Internal displacement and elastic properties of the silicon Tersoff model

Martin's method, which is used to determine the internal displacement of atomic systems and elastic constants, is applied to the Tersoff potential. The potential is modified to provide an accurate description of the high-temperature elastic properties of silicon. The elastic constants of crystalline silicon were investigated at both low and high temperatures. Results were verified using the statistical thermodynamic method, i.e., 'Fluctuation formula'. It was found that values of elastic constants and the influence of the internal displacement are valid. However, at high. temperatures the gap becomes larger owing to the thermal fluctuation. Since the convergence of the Martin's method is faster by about two orders, it is the more effective method. It was also found that the fluctuation term includes the effects of the internal displacement and thermal fluctuation.