ATAT - A software toolkit for modeling coupled configurational and ...

Automated Cluster Expansion Construction

Temperature scale problemhcp TiLikely source of the discrepancy:Vibrational entropy.Fultz, Nagel, Antony, et al. (1993-1999)Ceder, Garbulsky, van de Walle (1994-2002)de Fontaine, Althoff, Morgan (1997-2000)DO 19Ti 3AlZunger, Ozolins, Wolverton (1998-2001)Van de Walle, Asta and Ceder (2002),Murray (1987) (exp.)Many other examples…

The Cluster Expansion Formalismwith Coarse-GrainingE 1 ,, n F 1 , , n J T

Coarse-Graining of the Free EnergyGraphically:Formally: (Ceder (1993), Garbulski and Ceder (1994-1996))F 1 ln ie E i 1 ln ie E i 1 ln e FwhereF 1 ln ie E i k B T 1

First-principles lattice dynamicsFirst-principles dataComputationallyintensive!Least-squares fit toSpring modelMust be done formany configurations!Phonon density of statesThermodynamicPropertiesDirect force constant method(Wei and Chou (1992), Garbuski and Ceder (1994),among many others)

Transferable Force ConstantsChemical bond type andbond length:Good predictorof nearest-neighbor force constants(stretching and bending terms)Relationship holds acrossdifferent structures on thesame lattice (here fcc isshown).van de Walle and Ceder (2000,2002)

Au-Au bondsFurther tests...Wu, Ceder, van de Walle (2002)Cu-Cu bondsAu-Pd bondsPd-Pd bondsCu-Pd bondsAu-Cu bondsAccuracy ~ 0.03 k B

van de Walle and Ceder (2000,2002)Length-Dependent TransferableForce Constants (LDTFC)

Quasi-harmonic modelF(T,V) = E(V) + F H (T,V)Energy of a relaxed motionless latticewith externally imposed volume VVibrational free energy of a harmonic solidat temp. T with externally imposed volume VThermal expansion:V*(T) = arg min V F(T,V)“True” free energy:F(T) = F(T,V*(T))Ideal for use with length-dependent transferable force constants

Calculated Ti-Al Phase DiagramAssessed Phase Diagram:I. Ohnuma et al., ActaMater. 48, 3113 (2000)1 st -Principles Calculations:van de Walle and Asta

Ti-Al Thermodynamic Properties1 st -Principles Calculations vs.MeasurementsHeats of FormationGibbs Free Energies (T=960 K)0-5-10Calorimetry(Kubaschewski and Dench, 1955)0-5EMF Measurements(Samokhval et al., 1971)∆H (kJ/mole)-15-20-25-30-35-40FLMTO-LDAVASP-GGA∆G (kJ/mole)-10-15-20-25αMonte-CarloCalculationsα 2-450 0.1 0.2 0.3 0.4 0.5Al Concentration-300 0.1 0.2 0.3 0.4Al Concentration

Ordering in the Cu-Li system?Widely used assessmentsdo not include ordered phases(Pelton (1986), Saunders (1998)).Evidence from EMF measurementsOrdered Cu 4 Li phase also suggested byBorgsttedt & Gumiński (1996),Krauss, Mendelson, Gruen, et al. (1986),Old & Trawena (1981).

Calculated Thermodynamic datafor Cu-Li systemPhase diagramElectromotive Force (EMF)fcc1 st order transitionbcc2 nd order transitionB32T simulation = 950 KT measurement = 885 K2 adjustable parameters:T simulation+ chemical potential of Li (liq)

Thermodynamic dataLattice model &Monte Carlo SimulationsConfigurational disorderElectronicLattice vibrationsexcitationsElectronic excitationsQuantum Mechanical Calculations

Electronic ExcitationsFinite-temperature DFTT-independent DOS and charge densityAdvantage: Get F elec “for free”Electronic DOSFermi-Dirac DistributionElectronic Free energyF elec T E elec T E elec 0 TS elec TDensity of States876543210f ,T -4 -2 0Energy (eV)gE elec T f ,T gdS elec T k B f ,T ln f ,T 1 f ,T ln1 f ,T gdCluster expansion:F 1 , , n J T

Using ATAT• Overview of the input/output files• Syntax of the files• Sample output

File structureFiles:ABlat 0lat.invasp.wrap 5eci.outclusters.outgs.outmaps.logstrnames.inslsprings.outTrange.in. . .fvib.eciteci.outstr.outstr.out0.2_0_00.2_0_10.2_0.5_00.2_0.5_1Commands:energy str_relax.outenergy str_relax.outstr.out force.outstr.out force.outstr.out force.outstr.out force.outfvibfvibPerturbationsmaps -drun ab initio codefitsvsl -drun ab initio codefitsvsl -fforeachfile str.out svsl -dclusterexpand fvibmkteci fvib.eci

Example of input filesSimple lattice input fileSimple ab initio code input file

Clusters and ECI filesclusters.out eci.out fvib.eci10.0000000T maxteci.out2000 21# divisionmultiplicitydiameter# of pointssites(using coordinatesystem in lat.in)20.00000011.000000 1.000000 1.00000062.93999920.666667 0.333333 0.5000001.000000 0.000000 1.00000062.94000420.666667 0.333333 0.500000-0.333333 -0.666667 0.5000000.229683-0.3502750.0479380.041720etc.0.0826-0.0008-0.0006-0.0005...0.0793-0.0008-0.0006-0.0006...T=0KT=100Ketc.0.312346-0.3510770.04733490.0411423...0.308527-0.3509030.04725380.0410874...etc.

maps graphical output

Search for new compoundsin the Al-Mo-Ni systemMo (bcc)Ni (fcc)Al (fcc)EMoNiAlNi 3 Al (L1 2 )NiAl (B2)plotted with MEDIT, INRIA-Rocquencourt.

Predicted CompoundNiAl(fcc)(bcc)AlMo 2Ni 2Moplotted with MEDIT, INRIA-Rocquencourt.

Force constant (eV/Å 2 )1.61.41.210.80.60.40.20fitsvsl graphical outputAl-Als'f_Al-Al.dat' u 1:2b'f_Al-Al.dat' u 1:32.8 2.82 2.84 2.86 2.88 2.9length (Å)Force constant (eV/Å 2 )32.521.510.5021.510.50-0.5Ti-Ti2.8 2.85 2.9 2.95 3length (Å)Al-Tis'f_Al-Ti.dat' u 1:2b'f_Al-Ti.dat' u 1:32.84 2.86 2.88 2.9 2.92 2.94s'f_Ti-Ti.dat' u 1:2b'f_Ti-Ti.dat' u 1:3length (Å)

emc2 graphical outputT1400'mc1.out' u 4:1120010008006004002000.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8xOther outputs:1) T: Temperature2) mu: chemical potential3) E-mu*x: Average energy4) x: Average Concentration5) phi: grand canonical potential6) E2: heat capacity7) x2: susceptibility8) E_lte-mu*x_lte: from LTE9) x_lte10) phi_lte11) E_mf-mu*x_mf: from MF12) x_mf13) phi_mf14) E_hte-mu*x_hte: from HTE15) x_hte16) phi_hte17) lro: Long Range Order parameter18-) corr: correlations

Miscellanea (I)ATATUtilitesmaps : Cluster expansion buildermmaps : Multicomponent version of mapsemc2 : General purpose Monte Carlo codephb : Phase-transition-tracing Monte Carlo codecheckrelax : Excessive relaxation detectorcorrdump : Cluster generator/correlation calculatorclusterexpand : Manual cluster expansion generatorgenstr : Super structure generatorgensqs : Special Quasirandom Structure generatorpdef : Point defect supercells generatorcsfit : Constituent strain calculatorcellcvrt : General crystal structure file format conversion utilitylsfit : Least-squares fitting codefitfc : Phonon calculation with direct force methodfitsvsl : Length-Dependent Transferable Force Constants generatorsvsl : Phonon calculations using LDTFCfelec : Electronic free energy calculator

Miscellanea (II)runstruct_vasp : Interface with vasprunstruct_abinit : Interface with abinitrunstruct_pwscf : Interface with pwscfrunstruct_gulp : Interface with gulpab initioempirical potentialATATUtilitespollmach : A job dispatcher for computer clustersforeachfile : A “loop over directories” utilitystr2xyz : File conversion utility for viewing with rasmolmakelat : Database of crystal structuresgetvalue, (just)after, (just)before, (just)between sspp : Text extractorsmemc2 : Multicomponent version of emc2 (in development)Getting Help• Run command without any argument to get usage help• Use –h option to get detailed help• http://cms.northwestern.edu/atat/manual/manual.html

References• A. van de Walle and G. Ceder. The effect of lattice vibrations onsubstitutional alloy thermodynamics. Rev. Mod. Phys., 74:11, 2002.• A. van de Walle, M. Asta, and G. Ceder. The alloy theoreticautomated toolkit: A user guide. CALPHAD Journal, 26:539, 2002.• A. van de Walle and G. Ceder. Automating first-principles phasediagram calculations. Journal of Phase Equilibria, 23:348, 2002.• A. van de Walle and M. Asta. Self-driven lattice-model monte carlosimulations of alloy thermodynamic properties and phase diagrams.Modelling Simul. Mater. Sci. Eng., 10:521, 2002.• Web site: http://cms.northwestern.edu/atat• This afternoon’s tutorial: http://cms.northwestern.edu/atat/tutorial