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ATAT - A software toolkit for modeling coupled
configurational and vibrationaldisorder in alloy systems
This work was supported by:NSF under program DMR-0080766 and DMR-0076097.DOE under contract no. DE-F502-96ER 45571.AFOSR-MEANS under grant no. F49620-01-1-0529
Axel van de WalleMaterials Science and Engineering Department
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A matter of time...Ti
me
Human
Computer
1980 2005
Time needed to complete a given first-principles calculation
The procedure needs to be automated
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Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrations
First-principles Thermodynamic Calculations
http://cms.northwestern.edu/atat
Configurational disorder
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Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderConfigurational disorder
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Coupled SublatticesMulticomponent Cluster Expansion
Example: binary fcc sublattice withternary octahedral sites sublattice
Occupation variables:
1 2
1 1
“Decorated” clusters:
i 0, ,ni 1
1 , ,n
i 0, ,ni 1
E1 , ,n J
2, ,
i
1 11 1 i
3, ,
i
1 1 11 1
2 12
0 32 3
2
i
i ni, i, i
Same basic form:
“Not in cluster”
Sanchez, Ducastelle and Gratias (1984)Tepesch, Garbulski and Ceder (1995)
# components
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Automated Cluster Expansion Construction
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Van de Walle, Asta and Ceder (2002),Murray (1987) (exp.) Many other examples…
hcp Ti
DO19Ti3Al
Likely 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)
Zunger, Ozolins, Wolverton (1998-2001)
Temperature scale problem
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Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderLattice vibrations
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The Cluster Expansion Formalismwith Coarse-Graining
E1, ,n
F1, ,n JT
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Coarse-Graining of the Free EnergyGraphically:
Formally: (Ceder (1993), Garbulski and Ceder (1994-1996))
F 1 ln i eEi 1 ln i eEi
1 ln eF
F 1 ln i eEiwhere
kBT1
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First-principles lattice dynamics
Least-squares fit toSpring model
First-principles data
ThermodynamicProperties
Phonon density of states
Computationallyintensive!
Direct force constant method(Wei and Chou (1992), Garbuski and Ceder (1994), among many others)
Must be done formany configurations!
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Transferable Force Constants
van de Walle and Ceder (2000,2002)
Relationship holds across different structures on the same lattice (here fcc is shown).
Chemical bond type andbond length:Good predictorof nearest-neighbor force constants(stretching and bending terms)
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Further tests...Wu, Ceder, van de Walle (2002)
Au-Au bonds
Pd-Pd bonds
Cu-Cu bonds
Cu-Pd bonds
Au-Pd bonds
Au-Cu bonds
Accuracy ~ 0.03 kB
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Length-Dependent TransferableForce Constants (LDTFC)
van de Walle and Ceder (2000,2002)
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Quasi-harmonic model
F(T,V) = E(V) + FH(T,V)
V*(T) = arg minV F(T,V)
F(T) = F(T,V*(T))
Energy of a relaxed motionless latticewith externally imposed volume V
Vibrational free energy of a harmonic solidat temp. T with externally imposed volume V
Thermal expansion:
“True” free energy:
Ideal for use with length-dependent transferable force constants
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Calculated Ti-Al Phase Diagram
Assessed Phase Diagram:I. Ohnuma et al., ActaMater. 48, 3113 (2000)
1st-Principles Calculations:van de Walle and Asta
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Ti-Al Thermodynamic Properties1st-Principles Calculations vs.
Measurements
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
0 0.1 0.2 0.3 0.4 0.5Al Concentration
∆H
(kJ/
mol
e)
Calorimetry(Kubaschewski and Dench, 1955)
FLMTO-LDA
VASP-GGA
-30
-25
-20
-15
-10
-5
0
0 0.1 0.2 0.3 0.4
Al Concentration
∆G
(kJ/
mol
e)
α
α2
EMF Measurements(Samokhval et al., 1971)
Monte-CarloCalculations
Gibbs Free Energies (T=960 K)Heats of Formation
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Ordering in the Cu-Li system?
Ordered Cu4Li phase also suggested by
Borgsttedt & Gumiński (1996),
Krauss, Mendelson, Gruen, et al. (1986),
Old & Trawena (1981).
Widely used assessments
do not include ordered phases
(Pelton (1986), Saunders (1998)).
Evidence from EMF measurements
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Calculated Thermodynamic datafor Cu-Li system
Tsimulation = 950 KTmeasurement = 885 K
2 adjustable parameters:Tsimulation + chemical potential of Li (liq)
bcc
fcc
B32
1st order transition
2nd order transition
Phase diagram Electromotive Force (EMF)
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Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderElectronic excitations
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Electronic Excitations
F1, ,n JT
Electronic DOS
Finite-temperature DFT
Fermi-Dirac Distribution
012345678
-4 -2 0Energy (eV)
Den
sity
of S
tate
s
T-independent DOS and charge density
Electronic Free energy
Advantage: Get Felec “for free”
FelecT EelecT Eelec0 TSelecT
EelecT f,Tgd
SelecT kB f ,T ln f ,T 1 f ,T ln1 f,Tgd
g
f,T
Cluster expansion:
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Using ATAT
• Overview of the input/output files
• Syntax of the files
• Sample output
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Commands:
File structureABlat 0
5
. . .
str.out energy str_relax.out
str.out energy str_relax.out
0.2_0_0
0.2_0_1
0.2_0.5_0
0.2_0.5_1
str.out
str.out
str.out
str.out
force.out
force.out
force.out
force.out
lat.invasp.wrap
maps -drun ab initio codefitsvsl -d
fitsvsl -f
run ab initio code
slsprings.outstrnames.in
eci.outclusters.outgs.outmaps.log Perturbations
clusterexpand fvibforeachfile str.out svsl -d
fvib
fvib
Trange.infvib.eci
mkteci fvib.eci
teci.out
Files:
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Example of input filesSimple lattice input file
Simple ab initio code input file
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Clusters and ECI files
10.0000000
20.00000011.000000 1.000000 1.000000
62.93999920.666667 0.333333 0.5000001.000000 0.000000 1.000000
62.94000420.666667 0.333333 0.500000-0.333333 -0.666667 0.500000
etc.
0.229683-0.3502750.0479380.041720
etc.
multiplicitydiameter
# of pointssites
(using coordinatesystem in lat.in)
clusters.out eci.out fvib.eci
0.0826-0.0008-0.0006-0.0005...
0.0793-0.0008-0.0006-0.0006...
T=0K
T=100K
etc.
teci.out
2000 21
0.312346-0.3510770.04733490.0411423...
0.308527-0.3509030.04725380.0410874...
Tmax # division
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maps graphical output
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Search for new compoundsin the Al-Mo-Ni system
E
AlNi
Al (fcc)
Mo (bcc)
Ni (fcc)
NiAl (B2)Ni3Al (L12)
Mo
plotted with MEDIT, INRIA-Rocquencourt.
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Ni
Predicted Compound
Al
MoAlMo2Ni2
(fcc)
(bcc)
plotted with MEDIT, INRIA-Rocquencourt.
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fitsvsl graphical output
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
2.8 2.82 2.84 2.86 2.88 2.9
Al-Al
s'f_Al-Al.dat' u 1:2
b'f_Al-Al.dat' u 1:3
-0.5
0
0.5
1
1.5
2
2.84 2.86 2.88 2.9 2.92 2.94
Al-Ti
s'f_Al-Ti.dat' u 1:2
b'f_Al-Ti.dat' u 1:3
0
0.5
1
1.5
2
2.5
3
2.8 2.85 2.9 2.95 3
Ti-Ti
s'f_Ti-Ti.dat' u 1:2
b'f_Ti-Ti.dat' u 1:3
length (Å)
Forc
e co
nsta
nt (e
V/Å
2 )
Forc
e co
nsta
nt (e
V/Å
2 )
length (Å)
length (Å)
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emc2 graphical output
200
400
600
800
1000
1200
1400
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
'mc1.out' u 4:1
T
x
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
Other outputs:
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Miscellanea (I)maps : 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
ATATUtilites
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Miscellanea (II)runstruct_vasp : Interface with vasprunstruct_abinit : Interface with abinitrunstruct_pwscf : Interface with pwscfrunstruct_gulp : Interface with gulp
pollmach : A job dispatcher for computer clustersforeachfile : A “loop over directories” utilitystr2xyz : File conversion utility for viewing with rasmol
makelat : Database of crystal structures
getvalue, (just)after, (just)before, (just)between sspp : Text extractors
memc2 : Multicomponent version of emc2 (in development)
ATATUtilites
ab initio
empirical potential
• Run command without any argument to get usage help • Use –h option to get detailed help• http://cms.northwestern.edu/atat/manual/manual.html
Getting Help
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References
• A. van de Walle and G. Ceder. The effect of lattice vibrations on substitutional alloy thermodynamics. Rev. Mod. Phys., 74:11, 2002.
• A. van de Walle, M. Asta, and G. Ceder. The alloy theoretic automated toolkit: A user guide. CALPHAD Journal, 26:539, 2002.
• A. van de Walle and G. Ceder. Automating first-principles phase diagram 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