Thermo-Calc Anwendertreffen Aachen, 3-4 September 2015

Thermodynamic and Transport Properties Determined

from Ab Initio and Forcefield Simulations using MedeA®

Erich Wimmer Materials Design

© Materials Design, Inc. 2015

Outline

Materials Design company profile

Scientific and technological context – ICME

Examples • Ni-Cr phase diagram

• Effect of alloying elements and impurities on strength of grain boundaries

• Interface energy

• Heat capacity

• The Zr-H system

• Precipitation of TiC in steel

• Diffusion and melting

• Boron carbide

• Viscosity of molten Ni

• Surface tension of molten Cu

Discussion © Materials Design, Inc. 2015 2

Materials Design, Inc. Company Profile

Founded in 1998

Business: MedeA® software, support, and contract research

Over 400 customers in Industry, Universities, and Government Laboratories including the world’s largest companies in • Automotive

• Chemical

• Electronics

• Oil and gas

• Energy

Global: USA (San Diego, Angel Fire), Europe (Paris, Stockholm), business partners in Japan, Korea, China, Taiwan, Singapore, and India

3 © Materials Design, Inc. 2015

Company Profile

Technology Chain

4 © Materials Design, Inc. 2015

Materials Properties

Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security, National Research Council (2008)

http://www.nap.edu/catalog/12199.html

Thermodynamics Diffusion models Microstructure FE structural analysis CFD Process models Corrosion models Device models

Experiments Atomistic Simulations

MedeA®

Design – Manufacturing – Reliability

Phase Stability in Ni-Cr Alloys

asdf

CrNi2 phase embrittles Prediction of long-range-ordered phase from atomistic simulations

© Materials Design, Inc. 2015 5

Cr-Ni Enthalpies from Cluster Expansion

© Materials Design, Inc. 2015 6

CrNi2

MedeA®-VASP-UNCLE

CrNi2

© Materials Design, Inc. 2015 7

Unit cell of antiferromagnetic CrNi2

P2/m

Antiferromagnetic ordering in Cr-chains is a key factor stabilizing CrNi2

Strength of Ni Grain Boundaries

strengthening

weakening

mo

no

crys

talli

ne

Ni

Σ5

gra

in b

ou

nd

ary

in p

ure

Ni

Grain boundaries with impurities

Result of Computations: Ranking of Impurities and Alloying Elements

© Materials Design, Inc. 2015 8

MedeA®-VASP

Interface Energy: Al/Si3N4

9

MedeA®-VASP

Heat Capacity

Cp(T) …… heat capacity at constant pressure

Cv(T) …… heat capacity at constant volume

αV(V,T) … thermal expansion coefficient

B(T) ……. bulk modulus

T ………. temperature

V0 ………. volume

All thermodynamic properties computed from first principles within the quasi-harmonic approximation

Computed with MedeA®-VASP, MedeA®-Phonon, and MedeA®-MT

J. Wróbel, L.G. Hector, W. Wolf, S. L. Shang, Z. K. Liu, and K. J. Kurzydłowski, J. Alloys and Compounds 512, 296 (2012)

Mg MedeA®-VASP-Phonon-MT

Zr-H Phase Diagram

11

µ ´

γ

ε-ZrH2 I4/mmm EOF/atom: -54 kJ/mol a = 3.537 Å (+0.48%) c = 4.458 Å (+0.21%) c11 = 225 GPa c12 = 88 GPa c33 = 157 GPa c13 = 108 GPa c44 = 30 GPa B = 130 GPa G = 24 GPa E = 68 GPa

Zr P6_3/mmc

δ-ZrH2 Fm-3m

EOF/atom: -53 kJ/mol a = 4.821 Å (+0.92%) Elastically unstable with 1:2 stoichiometry

γ-ZrH I-4m2 EOF/atom: -31 kJ/mol a = 3.283 Å (+1.23%) c = 5.012 Å (+1.30%)

ZrH P4_2/mmc

EOF/atom: -40 kJ/mol a = 3.243 Å (+0.00%) c = 5.022 Å (+1.50%)

S2

ζ-Zr2H P-3m1

EOF/atom: -20.2 kJ/mol a = 3.263 Å (-1.1%) c = 10.824 Å (+5.2%)

Zr2H Pn-3m

EOF/atom: -23.7 kJ/mol a = 4.660 Å

© Materials Design, Inc. 2015

Elastic Properties of ZrHx

12 © Materials Design, Inc. 2015

MedeA® provides properties where experimental data are lacking

MedeA®-VASP-MT

Solubility of H in Zr

Computed Measured

Computed

© Materials Design, Inc. 2015 13

MedeA®-VASP, Phonon

Nucleation of Dislocation Loops

MedeA®-LAMMPS/EAM

© Materials Design, Inc. 2015 14

Expansion in <a> Shrinkage in <c> Consistent with experimental data on radiation-induced growth

The diffusion coefficient of H in Ni computed from first-principles has similar accuracy as experimental data at ambient and medium temperatures Isotope effects are well explained and quantitatively described

Diffusion of H in Ni

E. Wimmer, W. Wolf, J. Sticht, P. Saxe, C. B. Geller, R. Najafabadi, and G. A. Young, “Temperature-dependent diffusion coefficients from ab initio computations: Hydrogen, deuterium, and tritium in nickel”, Phys. Rev. B 77, 134305 (2008)

15 © Materials Design, Inc. 2015

MedeA®-VASP, Phonon

Precipitation MedeA®-VASP

Computed vs. Experimental Solubility Product

Computed solubility product of TiC in ferritic Fe-Cr steel is similar to available experimental data

Accurate electronic energies, inclusion of vibrational entropy (full phonon spectra) and thermal expansion are critical

Ab initio calculations provide quantitative materials property data for alloy engineering

Wolf et al. (unpublished)

T

HAXM −=]][log[

MedeA®-VASP

Boron Carbide

High melting point at ~ 3000 K

Extremely hard (Vickers hardness 38 GPa)

• third hardest substance known (after diamond and boron nitride)

• brake linings

• bulletproof vests

• tank armor

© Materials Design, Inc. 2015 18

MedeA®-VASP-UNCLE

Boron Carbide

Distribution of carbon and boron on the lattice?

How does this influence hardness?

© Materials Design, Inc. 2015 19

?

MedeA®-VASP-UNCLE

Boron Carbide Cluster Expansion

CE for 0 at.% - 20 at.% carbon

Max. 1 unit cells (15 sites)

CVS: 2.4 meV/atom

14 DFT inputs, 81 CE predictions

© Materials Design, Inc. 2015 20

MedeA®-VASP-UNCLE

Boron Carbide Cluster Expansion

© Materials Design, Inc. 2015 21

Minimum carbon solubility in agreement with experimental phase diagram

MedeA®-VASP-UNCLE

Boron Carbide Cluster Expansion + MT

© Materials Design, Inc. 2015 22

B

Elastic properties of the three ground state structures with MT

Hardness increases with carbon concentration

Bulk modulus (Hill) 253 240 238 [GPa] Young’s modulus 595 526 533 [GPa] c11 669 612 566 [GPa] c44 282 174 206 [GPa]

hardness

MedeA®-VASP-UNCLE

Phonon Dispersions of Stable B4C

23 © Materials Design, Inc. 2014

Phonon calculations prove that the structure is dynamically stable

MedeA®-Phonon

Viscosity of Molten Ni

24 © Materials Design, Inc. 2015

MedeA®-LAMMPS

Cu Surface Tension with MedeA-LAMMPS

25 © Materials Design, Inc. 2015

Experimental data from Matsumoto et al, JWRI 34, 29 (2005)

Surface tension using a slab model and an EAM (Zhou 2004) forcefield ³ = Lz(PN-PT) where Lz is the slab dimension in z, and PN and PT the mean normal and tangential pressure components respectively

MedeA®-LAMMPS

Thermal Conductivity

© Materials Design, Inc. 2015 26

Computational approach: Supercell containing 7605 atoms Reverse non-equilibrium molecular dynamics: set heat flux, compute temperature gradient 400 ps equilibration, 1 ns data collection Newly developed charge-optimized many-body (COMB3) forcefield [1] MedeA-LAMMPS Calculations performed on CRAY XC-40 using 640 cores; computing time approximately 24 hours

1. France-Lanord et al., to be published

MedeA®-LAMMPS-Transport

Materials Properties from Computations

27

Structural properties

• Density – crystalline, amorphous, liquid • Bond distances – bulk, surfaces, interfaces • Point defects • Stacking faults • Grain boundaries • Dislocations

Thermo-Mechanical properties • Elastic moduli • Speed of sound • Debye temperature • Stress-strain behavior • Thermal expansion coefficients

Thermodynamic properties • ∆U, ∆H, ∆S, ∆G, heat capacity • Binding energies • Solubility • Melting temperature • Vapor pressure • Miscibility • Phase stability • Surface tension

Chemical properties

• Chemical reaction rates • Reactivity on surfaces • Solid-solid reactions • Photochemical reactions

Transport properties • Mass diffusion coefficient • Permeability • Thermal conductivity • Viscosity

Electronic, optical, and magnetic properties

• Electron density distribution - electrical moments • Polarizabilities, hyperpolarizabilities • Optical spectra • Dielectric properties • Piezoelectric properties • Electrostatic potential • Spin density distribution, magnetic moments • Energy band structure • Band gaps, band offsets at hetero-junctions • Effective masses • Ionization energies and electron affinities • Work function

© Materials Design, Inc. 2014

MedeA®

Materials properties from atomistic simulations

www.materialsdesign.com