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

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 T=20.5 K.