Elastic constants of crystalline sodium from molecular dynamics

We have used molecular-dynamics simulations to calculate the elastic constants $C_{11}$, $C_{12}$, and $C_{44}$ of bcc sodium based on a pseudopotential model, at approximately zero pressure and for temperatures to near melting. Our procedure requires evaluation of average fluctuations of position and volume derivatives of the ion-ion interaction potential. The agreement with experiment is good for the magnitudes of $C_{11}$ and $C_{12}$, and for the temperature dependences of all three elastic constants. The calculated $C_{44}$ is consistently smaller than experiment, and we attribute this to a neglect of theoretical contributions of higher than second order in the pseudopotential. We find that important contributions to the pressure and elastic constants of a metal result from the strictly volume-dependent binding potential, and also from the volume dependence of the ion-ion interaction potential.