Second-order elastic constants for the Lennard-Jones solid

The elastic constants of a classical nearest-neighbor Lennard-Jones solid are evaluated with the use of molecular-dynamics calculations in order to make comparisons with similar quantities derived from Monte Carlo calculations. Following Parrinello and Rahman, we use both strain fluctuations in the ($p,H,N$) ensemble and uniaxial loading to obtain the adiabatic elastic compliances and hence the elastic constants. While there is broad agreement between the three methods, Monte Carlo evaluation seems to be the most efficient procedure. The relationship between the elastic constants of the fcc and hcp solids is also discussed.