore in some circumstances it may be convenient to refer to a species in a lon
216. ven if the default energy units are changed by giving one of these keywords the temperature appearing in the Arrhenius expression of Eq 35 i e in T raised to the 8 power and in the denominator of the activation energy term is still in Kelvins 59 5 5 1 SURFACE REACTION DATA Each reaction line is divided into two fields where a line may take up two or more physical lines if it is more than 80 characters long A reaction data line is continued on the next line using the special character any information following the amp symbol on the same line is ignored The first field in the reaction line contains the symbolic description of the reaction which the second contains the Arrhenius rate coefficients Both fields are format free and blank spaces are ignored All characters on a line following an exclamation mark are considered comments and are ignored Blank lines are also ignored The reaction description given in the first field must be composed of the species symbols coefficients and delimiters as summarized below Symbols Each species name in a reaction is described with a unique sequence of characters as they appear in the species data and the thermodynamic data Coefficients A species symbol may be preceded by a positive integer or real coefficient This coefficient is interpreted as the number of moles of the particular species present as either a reactant or a product e g 20H is
217. ven material and the second dimension large enough to hold the number of materials input to the problem Sample logic that might appear in an application program to handle multiple materials is given in Fig 16 Typically the application program would store the data space needed for all of the different materials in three long real integer and character arrays with pointers to the starting locations of the work space particular to each material e g the arrays IMRSK N IMISK N and IMCSK N point to the starting locations for material N in the example shown in Fig 16 After such information is set up calls to most SURFACE CHEMKIN subroutines look like before but use off sets into the work arrays for the material of interest For example to get an array of the molecular weights of all species in the mechanism for material NMAT the call would look like CALL SKWT I IMISK NMAT R IMRSK NMAT WT 1 NMAT 77 ELEMENTS SI CL SPECIES E E AL CHEMKIN INTERPRE H CL2 CL SICL4 SICL2 CL ATI ER INPUT SURFACE CHEMKIN INTERPRETER INPUT ERIAL WAFER SITE POLY SDEN 2 25e 9 SI S SICL S SICL2 S SICL3 S END BULK SI B 2 33 REACTIONS MWOFF CL SI S gt SICL S STICK E CL2 2SI S gt 2SICL S BOHM E CL SICL3 S SI B gt

Surface Chemkin User Manual - CVD Group

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