Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations...

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Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio modeling First-principles (or ab initio) calculations based on Density Functional Theory (DFT).

Transcript of Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations...

Page 1: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Experimental data

Analysis

Predictions

Simulations

Microscopic parameters

Quantum mechanical calculations

Validation

Traditional vs. ab initio modeling

First-principles (or ab initio) calculations based on

Density Functional Theory (DFT).

Page 2: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Microscopic parametersgoverning materials properties

Example: nucleation and growth of precipitate

Page 3: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Outline

• Example of ab initio calculations• Why ab initio Thermodynamics?• Methods• Applications

Page 4: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Self-Assembling Ge/Si(001) Quantum Dots

Goal: quantify thestrain-dependence of

the parameters governingGe adatom diffusion

Related works: Roland and Gilmer (1992), Spjut and Faux (1994), Schroeder and Wolf (1997),Ratsch et al. (1997), Zoethout et al. (2000), Shu et al. (2001), Penev et al. (2001).

Si (001) substrate

Ge wetting layerGe quantum dot

Ge

Strain field(Medeiros-Ribeiro, et al., 1998)

adatom

(top view)

Page 5: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Unwanted Coarsening

• Thermodynamic effect

• Kinetic effect (?)

Lower surface/volume(capillarity)

µ

DHigher adatom mobility

(Lower barrier foradatom attachement)e.g. Koduvely and Zangwill (1999)

Larger island:

Near Larger island:

Page 6: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Saddle pointBinding site

Ge Adatom Diffusion on Ge (001)

Ge (001) Surface c(4x2) Reconstruction

Schematic top viewisoelectronic density plot 3D schematic

Page 7: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

0 % strain = Si lattice param. 4 % strain = Ge lattice param.

Strain dependence

Diffusion-driven kinetic coarsening

Binding Site (Eb) Saddle point (Ea+Eb ) Activation barrier (Ea)

Page 8: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Magnitude of the effect

0.038Si2/Si(001)Zoethout et al. (2000)

0.007-0.028Ag/Ag(111)Ratsch et al. (1997)

-0.023Si/Si(001)Roland et al. (1992)

-0.0220.002Ge/Si(001)PresentGe/Ge(001)/Si

Si/Si(001)

In/GaAs(001)

Systemadatom/subst.

-0.1280.212Present

-0.050Shu et al. (2001)

-0.020-0.050Penev et al. (2001)

dEa/de(eV/%)

dEb/de(eV/%)

Reference

Page 9: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

The “Virtual” Laboratory

Advantages

• Absolute control over “experimental’’ conditions• Unlimited “characterization’’ capabilities• Ability to perform thought experiments • Automation of repetitive tasks• “Materials by design”

• Limited by computational resources• Cannot predict effects not included in simulation

Weaknesses

Page 10: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Outline

• Example of ab initio calculations• Why ab initio Thermodynamics?• Methods• Applications

Page 11: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

From a virtual to a real material...Useless material

Wonderful compound

We need a way to predict phase stability:

First-principles phase diagram calculations

Page 12: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Outline

• Example of ab initio calculations• Why ab initio Thermodynamics?• Methods• Applications

Page 13: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Thermodynamic data

Quantum Mechanical Calculations

Lattice model &Monte Carlo Simulations

Electronic excitationsLattice vibrations

•Large number of atoms•Many configurations

•Small number of atoms•Few configurations

First-principles Thermodynamic Calculations

http://cms.northwestern.edu/atat

Configurational disorder

Page 14: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Thermodynamic data

Quantum Mechanical Calculations

Lattice model &Monte Carlo Simulations

Electronic excitationsLattice vibrationsConfigurational disorder

Page 15: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

The Cluster Expansion Formalism

Sanchez, Ducastelle and Gratias (1984)

Page 16: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Coupled Sublattices MulticomponentCluster Expansion

Example: binary fcc sublattice withternary octahedral sites sublattice

Occupation variables: i 0, ,ni 1

E1 , ,n JSame basic form:

Sanchez, Ducastelle and Gratias (1984)Tepesch, Garbulski and Ceder (1995)

Page 17: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Cluster expansion fit

Which structures andwhich clustersto include in the fit?

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Cross-validation

Example of polynomial fit:

Page 19: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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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Automated Cluster Expansion Construction

Page 21: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Application to Ti-Al AlloysSimple lattice input file

Simple ab initio code input file

Page 22: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Ground States Search

Page 23: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Thermodynamic data

Quantum Mechanical Calculations

Lattice model &Monte Carlo Simulations

Electronic excitationsLattice vibrationsConfigurational disorder

Page 24: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Monte Carlo output:Free energies

Cao-MgO system Ti-Al system

Page 25: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Calculated phase diagram

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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

Page 27: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Thermodynamic data

Quantum Mechanical Calculations

Lattice model &Monte Carlo Simulations

Electronic excitationsLattice vibrationsConfigurational disorder

Page 28: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

The Cluster Expansion Formalism

E1, ,n

F1, ,n JT

Page 29: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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

Page 30: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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!

Page 31: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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)

Page 32: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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

Page 33: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Length-Dependent TransferableForce Constants (LDTFC)

van de Walle and Ceder (2000,2002)

Page 34: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Calculated Ti-Al Phase Diagram

Assessed Phase Diagram:I. Ohnuma et al., ActaMater. 48, 3113 (2000)

1st-Principles Calculations:van de Walle and Asta

Page 35: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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

Page 36: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Thermodynamic data

Quantum Mechanical Calculations

Lattice model &Monte Carlo Simulations

Electronic excitationsLattice vibrationsConfigurational disorder

Page 37: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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: Or: any other model of electronic entropy

Page 38: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Outline

• Example of ab initio calculations• Why ab initio Thermodynamics?• Methods• Applications

Page 39: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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

Page 40: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

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)

Page 41: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Antiphase Boundary

Diffuse Antiphase Boundary

Creation of a plane with easy dislocation motion:Work softening

after passage of 1 dislocation after passage of 2 dislocations

after passage of 1 dislocation after passage of 2 dislocations

Page 42: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Short-range order and diffuse antiphaseboundary energy calculations

Calculated diffuse X-ray scattering in Ti-Al hcp solid-solution

Energy cost of creating a diffuse anti-phase boundary in a Ti-Al hcp short-range ordered alloy by sliding k dislocations

Neeraj (2000)

Page 43: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Phase Field Modeling of System

Zhu, Wang, Ardell, Zhou, Liu & Chen (2004)

L12 Ni3AlNi-rich fccsolid solution

Free energy:

Thermodynamic term “gradient energy” termphase fields

Input parameters needed: Bulk thermodynamic data, Kinetic coefficients,Interfacial free energy,Interface width

Page 44: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Interface Width & CoalescenceIn phase field modeling:

Interface width usually a numerical parameter.

Can get correct behavior with a larger-than-physical width

except if modeling of coalescence required.

φ

x

φ

x

Wider Interface Increased coalescence

Page 45: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Ni3Al/Ni (001)

Lattice model

Diffuse Coherent Interface

Page 46: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Interfacial ThermodynamicsNi3Al/Ni (001) diffuse coherent interface

Interfacial free energy Interface width

Important input for mesoscale phase field simulations:

provides the “gradient energy” term

1 nm

Page 47: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Search for new compounds

Hart, Blum, Walorski & Zunger, Nat. Mat. 4, 391 (2005)

Page 48: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Search for new compounds in theAl-Mo-Ni system

E

AlNi

Al (fcc)

Mo (bcc)

Ni (fcc)

NiAl (B2)Ni3Al (L12)

Mo

plotted with MEDIT, INRIA-Rocquencourt.

Page 49: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Ni

Predicted Nano-StructuredCompound

Al

MoAlMo2Ni2

1 nm

(fcc)

(bcc)

plotted with MEDIT, INRIA-Rocquencourt.

Page 50: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

x

y

Nanostructured Electrolyte(for fuel cell applications)

Superlattices

70000-atom simulation

Material: CexSm1-xOyVac2-y

Optimal composition

~25 nm

CexSm1-xOy

O

Interface

Forbidden composition

van de Walle & Ellis, Phys. Rev. Lett. 98, 266101 (2007)

Page 51: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

First-principles determination ofStructure-Property Relationships

Example: Configuration-strain coupling

Page 52: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

More Structure-Property Relationship!

Useful input for design and optimization of optoelectronic devices

Page 53: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Interatomic Potential Constructionfrom Quantum-Mechanics

Radiation damage in nuclear fuel for advanced burner Reactors: modeling and experimental validation (PI: N. Jensen, UC Davis; Student: P. Tiwary)

E

d

Page 54: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Calculated phase diagramsTi-Al

fcc + L12

T (K)

Page 55: Traditional vs. ab initio modeling · Experimental data Analysis Predictions Simulations Microscopic parameters Quantum mechanical calculations Validation Traditional vs. ab initio

Locating Phase Transitions andEquation of State (EOS) Calculations

T

P

solid

liquid

Ramalingam, Asta, van de Walle & Hoyt, Interface Sci., 10: 149, 2002

Phase coexistence method Free Energy Equalization

dPdT 1

THBHA

VBVA

T,P

G

Boundary tracing:

A B

V

P

T

Equation of state

PSAAP Center for the Predictive Modeling and Simulation of High Energy DensityDynamic Response of Materials (PI: M. Ortiz, Caltech).


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