Elastic Constants from Energy versus Unit Cell Data
These are formula for obtaining the Bulk Modulus (B) and the
shear elastic constant (C').
E is the
energy per atom
(in ergs),
a is a lattice parameter
(which can be either
unit cell length,
nearest neighbor distance or
some other linear distance measurement measured in cm),
V is the equilibrium volume per atom
(in cm3), and
a0 is the
equilibrium lattice parameter.
Bulk Modulus
To calculate the bulk modulus, expand the lattice uniformly
in the x,y,z directions
and record the energy E as a function of some lattice
parameter a. The bulk modulus B is then given by
Shear Elastic Constant
To calculate the shear elastic constant
C', expand the lattice
by u in the x direction and by -u in the
y direction
and record the energy E as a function of lattice
parameter a.
The shear elastic constant C'
is then given by
