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The Alloy-Theoretic Automated Toolkit (ATAT): A User Guide

1. 3 Optionally it is instructive to verify that the magnitude of the ECI decays as a function of the diameter of the corresponding cluster and as a function of the number of sites it contains 5 4 Monte Carlo simulations The emc2 code implements semi grand canonical Monte Carlo simulations 2 8 5 where the total number of atoms is kept fixed while the concentration is allowed to adapt to an externally imposed difference in the chemical potential of the two types of atoms The chemical potential difference will be simply referred to as the chemical potential in what follows This ensemble offers the advantage that for any imposed 24 CHAPTER 5 USER GUIDE Figure 5 2 Output of the maps Code as reported by the mapsrep command a Energies predicted from the cluster expansion as a function of composition for each structure generated known str denotes structures whose energy has been calculated from first principles known gs indicate the ground states that have so far been confirmed by first principles calculations and the dashed line outlines the convex hull of the ground states which serves as a threshold to detect other candidate ground states predicted denotes structures whose energy has not yet been calculated from first principles predicted gs are structures that are predicted by the cluster expansion to be ground states although this prediction has not yet been confirmed by first principles calculations
2. 7 1 MAN PAGES 41 The values of mu are found by linear extrapolation If the abs option is specified the value of mu are in units of energy per spin value as in the output file The ground states are read in from the file gs_str out If there are only two ground states the only correction performed is to shift mu so that mu 0 stabilizes a two phase equilibrium between the two ground states If there are less than 2 ground states no correction is made dmu chemical potential step expressed in the same units as mu0 and mui NOTE If mu is omitted only a scan through T is performed keeping mu mu0 If T1 is omitted only scan through mu is performed keeping T TO gs Gives the index of the ground state to use as an initial spin configuration the leftmost pure element is numbered 0 If the index is 1 the disordered state with an average spin of zero is used as the starting configuration phiO value of the grand canonical potential at the initial point of the run If left unspecified it is set to the grand canonical potential of given by either the 1 spin Low Temperature Expansion or the High Temperature Expansion depending whether the initial state is an ordered or a disordered phase er enclosed radius The Monte Carlo cell will the smallest possible supercell of unit cell of the initial configuration such that a sphere of that radius fits inside it This allows you to specify the system size in a struc
3. Williams method 4 While the algorithms underlying the maps code are described in 23 the present section focuses on its practical use 5 3 CLUSTER EXPANSION CONSTRUCTION USING THE MAPS CODE 19 Figure 5 1 Methodology implemented in atat for the computation of thermodynamic properties from first principles The automated construction of the cluster expansion is performed by the maps code Whenever needed maps requests the calculation of the formation energy of various atomic configurations by a first principles code such as vasp The necessary input files are created and the resulting output files are parsed without requiring user intervention The output of maps is a set of effective cluster interactions that define a computationally efficient Hamiltonian that can be used to perform Monte Carlo simulations with the emc2 code These simulations provide thermodynamic properties and phase diagrams that can be used to create thermodynamic databases or supplement existing ones Lattice geometry Ab initio code parameters MAPS MIT Ab initio Ab initio code Phase Stability Code Cluster expansion construction Effective cluster interactions ECI 4 Emc2 ex VASP Easy Monte Carlo Code Monte Carlo Simulations Phase diagrams Thermodynamic quantities 5 3 1 Input files The maps code needs two input files one that specifies the geometry of the parent lattice lat in and one that provides the parameters of
4. import structures from another source into MAPS A word of caution the imported structures must be unrelaxed and no effort is made to rotate or scale them in order to match the lattice aside from space group symmetry operations 7 1 11 mesqs This code uses a Monte Carlo algorithm to find a Special Quasirandom Structure SQS In writing this code Axel van de Walle benefited from the input of Alexey Dick Dongwon Shin and Yi Wang If you use this code in a publication please cite A van de Walle P Tiwary M de Jong D L Olmsted M Asta A Dick D Shin Y Wang L Q Chen Z Efficient stochastic generation of special quasirandom structures Calphad Journal 42 pp 13 18 2013 gt This code requires 2 input files 1 A file defining the random state by default rndstr in in a format similar to the lat in that is needed for maps or corrdump but with partial occupation of the sites see below 2 A cluster file by default clusters out generated for instance with the command line mcsqs 2 3 etc where 2 3 indicate the range of pairs triplets etc The code display the clusters found format nb of points diameter multiplicity Internally this actually calls the command corrdump l rndstr in ro noe nop clus 2 3 getclus Note that the new ro option allows corrdump to read the same input file as mcsqs here rndstr The noe and nop skip the empty and point clusters that are not u
5. 14 see the command reference for csfit atat can also calculate nonconfigurational contributions to the free energy such as lattice vibrations and electronic excitations see the command reference for fitsvsl svsl fitfc and felec 5 6 Conclusion The Alloy Theoretic Automated Toolkit ATAT drastically simplifies the practical implementation of the Connolly Williams method in combination with semi grand canonical Monte Carlo simulations thus pro viding a high level interface to the calculation of thermodynamic properties from first principles This toolkit enables researcher to focus on higher level aspects of first principles thermodynamic calculations by encap sulating the intricate details of the calculations under an easy to use interface It also makes these powerful methodologies readily available to the wide community of researchers who could benefit from it 30 CHAPTER 5 USER GUIDE Bibliography 10 11 12 13 14 15 16 17 M Asta V Ozolins and C Woodward A first principles approach to modeling alloy phase equilibria JOM Journal of the Minerals Metals amp Materials Society 53 16 2001 K Binder and D W Heermann Monte Carlo Simulation in Statistical Physics Springer Verlag New York 1988 G Ceder A van der Ven C Marianetti and D Morgan First principles alloy theory in oxides Modelling Simul Mater Sci Eng 8 311 2000 J W Connolly and A R Williams Density funct
6. A Kirov Crystallography online Bilbao Crystallographic Server Bulg Chem Commun 43 2 183 197 2011 M I Aroyo J M Perez Mato C Capillas E Kroumova S Ivantchev G Madariaga A Kirov and H Wondratschek Bilbao Crystallographic Server I Databases and crystallographic computing programs Z Krist 221 1 15 27 2006 doi 10 1524 zkri 2006 221 1 15 M I Aroyo A Kirov C Capillas J M Perez Mato and H Wondratschek 7 2 COMMAND LINE OPTIONS 81 Bilbao Crystallographic Server II Representations of crystallographic point groups and space groups Acta Cryst A62 115 128 2006 doi 10 1107 S0108767305040286 7 2 41 getproto GET PROTOtypes from database by Axel van de Walle Syntax getproto string Returns all structure prototypes matching string in ATAT s prototype database string can be a regular expression e g A3 The last 2 columns of the output can be used as arguments to the wycked code to generate the structure up to some adjustable parameters not constrained by symmetry ACKNOWLEDGEMENTS This file contains processed data from the index of the Landolt Bornstein database available at http www springermaterials com If using this data please cite Villars P Cenzual K Daams J Gladyshevskii R Shcherban 0 Dubenskyy V Melnichenko Koblyuk N Pavlyuk 0 Stoiko S Sysa L Landolt Bornstein Group III Condensed Matter Numerical Data and Functional Relationships in Scien
7. MAN PAGES 5l for elastic constants ONO NU e 13 Symmetry file format sym out number of symmetry operations 3x3 matrix point operation 1x3 matrix translation repeat etc Note that if you enter more than one unit cell of the lattice sym out will contain some pure translations as symmetry elements Cluster file format clusters out for each cluster multiplicity length of the longest pair within the cluster number of points in cluster coordinates of 1st point number of possible species 2 cluster function coordinates of 2nd point number of possible species 2 cluster function etc keyword describing type object in the GCE for instance tensor object data repeat etc When the object is a tensor the object data is rank 3 s repeated rank times 3 rank elements of the tensor Multiplicity and length are ignored when reading in the clusters out file For each point the following convention apply The coordinates are expressed in the coordinate system given in the first line or the first 3 lines of the lat in file The number of possible species distinguishes between binaries ternaries etc Since each site can accomodate any number of atom types this is specified for each point of the cluster In multicomponent system the cluster function are numbered from 0 to number of possible species 2 In the simple of a binary syste
8. b The phb command generates temperature composition phase diagrams The calculational details underlying these results can be found in 23 PI a b Ti Al DO T K Ti Al 2000 1800 Ti G ev TiAl 0 56 1600 0 57 T K 1400 0 58 gt 400 1200 0 59 Z f 800 50 60 70 80 90 100 at Ti phb T T mu 4 gs1 0 gs2 1 dT 25 dx 1e 3 er 50 k 8 617e 5 o ph0d out phb T T mu 4 gs1 1 gs2 1 dT 25 dx 1e 3 er 50 k 8 617e 5 o phd1 out In the above example it is assumed that the new phase appearing is the disordered phase indicated by the number 1 which will usually be the case Of course it is also possible that a given two phase equilibrium terminates because one of the two phases disappears In this case only one new calculation needs to be started as in the following example phb T 7 mu y gs1 0 gs2 2 dT 25 dx 1e 3 er 50 k 8 617e 5 o phd1 out Note that phase 1 has been replaced by phase 2 Finally it is also possible that the two phase equilibrium terminates because the concentration of each phase converges to the same value a situation which requires no further calculations The user can easily distinguish these three cases by merely comparing the final composition of each phase 5 4 3 Interpreting the output files The output file of emc2 reports the value of all calculated thermodynamic functions for each value of tem perature and chemical potential scanned The quantities reported include
9. e Statistical averages over Monte Carlo steps such as energy concentration short range and long range order parameters e Integrated statistical averages such as the Gibbs free energy G or the semi grand canonical potential G pe e The result of common approximations namely the low temperature expansion LTE 6 11 B6 the mean field MF approximation and the high temperature expansion HTE see for instance 6 While quantities obtained from statistical averages over Monte Carlo steps are valid for all temperatures and chemical potentials caution must be exercised when interpreting the result of the various approximations or when looking at the integrated quantities The LTE MF and HTE approximations are only accurate in a limited range of temperature and it is the responsibility of the user to assess this range of validity 5For efficiency reasons the long range order parameters are only calculated when starting from an ordered phase 5 5 RECENT DEVELOPMENTS 29 Also the free energy or the semi grand canonical potential are obtained from thermodynamic integration and are thus only valid if the starting point of the integration is chosen appropriately By default the low temperature expansion value is used as a starting point whenever the phase of interest is a ground state while the high temperature expansion is used when the phase of interest is the disordered state Hence to obtain absolute values of the semi
10. is the name of the directory associated with this structure predstr out Contains the predicted energy per site of all structures maps has in memory but whose true energy is unknown Format one structure per line and each line has the following information concentration predicted_energy index status index is the structure number or 1 if not written to disk yet status is either b for busy being calculated e for error u for unknown not yet calculated or g if that structure is predicted to be a ground state g can be combined with the above To list all predicted ground states type grep g predstr out gs out Lists the ground state energies one structure per line and each line has the following information concentration energy fitted_energy energy fitted_energy index gs_connect out Indicates which ground states touch each face of the ground state convex hull gs_str out Lists the ground state structures in the same format as the n str out files see below Each structure is terminated by the word end on a line by itself followed by a blank line 7 1 MAN PAGES 67 chempot out This file contains i the values of the chemical potentials that stabilize all fixed composition multiphase equilibria of the system at OK e g in a n nary system all the n phase equilibria ii values of the chemical potentials that stabilize each of the ground states at OK This data is useful to set up Monte Carlo simula
11. temperatures in kelvins when energies are in eV You can also select this value by using the keV option mft Mean field threshold If the grand canonical potential obtained via the mean field approximation and the low temperature expansion are less than this threshold Monte Carlo simulation are skipped and mean field values are used instead They replace the MC values in the output file The column labelled use_mf is equal to 1 when this substitution is made Note When use_mf 1 the correlations in the output file are incorrectly set to their values in an ideal fully ordered structure All other columns are reliable 62 CHAPTER 7 COMMAND REFERENCE mftq Quantity that must meet the tolerance specified by mft O phi default 1 energy 2 long range order 3 concentrations Tricks To read parameters from a file use memc2 cat inputfile where inputfile contains the commands line options To selectively display a few of the output quantities use memc2 options cut f n1 n2 n3 where ni n2 n3 are the column number desired see below gt Input files control in range of temperature and chemical potentials to scan The first line of this file specifies the initial conditions and has the format temperature chemical_potentials_1 chemical_potentials_n where the chemical potentials are for each specie Each subsequent line of this file indicates one of the axes along which to scan and has
12. 0 Li Vac 0 3333 0 6667 0 0833 0 0 6667 0 3333 0 1667 Co Al 0 0 0 25 0 Running the above example requires the multicomponent version of maps called mmaps Optional input file ref_energy in Contains the reference energy per site to be subtracted to get formation energies The first line is the c 0 energy the second line is the c 1 energy If this file is omitted the energies of leftmost and rightmost structures on the concentration axis are taken Optional input file nbclusters in Allows the user to manually select which clusters to include in the fit 7 1 MAN PAGES 55 This file should contains number of pairs to include number of triplets to include etc This file can be changed while maps is running However you must type touch refresh to tell maps to reread it gt Output files maps log Contains possible warnings Not enough known energies to fit CE True ground states not fitted ground states New ground states predicted see predstr out These warning should disappear as more structural energies become available and the following messages should be displayed Among structures of known energy true and predicted ground states agree No other ground states of xx atoms unit cell or less exist This file also gives the crossvalidation score of the current fit before the weighting is turned on in order to get the correct ground states fit out Contains the results of the
13. 2 PI 1 s m function 1 sin 2 PI 1 s m cos 2 PI m 2 s m sin 2 PI m 2 s m lt the last sin is omitted if m is even where the occupation variable s can take any values in 0 m 1 and denotes the round down operation Note that these functions reduce to the single function 1 s in the binary case 38 CHAPTER 7 COMMAND REFERENCE Special options sym Just find the space group and then abort clus Just find space group and clusters and then abort z To find symmetry operations atoms are considered to lie on top of one another when they are less than this much apart sig Number of significant digits printed gt Cautions When vacancies are specified the program may not be able to warn you that the structure and the lattice just don t fit Carefully inspect the corrdump log file If the structure has significant cell shape relaxations the program will be unable to find how it relates to the ideal lattice The problem gets worse as the supercell size of the structure gets bigger There is no limit on how far an atom in a structure can be from the ideal lattice site The program first finds the atom that can be the most unambiguously assigned to a lattice site It then finds the next best assignement and so on This is actually a pretty robust way to do this But keep in mind that the z option does NOT control this process 7 1 2 cv Help for cv Command line option
14. 4 1 n 1 a_ 4 2 n 1 a_ 4 1 7 1 MAN PAGES 73 a_ 6 0 a_ 6 1 n 1 a_ 6 2 n 1 a_ 6 1 etc Additional output files cs log Contains the constituent strain energy cse of superstructures along the specified directions as a function of concentration Format concentration cse along direction 1 of dir in cse along direction 2 of dir in etc repeat for each concentration csdebug out Contains the raw energies for each calculation The outer loop is on the directions of the dir in file The middle loop is on the element which pure end member The inner loop is on the stretching perpendicular to the k vector Each line contains the energy for various amount of stretching along the direction parallel to the k vector 7 1 16 svsl This code calculates the vibrational free energy of a structure using the Stiffness VS Length method Before using this code you will probably first need to use the fitsvsl code which generates the length dependent force constants that the present needs as an input It requires as an input 3 files 1 A relaxed structure the default file name is str_relax out but it can be overridden with the rs option This provides the actual atomic positions used in the calculations The format of this file is as described in the maps documentation see maps h 2 An unrelaxed structure the default file name is str out but it can be overridden with the us op
15. Thanks to Ruoshi Sun and Mike Widom for updating the script for recent versions of gnuplot 7 2 31 str2xyz Utility to convert structure files into xyz files suitable for viewing with rasmol Syntax str2xyz v na nb nc scale infile v optional calls rasmol otherwise xyz file is written to stdout na nb nc define the number of periodic repetition to plot scale optional scales the structure to adjust which bonds are plotted 7 2 COMMAND LINE OPTIONS 79 7 2 32 makelat MAKE LATtice by Axel van de Walle Utility setting up directories with maps input files for a given alloy system and for one or multiple lattices Syntax makelat o s scale atom1 atom2 lattice1 lattice2 Make sure that there are commas but no spaces between atoms and similarly between the lattices Examples makelat Al Ni bcc fcc makelat Ca Mg 0 rocksalt note the to separate sublattices The default scale is 1 It can be changed to allow for units other than angstroms The o option outputs to strout Lattices available B2 bcc bcc oct bcc tet diamond fcc fcc oct fcc octtet fcc tet hcp hcp oct hcp tet L11 rocksalt sc wurtz Other lattices can be added in the home avdw avdw atat data directory or new atomic radius can be added in the home avdw avdw atat data radii in file 7 2 33 clusterexpand Syntax clusterexpand e pa s 1 0 1 filename Cluster expands the quantity stored in filename Uses the clusters in clusters out
16. The origin of these routines dates back to a FORTRAN code by R C Singleton in 1968 later converted to C and subsequently improved by Mark Olesen and John Beale in 1995 These routines are http www its caltech edu avdw atat http www mit edu avdw ttp www mit edu avdw maps http burgaz mit edu ttp cms northwestern edu ttp www sst nrel gov http est www nrlnavy mil lattice eg 5 gi aa fea fe a 6 CHAPTER 2 CREDITS AND LICENCE included in the atat package for sole purpose of providing users with the convenience of avoiding a separate download Axel van de Walle does not claim any ownership of them or intellectual credit for them Some of the basic numerical routines were inspired by Numerical Recipes in C although they were completely re written according to the ATAT code style conventions for instance to use 0 indexed arrays and make better use of C features Gao Zhe has contributed an interface to PWSCF aka Quantum Espresso that can be found in atat glue qe Matt Probert has contributed an interface to CASTEP that can be found in atat glue castep 2 2 Financial Support The development of MAPS was supported by the U S Department of Energy Office of Basic Energy Sciences under contract no DE F502 96ER 45571 Gerbrand Ceder acknowledges support of Union Mini re through a Faculty Development Chair Axel van de Walle acknowledges support of the Nat
17. deleted We are now ready to automate the calculations Type chl and as indicated on the screen open the file machines rc with a text editor This file contains numerous comment lines explaining the format of the file and a few examples The commands in the first column before the must print a single number indicating the load of the machine It is a good check to copy and paste each of these command one at the time into a shell window to see if the output is a single number In order to extract a single number out of a complicated output the command getvalue is provided It extracts the single number following the token given as an argument The first entry with the none keyword after the indicates the threshold load above which a machine is considered too busy to be usable Note that the load checking commands may quite elaborate if for instance you need to rescale the load of some machines because they have a different reporting scheme or if you want to tweak the priority given to each machine The second column after the give the command prefix needed to run on each remote machine These prefix will usually consist of the command node described above It is very important that the command prefix be such that the current directory in the remote machine when the command is run is the same as on 3 3 INTERFACING MAPS WITH OTHER FIRST PRINCIPLES CODES 13 the local machine The best way to test that is to try the prefix i
18. eci They have already been divided by multiplicity The corresponding clusters are in clusters out clusters out For each cluster the first line is the multiplicity the second line is the cluster diameter and the third line is the number of points in the cluster The remaining lines are the coordinates of the points in the cluster in the coordinate system specified in the input file defining the lattice A blank line separates each cluster n str out Same format as the lattice file except that The coordinate system is always written as 3x3 matrix Only one atom is listed for each site ref_energy out Reference energies used to calculate formation energies Usually energy of the pure end members OR values given in ref_energy in if provided The standard output reports the current progress of the calculations During the fit of the cluster expansion each line of numbers displayed has the following meaning 1 The current number of point pair triplet etc clusters 2 An indicator of whether the predicted ground states agree with the true ones 1 or not 0 3 The CV score gt Communication protocol between maps and the script driving the energy method code e g ab initio code Only those who want to customize the code need to read this section The scripts described in this section are provided with the atat distribution in the glue subdirectory Unless otherwise specified all files mentioned reside in the di
19. emc2 or phb by using the ks cs option CONVENTIONS We expand the concentration dependent reciprocal space ECI associated with constituent strain as J_ CS x k sum_ 1 0 2 4 a_ 1 x K_ 1 k where K_ 1 k 2 is normalized to integrate to one over the unit spherical shell kl 1 By combining Equations 12 and 19 in V Ozolins C Wolverton and A Zunger Phys Rev B 57 6427 1998 we see that the coefficients a_ l x are related to the c_ l x coefficients defined in this paper through a_ 1 x c_ 1 x 4x 1 x The configuration dependent constituent strain energy is given by Delta E_ CS sigma sum_ k Delta J_ CS x k S sigma k 2 exp k 2 k_c 2 see Equation 22 in C Wolverton V Ozolins A Zunger J Phys Condems Matter 12 2749 2000 The S sigma k is computed according to the following convention S sigma k sum_ j in unit cell of structure S_j exp i 2 pi k R_j number of atom in unit cell of parent lattice number of atom in unit cell of structure Delta E_ CS sigma is thus given per unit cell of the parent lattice 1 kc is given in the same unit of length as in the lat in file for instance Angstroms The ouput file cs in contains 1 k_c set to 0 to turn off attenuation Number of kubic harmonic to use e g 2 to use K_O and K_4 Number n of mesh point in concentration grid including x 0 and x 1 a_ 0 0 a_ 0 1 1 a_ 0 2 n 1 LORD a_ 4 0 a_
20. er given here are typical values The user should ensure that these values are such that the results are converged Note that thanks to the way these precisions parameters are input if satisfying values have been found for one simulation the same values will provide a comparable accuracy for other simulations of the same system The option innerT indicates that the inner loop of the sequence of simulations scans the temperature axis while the outer loop scans the chemical potential In this fashion the point of highest temperature in the region of stability of the phase will be known early during the calculations If the user is more interested in obtaining solubility limits early on this option can be omitted and the inner loop with scan the chemical potential axis In either cases the code exits the inner loop and the outer loop if appropriate when it encounters a phase transition The emc2 code thus enables the automated calculation of the whole free energy surface of a given phase as illustrated in Figure 5 4h Such free energy surfaces can be used as an input to construct thermodynamic databases or supplement existing ones To facilitate this process a utility that converts the output of emc2 into input files for the fitting module of ThermoCalc is provided While the above examples focus on the calculation of a phase s thermodynamic properties over its whole region of stability one may be interested in directly computing the temperature
21. for more information type pollmach runstruct_vasp h gt Format of the input file defining the lattice specified by the l1 option First the coordinate system a b c is specified either as a b c alpha beta gamma or as ax ay az bx by bz cx cy cz Then the lattice vectors u v w are listed expressed in the coordinate system just defined ua ub uc va vb vc wa wb wc Finally atom positions and types are given expressed in the same coordinate system as the lattice vectors atomia atom1b atomic atomitypes atom2a atom2b atom2c atom2types etc The atom type is a comma separated list of the atomic symbols of the atoms that can sit the lattice site When only one symbol is listed this site is ignored for the purpose of calculating correlations but not for determining symmetry Examples The fcc lattice of the Cu Au system 3 8 3 8 3 8 90 90 90 5 0 5 5 Ogro oun OO Q O m E e a e Q u Au 7 1 MAN PAGES 65 A 0 O O oooo o Op lattice for the Li_x Co_y Al_ 1 y 0_2 system 707 0 707 6 928 90 90 120 3333 0 6667 0 3333 6667 0 3333 0 3333 3333 0 3333 0 3333 0 0 Li Vac 3333 0 6667 0 0833 0 6667 0 3333 0 1667 Co Al 0 0 25 0 tional input file ref_energy in Contains the reference energy per active site i e those that can host more than one specie to be subtracted to get formation energies The atomic
22. g a shell script called runstruct_xxx where xxx is any name of your choice This script should read from the current directory the file str out describing the geometry of the structure and create the appropriate input files for the first principles code It should then execute the command s needed to run the code If a multiple machine environment is used the script should use the first argument passed to the script 1 as command prefix to put in front of any command in order for them to be run on a remote machine That is if the first principle code is called myfp the script should execute 1 myfp Once the first principles code has terminated the script should e Create a file called energy containing the energy of the structure per unit cell of the structure not the lattice this is what first principles code usually give anyways e If the calculation fails no energy file should not be created Instead an empty file called error should be created The above files must all reside in the current directory from where the script was invoked To follow the philosophy of the package the additional input parameters besides the structure geometry needed by the first principles code should be contained in a file called xxx wrap located one or two levels up in the directory hierarchy relative to the current directory As a starting point to write this script have a look at the file atat glue vasp runstruct_vasp 14 CHAPTE
23. in file sets the composition of each sublattice correctly This can be verified by looking at the point correlations output HH HH HH HOH OH this looks for possible sqs of 8 atoms cell gensqs n 8 gt sqs8 out corrdump 2 anotherradius 3 anotherradius noe s sqs8 out this helps you decide which sqs is best based on other correlations associated with clusters pairs and triplets of diamter less than anotherradius Caution gensqs only generates structures containing exactly the number of atoms per unit cell specified by the If an SQS with a smaller unit cell exists it will not be listed If you give too many correlations to match the code may not output anything Finding an 8 atom sqs takes a few minutes an 16 atom sqs a few hours and a 32 atom sqs a few days The exact speed depends on the symmetry of the lattice and on your computer 7 1 10 maps gt What does this program do It gradually constructs a increasingly more accurate cluster expansion A user provided script running concurrently is responsible for notifying maps when computer time is available maps creates files describing structures whose energy should be calculated The user provided script sets up the runs needed to calculate the energy of these structures As maps becomes aware of more and more structural energies it gradually improves the precision of the cluster expansion which is continously written to an output file The code
24. mismatch e Tensorial cluster expansions gce e Elastic constant calculations calcelas e Structure conversion utilities subcells supercells coordinate system changes file format etc cell cvrt wycked etc e Scripts to automate tasks foreachfile sspp getvalue getlines etc e Codes to generate CALPHAD databases sqs2tdb e Utilities to interface the above tools with first principles codes such as VASP runstruct_vasp run struct_abinit runstruct_gulp etc e Job control utilities that enable the efficient use of a cluster of workstations to run the first principles codes that provide the input to the above codes pollmach CHAPTER 1 FEATURES CAPABILITIES Chapter 2 Credits and Licence The Alloy Theoretic Automated Toolkit ATAT is a generic name that refers to a collection of alloy theory tools developped by Axel van de Walld in collaboration with various research groups 2 1 Collaborators and Credits The MAP MIT Ab initio Phase Stability code which automatically constructs a cluster expansion from the result of first principles calculations was developped by Axel van de Walle in collaboration with Prof Gerd Ceder s grou 14 from the Department of Materials Science and Engineering at the Massachusetts Institute of Technology MAPS consists of the following codes maps corrdump genstr checkcell kmesh cv The EMC2 Easy Monte Carlo Code which automate the calculation of alloy thermody
25. section atat consists of two main computer programs see Figure 5 1 The cluster expansion construction is performed by the MIT Ab initio Phase Stability MAPS code 23 while the Monte Carlo simulations are driven by the Easy Monte Carlo Code EMC2 developed at Northwestern University 21 Each of these codes will be discussed in turn While the present user guide describes how the atat software can be used to carry out all the steps necessary for the calculation of thermodynamic properties from first principles it must be emphasized that each part of the toolkit can be used as a stand alone code For instance many users may have access to an existing cluster expansion obtained through the SIM or other popular methods such as concentration wave based methods see for instance 7 6 20 It is then staightforward to setup the appropriate input files to run the emc2 Monte Carlo code Alternatively after obtaining a cluster expansion using the maps code users could choose to calculate thermodynamic properties with the cluster variation method CVM 10 6 as implemented in the IMR CVM code I9 The modularity of the toolkit actually extends below the level of the maps and emc2 codes many of the subroutines underlying these codes can be accessed through stand alone utilities 22 5 3 Cluster expansion construction using the MAPS code The maps code implements the so called Structure Inversion Method SIM also known as the Connolly
26. sqs2tdb could be echo Al Ni gt species in sqs2tdb cp 1 FCC_A1 lv 1 sqs2tdb cp 1 FCC_A1 lv 1 cd FCC_A1 foreachfile wait pwd runstruct_vasp sqs2tdb fit Edit the file terms in to read 1 0 2 0 sqs2tdb fit cd repeat the above for other lattices if necessary sqs2tdb tdb The file AL_NI tdb would contain a valid tdb file gt In a more advanced example the runstruct_vasp command could be replaced by a job script submission containing the runstruct_vasp command 7 2 COMMAND LINE OPTIONS 83 gt When there are lattice instabilities the runstruct_vasp could be replaced by robustrelax_vasp mk this is to be run only once see robustrelax_vasp h for instructions robustrelax_vasp neb gt If phonons are to be included for end members one could do foreachfile endmem pwd fitfc si str_relax out ernn 4 ns 1 nrr foreachfile d 3 wait runstruct_vasp w vaspf wrap where vaspf wrap contains parameters for a static run to calculate forces foreachfile endmem pwd fitfc si str_relax out f frnn 2 foreachfile endmem pwd robustrelax_vasp vib sqs2tdb fit 7 2 43 symbrklib Usage symbrklib s fraction element initial_structure final_structure Currently the initial and final structures can be one of bcc fcc hcp The s option optional indicates to just generate a small distortion a given fraction along the inst This command is intended to be run before robustrelax_xxxx 7
27. terminates when a stop file is created by typing for instance touch stop NOTE Fully functional scripts are included with the package pollmach and runstruct_vasp For for more information type pollmach runstruct_vasp h 54 CHAPTER 7 COMMAND REFERENCE gt Format of the input file defining the lattice specified by the 1l option First the coordinate system a b c is specified either as a b c alpha beta gamma or as ax ay az bx by bz cx cy cz Then the lattice vectors u v w are listed expressed in the coordinate system just defined ua ub uc va vb vc wa wb wc Finally atom positions and types are given expressed in the same coordinate system as the lattice vectors atomia atom1b atomic atomitypes atom2a atom2b atom2c atom2types etc The atom type is a comma separated list of the atomic symbols of the atoms that can sit the lattice site The first symbol listed is assigned a spin of 1 and the second a spin of 1 When only one symbol is listed this site is ignored for the purpose of calculating correlations but not for determining symmetry Examples The fcc lattice of the Cu Au system 3 8 3 8 90 90 90 5 foe 5 5 oOo OOO WwW oo0oo0oo O 0O O oO n qu u Au A lattice for the Li_x Co_y Al_ 1 y 0_2 system 0 707 0 707 6 928 90 90 120 0 3333 0 6667 0 3333 0 6667 0 3333 0 3333 0 3333 0 3333 0 3333 0 0
28. the format temperature chemical_potentials_1 chemical_potentials_n number_of_steps where number_of_steps is the the number of steps made between the initial conditions and the final conditions given on the line Example to scan the region in T mu1 mu2 mu3 space defined by 100 lt T lt 200 and O lt mui lt 1 0 and O lt mu2 lt 0 5 and mu3 0 0 with a 10x5x5 grid the control in file should be 100 0 0 0 0 0 0 200 0 0 0 0 0 0 10 100 0 0 0 5 0 0 5 100 1 0 0 0 0 0 5 Note Temperatures are given in units of energy unless the k or eV options are set By default the finals conditions are excluded from the scan in the example above the chemical potentials scanned in the last line are 0 0 0 2 0 4 0 6 0 8 This behavior can be changed with the il option to give 0 0 0 25 0 5 0 75 1 0 Alternatively the hf option gives 0 1 0 3 0 5 0 7 0 9 NOTE The mmaps code generates a file called chempot out which contains special values of the chemical potential that stabilize various types of equilibria These values are useful guidelines to select relevant regions in mu space to scan gt Other input files lat in description of the lattice clusters out describes the clusters eci out provides the ECI gs_str out a list of ground states in no particular order These 4 files can be created by maps See maps documentation maps h for a description of the formats gt Optional input files 7 1 MAN PAGES 6
29. the program 1 Dane Morgan University of Wisconsin Paul Dalach Northwestern Dinesh Balachandran MIT Gerd Ceder s group Ben Burton National Institute of Standards and Technology Gautam Ghosh Northwestern University Nikolai Andreevich Zarkevich University of Illinois at Urbana Champaign Duane Johson s group Volker Blum NREL Alex Zunger s group Chris Woodward Northwestern University Air Force oO AN DoT A WwW N Zhe Liu Northwestern University Mark Asta s group Yi Wang and Raymundo Arroyave Pennsylvania State University Long Qing Chen and Zi Kui Liu s group 11 Elif Ertekin University of California at Berkeley Daryl Chrzan s group 12 Rodrigo Barbosa Capaz University of California at Berkeley 13 Sundar Amancherla General Electric http www cryst ehu es http www springermaterials com mailto avdw alum mit edu CHAPTER 2 CREDITS AND LICENCE Chapter 3 Getting started 3 0 1 Requirements You need the following utilities installed e g version 2 7 2 or later Type g version to verify this This package can be downloaded from http www gnu org GNU make any version Type make version to verify this On some systems this command may be called gmake or gnumake This package can be downloaded from http www gnu org e A first principle electronic structure calculation code such as VASE e You may want to use gnuplot t
30. the wrap file is not found in the current directory it searches in the parent directories up to number specified by depth default is 5 For a description of the syntax of the vasp wrap file type ezvasp h and look for options under the INCAR section p means preserve vasp output file lu means look up one directory for WAVECAR to use as starting point ng means do not generate a vasp in file use the existing one nr means do not run vasp just generate input files ex means do not generate vasp in do not run vasp but extract info from vasp output file cmdprefix is the prefix needed for vasp to run on a remote machine such as node s node2 7 2 57 ezvasp Syntax ezvasp c s n p input_file c Cell patch This option will convert the cell you entered into a cell that has the symmetry needed vasp to work properly The atom positions are altered correspondingly s Static run After the relaxations are completed this option makes vasp start again turning off re and turning on tetrahedron integration with bloech correction Can acheive the same effect by including DOSTATIC in the INCAR portion of the input file n do Not run vasp If you want to create the input files now and run them later perhaps on another m p name of the vasp command vasp by default You can include addition prefix such as ezvasp p rsh remote machine nice 5 usr local bin vasp vasp in Here is an example of input fil
31. wc Finally atom positions and types are given expressed in the same coordinate system as the lattice vectors atomia atom1b atomic atomitype atom2a atom2b atom2c atomitype etc In the lattice file The atom type is a comma separated list of the atomic symbols of the atoms that can sit the lattice site In a binary the first symbol listed is assigned a spin of 1 In general ordering of the atom symbol corresponds to value of s 0 1 in the table gt Convention used to calculate the correlations below When only one symbol is listed this site is ignored for the purpose of calculating correlations but not for determining symmetry The atomic symbol Vac is used to indicate a vacancy In the structure file The atom type is just a single atomic symbol which of course has to be among the atomic symbols given in the lattice file Vacancies do not need to be specified Examples The fcc lattice of the Cu Au system 1 1 1 90 90 90 0 0 5 0 5 0 5 0 0 5 0 5 0 5 O O O O Cu Au The Cu3Au L1_2 structure 1 1 1 90 90 90 100 010 001 0 0 0 Au 0 5 0 5 0 Cu 0 5 0 0 5 Cu 0 0 5 0 5 Cu A lattice for the Li_x Co_y Al_ 1 y 0_2 system 0 707 0 707 6 928 90 90 120 0 3333 0 6667 0 3333 0 6667 0 3333 0 3333 0 3333 0 3333 0 3333 0 0 0 Li Vac 7 1 MAN PAGES 37 0 3333 0 6667 0 0833 0 0 6667 0 3333 0 1667 Co Al 0 0 0 25 0 Symmetry file format sym out number of symmetry operati
32. 1 3 1 1 is specified only pair clusters shorter than 2 1 units and triplet clusters containing no pairs longer than 1 1 will be selected This produces a generalized cluster expansion GCE representating a relationship between a property of type object and a crystal structure The object can be anything obeying well defined symmetry rules By default the object is a tensor of rank defined in the file gcetensor in see below for format It writes all clusters found to clusters out If the c option is specified clusters are read from clusters out instead It reads the structure file specified by the s option It determines for that structure the correlations associated with all the clusters chosen earlier This information is then output on one line in the same order as in the clusters out file See below for conventions used to calculate correlations It writes the files corrdump log containting the list of all adjustements needed to map the possibly relaxed structure onto the ideal lattice gt File formats Lattice and structure files Both the lattice and the structure files have a similar structure First the coordinate system a b c is specified either as a b c alpha beta gamma or as ax ay az bx by bz cx cy cz Then the lattice vectors u v w are listed expressed in the coordinate system just defined ua ub uc va vb vc wa wb wc Fin
33. 2 44 getvalue Syntax getvalue label Script that scans standard input for a given label and write to standard output the numerical value following every occurence of that label Any number of spaces or tabs can separate the label and the number Example getvalue Final energy lt gulp output 7 2 45 getlines Syntax getlines h af bf bt jaf jbf bt stringi string2 Copies selected lines of standard input to standard output h print this help af print all lines located after a line containing string1 bf print all lines located before a line containing string1 bt print all lines located between a line containing stringi and a line containing string2 If there are multiple blocks of lines braketed by begin string and end string they are all copied The prefix j means just indicating that the line s containing the matching string s is are ommit Don t forget to quote your strings if they contain spaces 7 2 46 niltoblank Converts each newline character to a space 7 2 47 blanktonl Converts each contiguous sequence of blanks to a newline character 84 CHAPTER 7 COMMAND REFERENCE 7 2 48 foreachfile Syntax foreachfile e d depth filename command Execute the specified command in every first level subdirectory containing the file filename The e option cause foreachfile to skip directories containing the file error The d option specifies to go down to lower level subdir
34. 3 teci out if present provides temperature dependent eci overrides eci out Note that even when the teci out file is used column 6 of the output file reflects only the configurational contribution to the heat capacity The format this file is maximum temperature Tm number of temperatures where eci are provided nT ECIs for temperature 0 ECIs for temperature Tm nT 1 ECIs for temperature 2 Tm nT 1 ECIs for temperature Tm Note that these numbers can be seperated by blanks or newlines as desired conccons in Specifies linear constraints on the composition that spin flips must obey The code will generate multi spin flips if necessary Here is an example of such file 1 0 Al 1 0 Li 0 1 Co 0 5 Please use rational numbers only infinite loop will result otherwise Composition is determined by the user supplied initial configuration via the g or is options gt Format of the output file The file mcheader out gives the content of column of the output file The following abreviations are used T temperature mu A chemical potentials of specie A x A concentration of specie A E energy per active site Egc grand canonical energy per active site i e E sum_i mu i x i lro long Range Order parameter of the initial ordered phase 0 if initial phase is disordered F Helmholtz free energy per active site phi grand canonical potential F sum_i mu i x i use_mf flag that is 1
35. D B Laks L G Ferreira S Froyen and A Zunger Efficient cluster expansion for substitutional systems Physical Review B 46 12587 1992 M Laradji D P Landau and B Diinweg Structural properties of Si _ Ge alloys A monte carlo simulation with the stillinger weber potential Phys Rev B 51 4894 1995 M E J Newman and G T Barkema Monte Carlo Methods in Statistical Physics Clarendon Press Oxford 1999 V Ozolins C Wolverton and A Zunger Cu au ag au cu ag and ni au intermetallics First principles study of temperature composition phase diagrams and structures Phys Rev B 57 6427 1998 31 32 18 19 20 21 22 23 24 25 26 27 28 BIBLIOGRAPHY J M Sanchez F Ducastelle and D Gratias Generalized cluster description of multicomponent sys tems Physica 128A 334 1984 M H Sluiter Imr cvm code 2000 http www lab imr tohoku ac jp marcel cvm cvm html P E A Turchi In J H Westbrook and R L Fleisher editors Intermetallic Compounds Principles and Practice volume 1 page 21 New York 1995 John Wiley A van de Walle and M Asta Self driven lattice model monte carlo simulations of alloy thermodynamic properties and phase diagrams Modelling Simul Mater Sci Eng 10 521 2002 A van de Walle M Asta and G Ceder Invited paper The alloy theoretic automated toolkit A user guide CALPHAD Journal 26 539 2002 A van de Walle and G Ceder Auto
36. ENCE The temperature step for instance dT 50 The enclosed radius which sets the system size for instance er 35 see emc2 documentation for more information The precision of the calculation This is expressed as the desired precision of the average concentration For instance dx 1le 3 The code automatically finds the equilibration time and the number Monte Carlo steps needed to obtain the target standard deviation of the average concentration There are a number of optional parameters as well ltep The low temperature expansion is used to find the free energy at low temperature ltep gives the maximum error allowed before Monte Carlo is used instead of LTE dmu The step in chemical potential used when scanning in search of the phase boundary for instance dmu 0 005 Sometimes the algorithm looses track of the phase boundary because of statistical errors When that happens it scans a range of values of the chemical potential in search of the boudary of the hysteresis loop associated with the first order transition of interest It then position itself in the middle of it dmu is the step size used for that search Note that the code will automatically shrink dmu if needed By default dmu is automaticaly set to the formation energy of a disordered alloy times 0 01 mug lets you specify a small difference in chemical potential between the phases to make the code less sensitive to accidental phase transit
37. Maps replies Finding best structure To find the structure just created wait for done to appear and type ls wait to observe that directory 0 has been created This directory contains a file str out which describes the structure whose energy needs to be calculated The file wait is just a flag that allows you to find the newly created directory Let s pretend that we have computed the energy of that structure We need to let maps know about it Type for instance echo 1 1 gt O energy If 1 1 is the energy of the structure rm O wait Maps responds by Finding best cluster expansion followed by done You can repeat the process touch ready etc to add more structures Maps will update the current cluster expansion every time a new energy becomes known By default maps checks every 10 sec For a description of the output files type maps h more or refer to section A nice utility called mapsrep allows you to plot the results using gnuplot To stop maps cleanly type touch stop Suggestion to clarify the output of the program it is recommended that you run maps in one terminal window and type all other command in another terminal window 3 1 Install the interface between MAPS and VASP Type ezvasp and follow the instructions posted on the screen to configure this command To test this interface change to a directory of your choice and type maps d amp unless maps is running already in that same director
38. Outputs to filename eci filename ecimult ecimult contains the eci multiplied by multiplicity the option e causes the structures flagged with an error file to be ignored the option pa indicates that the quantity is per atom already so that the code must NOT divide it by the number of atoms the option s lets you select which cluster to include 1 or exclude 0 the option g selects a generalized tensor cluster expansion 7 2 34 mkteci Syntax mkteci filel eci where filel eci etc is a list of T dependent eci files obtained with the clusterexpand command e g clusterexpand fvib in the case of vibrational free energy or clusterexpand felec in the case of electronic free energy Usually the file list is fvib eci felec eci vibrational electronic free energy 7 2 35 clusterpredict Syntax clusterpredict pa file see clusterexpand for more info 7 2 36 checkrelax Prints the amount of relaxation each structure in str_relax out has 80 CHAPTER 7 COMMAND REFERENCE undergone relative to str out or str_sup out if it exists Typically values above 0 1 are considered too much for the cluster expansion to be applicable and the offending structures should be disabled using the command touch structure_number error where structure_number is the appropriate directory name The option 1 checks relaxations for one structure only in the current directory This command measures the magnitude of the strain that need to be a
39. R 3 GETTING STARTED Chapter 4 Version History and Bugs 1 50 constituent strain allow any structure names allow new structures to be added at all times 1 66 unit cell in symmetric form ready for ab initio codes constituent strain fitting code temperature dependent ECI in Monte Carlo code manual in tex html reciprocal space Monte Carlo BETA easy to configure job control scripts 2 03 vibrational and electronic entropy included 2 50 mixed canonical grandcanonical multicomponent monte carlo 2 53 reciprocal space multicomponent monte carlo for electrostatics 2 54 automated patching system for c language qwirks 2 70 tensorial generalized cluster expansion gce utility 2 71 fixed bug in multisublattice structure enumeration routine only affects cases where a pure translation maps one sublattice onto another omits some structures with lattice vector equal to one of the unit cell lattice vectors cluster expansions not affected but perhaps missed ground states or SQS but unlikely 15 16 CHAPTER 4 VERSION HISTORY AND BUGS Chapter 5 User guide 5 1 Introduction First principles calculations of alloy thermodynamic properties have been successfully employed in a variety of contexts for metallic semi conductor and ceramic systems including the computation of composition temperature phase diagrams thermodynamic properties of stable and metastable phases short range order in sol
40. The Alloy Theoretic Automated Toolkit ATAT A User Guide Axel van de Walle July 14 2015 Chapter 1 Features Capabilities The Alloy Theoretic Automated Toolkit ATAT is a generic name that refers to a collection of alloy theory tools e Codes to construct cluster expansions from first principles maps and mmaps A cluster expansion is a very compact and efficient expression giving the energy of an substitutional alloy as a function of its configuration i e which type of atom sits where on the lattice e Codes to perform Monte Carlo simulation emc2 and memc2 of lattice models in order to compute thermodynamic properties of alloys starting from a cluster expansion e Codes to perform lattice dynamics calculations fitfc fitsvsl svsl e Codes to calculate electronic and magnetic free energy contributions felec fmag fempmag using simple physical or semiempirical models e Utilities to combine all of the above to generate free energies that include configurational vibrational and electronic contributions mkteci e Codes to generate Special Quasirandom Structures SQS to model disordered solid solutions mcsgqs gensqs and to enumerate structures genstr e A large library of pre computed SQS and structure prototypes e Extension of the two above tools that allow the construction of so called reciprocal space cluster ex pansion which are useful to model the energetics of alloys exhibiting a large atomic size
41. Z Krist 221 15 2006 M I Aroyo A Kirov C Capillas J M Perez Mato and H Wondratschek Bilbao Crystallo graphic Server II Representations of crystallographic point groups and space groups Acta Cryst A62 115 2006 9 The getproto code uses processed data from the index of the Landolt Bornstein databasd4 This data is available upon request by contacting avdw alum mit ed 4 if you can show that you have access to this database Also if using this data please cite Villars P Cenzual K Daams J Gladyshevskii R Shcherban O Dubenskyy V Melnichenko Koblyuk N Pavlyuk O Stoiko S Sysa L Landolt Brnstein Group III Condensed Matter Numerical Data and Functional Relationships in Science and Technology Edited by Villars P and Cenzual K SpringerMaterials The Landolt Brnstein Database Volume 43A1 43A10 2013 The files included in this distribution cannot be further distributed either in their original or in a modified form without consent of the author Axel van de Walle avdw alum mit edu Users are free to modify the code solely for their personal use and are encouraged to share their improve ments with the author at avdw alum mit ed Their contributions will be acknowledged in the present section in future versions of this manual 2 4 Beta testers The following researchers have provided numerous constructive comments that have proven extremely useful to improve the quality of
42. a stop file is created Note that the script can ask maps to create new structure directories even before the energy of the current structure has been found Note that human intervention is allowed an n error file can be manually created if an error is later found in a run Users can also manually step up all runs if they wish so as long as they follow the protocol Example of script portions in have to be filled in with the appropriate code bin csh while e stop check machine load here if load low enough then touch ready while e ready sleep 30 end cd ls wait sed st g head 1 rm f wait convert str out to the native format of ab initio code in background run code and create either energy file or error file cd endif sleep 180 end gt Using maps with vasp The script runstruct_vasp when run from within directory n 1 converts vasp wrap and n str out into all the necessary files to run vasp 2 runs vasp 3 extract all the information from the output files and writes in a format readable by maps An example of vasp wrap is INCAR PREC high ISMEAR 1 7 1 MAN PAGES 69 SIGMA 0 1 NSW 41 IBRION 2 ISIF 3 KPPRA 1000 DOSTATIC See ezvasp documentation for more information gt Importing structures into maps MAPS continuously scans all the first level subdirectories containing a file called
43. a function of the diameter of their associated cluster defined as the maximum distance between any two sites in the cluster Pairs triplets etc are plotted consecutively This plot is useful to assess the convergence of the cluster expansion When the magnitude of the ECI for the larger clusters has clearly decayed to a negligible value relative to the nearest neighbor pair ECI this is indicative of a well converged cluster expansion e A plot of the residuals of the fit i e the fitting error for each structure This information is useful to locate potential problems in the first principles calculations Indeed when first principles calculations exhibit numerical problems this typically results in calculated energies that are poorly reproduced by the cluster expansion When the user is satisfied with the results which are constantly updated maps can be stopped by creating a file called stop in the current directory using the command touch stop while the job dispatching system can be stopped by typing touch stoppoll A cluster expansion can be considered satisfactory when 1 All ground states are correctly reproduced and no new ground states are predicted The log out file would then indicate that Among structures of known energy true and predicted ground states agree No other ground states of n atoms unit cell or less exist 2 The crossvalidation score as given in the log out file is small typically less than 0 025 eV
44. ained by the amount needed for the str out file to be identical to the str_relax out file The phonon frequencies are output in the eigenfreq out file Other parameters can be altered if needed The physical constants are set by default for force constants input in eV Angstrom 2 temperature in K free energy in eV frequencies in Hz masses in a u They can be altered by the hb kb cfk and mu options By default the code give free energies per unit cell but the pa option gives them per atom 7 2 COMMAND LINE OPTIONS 75 The sc option can provide a multiplicative factor for other conventions e g per formula unit By default the code aborts whenever unstable modes are found unless the fn option is specified Contact the author for information about the df and sf options The output files are as follows svsl log a log file giving some of the intermediate steps of the calculations vdos out the phonon density of states for each lattice parameter considered unstable modes appear as negative frequencies svsl out gives along each row the temperature the free energy and the linear thermal expansion e g 0 01 means that the lattice has expansion by 1 at that temperature fvib gives only the free energy gt For including vibrations in phase diagram calculations You are likely to use this code as follow first create the Trange in file for up to 2000K in intervals of 100K echo 2000 21 gt Trange in Thi
45. ally atom positions and types are given expressed in the same coordinate system as the lattice vectors atomia atom1b atomic atomitype atom2a atom2b atom2c atomitype etc 50 CHAPTER 7 COMMAND REFERENCE In the lattice file The atom type is a comma separated list of the atomic symbols of the atoms that can sit the lattice site The first symbol listed is assigned a spin of 1 When only one symbol is listed this site is ignored for the purpose of calculating correlations but not for determining symmetry The atomic symbol Vac is used to indicate a vacancy In the structure file The atom type is just a single atomic symbol which of course has to be among the atomic symbols given in the lattice file Vacancies do not need to be specified Examples The fcc lattice of the Cu Au system 1 1 1 90 90 90 0 0 5 0 5 0 5 0 0 5 0 5 0 5 0 O O O Cu Au The Cu3Au L1_2 structure 1 1 1 90 90 90 100 010 001 0 0 0 Au 0 5 0 5 0 Cu 0 5 0 0 5 Cu 0 0 5 0 5 Cu A lattice for the Li_x Co_y Al_ 1 y 0_2 system 0 707 0 707 6 928 90 90 120 0 3333 0 6667 0 3333 0 6667 0 3333 0 3333 0 3333 0 3333 0 3333 0 0 0 Li Vac 0 3333 0 6667 0 0833 0 0 6667 0 3333 0 1667 Co Al 0 0 0 25 0 File format of gcetensor in rank list of pairs of indices indicating which simultaneous index permutations leave the tensor invariant next list etc Examples for strain or stress 2 O 1 7 1
46. ansion is that in practice it is found to converge rapidly An accuracy that is sufficient for phase diagram calculations can be achieved by keeping only clusters a that are relatively compact e g short range pairs or small triplets The unknown parameters of the cluster expansion the ECI can then be determined by fitting them to the energy of a relatively small number of configurations obtained through first principles computations This approach is known as the Structure Inversion Method SIM or the Collony Williams 4 method The cluster expansion thus presents an extremely concise and practical way to model the configurational dependence of an alloy s energy A typical well converged cluster expansion of the energy of an alloy consists of about 10 to 20 ECI and necessitates the calculation of the energy of around 30 to 50 ordered structures see for instance 24 9 T7 Once the cluster expansion has been constructed the energy of any configuration can be calculated using Equation at a very small computational cost This enables the use of various statistical mechanical techniques such as Monte Carlo simulations 2 the low temperature expansion LTE Ti 6 the high temperature expansion HTE 6 or the cluster variation method CVM 10 6 to calculate thermodynamic properties and phase diagrams The atat software implements Monte Carlo simulations the LTE and the HTE Paralleling the two step approach described in the previous
47. ative index gives the sine instead of cosine phase of the mode You can run your ab initio code in the subdirectory generated named vol_ p_uns_ lt dr gt _ lt kmesh gt _ lt numbe and rerun fitfc f fr If you see Warning p is an unstable mode then you have found a true instability If you only see Unstable modes found Aborting you may repeat the process until the message disappear or a truly unstable mode is found Note If you want to generate a phonon DOS even if there are unstable modes use the fn option The unstable modes will be shown as negative frequencies Phonon Dispersion curves The df inputfile option invokes the phonon dispersion curve module The syntax of the input file is nb of points kxi ky1 kz1 kx2 ky2 kz2 repeat Each line of input defines one segment kx1 ky1 kz1 kx2 ky2 kz2 along which the dispersion curve is to be calculated nb of points specifies the number of points sampled along the segment The coordinates are in multiple of the reciprocal cell defined by the axes in the file specified by the si option or by default in the str out file The k point coordinates are appropriately strained by the amount needed for the str out file to be identical to the str_relax out file The phonon frequencies are output in the eigenfreq out file in the vol_ subdirectories Output files fitic log A general log file 7 1 MAN PAGES 47 vol_ vdos out th
48. b Energies calculated from first principles known str and known gs are as in a except that the energy calculated from first principles is reported c Effective Cluster Interaction ECI as a function of the diameter of the associated cluster and as a function of the number of sites in the cluster i e pair triplet etc d Residuals of the fit that is the difference between the first principles energies and the energies predicted from the cluster expansion The abscissa refers to the line number within the output file fit out listing all the structures with known energies Fitted Energies Calculated Energies a b 0 A T T T T 0 ig T T T T 7 0 05 F5 g 1 0 05 FY 4 0 1 j o i t t f3 K 0 1 F v s i s 7 f y 4 0 15 geod TE p 0 15 FON i 36 9 a S f 7 0 2 Fo o e 2 J ng 7 Fe 0 25 f i s y 0 25 f S o y s N g t gt 0 3 Me ot o m 0 3 f y 3 a 1 0 35 E O 2 predicted 9 35 L Ye nr i g gt known str i a 8 Ep a z 0 4 Sig ec known gs a 0 4 F gt a m7 ee predicted gs x known gs a 0 45 i i i 0 45 i 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 c ECI vs cluster diameter d Residuals of the fit same order as in fit out 0 06 T T T T T T T T T T T T 0 08 T T es T T T 0 05 0 06 l 0 04 0 03 ee e o 0 02 F oo2 F e 0 01 es eee o
49. before the energy of the current structure has been found Note that human intervention is allowed an n error file can be manually created if an error is later found in a run Users can also manually step up all runs if they wish so as long as they follow the protocol Example of script portions in have to be filled in with the appropriate code bin csh while e stop check machine load here if load low enough then touch ready while e ready sleep 30 end cd ls wait sed st g head 1 rm f wait convert str out to the native format of ab initio code in background run code and create either energy file or error file cd endif sleep 180 end gt Using maps with vasp The script runstruct_vasp when run from within directory n 1 converts vasp wrap and n str out into all the necessary files to run vasp 2 runs vasp 3 extract all the information from the output files and writes in a format readable by maps An example of vasp wrap is INCAR PREC high ISMEAR 1 SIGMA 0 1 NSW 41 IBRION 2 ISIF 3 KPPRA 1000 58 CHAPTER 7 COMMAND REFERENCE DOSTATIC See ezvasp documentation for more information gt Importing structures into maps MAPS continuously scans all the first level subdirectories containing a file called str out and tries to map them onto superstructures of the lattice provided This lets you
50. bic symmetry or if you are willing to assume that thermal expansion is isotropic or if you only which to use the harmonic approximation the fitfc command should be invoked with the nrr option do Not ReRelax and you can now skip to step 3 7 1 MAN PAGES 45 2b 2c 3 4 Each volume subdirectory now contains a str out file which is stretched version of the main str_relax out file provided You then need to run the ab initio code to rerelax the geometry at the various levels of imposed strain and obtain the energy as a function of strain Typically this is acheived by typing pollmach runstruct_vasp amp make sure that the vasp wrap file is modified so that all degrees of freedom except volume are allowed to relax After this command each subdirectory will contain an energy and a str_relax out file Type touch stoppoll after all energies have been calculated The runstruct_vasp command can also be executed manually in each subdirectory or as follows foreachfile wait runstruct_vasp rm wait Now you need to reinvoke fitfc to generate perturbations of the atomic position for each level of strain fitfc er 11 5 ns 3 ms 0 02 dr 0 1 This is exactly the same commmand as before but the code notices the presence on the new files and can proceed further At this point the files generated are arranged as follows At the top level there is one subdirectory per level of strain vol_ where is the strain in percent an
51. called the remote machines only need to have VASP or any other ab initio code Before you start you must first make sure that it is possible to login from the master machine to the remote machines without entering a password This is essential for the program to be able to run on its 12 CHAPTER 3 GETTING STARTED own without your intervention Don t worry it is generally possible to do this without compromising the security of your system Two commands allow you to run a command on a remote machine If the master and remote machines are connected through a secure network e g a beowolf cluster having its own local network or if you don t care about security for now you can use rsh Otherwise ssh provides a secure way to command a machine remotely To set up rsh so that you can login without typing a password you must have the appropriate rhosts file on the remote machine For more information consult the rsh man page One important issue often not mentioned in the man pages its that you need to set the file permissions of the rhosts file so that noone else but you has write permission chmod og w rhosts To set up ssh so that you can login without typing a password consult the ssh man page especially the section on RSA based host authentication This is the feature that makes the login secure even if no password is needed In general setting this up involves creating a shosts file and generating a public
52. cates that a static run must be done after the relaxation run NSW tag is removed and t token are ajusted accordingly The output files named relax contain the result of the first relaxation run while the files named static contain the results of the second static run When DOSTATIC is not specified all output files are named static whether the VASP input paramet allow relaxations or not KSCHEME specifies the type mesh to use Gamma shift or Monkorst Pack The default is Gamma if KSCHEM MAGATOM is similar to the usual token MAGMOM used to specify the moment on each atom The novelty is moments in the POSCAR section In version 3 15 and above this token can be ommited Having spins s section turns this on automatically It also set ISPIN 2 automatically The usual MAGMOM token is still available but you cannot use both MAGMOM and MAGATOM USEPOT 88 CHAPTER 7 COMMAND REFERENCE selects the potentials used LDA GGA PAWLDA PAWGGA PAWPBE or any other potential defined in ezvasp By default LDA without PAW is used For backward compatibility you can also use the tag DOGGA instead of USEPOT GGA 6 The SUBATOM token lets you specify a sed like substitution command to be applied to the name of the atomic species For instance SUBATOM s Fe Fe_h g will cause ezvasp to use the Fe_h pseudopotential instead of the Fe one Multiple SUBATOM token can be given one for each substitution Don t forget the s and g and the aft
53. ce and Technology Villars P Cenzual K ed SpringerMaterials The Landolt Bornstein Database http www springermaterials com Volume 43A1 43A10 2013 7 2 42 sqs2tdb sqs2tdb version 3 16 by Axel van de Walle and with contributions to the SQS database from Ruoshi Sun Qijun Hong and Sara Kadkhodaei Usage sqs2tdb options where the available options are h More help cp Copy SQS from the database to the current directory Must specify lv level level indicates how fine of composition mesh to use 0 only end members 1 mid points etc 1 lattice Available lattices AUCU_L10 BCC_A2 BETASN_A5 CDI2_C6 CHI_A12 CR3SI_A15 CSCL_B2 CUPRITE_C3 CUPT_B22 DIAMOND_A4 FCC_A1 FE3SAL_D03 FLUORITE_C1 GAMMA_L12 HCP_A3 HEUSLER_D022 82 CHAPTER 7 COMMAND REFERENCE HEUSLER_L21 hidden LIQUID MGCU2_C15 NIAS_D81 OMEGA_C32 PEROVSKITE_E21 PYRITE_C2 REO3_D09 ROCKSALT_B1 RUTILE_C4 SIGMA_D8B WURTZITE_B4 ZINCBLENDE_B3 ZINTL_B32 ZIRCONIA_TET fit Fit solution model from SQS energies to be run within the desired lattice directory tdb Combine solution models from one or multiple lattices into a single tdb file mk Generate input file for SQS generation with mcsqs Usually not needed only for experts To be run in the SQS database directory home avdw avdw atat data sqsdb lattice name Note that h mk cp fit tdb are mutually exclusive EXAMPLES gt A simple session of
54. chines rc file is created the first time the chl command is run The format of the file is explained in the comments therein If no machines rc file exists command_to_run is run sequentially on the local computer in each directory containing a wait file This is the single machine mode When using this command with maps command_to_run will typically be runstruct_vasp The m option overrides the default machines rc it is optional The e option specifies that the command should terminate when no more wait files are to be found only works in single machine sequential mode when no machines rc file is given The f option forces the command to run even if of pollmach_is_running file exists The s option cause pollmach to self manage the load it does not poll the nodes for their loads but instead keeps track of where it sends a job and does not send any other job to that node until it i 86 CHAPTER 7 COMMAND REFERENCE The first column in the machine_configuration_file is ignored and can be omitted The w option tells pollmach to wait until all sub processes have finished before quitting To cleanly stop this program type touch stoppoll 7 2 55 fixeol converts text files to unix u or to pc p format Syntax fixeol ul p file1 file2 7 2 56 runstruct vasp runstruct_vasp w file d depth p lu ng nr ex cmdprefix where file is an optional alternate wrap file default vasp wrap If
55. composition phase boundary without first constructing a full free energy surface To accomplish this task a typical command line for the phb program would be phb gsi 0 gs2 1 dT 25 dx 1le 3 er 50 k 8 617e 5 ltep 5e 3 o ph01 out This command computes the two phase equilibrium between phase 0 and phase 1 starting at absolute zero and incrementing temperature in steps of 25 K The ltep option indicates that a Low Temperature Expansion LTE should be used instead of Monte Carlo simulation whenever its precision is better than 5 x 10 3 eV The output file phO1 out contains the temperature composition phase boundary of interest as well as the chemical potential stabilizing the two phase equilibrium as a function of temperature This output can be used to generate phase diagrams as illustrated in Figure 5 4p The program automatically terminates when the end of the two phase equilibrium has been reached If the two phase equilibrium disappears because of the appearance of a third phase two new two phase equilibria have to be separately calculated To do so one uses the final temperature T and chemical potential p given in the output file as a starting point for two new phb runs 28 CHAPTER 5 USER GUIDE Figure 5 4 Output of Monte Carlo codes a The emc2 provides free energy surfaces as a function of temperature T and composition x For clarity the common tangent construction thick lines is drawn over the calculated free energy
56. d in each subdirectory there are a number of subsubdirectories each containing a different perturbation The pertubation names have the form p lt gt lt dr gt _ lt er gt _ lt index gt where lt pertmag gt is the number given by the dr option lt er gt by the er option and lt index gt is a number used to distinguish between different pertubations Two perturbations that differ only by their signs are sometimes generated and are distinguished by a or prefix If you want to ensure that the third order force constants cancel out exactly in the fit you need to consider both perturbations Otherwise only the positive perturbation will be sufficient Note that whenever the third order terms cancel out by symmetry only the positive perturbation will be generated You then need to use the ab initio code to calculate reaction forces for each perturbation This will typically be accomplished by typing pollmach runstruct_vasp amp make sure that the vasp wrap file indicates that no degrees of freedom are allowed to relax and the smearing is used for Brillouin zone integration Do not use the DOSTATIC option Fitting the force constants and phonon calculations This mode is invoked with the f option In addition you need to specify the range of the springs included in the fit using the fr option 46 5 gt CHAPTER 7 COMMAND REFERENCE Usually the range specified with fr should be not mo
57. e INCAR SYSTEM FeNi ISPIN 2 PREC HIGH ISMEAR 1 NSW 41 7 2 COMMAND LINE OPTIONS 87 SIGMA 0 1 IBRIO IS 2 IF 3 ENMAX 400 ED ED IFF 1e 6 IFFG 1e 4 KPPRA 1000 USEPOT PAWGGA DO SUBATOM KSCHEME MAGATOM STATIC s Fe Fe_h g GAMMA POSCAR S OME TITLE 3 55 1 500000000 500000000 1 000000000 500000000 1 000000000 500000000 500000000 500000000 1 000000000 2 Direct 33333 33333 00000 Fe 5 00000 00000 00000 Vac 66667 66667 00000 Fe 5 End of example Note that there 5 new tokens in the INCAR section 1 2 3 4 5 KPPRA stands for K Point Per Reciprocal Atom This is a way to automatically set the k point mesh a number of similar systems Here is how it works If you know that you need 500 k points for a 2 at structure then you type in 1000 If you now try a similar structure with 4 atoms the code automati use 250 k points The mesh along the three axes is automatically chosen to make the mesh as uniform For the algorithm see atat src kmesh cc You can also specify KPPRA UPDIR which indicates that the KPOINTS file found one directory above should be used This is useful for cell distorsions used in elastic constant calculations of constituent strain run If this token is ommited you need to specify a KPOINT section in the input file that contains wha you want the KPOINT file to be DOSTATIC indi
58. e 93
59. e energy is accurate within the target precision specifified by tp aq Alternative quantity that must meet the tolerance specified by tp 0 energy default 1 long range order 2 concentations correlations gs Gives the index of the ground state to use as an initial spin configuration starting at 0 The ground states are listed in gs_str out If the index is 1 the disordered state with equiatomic composition is used If gs 1 the LTE and MF approximations are not calculated If you want the LTE and MF ouputs use one of the pure end members as a starting point tstat Critical value of the test for discontinuity The code is able to catch phase transformations most of the time when going from an ordered phase to another or to the disordered state This involves a statistical test which a user specified confidence level The default 3 corresponds to a 0 4 chance of finding a transition where there is none Refer to a standard normal table tstat 0 turns off this option Suggestion if a phase transition is undetected first try to reduce temperature or chem pot steps or increase n or decrease tp before toying around with this parameter Also beware of hysteresis sigdig Number of significant digits printed Default is 6 0 Name of the output file default mc out k Sets boltzman s constant default k 1 This only affects how temperatures are converted in energies k 8 617e 5 lets you enter
60. e phonon density of states for each volume considered vol_ fc out The force constants For each force constant a summary line gives i the atomic species involved ii the bond length iii the stretching and bending terms Then each separate component of the force constant is given and finally their sum vol_ svib_ht gives the high temperature limit of the vibrational entropy in units of kB atom in the harmonic approximation excluding the configuration independent contribution at each unit cell volume considered so this just 3 times the average log phonon frequency vol_ fvib gives the harmonic vibrational free energy in eV at that volume as a function of temperature The following 3 files give the output of the quasiharmonic approximation if ns gt 1 and the harmonic approximation if ns 1 fitfc out gives along each row the temperature the free energy and the linear thermal expansion e g 0 01 means that the lattice has expanded by 1 at that temperature fvib gives only the free energy svib gives only the entropy in energy temperature by default eV K eos0 out equation of state at OK one strain energy pair per line eos0 gnu gnuplot script to plot polynomial amp data 7 1 7 fitsvsl This code determines bond stiffness vs bond length relationship for the purpose of calculating vibrational properties with the svsl code It requires the following files as an input 1 A lattice file by de
61. e present and the code will look for all files of the form force out and force out and the corresponding files str out and str out The code will then use that information to create the length dependent force constants this may take a few minutes and ouputs them in slspring out Here is an example of the format of this file Al Al gives the type of bond 2 2 parameters linear fit is used 50 28971 polynomial coeficients of the stiffness vs length relationship for stretching term 7 88973 typically stiffness is in eV Angstrom 2 and length is in Angstrom 2 6 12722 idem for bending term 1 01641 Ti Al repeat for each type of chemical bond 3 etc The only option controling this process is op which specifies the order of the polynomial used to fit the length dependence by default op 1 and a linear fit is used Contact the author for information about the sf option Diagnostic files are also output fitsvsl log a log file fitsvsl gnu and f_ dat to plot the s vs 1 relationship 7 1 MAN PAGES 49 7 1 8 gce gt What does this program do 1 2 3 4 5 6 7 It reads the lattice file specified by the l option See format below It determines the space group of this lattice and writes it to the sym out file It finds all symmetrically distinct clusters object pairs that satisfy the conditions specified by the options 2 through 6 For instance if 2 2
62. e specific syntax of the job submission script because it is highly system dependent In a nutshell one would submit on job containing the following commands assuming the system is using a standard implementation of MPI some header specifying the number of nodes etc maps d amp note the amp to run in the background pollmach runstruct_vasp mpirun you may need to specify the number of processors as mpirun np number If your system does not allow a background commands in the script or if this would be very inefficient then you could put each command without amp in a separate script but making sure they run at the same time Either way parallelization occurs at the level of the vasp command If you wish to also parallelize by running multiple vasp commands simultaneously then you should submit yet another job script with some header specifying the number of nodes etc pollmach runstruct_vasp mpirun repeating this process as many times as you the number of simultaneous vasp processes you want note that there is still only one copy of maps running 3 2 2 Without queueing systems We now cover the case where there is no queueing system and the user has full power to run on any of the nodes in the cluster Networking problems can be tricky and we will test various thing as we go along You only need to perform this installation on your master machine that will run maps All other machine which we be
63. ectories as well the default is 1 7 2 49 calc Syntax calc mathematical expression 7 2 50 sspp Simple symbolic pre processor reads from stdin writes to stdout also writes temporary file tmp awk Interprets simple definitions and evaluates numerical expressions with constants definitions invoking sspp nb produces a output file where all blank lines have been removed input file syntax understands any C pre processor commands see man cpp also understands const vari value2 var2 value2 the variables vari can be used later in the file Expression to be evaluated must be enclosed in braces except when they are in a const declaration The brace characters are entered as and Understands c comment char Examples const x 2 3 14 The value is 1 cos x define PLUS x y x y The answer is PLUS 1 2 Braces are Implementation details Any line beginning with const or awk is interpreted as an awk command see man awk Expression in braces are awk expressions The file tmp awk is the file sent to awk for interpretation BUGS Never start a line with is not a comment character 7 2 51 chl chl m alternative_machine_config file Checks the load on the remote machines specified in the machines rc file or as overridden by the m option The first column of output is the load and the commands following the sign give the command prefix needed to run on that machi
64. em the occupation variables g take the value 1 or 1 depending on the type of atom occupying the site A particular arrangement of these spins on 17 18 CHAPTER 5 USER GUIDE the parent lattice is called a configuration and can be represented by a vector containing the value of the occupation variable for each site in the parent lattice Although we focus here on the case of binary alloys this framework can be extended to arbitrary multicomponent alloys the appropriate formalism is presented in 18 The cluster expansion then parametrizes the energy per atom of the alloy as a polynomial in the occupation variables E o X mado II n 5 1 ica where q is a cluster a set of sites i The sum is taken over all clusters a that are not equivalent by a symmetry operation of the space group of the parent lattice while the average is taken over all clusters a that are equivalent to a by symmetry The coefficients Ja in this expansion embody the information regarding the energetics of the alloy and are called the effective cluster interaction ECI The multiplicities Ma indicate the number of clusters that are equivalent by symmetry to a divided by the number of lattice sites It can be shown that when all clusters a are considered in the sum the cluster expansion is able to represent any function E of configuration o by an appropriate selection of the values of Ja However the real advantage of the cluster exp
65. er the first element name to avoid F matching Fe or Y matching Yb There are new features in the POSCAR section as well 1 The line that specify the number of atoms here 1 2 can be ommited it is ignored 2 The atomic species are specified to the right of the atom positions The corresponding POTCAR are automatically copied You can specify pseudopotentials like Li_h or O_s 3 The number following the species is the magnetic moment on the atom if MAGMOM is in the INCAR secti Identical species with different moments will be considered symmetrically distinct to allow for symmetry breaking relaxations 4 Do not specify selective dynamics It will be written to the INCAR file automatically if you include T s and F s after the atom species e g 0 50 5 0 5 ALTTF 5 The element Vac stands for vacancy It is ignored for everything but to compute the k point mesh with the KPPRA option 7 2 58 robustrelax vasp This command implements the inflection detection method introduced in The free energy of mechanically unstable phases by A van de Walle Q Hong S Kadkhodaei and R Sun Nat Com forthcoming 2015 It calculates the energy of a structure that is potentially mechanically unstable In a nutshell the method finds either a local minimum for a mechanically stable phase or the inflection point on a path joining the unrelaxed and fully relaxed structures for a mechanically unstable phase Syntax robustrelax_vasp op
66. fault lat in but this can be overridden with the l option which allows the code to determine what chemical bonds are present in the system The format is as described in the maps documentation see maps h 2 A list of directories containing structures that will be used to calculate force constants by default strname in but this can be overridden with the dn option Each of the listed directory must contain a a str out file containing an ideal unrelaxed structure that will be used to automatically determine the nearest neighbor shell b a str_relax out file containing the relaxed structure that will be used to calculate bond lengths and that the code will perturb in various ways to determine the force constants The code can operate in two modes a structure generation mode and a fitting mode indicated by the f option In structure generation mode All the above input files are needed and the option er must be specified in order to indicate the size of the supercells generated The er option indicates how far from each other a displaced atom must be from 48 CHAPTER 7 COMMAND REFERENCE its periodic images the code will infer the smallest supercell satisfying this constraint Typically er should be 3 or 4 times the nearest neighbor distance All of these distances are measured using the ideal structures str out The following parameters have reasonable default values which can be overridden dr specifies the displacemen
67. fault sqsparam in Read supercells from file sqscell out default generate internally and write to sqscell Index of current process for parallel operation Default 1 Collect best SQS among the outputs of prior parallel runs Default Off Select correlation functions default trigo Seed for random number generation default use clock Read parameter file every rt step default 10000 Generate only supercells in the plane of a b axes Default Off Number of significant digits to print in output files default 6 Display more help Default Off 7 2 20 memc2 src memc2 Command not found 78 CHAPTER 7 COMMAND REFERENCE 7 2 21 mmaps src mmaps Command not found 7 2 22 nnshell src nnshell Command not found 7 2 23 mnntouch src nntouch Command not found 7 2 24 pdef src pdef Command not found 7 2 25 phb src phb Command not found 7 2 26 strpath src strpath Command not found 7 2 27 svsl src svsl Command not found 7 2 28 triph src triph Command not found 7 2 29 getclus Syntax getclus e ecifile extracts from clusters out the cluster sizes lengths and multiplicities if ecifile is given it also prints the eci therein if e is specified it prints eci from eci out 7 2 30 mapsrep Display the output of maps in graphical form Syntax mapsrep e the optional switch e tells the code to plot structures flagged with error too
68. fcc lattice of the Cu Au system request for an SQS at composition 0 5 3 8 3 8 3 8 90 90 90 oO A lattice for the Li_x Co_y Al_ 1 y 0_2 system request for an SQS with different composition on each sublattice 0 707 0 707 6 928 90 90 120 60 CHAPTER 7 COMMAND REFERENCE 0 3333 0 6667 0 3333 0 6667 0 3333 0 3333 0 3333 0 3333 0 3333 0 0 0 Li 0 75 Vac 0 25 0 3333 0 6667 0 0833 0 0 6667 0 3333 0 1667 Co 0 25 Ni 0 25 A1 0 5 0 0 0 25 0 gt The objective function used is sum absolute difference from the disordered state correlations exp wd diameter of cluster wn n normalization for weights to sum up to 1 over clusters bigger than the smallest nonmatching cluster sum over p wr wn p 2 diameter of the smallest cluster of p points of less whose correlation does n The wr wn and wd are set through the wr wn and wd options respectively or as the 3 first numbers o The diameter of a cluster is the length of the longest pair contained in a cluster normalized by neare See routine calc_objective_func in mcsqs c for a more precise description This objective function reflect researchers desire to perfectly match all correlation up to some range Adding the absolute difference serves to guide the algorithm in the right direction to extend the range of perfect match This objective function is a generalization of the one found in the Calphad paper cited above reduces gt Post processing If you have ob
69. fit one structure per line and each line has the following information concentration energy fitted_energy energy fitted_energy weight index concentration lies between O and 1 energy is per site a site is a place where more than one atom type can lie weight is the weight of this structure in the fit gt index is the name of the directory associated with this structure predstr out Contains the predicted energy per site of all structures maps has in memory but whose true energy is unknown or has been flagged with error Format one structure per line and each line has the following information concentration energy predicted_energy index status index is the structure number or 1 if not written to disk yet energy is the calculated energy or 0 if unknown status is either b for busy being calculated e for error u for unknown not yet calculated or g if that structure is predicted to be a ground state g can be combined with the above To list all predicted ground states type grep g predstr out gs out Lists the ground state energies one structure per line and each line has the following information concentration energy fitted_energy index gs_str out 56 CHAPTER 7 COMMAND REFERENCE Lists the ground state structures in the same format as the n str out files see below Each structure is terminated by the word end on a line by itself followed by a blank line eci out Lists the
70. grand canonical potential one must ensure that the calculations are started at a sufficiently low temperature or sufficiently high temperature in the case of the disordered phase This can be checked by comparing the Monte Carlo estimates with the LTE or HTE estimates and verifying that they agree for the first few steps of the thermodynamic integration A user specified starting point for e g obtained from an earlier Monte Carlo simulation can be indicated using the option phid Note that unlike emc2 the phb code automatically makes use of the low temperature expansion whenever it is sufficiently accurate in order to save a considerable amount of computational time By default the code reports the thermodynamic quantities associated with the semi grand canonical ensemble such as the semi grand canonical potential The command line option can instructs the code to add px to all appropriate thermodynamic quantities so that the code outputs the more commonly used canonical quantities such as the Gibbs free energy G and the internal energy E 5 5 Recent developments The multicomponent version of maps is mmaps and the multicomponent version of emc2 is memc2 The phb code does not have a multicomponent version All other utilities can handle multicomponent systems Although the present tutorial does not discuss the topic atat also implements reciprocal space cluster expansions and in particular the constituent strain formalism
71. he initial chemical potential is optional when starting from absolute zero because the code can determine the required value from the ground state energies It can nevertheless be specified in absolute value with the mu y option if a finite temperature starting point is desired A list of the command line options of either the emc2 or phb codes can be displayed by simply typing either command by itself More detailed help is displayed using the h option 5 4 2 Examples We now give simple examples of the usage of these commands Consider the calculation of the free energy of the phase associated with ground state number 1 as a function of concentration and temperature Then the required commands could for instance be emc2 gs 1 mu0 1 5 mui 0 5 dmu 0 04 T0 300 T1 5000 dT 50 k 8 617e 5 dx 1e 3 er 50 innerT o mc10 out emc2 gs 1 mu0 1 5 mu1 2 5 dmu 0 04 T0 300 T1 5000 dT 50 k 8 617e 5 dx 1e 3 er 50 innerT o mc12 out The only difference in the two command lines is the value of mu1 and the output file name specified by the o option These commands separately compute the two halfs of the free energy surface corresponding to the values of the chemical potential below and above the middle value of 1 5 which stabilizes ground state 1 at absolute zero This natural separation allows you to run each half calculation on a separate processor and obtain the results in half the time The values of dmu dT dx and
72. he middle of the calculations finding the best cluster expansion or the best structures because MAPS only generates these clusters or structures when they are needed Q Where are the results A In a variety of files whose descriptions you can view by typing maps h more A utility called mapsrep lets you display the most useful output data using gnuplot Q What files do I need to get started with MAPS A A lat in files to specify the geometry of the lattice and a wrapping file that specifies the parameters of the first principles code If you are using vasp this file is usually called vasp wrap Examples of those files can be found in the example directory Q I already have structures and energies What if I just want to fit them A You need a lat in files to specify the geometry of the lattice and you need to create one subdirectory for each structure name them as you which In each subdirectory you need a str out file to specify the geometry of the structure and an energy file to indicate the energy of that structure For the format of those files type maps h more Note that the energy must per unit cell of the structure not the lattice Q When I type maps I only get the command line option help How can I run it A Type maps d to use all the default options You can also specify any option you want Either way the help message will not be displayed and the code will run If the help is still displayed it is because the
73. ic Automated Toolkit Calphad Journal 33 266 2009 5 As of version 2 81 the algorithm to generate superstructures has been improved based on the ideas in G L W Hart and R W Forcade Algorithm for generating derivative structured Phys Rev B 77 224115 2008 6 If the mcsqs code is used A van de Walle and P Tiwary and M M de Jong and D L Olmsted and M D Asta and A Dick and D Shin and Y Wang and L Q Chen and Z K Liu Efficient stochastic generation of Special Quasirandom Structured 4 Calphad Journal 42 13 2013 7 If the constituent strain extension is used D B Laks and L G Ferreira and S Froyen and A Zunger Phys Rev B 46 p 12587 1992 http arXiv org abs cond mat 0201511 1Chttp arXiv org abs cond mat 0201473 http Jarxiv org abs cond mat 0212159 http arxiv org abs 0906 1608 i 14 2 4 BETA TESTERS 7 8 The wycked code uses the Wyckoff position database from the Bilbao Crystallographic Serve Ac cordingly if you use this code you should also cite the following papers M I Aroyo J M Perez Mato D Orobengoa E Tasci G de la Flor A Kirov Crystallography online Bilbao Crystallographic Server Bulg Chem Commun 43 183 2011 M I Aroyo J M Perez Mato C Capillas E Kroumova S Ivantchev G Madariaga A Kirov and H Wondratschek Bilbao Crystallographic Server I Databases and crystallographic com puting programs
74. id solutions thermodynamic properties of planar defects including surfaces or antiphase and interphase boundaries and the morphology of precipitate microstructures 6 5 27 28 25 3 0 Although the formalism that allows the calculation of thermodynamic properties from first principles has been known for decades 6 5 27 its practical implementation remains tedious These practical issues limit the accuracy researchers are able to obtain without spending an unreasonable amount of their time writing input files for various computer codes monitoring their execution and processing their output These practical difficulties also limit the community of researchers that use these methods solely to those that possess the necessary expertise to carry out such calculations The Alloy Theoretic Automated Toolkit ATAT drastically simplifies the practical use of these methods by implementing decision rules based on formal statistical analysis that free the researchers from a constant monitoring during the calculation process and automatically glues together the input and the output of various codes in order to provide a high level interface to the calculation of thermodynamic properties from first principles In order the make this powerful toolkit available to the wide community of researchers who could benefit from it this article present a concise user guide to this toolkit 5 2 Theoretical Background While there exist numerous methodol
75. if mf values have been used instead of mc values corr_n_d the average correlations associated with each cluster n is the number of points in the cluster d is the diameter of the cluster Suffixes _lte obtained with low temperature expansion _mf obtained with mean field approximation _mc obtained with Monte Carlo simulations NOTE to obtain canonical rather than grand canonical quantities adding mu x to all free energies use the g2c option NOTE an active site is one that can host more than one possible atom type Energy and free energy are reported per active site not per total sites 64 CHAPTER 7 COMMAND REFERENCE 7 1 13 mmaps gt What does this program do This is the multicomponent version of the maps code It gradually constructs a increasingly more accurate cluster expansion A user provided script running concurrently is responsible for notifying maps when computer time is available maps creates files describing structures whose energy should be calculated The user provided script sets up the runs needed to calculate the energy of these structures As maps becomes aware of more and more structural energies it gradually improves the precision of the cluster expansion which is continously written to an output file The code terminates when a stop file is created by typing for instance touch stop NOTE Fully functional scripts are included with the package pollmach and runstruct_vasp For
76. ion k sets boltzman s constant see emc2 documentation keV dn indicates that the boundary must be folowed downward decreasing T Output file Column Value temperature chemical potential concentration of phase 1 in 1 1 concentration of phase 2 in 1 1 energy of phase 1 energy of phase 2 Onan RWN Ee 7 1 MAN PAGES 71 7 1 15 predcs This code fits a reciprocal space cluster expansion of the constituent strain energy for binary systems with cubic symmetry USAGE csfit needs as an input 4 files 1 A lat in file defining the geometry of the lattice same format as maps 2 Two str_relax out residing in given directories pa and pb options or by default 0 and 1 and providing the relaxed geometry of the two pure end members for the system 3 A dir in file listing the directions along which to compute epitaxial deformation energy in order to fit the expansion Directions are specified as miller indices in the coordinate system defined in lat in Each index must be separated by a space and each direction must be on a separate line The code then generates subdirectories in 0 and 1 or any other directory you specify with deformed structures whose energy will be used to fit the expansion The np and nl options let you control the number of structures generated np provides the number of intermediate epitaxial strain perpendicular to specified directions considered between the lattice parameter
77. ional Science Foundation under program DMR 0080766 and DMR 0076097 during his stay at Northwestern University The development of EMC2 was supported by the NSF under program DMR 0080766 The development of the CSE is supported by the NSF under program DMR 0080766 The development of the tensorial cluster expansion GCE and gencs code is supported by the Center for the Science and Engineering of Materials at Caltech an NSF funded MRSEC and by the NSF CMMT grant DMR 0907669 The development of the wycked and getproto codes is supported by the NSF CAREER grant DMR 1154895 The development of the mcsqs code is supported by ONR grants N00014 11 1 0886 and N00014 11 1 0886 2 3 Licence and Agreements Any scientific article or book whose results were obtained with the codes described above must properly acknowledge their use by citing the following papers 1 A van de Walle and G Ceder Automating First Principles Phase Diagram Calculationd Journal of Phase Equilibria 23 348 2002 2 A van de Walle and M Asta Self driven lattice model Monte Carlo simulations of alloy thermody namic properties and phase diagram Modelling Simul Mater Sci Eng 10 521 2002 3 A van de Walle M Asta and G Ceder The Alloy Theoretic Automated Toolkit A User Guidad CALPHAD Journal 26 539 2002 4 A van de Walle Multicomponent multisublattice alloys nonconfigurational entropy and other addi tions to the Alloy Theoret
78. ional theory applied to phase transformations in transition metal alloys Phys Rev B 27 8 5169 1983 D de Fontaine Cluster approach to order disorder transformation in alloys Solid State Phys 47 33 1994 F Ducastelle Order and Phase Stability in Alloys Elsevier Science New York 1991 F Ducastelle and F Gautier Generalized perturbation theory in disordered transitional alloys application to calculation of ordering energies Journal of Physics F Metal Physics 6 2039 1976 B Diinweg and D P Landau Phase diagram and critical behavior of the si ge unmixing transition A monte carlo study of a model with elastic degrees of freedom Phys Rev B 48 14182 1993 G D Garbulksy and G Ceder Linear programming method for obtaining effective cluster interactions in alloys from total energy calculations application to the fcc pd v system Phys Rev B 51 1 67 1995 R Kikuchi A theory of cooperative phenomena Phys Rev 81 988 1951 A F Kohan P D Tepesch G Ceder and C Wolverton Computation of alloy phase diagrams at low temperatures Comput Mater Sci 9 389 1998 G Kresse and J Furthmiiller Efficiency of ab initio total energy calculations for metals and semicon ductors using a plane wave basis set Comput Mater Sci 6 15 1996 G Kresse and J Furthmiiller Efficient iterative schemes for ab initio total energy calculations using a plane wave basis set Phys Rev B 54 11169 1996
79. it Crossvalidation score s This provides the predictive power of the cluster expansion It is analo gous to the root mean square error except that it is specifically designed to estimate the error made in predicting the energy for structures not included in the least squares fit 23 It is defined as 2 a 1 2 CV Se w i 1 5 4 MONTE CARLO SIMULATIONS 23 where E is the calculated energy of structure i while Ew is the predicted value of the energy of structure 7 obtained from a least squares fit to the n 1 other structural energies The maps code also outputs quantitative data in various output files The simplest way to analyze this data is by typing mapsrep As illustrated in Figure 5 2 this command displays in turn e The log out file described earlier e The formation energy of all structures whose energy is known from first principles calculations as well as the predicted energy of all structures maps has in memory The convex hull of the ground states among structures of known energy is overlaid while the new predicted ground states if any are marked by an x Note that this ground state line is only meaningful if the log out file contains Among structures of known energy true and predicted ground states agree e The formation energy of all structures calculated from first principles and associated ground state line e A plot of the magnitude of the Effective Cluster Interactions ECI as
80. key files to be copied onto the remote machines If your username is different on the remote machine and if you use ssh use the syntax node username host instead If you use rsh use the syntax node 1 username host Once you are able to run either rsh node2 1s or ssh node2 1s and get the content of your home directory on the remote machine assuming that you have a remote machine called node2 you can proceed to the next step Do you have the same home directory on the master and remote machines and does it have the same access path To check this cd to some arbitrary subdirectory and type node node2 1s where node is a command provided with ATAT and node is the name of the remote machine If you want to use ssh instead type node s node2 1s This should print the content of the current directory on the master machine not your home directory If you get an error message or if you get the content of another directory you will need to check if the following works Make sure you are in a directory that does not contain too many files If you want to use rsh type node r node2 1s while if you want to use ssh node s r node2 ls In either case you should get the content of the current directory before continuing on The node r command works by copying the content of the current directory on the remote machine in a temporary directory Once the command has terminated the new content is copied back and the remote temporary directory is
81. lay a few of the output quantities use emc2 options cut f ni n2 n3 where ni n2 n3 are the column number desired see below Input files lat in description of the lattice clusters out describes the clusters eci out provides the ECI gs_str out a list of ground states in increasing order of concentration These 4 files can be created by maps See maps documentation maps h for a description of the formats Optional input file teci out if present provides temperature dependent eci overrides eci out Note that even when the teci out file is used column 6 of the output file reflects only the configurational contribution to the heat capacity The format this file is maximum temperature Tm number of temperatures where eci are provided nT ECIs for temperature 0 ECIs for temperature Tm nT 1 ECIs for temperature 2 Tm nT 1 ECIs for temperature Tm Note that these numbers can be seperated by blanks or newlines as desired Format of the output file Each line contains in order 1 T Temperature 2 mu chemical potential derivative of the free energy wrt to average spin 3 E mu x Average energy per spin 4 x Average Concentration ranges from 1 to 1 5 phi grand canonical potential 6 E2 Variance of the energy proportional to heat capacity 7 x2 Variance of the concentration proportional to susceptibility 7 1 MAN PAGES 43 8 E_lte mu x_lte calcula
82. ll of the structure that is in the way a first principles code usually gives it e Errors in the lat in file Use the corrdump sym more sym out command to analyse the symmetry of the lattice and see if it correspond to your expectations You can also use corrdump 2 10 clus more clusters out to verify the symmetrically distrinct pairs are what you expect them to be e When the structures are not generated by MAPS i e you typed them it beware of typos MAPS will detect if a structure is incompatible with the lattice but it will not detect another very common mistake putting the energy and str out files that correspond to different structures in the same directory To check for this error look at the residual plot generated by mapsrep e When copying the lat in files provided as examples make sure you make all the required changes i Change the atom names ii Set the lattice parameters first 3 numbers in the file to values that are at least as large as the true lattice parameter otherwise first principles code can be unable to properly relax the geometry of the structure is the atoms are too close to one another initially Chapter 9 Organization of the Toolkit e src source code e glue utilities to interface MAPS with other codes e glue jobctrl utilities allowing maps to automatically lauch jobs e glue vasp interface between vasp and maps e doc user guide and documentation regarding the inner workings of the cod
83. m number of possible species 2 cluster function are just 0 0 For a ternary the possible values are 1 0 and 1 1 All the utilities that are not yet multicomponent ready just ignore the entries number of possible spe Convention used to calculate the correlations 52 CHAPTER 7 COMMAND REFERENCE The cluster functions in a m component system are defined as function 0 cos 2 PI 1 s m function 1 sin 2 PI 1 s m cos 2 PI m 2 s m sin 2 PI m 2 s m lt the last sin is omitted if m is even where the occupation variable s can take any values in 0 m 1 and denotes the round down operation Note that these functions reduce to the single function 1 s in the binary case Special options sym Just find the space group and then abort clus Just find space group and clusters and then abort 2 To find symmetry operations atoms are considered to lie on top of one another when they are less than this much apart sig Number of significant digits printed gt Cautions When vacancies are specified the program may not be able to warn you that the structure and the lattice just don t fit Carefully inspect the corrdump log file If the structure has significant cell shape relaxations the program will be unable to find how it relates to the ideal lattice The problem gets worse as the supercell size of the structure gets bigger There is no limit on how far an atom i
84. mating first principles phase diagram calculations Journal of Phase Equilibria 23 348 2002 A van der Ven M K Aydinol G Ceder G Kresse and J Hafner First principles investigation of phase stability in li coog Phys Rev B 58 2975 1998 C Wolverton V Ozolins and A Zunger Short range order types in binary alloys a reflection of coherent phase stability J Phys Condens Matter 12 2749 2000 C Woodward M Asta G Kresse and J Hafner Density of constitutional and thermal point defects in L1g AlsSc Phys Rev B 63 094103 2001 A Zunger First principles statistical mechanics of semiconductor alloys and intermetallic compounds In P E Turchi and A Gonis editors NATO ASI on Statics and Dynamics of Alloy Phase Transformation volume 319 page 361 New York 1994 Plenum Press A Zunger Spontaneous atomic ordering in semiconductor alloys Causes carriers and consequences MRS Bull 22 20 1997 Chapter 6 Interfacing with ThermoCalc A description of the steps necessary to convert the output of the Monte Carlo code emc2 to input files suitable for the PARROT module of ThermoCalc are described in an online tutorial by Gautam Ghosh available in atat doc emc2tc pdf These steps are partially automated in the script atat glue tc emc2tc included in the ATAT distribution 33 34 CHAPTER 6 INTERFACING WITH THERMOCALC Chapter 7 Command Reference 7 1 Man pages 7 1 1 corrdump gt What does
85. minimal cluster expansion containing only nearest neighbor pair interactions and test its accuracy Thus the first cluster expansion is typically constructed after at least 4 structural energies have been computed this number may vary as a function of the symmetry of the lattice Among structures of known energy true ground states differ from fitted ground states The current cluster expansion incorrectly predicts which structures have the lowest energy for given concentrations among structures whose first principles energy is known The code has built in checks to avoid this However in rare instances it may be mathematically impossible to satisfy all the constraints that the code imposes for a cluster expansion to be acceptable This problem becomes increasingly unlikely as the number of calculated structural energies increases so the user should just wait until the problem fixes itself Among structures of known energy true and predicted ground states agree Opposite of the previous message When this message is displayed maps also displays either one of the following two messages New ground states of volume less or equal to n predicted see predstr out This indi cates that the cluster expansion predicts that at some concentration there exist other structures that should have an energy even lower than the one of the structures whose energy has been calculated from first principles In this case maps will investigate the matter by gene
86. n a structure can be from the ideal lattice site The program first finds the atom that can be the most unambiguously assigned to a lattice site It then finds the next best assignement and so on This is actually a pretty robust way to do this But keep in mind that the z option does NOT control this process 7 1 9 gensqs IMPORTANT NOTE Please see mcsqs command for a better easier to use SQS generator This code requires 3 input files 1 A lattice file by default lat in in the same format as for maps or corrdump 2 A cluster file by default clusters out as generated with the corrdump utility 3 A target correlation file by default tcorr out which contains the value of desired correlations for each of the clusters listed in the cluster file A typical caling sequence would be 7 1 MAN PAGES 53 the following command can be used to generate the target correlation file tcorr out corrdump noe 2 maxradius rnd s conc in gt tcorr out where maxradius is the length of the longest pair desired and where conc in contains an ordered structure having the desired concentration The geometry of the structure in the conc in file is not crucial only the average concentration on each sublattice will be used CAUTION Here a sublattice is a set of symmetrically equivalent point clusters If your system contains multiple sublattices as evidenced by multiple point clusters in clusters out make sure that your conc
87. n front of the 1s command and verify that what is printed is indeed the content of the current local directory Once you are done with entering the information for each of your machines you can also enter only a few and come back later to add the remaining ones make sure to comment out the examples provided placing a at the beginning of the unwanted line Do not comment out the first line which contains the none keyword Once you have edited the machines rc file type chl This should give a list of the load of all machines in the first column and a list of command prefix in the second Next try the command minload It should give the command prefix that let you access the machine with the minimum load or none if no machine is available To check once again that the command prefix are correct type minload 1s make sure you use backward quotes This should print the content of the current directory unless there are no machines available This approach could also be used with a queueing system but this is much more advanced and requires good knowledge of scripting languages You could read the node list file the queueing system assigned to the job and create a local machine rc file on the fly The s option of pollmach could prove helpful to ensure two vasp runs do run on the same processors and avoids the need for load balancing code 3 3 Interfacing MAPS with other first principles codes You need to provide a command e
88. namic properties via Monte Carlo simulations of lattice models were developped by Axel van de Walle in collaboration with Prof Mark Asta s group from the Department of Materials Science and Engineering at Northwestern University EMC2 consists of the following codes emc2 phb The CSE Constituent Strain Extension to both the MAPS and EMC2 codes which implement the constituent strain formalism based on a reciprocal space cluster expansion was developped by Axel van de Walle in collaboration with Alex Zunger s Solid State Theory See at the National Renewable Energy Laboratory in Golden Colorado and in collaboration with Gus Hart from the Department of Physics and Astronomy at Northern Arizona University CSE conssists of the following files csfit cc predcs cc predrs cc kspacecs cc Mayeul D Avezac at NREL has provided all the changes needed for ATAT to compile with g versions 4 1 and later as well as intel s c compiler Volker Blum at NREL has contributed to improve the portability of the package by providing a perl version of the ch1 utility Dongwon Shin at Penn State has converted a large number of common lattices found at the NRL navy web sitd into the atat format See directory data str Greg Pomrehn has improved the efficiency of the structure enumeration algorithm and contributed the script mmapsrep The FFT routines in the files fftn cc and fftn h were obtained from the NIST Guide to Available Math Software GAMS
89. ne 7 2 COMMAND LINE OPTIONS 85 A default machines rc is created the first time the command is run See comments therein for the format of the file 7 2 52 minload Syntax minload m alternate_machine_config file w Returns the command prefix needed to run a command on the remote machine having the minimum load among the machines listed in the machines rc file or as specified by the m option A default machines rc file is created the first time the chl command is run and the file format is described in the comments therein 7 2 53 node This command is basically like rsh except that the command makes sure that the current directory on the remote machine is the same as on the local machine If the two machines do not share the same disk space use the r option Syntax node s r user host command s use ssh instead of rsh r copy files in current directory to remote host before running command if user is the same on remote host use may use node s r host command 7 2 54 pollmach Syntax pollmach f e m alternate_machine_configuration_file s w command_to_run This command periodically checks the load on various machines specified in the file machines rc and looks for subdirectories containing a file called wait If the load on a machine is sufficiently low it executes command_to_run on that machine in the directory where the oldest wait file lies A default ma
90. ng the simulation are specified as command line options The first input param eter s needed by the code are the phase s whose thermodynamic properties are to be determined There are two ways to invoke the Monte Carlo simulation code When the command emc2 is used a single Monte Carlo simulation is run to allow the calculation of thermodynamic properties of a single phase for the whole region of chemical potential and temperature where that phase is stable The phase of interest is specified by a command line option of the form gs n where n is a number between 1 and G 1 inclusive where G is the number of ground states The value 1 indicates the disordered phase while values ranging from 0 to G 1 indicate the phases associated with each ground states 0 denoting the ground state with the smallest composition When the command phb is used two Monte Carlo simulations are run simultaneously to enable the determination of the temperature composition phase boundary associated with a given two phase equilibrium The two phases are specified by gsl n gs2 np It is possible to compute a two phase equilibrium between phases defined on a different parent lattice In this case the user needs to specify the directories where the cluster expansions of each lattice resides using the options of the form di directory 1 d2 directory 2 The accuracy of the thermodynamic properties obtained from Monte Carlo simulations is determined b
91. nge c These defaults can be overridden by the TO T1 and dT options The output files contain the free energy per unit cell felec log contain temperature and corresponding free energy on each line felec contains the free energies only plotdos out contains the dos col 1 energy normalized so that Ef 0 col 2 DOS gt For including electronic entropy in phase diagram calculations You are likely to use this code as follow first create the Trange in file for up to 2000K in intervals of 100K echo 2000 21 gt Trange in This executes the svsl code in each subdirectory containing dos out but no error file foreachfile e dos out pwd felec options if desired constructs a cluster expansion of the electronic free energy eci are in felec eci clusterexpand felec 44 CHAPTER 7 COMMAND REFERENCE add the energetic eci from eci out to the electronic eci from felec eci and create the teci out file that will be read by the Monte Carlo code mkteci felec eci you can even combine vibrational and electronic eci mkteci fvib eci felec eci 7 1 5 fempmag I Ohnuma et al Phase equilibria in the Fe Co binary system Acta Materialia 50 2002 379 7 1 6 fitfc Calculates vibrational properties by fitting a spring model to reaction forces resulting from imposed atomic displacements The examples below are given assuming that one uses the vasp code although other ab initio codes would work as well The calculations pr
92. o ONE CO a T A 0 Seavey Lees eee ARENS P PEENE 22 Seles dele ae e o p o m g 0 01 092 a bo 0 02 1 1 1 i i L L L 1 J 1 1 0 04 1 roe 1 1 a 1 pair 5 10 15 trip 5 10 I5quad 5 10 15 0 10 20 30 40 50 60 chemical potential the equilibrium state of the system is a single phase equilibrium free of interfaces It also simplifies the process of calculating free energies through thermodynamic integration While a detailed description of the algorithm underlying this code can be found in 2I the current section focuses on the practical usage of the code 3If the simulation cell is commensurate with the unit cell of the phase under study a requirement that the code automatically ensures 5 4 MONTE CARLO SIMULATIONS 25 5 4 1 General input parameters The Monte Carlo code needs the following files as an input 1 A lattice geometry file lat in which is the same as the input for maps see Table 1 2 Files providing the cluster expansion the clusters used are listed in the clusters out file while the corresponding ECI are listed in the eci out file These files are automatically generated by maps although users can supply their own cluster expansion if desired A description of the format of these files is available by typing maps h 3 A list of ground states gs_str out which merely provide convenient starting configurations for the simulations maps also automatically creates this file The parameters controlli
93. o plot the output of the code Type gnuplot and check the program starts Type q to quit If not it can be downloaded from http www gnuplot info e You may need ssh if you have multiple machines and they are connnected through an unsecure network e g the internet This package can be downloaded from http www openssh com 3 0 2 Installation If you have an earlier version of ATAT installed please delete or rename the former atat directory before proceeding e g mv atat atatold Then type gunzip atatX_XX tar gz tar xvf atatX_XX tar gz where X_XX is the current version number These commands create a directory called atat in the current directory It contains the whole package For future reference Pll call the whole access path to this directory atat Type cd atat and open the file makefile with a text editor and look for the line BINDIR HOME bin Change HOME bin to point wherever you want to put the executables Type make If no error message appears proceed with the next steps otherwise consult Chapter 8 make install rehash not necessary with bash shell http cms mpi univie ac at vasp 10 CHAPTER 3 GETTING STARTED 3 0 3 Test MAPS with a simple example Change to a directory of your choice preferably empty and type cp atat examples cuau in lat in maps d amp Maps is running and waiting for a signal Type touch ready to indicate that you are ready to for maps to generate a structure
94. oceed as follows 1 You first need to fully relax the structure of interest The code expects the relaxed geometry in the file str_relax out It also expects a str out file containing the unrelaxed geometry which may be the same as the relaxed geometry if you wish The unrelaxed geometry will be used to determine the neighbor shells and measure distances between atoms Typically the user would specify the str out file then obtain the str_relax out file by runing an ab initio code with a command of the form runstruct_vasp making sure the vasp wrap file indicates that all degrees of freedom must be relaxed 2 Generation of the pertubations 2a A typical command line is as follows fitfc er 11 5 ns 3 ms 0 02 dr 0 1 er specifies how far apart the periodic images of the displaced atom must be The code then finds the size of the supercell satisfying this constraint Distances are measured according to the atomic positions given in str out and in the same units ns specifies the number of different strain at which phonon calculations will be performed ns 1 implies a purely harmonic model the default while values greater than 1 will invoke a quasiharmonic model ms specifies the maximum strain 0 02 signifies a 2 elongation along every direction dr the magnitude of the displacement of the perturbed atom The above command writes out a series of subdirectories vol_ one for each level of strain If the structure has cu
95. ogies that enable the calculation of thermodynamic properties from first principles we will focus on the following two step approach see Figure 5 1 First a compact representation of the energetics of an alloy known as the cluster expansion 18 6 5 27 is constructed using first principles calculations of the formation energies of various atomic arrangements Second the cluster expansion is used as a Hamiltonian for Monte Carlo simulations 16 2 8 5 that can provide the thermodynamic properties of interest such as the free energy of a phase or short range order parameters as a function of temperature and concentration This two step approach is essential because the calculation of thermodynamic quantities through Monte Carlo involves averaging the property of interest over many different atomic configurations and it would be infeasible to calculate the energy of each of these configurations from first principles The cluster expansion enables the prediction of the energy of any configuration from the knowledge of the energies of a small number of configurations typically between 30 and 50 thus making the procedure amenable to the use of first principles methods Formally the cluster expansion is defined by first assigning occupation variables g to each site 7 of the parent lattice which is defined as the set of all the atomic sites that can be occupied by one of a few possible atomic species In the common case of a binary alloy syst
96. ommand not found Command not found 7 2 18 maps src maps Command not found 7 2 19 mesqs Monte Carlo generator of Special Quasirandom Structures 3 16 by Axel van de Walle n int nb of atom unit cell Default 0 If n is not specified generate clusters of the following sizes 2 real 3 real 4 real 5 real 6 real 1 string cf string tcf string tol real wr real wn real wd real T real pf string rc ip int best crf string sd int rt int 2d sig int h Maximum distance between two points within a pair Default 0 Maximum distance between two points within a triplet Default 0 Maximum distance between two points within a quadruplet Default 0 Maximum distance between two points within a quintuplet Default 0 Maximum distance between two points within a sextuplet Default 0 Input file defining the random structure default rndstr in Input file defining the clusters default clusters out Input file defining the target multibody correlations default internally calculated va Tolerance for matching correlations default 1e 3 Weight assigned to range of perfect correlation match in objective function default 1 Multiplicative decrease in weight per additional point in cluster default 1 Exponent of decay in weight as function of cluster diameter default 0 Temperature default 1 Input file defining the optimization parameters de
97. on in the glue subdirectory Unless otherwise specified all files mentioned reside in the directory where maps was started All paths are relative to the startup directory The script should first wait for computer time to be available before creating a file called ready Upon detecting that the ready file has been created maps responds by creating a subdirectory n where n is a number and a file n str out containing a description of a structure whose energy needs to be calculated maps creates a file called n wait to distinguish this directory from other ones created earlier maps deletes the ready file 68 CHAPTER 7 COMMAND REFERENCE Upon detecting that the ready file has disappeared the script should now look for the n wait file start the calculations in the directory n and delete file n wait If anything goes wrong in the calculations the script should create a file n error When the calculations terminate successfully the energy per unit cell of the structure should be copied to the file n energy NOTE use energy per unit cell of the structure NOT per unit cell of the lattice maps continuously scans all the subdirectories n for n energy or n error files and updates the cluster expansion accordingly maps updates the cluster expansion whenever a file called refresh is created maps then deletes it maps terminates when
98. ons 3x3 matrix point operation 1x3 matrix translation repeat etc Note that if you enter more than one unit cell of the lattice sym out will contain some pure translations as symmetry elements Cluster file format clusters out for each cluster multiplicity length of the longest pair within the cluster number of points in cluster coordinates of 1st point number of possible species 2 cluster function coordinates of 2nd point number of possible species 2 cluster function etc repeat etc Multiplicity and length are ignored when reading in the clusters out file For each point the following convention apply The coordinates are expressed in the coordinate system given in the first line or the first 3 lines of the lat in file The number of possible species distinguishes between binaries ternaries etc Since each site can accomodate any number of atom types this is specified for each point of the cluster In multicomponent system the cluster function are numbered from 0 to number of possible species 2 In the simple of a binary system number of possible species 2 cluster function are just 0 0 For a ternary the possible values are 1 O and 1 1 All the utilities that are not yet multicomponent ready just ignore the entries number of possible spe Convention used to calculate the correlations The cluster functions in a m component system are defined as function 0 cos
99. pecified by rc vc cc sc can be set to empty to skip the corresponding calculation step useful to restart an aborted run This command does the following 1 2 3 4 5 6 Fully relax the structure in str_hint out or str out to create str_relax out just like runstruct_vasp If the relaxation cutoff c no exceeded stop Typically should be set to c 0 05 Relax the volume only of structure in str_sup out or str out Results are in directory 00 Do a neb calculation between the two structures obtained in step 1 and 3 if neb is specified or just a linear interpolation between them Results are in directories Note that you need VIST Tools from http theory cm utexas edu vtsttools for the neb method with variable cell shape Do static calculations in each directory Find the inflection point on the path optimized in step 4 If it does not exist find the minimum energy along that path 7 Report the energy found in 6 in the file energy and the corresponding geometry in str_relax out Notes 1 str_beg out and str_end out contain the extremities of the path 2 If you want to restart from scratch delete these files For high symmetry phases e g bcc fcc hcp you may need to break the symmetry of the phase for it t For that purpose you can use e g symbrklib fcc bcc W or cellcvrt ja 0 01 jc 0 01 lt str out gt str_hint out Sometimes a supercell is needed a phonon analysis will tell you tha
100. pplied to the unit cell of str cell to get the unit cell of str_relax out neglecting i isotropic scaling and ii rigid rotation The numbers reported are the sqrt of the sum of each element of the strain tensor squared 7 2 37 calcbulk Calculates bulk modulus Syntax calcbulk mins maxs ds runcommand where mins and maxs are the minimum and maximum strains e g 0 00 0 01 ds is the step size e g 0 005 runcommand is the command to run the ab initio code e g runstruct_vasp 7 2 38 mecdroplast This script reads the output file of a mc run and deletes the last data point of each inner loop The point after a phase transition occured Same effect as the dl option of emc2 7 2 39 str2cif Converts an ATAT structure file from stdin to the CIF format stdout 7 2 40 wycked WYCKoff position EDitor by Axel van de Walle Syntax wycked spcgrp list_of_wyckoff_position_letter_without_seperators The output is meant to first be edited to set the free parameters a b c alpha beta gamma x y z etc in each of the lines starting with const and processed by sspp to create a valid ATAT structure file ACKNOWLEDGEMENTS This code makes use of a Wyckoff position database downloaded from the Bilbao Crystallographic Server at http www cryst ehu es Accordingly if you use this code you should cite in addition to the usual ATAT citations the following papers M I Aroyo J M Perez Mato D Orobengoa E Tasci G de la Flor
101. r in Line minimization Default 2 eil int Epicycle maximum number of Iterations in Line minimizations Default 40 eic int Epicycle maximum number of Iterations in Conjugate gradient Default 40 ebf int Epicycle motion Bad step Forgiveness Default 1 el real Epicycle Length Default 0 01 ism real Ion motion Steepest descent Multiplier Default 0 01 isi int Ion motion Steepest maximum number of Iterations Default 0 igt real Ion motion Gradient Tolerance Default 1 its real Ion motion Trial Step Default 0 003 ims real Ion motion Maximum Step Default 0 01 iml real1 Ion motion Multiplier in Line minimization Default 2 iil int Ion motion maximum number of Iterations in Line minimizations Default 40 iic int Ion motion maximum number of Iterations in Conjugate gradient Default 40 ibf int Ion motion Bad step Forgiveness Default 1 7 2 COMMAND LINE OPTIONS TI ics real ff real st int r db aex t1 real t2 real d Ion motion Curvature constraint Stiffness O automatic Default 0 Force scale Factor Default 4 Sleep Time between read access Default 5 Relax to minimum for debugging only Default Off debug Default Off Analytical Example for debugging Default Off Temp param 1 Default 1 9 Temp param 2 Default 2 Use all default values Default Off 7 2 16 kmesh src kmesh 7 2 17 I sfit src 1sfit C
102. rating those structures and requesting that their energy be calculated Once again the user should just wait for the problem to fix itself The predicted ground states are flagged by a g in the predstr out file so that you can display their energy by typing grep g predstr out No other ground states of n atoms unit cell or less exist The energies of all ground states predicted by the cluster expansion have been confirmed by first principles calculations Because it can be computationally intensive to perform a full ground state search when interactions extend beyond the nearest neighbor shell 6 maps uses a search algorithm that merely enumerates every possible structures having n atoms or less per unit cell and uses the cluster expansion to predict their energies The upper limit n increases automatically as calculations progress The log out file also contains two other pieces of information Concentration range used for ground state checking a b This displays the user selected range of concentration over which ground state checking is performed which can be specified as a command line option of the maps command c0 a c1 b It may be useful to relax the constraints that ground states be correctly reproduced over the whole concentration range when it is known that other parent lattices are stable in some concentration range In this fashion the code can focus on providing a higher accuracy in the concentration range where the user needs
103. re is 91 92 CHAPTER 8 TROUBLESHOOTING an error in the options you specified Q When I superimpose the energies of fit out with the energies obtained from the Monte Carlo code I can see that they don t match What is happening A The energies given by the Monte Carlo code are in fact E ux so you need to add ux to get the true energy Use the g2c option to tell the Monte Carlo code to output the true energy Q How can I verify that the structures do not relax to a superstructure of a different type of lattice e g fcc becoming bec A Run the utility called checkrelax It will give you a list all structures along with a measure of the strain they each experienced during relaxation Q When I look at the calculated and fitted energies in the fit out file there are structures where the difference is very large A Make sure that these structures have properly relaxed A common problem is to start the first principles calculations with an unrelaxed geometry where the atoms are too close to one another Restart the energy calculations of the offending structures by using larger starting volumes Q My input files seem correct but ATAT utilities crash while reading them A Make sure your files have unix style end of lines The fixeol u yourinputfile command should fix that issue 8 3 Common mistakes e Write the energy per atom or per unit cell of the lattice in the energy files One should write the energy per unit ce
104. re than half the distance specified with the er option ealier Distances are measured according to the atomic positions given in str out and in the same units It is a good idea to try different values of fr starting with the nearest neighbor bond length and check that the vibrational properties converge as fr is increased Sometimes you will get the message Unstable modes found Aborting This indicates that the structure considered may be mechanically unstable If in addition you see the warning Warning p is an unstable mode then the structure is certainly unstable Otherwise it may be a artifact of the fitting procedure To find out you can tell the code to generate perturbations along the unstable directions and let your ab initio code calculate the reaction forces which can then be included in the fit to settle this issue First to view the unstable modes use the fu option the output is in vol_ unstable out and has the form u index nb_atom kpoint branch frequency displacements where index is a reference number nb_atom is the size of the supercell needed to represent this mode the other entries are self explanatory If this file contains only entries with nb_atom too_large you need to increase the mau option beyond its default of 64 You can pick one of these modes to written out to disk with the option gu index where index is the one reported in the unstable out file Using a neg
105. rectory where maps was started All paths are relative to the startup directory The script should first wait for computer time to be available before creating a file called ready Upon detecting that the ready file has been created maps responds by creating a subdirectory n where n is a number and a file n str out containing a description of a structure whose energy needs to be calculated maps creates a file called n wait to distinguish this directory from other ones created earlier maps deletes the ready file Upon detecting that the ready file has disappeared the script should now look for the n wait file start the calculations in the directory n and delete file n wait If anything goes wrong in the calculations the script should create a file n error 7 1 MAN PAGES 57 When the calculations terminate successfully the energy per unit cell of the structure should be copied to the file n energy NOTE use energy per unit cell of the structure NOT per unit cell of the lattice maps continuously scans all the subdirectories n for n energy or n error files and updates the cluster expansion accordingly maps updates the cluster expansion whenever a file called refresh is created maps then deletes it maps terminates when a stop file is created Note that the script can ask maps to create new structure directories even
106. reference energies must be in the same order as in the atoms out file If this file is omitted the energies of the structures with the most extreme compositions are used to determine the reference energies which are then output to the ref_energy out file Optional input file nbclusters in Allows the user to manually select which clusters to include in the fit This file should contains number of pairs to include number of triplets to include etc This file can be changed while maps is running However you must type touch refresh to tell maps to reread it Optional input file crange in or as specified by the cr option If present this file selects the range of concentration over which the cluster expansion is to be fitted This controls both where the correct ground states are inforced in the fitting process and the range of concentration of the generated structures Occasionally a structure outside that range is generated to verify the ground state hull Here is an example of such file 1 0 Al 1 0 Li 0 1 Co gt 0 5 Multiple constraints can be listed on separate lines Make sure to include a numerical prefactor for each species even if it is 1 0 Do not put a space between and a number Note that the crange in file is read if present even if the cr option is not specified Optional input file weights in Forces specific weights to assign to each structure when fitting its energy These weights may be
107. s g Favor cluster choices where the ground state line is correct It is suggested to turn this feature on if you have trouble getting the right ground states w Weight structures by w struct_energy gs_energy w recommended value start with 1 and decrease down to about 0 010 eV if you have trouble getting the correct ground states Default all structure have equal weight p Penality for structures that lie below the ground state line recommended value start with 1 and increase up to about 20 if you have trouble getting the correct ground states Default 0 gt corr in table of correlations one structure per line exactly the output of corrdump gt energy in column of energy values one per line in the same order as in the corr in file If energy is unknown put x 7 1 MAN PAGES 39 gt include in This file can be omitted It gives a list of clusters than must be part of the cluster expansion Each number in this file indicates a column in the corr in file gt weight in This file can be omitted It indicates the weight that must be given to each structure Usually this file is copied from the weight_sug out file obtained from a previous run Each weight in this file is multiplied by gs_prec structure_energy ground_state_energyt tgs_prec see above gt clusters out A list of the clusters in the same format as generated by either maps or corrdump OUTPUT FILES gt fi
108. s of the 2 pure elements while nl provides the number of different values of strain along the directions specified The range of strains spanned is given by the ml option that value 0 strain being the strain that keeps volume constant The ns option controls the numerical energy minimization it is the number of mesh points used in the search for a minimum and has no effect of the number of generated structures All default values are very reasonable You may want to increase ml and nl for systems with a large size mismatch The files generated are compatible with the pollmach automatic job control utility If you use vasp you would typically type csfit d amp pollmach runstruct_vasp w csvasp wrap amp where the csvasp wrap contains the parameters needed for a vasp run that does not relax the structure geometry see atat examples directory WARNING you are free to rerun csfit many times adding new lines in dir in but you CANNOT rerun it with different ml np nl settings without first deleting the subdirectories generated The csfit programs waits until all calculations are done and then fits the expansion and writes the results to the cs in file The cs log contains the constituent strain as a function of concentration rows for long period superlattices along the specified directions columns You can use the resulting expansion in maps by using the p cs option 72 CHAPTER 7 COMMAND REFERENCE and in
109. s executes the svsl code in each subdirectory containing str_relax out but no error file foreachfile e str_relax out pwd svsl options if desired constructs a cluster expansion of the vibrational free energy eci are in fvib eci clusterexpand fvib add the energetic eci from eci out to the vibrational eci from fvib eci and create the teci out file that will be read by the Monte Carlo code mkteci fvib eci 7 2 Command line options 7 2 1 cellevrt src cellcvrt Command not found 7 2 2 checkcell src checkcell Command not found 7 2 3 corrdump src corrdump Command not found 7 2 4 csfit src csfit Command not found 7 2 5 CV src cv Command not found 76 CHAPTER 7 COMMAND REFERENCE 7 2 6 emc2 src emc2 Command not found 7 2 7 felec src felec Command not found 7 2 8 fitfc src fitfc Command not found 7 2 9 fitsvsl src fitsvsl Command not found 7 2 10 fixcell src fixcell Command not found 7 2 11 gce src gce Command not found 7 2 12 gencs src gencs Command not found 7 2 13 gensqs src gensqs Command not found 7 2 14 genstr src genstr Command not found 7 2 15 infdet INFlection DETection method 3 16 by Axel van de Walle egt real Epicycle Gradient Tolerance Default 1 ets real Epicycle Trial Step Default 0 1 ems real Epicycle Maximum Step Default 0 785398 eml real Epicycle Multiplie
110. sed by mcsqs clus indicates to generate clusters only 2 3 indicate the range of pairs triplets etc getclus just indicates to write out the clusters nb of points length multiplicity See corrdump h for more info gt Output files bestsqs out The best SQS found so far in stardard ATAT structure file format see mmaps h for a description bestcorr out For each of the clusters selected its number of pointd 1st column its diameter 2nd column the correlations of the best SQS found so far 3rd column along with the target disordered state correlation 4th column and the difference between the two 5th column rndstrgrp out A file containing the same info as the input file defining the random state rndstr in but with symmetrically equivalent sites grouped together and separated by blank lines This helps determine which sites can have the same occupations 7 1 MAN PAGES 59 mcsqs log A log file The code stops if a perfect match is found all correlations requested match the disordered state but this may never happen if there are too many clusters in clusters out or n the number of atoms is In any case the bestsqs out and bestcorr out always contain the best solution found so far Stopping the code prematurely if the solution is satisfactory is fine gt Optional files Creating a file called stopsqs stops the code cleanly Creating a file called sqsparam in or as specified by the pf option wi
111. str out and tries to map them onto superstructures of the lattice provided This lets you import structures from another source into MAPS A word of caution the imported structures must be unrelaxed and no effort is made to rotate or scale them in order to match the lattice aside from space group symmetry operations 7 1 14 phb This is Monte Carlo code which automatically follows a given phase boundary Input files see maps documentation lat in describes the lattice gs_str out lists the ground states eci out ECI clusters out clusters You have to provide on the command line the following parameters The two phases which are in equilibrium For instance gs1 0 gs2 1 If there are n ground states phases are numbered from 0 to n 1 These ground states are read in from gs_str out The disordered state is labelled by the number 1 If the two phases are on different lattices you need to specify the path that give access to the files lat in gs_str out eci out clusters out for each lattice For instance di fcc d2 hcp If either or both options are omitted the files are read from the current directory The starting temperature and chemical potential for instance T 100 mu 0 125 Make sure to set blotzmann s constant appropriately If you tracing the phase boundary between two ordered phases starting from OK you do not need to specify a starting T and mu 70 CHAPTER 7 COMMAND REFER
112. t or symbrklib for bcc fcc hcp 90 CHAPTER 7 COMMAND REFERENCE Chapter 8 Troubleshooting 8 1 Forum Please see the new ATAT forum at http alum mit edu www avdw forum for answers to common and uncommon questions 8 2 FAQ Q I can do a least squares by hand with a much lower mean square error MSE than MAPS can Yet you claim that MAPS is optimal How is this possible A The MSE is not a very good measure of the predictive power of a cluster expansion It can be made arbitrarily close to zero but merely including enough ECI in the fit But having a small MSE is no guarantee that the error on the predicted energy of structures not inlcuded in the fit is small The cross validation CV score which is used in MAPS is a better measure of the predictive power of a least squares fit The CV score does not systematically decrease as the number of ECI increases and it has been shown that choosing the number of ECI such that the CV score is minimized is an asymptotically optimal strategy Researchers often have a tendency to use too many ECI because this appears to reduce the error but this is a illusion MAPS gives you an unbiased estimaqte of the prediction error and the magnitude of that number is larger than many would like to believe Q MAPS is frozen What is going on A MAPS sometimes needs a few minutes to generates new clusters or structures This is a complex operation be patient This generation can occur in t
113. t of the perturbed atom which is 0 2 Angstrom by default ms specifies the maximum linear expansion of the structures for the purpose of lengthing the bond lenght For instance ms 0 01 the default indicates that the supercells will be stretched by up to 1 isotropically ns indicates the number of intermediate lattice parameters sampled by default 2 which is the minimum in order to be able to determine the length dependence of bond stiffness After the structure generation step Each of the directory specified in strname in will contain multiple subdirectories each of which contains a the ideal unrelaxed supercell in a str_ideal out file b the relaxed but unperturbed supercell in a str_unpert out file c the actual geometry of perturbed supercell calculation in a str out file The appropriate first principles calculations can be performed using the other utilities in the atat package such as runstruct_vasp Of course a corresponding vasp wrap file must given in order to provide the input parameters for the first principles calculations Make sure that these parameters indicate a static run no relaxations After all or some of these calculations are done each subdirectory will contain a force out file containing the forces acting on each atoms a str_relax out file containing the atomic positions in the same order as in force out The fitting mode f option of ftsvsl then needs to be used The lattice file e g lat in must b
114. t out Contains the results of the fit one structure per line and each line has the following information concentration energy fitted_energy weight index gt concentration lies between O and 1 energy is the true formation energy gt fitted_energy is the predicted formation energy gt weight is the weight of this structure in the fit index is the structure number not counting structure of unknown energies gt predstr out Contains the predicted energy of all structures whose true energy is unknown Format one structure per line and each line has the following information concentration predicted_energy 1 status the 1 is for compatibility with maps status is u for compatibility with maps and a g is appended to status if that structure is predicted to be a ground state To list all predicted ground states type grep g predstr out gt gs out The ground states as determined by energies given in energy in Each line is a concentration energy pair gt gs_fitted out The ground states as determined by energies predicted from the cluster expansion Structures for which the true energy is unknown are omitted Each line is a concentration energy pair 40 CHAPTER 7 COMMAND REFERENCE gt weight_sug out If the ground states are incorrectly predicted by the cluster expansion this file contains suggested weight that should correct the problem just type cp weight_sug ou
115. t weight in and rerun the program gt weight_used out Weights actually used to do the fit gt fit gnu A gnuplot script that display all the relevant information Just type gnuplot fit gnu gt eci out The values of the fitted eci in the same order as in the corr in file 7 1 3 emc2 Easy Monte Carlo Code emc2 by Axel van de Walle Command line parameters TO initial temperature T1 final temperature dT temperature step db inverse temperature step Temperatures are given in units of energy unless the k option is set dT and db are mutually exclusive Which option you use determines whether T or 1 T are unformly spaced The output file always shows T Avoid setting TO or T1 to 0 The output will be nonsensical k Sets boltman z constant default k 1 This only affects how temperatures are converted in energies k 8 617e 5 lets you enter temperatures in kelvins when energies are in eV You can also select this value by using the keV option mu0 initial chemical potential mu final chemical potential By default these are input as dimensionless values defined as follows If x is integer x is the chemical potential that stabilizes a two phase equilibrium between ground state x 1 and x Ground states are numbered starting at 0 Fractional values interpolate linearly between these integer values Negative values or values larger than the number of ground states 1 are allowed
116. tained an SQS and would like to see how good bad the correlations you have NOT included in the objective function are you can use a command of the form corrdump l rndstr in ro noe 2 3 s bestsqs out and compare to the output for a perfectly random solid solution of corrdump l rndstr in ro noe 2 3 s bestsqs out rnd Beware that the above commands overwrite the clusters out file Make sure to NOT include the nop option which is incompatible with the rnd option The getclus command is useful to get a summary of what the clusters are number of points diameter mu 7 1 12 memc2 MultiComponent Easy Monte Carlo Code emc2 by Axel van de Walle Command line parameters er enclosed radius The Monte Carlo cell will the smallest possible supercell of unit cell of the initial configuration such that a sphere of that radius fits inside it This allows you to specify the system size in a structure independent fashion 7 1 MAN PAGES 61 cf Control file specifying the ranges of temperature and chemical potentials scanned default control in See file format below eq number of equilibration passes Equilibration is performed at the beginning of each step of the outer loop n number of Monte Carlo passes performed to evaluate thermodynamic quanties at each step of the inner loop tp instead of specifying eq and n you can ask the code to equilibrate and run for a time such that the averag
117. ted with a one spin Low Temperature Expansion 9 x_lte 10 phi_lte 11 E_mf mu x_mf calculated with the Mean Field approximation 12 x_mf 13 phi_mf 14 E_hte mu x_hte calculated with a High Temperature Expansion ideal solution polynomial in x 15 x_hte 16 phi_hte 17 lro Long Range Order parameter of the initial ordered phase 0 if initial phase is disordered 18 corr the average correlations associated with each cluster NOTE to obtain canonical rather than grand canonical quantities use the g2c option This has the effect of adding mu x to columns 3 5 8 10 11 13 14 16 7 1 4 felec This code calculates the electronic free energy within the one electron and temperature independent bands approximations It needs an dos out input file whose name can be changed with dos option that has the following format number of electron in unitcell energy width of each bins used to calculate the dos a multiplicative scale factor to adjust units the density in each bin in states unit cell energy lt repeated The code calculates the electronic free energy from temperature TO to T1 in steps of dT a The defaults are TO 0 T1 2000 dT 100 b If a file Trange in exists in the upper directory it is used to set TO T1 dT Trange in must contain two numbers on one line separated by a space T1 T1 dT 1 Note that TO 0 always For phase diagram calculations you must use this method to specify the temperature ra
118. th 4 numbers in it allows you to set the wr wn wd and T options during runtime for backward compatibility if 2 numbers are specified they set the wr and T options while the remaining options are set to their defaults The rc option lets you specify supercells to use via a sqscell out file Useful if brute force enumeration takes too long The sqscell out usually comes from a previous mcsqs run but you can create it yourself Note that the sqscell out file must start with the number supercells you will provide and that supercells must be expressed in multiple of the axes defined in the rndstr in file in particular all numbers entered should be integers If your are using a version prior to 3 07 these should be entered in cartesian coordinates gt Format of the input file defining the lattice specified by the l1 option First the coordinate system a b c is specified either as a b c alpha beta gamma or as ax ay az bx by bz cx cy cz Then the lattice vectors u v w are listed expressed in the coordinate system just defined ua ub uc va vb vc wa wb wc Finally atom positions and types are given expressed in the same coordinate system as the lattice vectors atomta atomtb atomic atomtype11 occupation11 atomtype12 occupation12 atom2a atom2b atom2c atomtype21 occupation21 atomtype22 occupation22 etc Examples The
119. th the command line option k kp A value of 8 617 x 1075 corresponds to energies in eV and temperatures in Kelvin With emc2 the range of chemical potentials to be scanned needs to be specified Once again only the starting point really matters because the code will stop when a phase transition is reached By default chemical potentials are given in a dimensionless form so as to facilitate the link between the value of the chemical potential and the phase that it stabilizes For instance a chemical potential equal to 3 0 is such that it would stabilize a two phase equilibrium between phase number 2 and phase number 3 at absolute zero see Figure 5 3b A chemical potential between 3 0 and 4 0 stabilizes phase number 3 at absolute zero While these ranges of stability are no longer exact at finite temperature this dimensionless chemical potential still provides easy to interpret input parameters The syntax is 4Temperature steps in reciprocal temperature are not needed because a two phase equilibrium never extents up to infinite temperature 5 4 MONTE CARLO SIMULATIONS 27 mu0 p9 mui 4 dmu Ap where Ay is the chemical potential step between each new simulation Chemical potentials can also be entered in absolute value say in eV if the energies are in eV by specifying the abs option Note that the output files always give the absolute chemical potentials so that thermodynamic quantities can be computed from them With phb t
120. the first principles calculations xxxx wrap where xxxx is the name of the first principles code used The clear separation between the thermodynamic and first principles calculations is a distinguishing feature of atat that enables the package to be easily interfaced with any first principles code Table B I gives two annotated examples of a lattice geometry input file The package includes ready made lattice files for the common lattice types e g bec fcc hep It also includes an utility that automatically constructs multiple lattice geometry input files for common lattices For instance makelat Al Ti fcc bcc hcp creates 3 subdirectories containing the appropriate input files for each specified lattice The first principles input file is usually less than 10 lines long thanks to the dramatic improvements in the user friendliness of most modern first principles codes For instance in the case of the widely used VASP code 3 2 a typical input file is given in Table 5 2 Examples of such input files are provided with the package Note that atat contains a utility that enables the automatic construction of k point meshes from a single parameter defining the desired target k point density the number of k point per reciprocal atom KPPRA 5 3 2 Running the code The maps code is started using the command 20 CHAPTER 5 USER GUIDE Table 5 1 Examples of lattice geometry input file lat in Typically the coordinate system entry is used
121. the options 26 CHAPTER 5 USER GUIDE Figure 5 3 Definitions of the quantities used to specify a the simulation cell size and b the chemical potential a Simulation Cell x Unit cell 0 0 2 0 4 0 6 0 8 1 Concentration TegFNeq N Navg The Monte Carlo code also needs additional parameters that specify which portion of a phase s free energy surface needs to be computed With emc2 the range of temperatures to be scanned are specified in either one of the following two ways T0 Tp T1 7 dT AT for steps in direct temperature or TO Ty T1 T db A 1 T for steps in reciprocal temperature The temperature steps in reciprocal temperature A 1 T can be useful when calculations are started from infinite temperatures down to a finite temperature The T1 and dT or db options can be omitted if calculations at a single temperature are desired Since the program automatically stops when a phase transition is detected it is not necessary to know in advance the temperature range of stability of the phase The user only needs to ensure that the initial temperature lies within the region of stability of the phase of interest An obvious starting point is T 0 since the ground state is then stable by definition With the phb code the syntax is T T dT AT If the T option is omitted calculations start at absolute zerol The energy and temperature units used are set by specifying the Boltzman s constant wi
122. this program do 1 It reads the lattice file specified by the l option 2 It determines the space group of this lattice and writes it to the sym out file 3 It finds all symmetrically distinct clusters that satisfy the conditions specified by the options 2 through 6 For instance if 2 2 1 3 1 1 is specified only pairs shorter than 2 1 units and triplets containing no pairs longer than 1 1 will be selected 4 It writes all clusters found to clusters out If the c option is specified clusters are read from clusters out instead 5 It reads the structure file specified by the s option 6 It determines for that structure the correlations associated with all the clusters chosen earlier This information is then output on one line in the same order as in the clusters out file See below for conventions used to calculate correlations 7 It writes the files corrdump log containting the list of all adjustements needed to map the possibly relaxed structure onto the ideal lattice gt File formats Lattice and structure files Both the lattice and the structure files have a similar structure First the coordinate system a b c is specified either as a b c alpha beta gamma or as ax ay az 35 36 CHAPTER 7 COMMAND REFERENCE bx by bz cx cy cz Then the lattice vectors u v w are listed expressed in the coordinate system just defined ua ub uc va vb vc wa wb
123. tice parameters from the OK value to the itms larger where ms is the number specified in the ms option The ns option gives the number of volumes considered Setting ns 1 selects the harmonic instead of the quasiharmonic approximation The code calculates the vibrational free energy from temperature TO to T1 in steps of dT a The defaults are TO 0 T1 2000 dT 100 b If a file Trange in exists in the upper directory it is used to set TO T1 dT Trange in must contain two numbers on one line separated by a space T1 T1 dT 1 Note that TO 0 always For phase diagram calculations you must use this method to specify the temperature range c These defaults can be overridden by the TO T1 and dT options The kpoint sampling is specified with the kp option The actual number of kpoints used is the number give divided by the number of atoms in the cell gt Phonon Dispersion curves The df inputfile option invokes the phonon dispersion curve module The syntax of the input file is nb of points kx1 ky1 kz1 kx2 ky2 kz2 repeat Each line of input defines one segment kx1 ky1 kz1 kx2 ky2 kz2 along which the dispersion curve is to be calculated nb of points specifies the number of points sampled along the segment The coordinates are in multiple of the reciprocal cell defined by the axes in the file specified by the us option or by default in the str out file The k point coordinates are appropriately str
124. tion This provides the ideal atomic positions that are used to automatically determine which atoms lie in the nearest neighbor shell This file can be the same as the relaxed structure but then the determination of the nn shell may be less reliable 3 A spring constant file the default is to lookup in slspring out and slspring out but this can be overridden with the sp option This file provides the bond stiffness vs bond length relationships that are used to determine the force constants of the springs joining neighboring atoms The format of this file is described in the documentation of the fitsvsl code which is 74 CHAPTER 7 COMMAND REFERENCE a utility that fits such spring constants A number of optional files can be given as well 4 An input file defining the atomic masses By default the code looks up in the atat rc file to determine the directory where atat is installed and then loads the file data masses in This behavior can be overridden with the m option 5 By default the bulk modulus is calculated from the force constants but it can also be read from a file whose name is specified with the bf option or specified on the command line with the b option The parameters that govern the accuracy of the calculations are as follows The default values are all reasonable The code uses the quasiharmonic approximation account for thermal expansion For this purpose it calculates the vibrational free for a range of lat
125. tions command_prefix where options are id Inflection Detection method idop options Options passed to the infdet command neb Use the Nudged Elastic Band method to find minimum energy path Otherwise simply interpolate linearly ex Only extract data form VASP files Do not run anything c real Relaxation magnitude cutoff needed to activate robust relax algorithm default 0 ni integer Number of images in the minimum energy path default 6 rc string Command for full relaxation Default runstruct_vasp w vasp wrap vc string Command for volume only relaxation Default runstruct_vasp w vaspvol wrap cc string Command for chain neb calculations Default runstruct_vasp w vaspneb wrap sc string Command for static runs Default runstruct_vasp w vaspstatic wrap ic string Command for inflection detection runs id option Default runstruct_vasp p w vas idf real Starting point fraction for inflection detection default 0 5 ja jc By how much to jitter atoms ja and cell parameters jt for the initial condition for inflection detection method vib Update vibrational data in svib_ht file from vol_0 svib_ht file 7 2 COMMAND LINE OPTIONS 89 mk Make auxiliary vasp input files vaspvol wrap vaspneb wrap vaspstatic wrap vaspf w Do not run anything d Use all defaults values command_prefix Prefix needed for vasp to run on a remote machine or in parallel e g mpirun Note the commands s
126. tions with the memc2 code eci out Lists the eci They have already been divided by multiplicity The corresponding clusters are in clusters out clusters out For each cluster the first line is the multiplicity the second line is the cluster diameter and the third line is the number of points in the cluster The remaining lines are the coordinates of the points in the cluster in the coordinate system specified in the input file defining the lattice A blank line separates each cluster n str out Same format as the lattice file except that The coordinate system is always written as 3x3 matrix Only one atom is listed for each site ref_energy out Reference energies used to calculate formation energies Usually energy of the pure end members OR values given in ref_energy in if provided The standard output reports the current progress of the calculations During the fit of the cluster expansion each line of numbers displayed has the following meaning 1 The current number of point pair triplet etc clusters 2 An indicator of whether the predicted ground states agree with the true ones 1 or not 0 3 The CV score per atom as of version 2 88 per cell earlier gt Communication protocol between maps and the script driving the energy method code e g ab initio code Only those who want to customize the code need to read this section The scripts described in this section are provided with the atat distributi
127. to define the conventional unit cell so that all other entries can be specified in the normalized coordinates that are the most natural for the symmetry of the lattice The input lattice parameters do not need to be exact as the first principles code will optimize them Example 1 hcp Ti Al system 3 1 3 1 5 062 90 90 120 Coordinate system a b ca 8 y notation 100 Primitive unit cell one vector per line 010 expressed in multiples of the above coordinate 001 system vectors 000 Al Ti Atoms in the lattice 0 6666666 0 3333333 0 5 Al Ti Example 2 rocksalt CaO MgO pseudobinary system 4 1 4 1 4 1 90 90 90 00 5 0 5 0 50 0 5 0 5 0 5 0 0 0 0 Ca Mg Active atoms in the lattice 0 5 0 5 0 5 0 spectator ion Table 5 2 Examples of first principles code input file example given for the vasp code It is especially important to verify that the KPPRA parameter is set sufficiently large for the system under study INCAR PREC high ENMAX 200 ISMEAR 1 SIGMA 0 1 NSW 41 IBRION 2 ISIF 3 See vasp manual for a description of the above 6 parameters KPPRA 1000 Sets the k point density K Point Per Reciprocal Atom DOSTATIC Performs a static run see vasp manual maps d amp where the option d indicates that all default values of the input parameters should be used which is what most users will ever need The optional parameters can be displayed by typing maps by itself and f
128. ture independent fashion innerT by default the inner loop is over values mu while the outer loop is over values of T This flag permutes that order eq number of equilibration passes Equilibration is performed at the beginning of each step of the outer loop n number of Monte Carlo passes performed to evaluate thermodynamic quanties at each step of the inner loop dx instead of specifying eq and n you can ask the code to equilibrate and run for a time such that the average concentration is accurate within the target precision specifified by dx tstat Critical value of the test for discontinuity The code is able to catch phase transformations most of the time when going from an ordered phase to another or to the disordered state This involves a statistical test which a user specified confidence level The default 3 corresponds to a 0 4 chance of finding a transition where there is none Refer to a standard normal table tstat 0 turns off this option Suggestion if a phase transition is undetected first try to reduce dT or dmu or increase n or decrease dx before toying around with this parameter Also beware of 42 CHAPTER 7 COMMAND REFERENCE hysteresis sigdig Number of significant digits printed Default is 6 0 Name of the output file default mc out Tricks To read parameters from a file use emc2 cat inputfile where inputfile contains the commands line options To selectively disp
129. updated by the code internally to better reproduce the ground state line Format one weight per line in the same order as in fit out This should only be used to fine tune the fit at the end when no new structures will be added since weights in would have to change every time a new structure us added gt Output files 66 CHAPTER 7 COMMAND REFERENCE maps log Contains possible warnings Not enough known energies to fit CE gt True ground states not fitted ground states New ground states predicted see predstr out These warning should disappear as more structural energies become available and the following messages should be displayed Among structures of known energy true and predicted ground states agree gt No other ground states of xx atoms unit cell or less exist This file also gives the crossvalidation score of the current fit before the weighting is turned on in order to get the correct ground states atoms out Lists all atomic species given in the input files fit out Contains the results of the fit one structure per line and each line has the following information concentration energy fitted_energy energy fitted_energy weight index gt concentration a vector of the atom fraction of all species in the same order as in atoms out gt energy is per site a site is a place where more than one atom type can sit gt weight is the weight of this structure in the fit gt index
130. ure Type cd 0 to go into the directory of the first structure Assuming that your first principles code is called xxxx type runstruct_xxxx amp After this command has successfully terminated display the energy of that structure and go back to the initial directory cat energy cd and edit the file defining the first principles code parameters emacs xxxx wrap amp so that the precision of the calculation is increased e g increase the k point density or the cut off of the plane wave energy Then you rerun the calculations to check by how much the calculated energy has changed cd 0 runstruct_xxxx amp cat energy After the calculations are completed cd This process is repeated until the user is satisfied with the precision of the calculation that is if the energy has become insensitive to changes in the input parameters within the desired accuracy A similar study should also be performed for the other pure structure labeled structure 1 and if one is really concerned with precision for a few structures with intermediate concentrations Once the appropriate ab initio code parameters have been determined the fully automated process can begin From within the directory where maps was started type pollmach runstruct_xxxx to start the job manager that will monitor the load on your local network of workstations and ask maps to generate new structures i e atomic arrangements whenever a processor becomes a
131. urther help is available via the command maps h The trailing amp character cause the command to execute in background mode In this fashion maps can continuously be on the lookout responding to various signals while the user performs other tasks The ongoing discussion assumes that the code is run under a UNIX environment within a shell such as sh csh tcsh or bash The process of constructing a cluster expansion from first principles calculations can be summarized as follows 1 Determine the parameters of the first principles code that provide the desired accuracy 2 Let maps refine the cluster expansion 3 Decide when the cluster expansion is sufficiently accurate 5 3 CLUSTER EXPANSION CONSTRUCTION USING THE MAPS CODE 21 Typically one calibrates the accuracy of the first principles calculations using the pure structures of the alloy system of interest To generate the two pure structures type touch ready This creates a file called ready which tells maps that you are ready to calculate the energy of a structure Within 10 seconds maps replies with Finding best structure done maps has just created a directory called 0 and within it a file called str out that contains the geometry of one of the two pure structures If you type touch ready once more the other pure structure is written to 1 str out You now need to launch the first principles code to calculate the energy of each struct
132. vailable Note that the first time the command is run instructions will appear on screen that explain how to configure the job dispatching system in accordance to your local computing environment Once this configuration is complete the above command should be invoked in the background by appending a amp to it lIn the case of pseudobinary alloys with spectator ions e g the MgO CaO system the pure structures would correspond to the structures where the sublattice of interest is entirely filled with a single type of atom 2A key number to keep in mind is that an error of 25meV corresponds to 300K on a temperature scale 22 CHAPTER 5 USER GUIDE 5 3 3 Output of MAPS While the calculations are running you can check on the status of the best cluster expansion obtained so far The file Log out contains a brief description of the status of the calculations such as the accuracy of the cluster expansion and various warning messages Most of the messages pertains to the accurate prediction of the so called ground states of the alloy system The ground states which are the structures that have the lowest energy for each given concentration are extremely important to predict accurately because they determine which phases will appear on the phase diagram The four possible messages are described below Not enough known energies to fit CE Before displaying any results maps waits until enough structural energies are known to fit a
133. y While MAPS automatically create files that describe the geometry of the structures calledn str out where n is the structure name we need to provide a file containing all the other parameters needed by the first principles code Type cp atat glue vasp vasp wrap to copy an example of such file in the current directory For a description of these parameters type ezvasp h more Let s say you have a new structure in directory 0 created by typing touch ready Type 3 2 INSTALL AND TEST THE JOB CONTROL UTILITIES 11 cd 0 runstruct_vasp When the command has terminated the directory 0 will contain a file energy giving the energy of the structure If error messages appear consult Chapter 8 If no error messages appear you can proceed another level up in automation Type cd to go back into the main directory pollmach runstruct_vasp amp This script will automatically call the above command repeatedly To stop it cleanly type touch stoppoll Disregard the warning message If you only have access to one machine this is as good as it gets if you have more than one machine read the next section If you want to use another code than VASP read section 3 3 3 2 Install and test the job control utilities This section requires some knowledge of UNIX but it is worth it 3 2 1 With queueing systems Let s start with the simple and common case of a computer cluster with a queueing system We don t give here th
134. y two parameters The size of the simulation cell and the duration of the simulation The size of the simulation cell is specified by providing the radius r of a sphere through the command line option er r As illustrated in Figure 53h the simulation cell size will be the smallest supercell that both contains that sphere and that is commensurate with the unit cell of the ground state of interest This way of specifying the simulation cell size ensures that the system size is comparable along every direction regardless of the crystal structure of the ground state of interest It also frees the user from manually checking the complicated requirement of commensurability It is important that the user check that the simulation cell size is sufficiently large for the thermodynamic properties of interest to be close to their infinite system size limiting value This can be done by gradually increasing the system size until the calculated quantities become insensitive to the further increases in system size within the desired accuracy The duration of the simulations is automatically determined by the code from a user specified target precision on the atomic composition of the phase indicated by a command line option of the form dx Avz Alternatively the user may also manually set the number neg of Monte Carlo steps the system is allowed to equilibrate before thermodynamic averages are computed over a certain number Nayg of Monte Carlo steps using

The Alloy-Theoretic Automated Toolkit (ATAT): A User Guide

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