Fluctuation method for calculation of elastic constants of solids

This paper derives a method for calculation of the elastic constants of a solid from computer simulation data on atomic displacement correlations at long range. It is shown that principal axes of the elastic constant tensor can be found from a Fourier analysis of the second-rank tensor of displacement correlations together with a numerical search in the reciprocal Fourier k space. The full fourth-rank tensor of elastic constants then can be obtained by rotations after the principal values are calculated. The method is not limited to special crystal symmetries, to pair-decomposable forces, to low temperatures, to thermodynamic states of only slight distortion from the minimum energy configuration, or to harmonic systems.