Could you please specify procedure to calculate elastic constants: C11, C12 and C44.
I have performed Monte Carlo simulations for metal system. Calculated other properties like cohesive energy, heat of mixing, lattice constants.
For fcc structure, these elastic constants are to be calculated. From existing properties can we directly obtain elastic constants?
Srikanth,
the main two methods to calculate the elastic constants from molecular (atomistic) simulations are: (i) to calculate variations of the crystal energy with respect to specific lattice distortions, and (ii) to obtain the phonon dispersion curves along specific branches and get the elastic constants from there. In both cases, the critical quantity to obtain are the second derivatives of the energy (density) of the crystal with respect to the displacement. In metals (or other systems) with cubic symmetry, the best strategy is to calculate the bulk modulus B, C', and C44 and get the other elastic constants using suitable relations. In all three cases, you obtain the energy of the crystal as a function of hydrostatic, tetragonal, and trigonal strains, and get each elastic constant from the second derivative of those curves.
In latex notation:
c_{\alpha\beta} = \frac{partial^2 U}{\partial \epsilon_{\alpha}\epsilon_{\beta}}
I hope this helps.
Srikanth,
the main two methods to calculate the elastic constants from molecular (atomistic) simulations are: (i) to calculate variations of the crystal energy with respect to specific lattice distortions, and (ii) to obtain the phonon dispersion curves along specific branches and get the elastic constants from there. In both cases, the critical quantity to obtain are the second derivatives of the energy (density) of the crystal with respect to the displacement. In metals (or other systems) with cubic symmetry, the best strategy is to calculate the bulk modulus B, C', and C44 and get the other elastic constants using suitable relations. In all three cases, you obtain the energy of the crystal as a function of hydrostatic, tetragonal, and trigonal strains, and get each elastic constant from the second derivative of those curves.
In latex notation:
c_{\alpha\beta} = \frac{partial^2 U}{\partial \epsilon_{\alpha}\epsilon_{\beta}}
I hope this helps.
Srikanth,
If you use LAMMPS (lammps.sandia.gov) they have an input script in the examples directory on calculating the elastic coefficients. LAMMPS is however a Molecular Dynamics code.
Best'
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