Post on 26-Jan-2020
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
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
Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrations
First-principles Thermodynamic Calculations
http://cms.northwestern.edu/atat
Configurational disorder
Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderConfigurational disorder
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
Automated Cluster Expansion Construction
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
Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderLattice vibrations
The Cluster Expansion Formalismwith Coarse-Graining
E1, ,n
F1, ,n JT
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
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!
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)
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
Length-Dependent TransferableForce Constants (LDTFC)
van de Walle and Ceder (2000,2002)
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
Calculated Ti-Al Phase Diagram
Assessed Phase Diagram:I. Ohnuma et al., ActaMater. 48, 3113 (2000)
1st-Principles Calculations:van de Walle and Asta
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
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
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)
Thermodynamic data
Quantum Mechanical Calculations
Lattice model &Monte Carlo Simulations
Electronic excitationsLattice vibrationsConfigurational disorderElectronic excitations
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:
Using ATAT
• Overview of the input/output files
• Syntax of the files
• Sample output
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:
Example of input filesSimple lattice input file
Simple ab initio code input file
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
maps graphical output
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.
Ni
Predicted Compound
Al
MoAlMo2Ni2
(fcc)
(bcc)
plotted with MEDIT, INRIA-Rocquencourt.
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)
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:
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
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
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