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
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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
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CrNi2
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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
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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
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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
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Elastic Properties of ZrHx
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MedeA® provides properties where experimental data are lacking
MedeA®-VASP-MT
Solubility of H in Zr
Computed Measured
Computed
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MedeA®-VASP, Phonon
Nucleation of Dislocation Loops
MedeA®-LAMMPS/EAM
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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
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
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MedeA®-VASP-UNCLE
Boron Carbide
Distribution of carbon and boron on the lattice?
How does this influence hardness?
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?
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
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MedeA®-VASP-UNCLE
Boron Carbide Cluster Expansion
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Minimum carbon solubility in agreement with experimental phase diagram
MedeA®-VASP-UNCLE
Boron Carbide Cluster Expansion + MT
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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
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
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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
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