## Third-order elastic from molecular dynamics: Theory and an example
calculation

Cagin-T and Ray-JR

Physical Review B**38**, 7940-7946(1988)

## ABSTRACT

In earlier work, fluctuation formulas have been derived which allow the
calculation of the second-order elastic constants of solids with use of
molecular-dynamics computer simulations; explicit calculations have
shown that these fluctuation formulas furnish an efficient method of
obtaining the second order elastic constants of crystalline and
amorphous solids. In this paper, we present the statistical fluctuation
formulas containing the isothermal and adiabatic third-order elastic
constants. As we show, these formulas also enable one to efficiently
calculate the third-order elastic constants of solids, using
molecular-dynamics computer simulation. We illustrate the usefulness of
these new fluctuation formulas by an explicit calculation of the
adiabatic second- and third-order elastic constants of argon at 20.5 K.
We also give the pressure derivatives of second-order elastic constants
at 20.5 K.