M. I. Baskes Los Alamos National Laboratory and University of California, San Diego



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M. I. Baskes


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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