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

Cagin-T and Ray-JR
Physical Review B38, 7940-7946(1988)


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.