M. I. Baskes Los Alamos National Laboratory and University of California, San Diego
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05.03.2018
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495 b.
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M. I. Baskes
M. I. Baskes
Los
Alamos National Laboratory
and
University of California, San Diego
Modified EAM (MEAM)
Modified EAM (MEAM)
Single Element
Alloys
EAM uses a linear superposition of spherically averaged electron densities
EAM uses a linear superposition of spherically averaged electron densities
MEAM allows the background electron density to depend on the local symmetry
Choose
Reference Structure
Choose Reference Structure
Assemble
Data Base
Associate/Fit Parameters with Data Base
Validate
Iterate
Simple Crystal Structure
Simple Crystal Structure
fcc
bcc
hcp
diamond cubic
Usually Equilibrium Ground State
Must Have Data
Relevant
to Simulations
Experiment (reference structure)
Experiment (reference structure)
Cohesive energy
Lattice constant
Elastic constants
Vacancy formation energy
Stacking fault energy
Thermal expansion
Other phases
First Principles (reference structure)
Energy vs. volume
Other phase relative energies
Transformation path
UEOS
UEOS
Cohesive energy (Ec)
Lattice constant (re)
Bulk modulus (α)
Thermal expansion (δ)
Partial
Electron Density Weights
Vacancy formation energy (t1)
Shear elastic constants (t2)
Stacking fault energy (t3)
Embedding Energy Strength (A)
Embedding Energy Strength (A)
Energy of other phases
Atomic Electron Density Decay
Energy of other phases (β0)
Surface relaxation (β1)
Shear elastic constants (β2)
c/a (β3)
Angular Screening
Energy of other phases
Shear elastic constants
Thermal
properties
Thermal properties
Expansion
Specific heat
Surfaces
Energy
Relaxation
Reconstruction
Point defects
Vacancy
mobility
Interstitial
Formation energy
Geometry
Migration energy
Liquid
Liquid
Heat of fusion
Density
Melting point
Solid
Relative stability
Lattice constants
Internal relaxation
Elastic constants
Transformation paths
Choose Reference Structure
Choose Reference Structure
Assemble Data Base
Associate/Fit Parameters with Data Base
Validate
Iterate
Simple Crystal Structure
Simple Crystal Structure
Preferably with 1NN of opposite type
B1 (rock salt –NaCl)
Equilibrium Ground State if Simple
Must Have Data
Relevant to Simulations
stoichiometry
Structure
Derive Analytic Expression
for Cross Pair Potential
Experiment or First Principles (reference structure)
Experiment or First Principles (reference structure)
Cohesive energy
Lattice constant
Elastic constants
Thermal expansion
Other Phases
Cohesive energy
UEOS (reference structure)
UEOS (reference structure)
Cohesive energy (Ec)
Lattice constant (re)
Bulk modulus (α)
Thermal expansion (δ)
Electron Density Scaling
Elastic constants (ρa0)
Other cohesive energies (ρa0, Cmin, Cmax)
Thermal properties
Thermal properties
Expansion
Specific heat
Surfaces
Energy
Relaxation
Reconstruction
Segregation
Point defects
Point defects
Vacancy (on A and B sub-lattices) mobility
Interstitial
Formation energy
Geometry
Migration energy
Liquid
Liquid
Heat of fusion
Density
Melting point
Solid
Relative stability
Lattice constants
Internal relaxation
Elastic constants
Transformation paths
Dilute heats of solution
Short
range order
There are a limited number of free parameters for multi-components
There are a limited number of free parameters for multi-components
For AB choose ρaB0
For AC choose ρaC0
There is no ρ to choose for BC
There are Cmin(A,B,C) and Cmax(A,B,C) to choose
All combinations of A, B, C
MEAM is Parameterized to Facilitate Relatively
Easy Function Determination
MEAM is Parameterized to Facilitate Relatively Easy Function Determination
MEAM Can Quantitatively Reproduce the Fe Data Base Including Phase Transformations
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