Investigating the temperature dependence of elastic constants by thermal fluctuation formula

The differences between the calculated values of elastic constants of materials and the experimental data are consistently restricting the application of thermal fluctuation formula to the mechanical properties of materials. In this work, the temperature dependence of elastic constants of many-body potentials is studied by thermal fluctuation formula. The differences between the calculated values and the experimental data are investigated in detail. Our studies show that the differences come from the thermal expansion of the materials: the calculated zero-stress states are bigger than the experimental zero-stress states of the materials, and this deviation makes Born terms of the thermal fluctuation formula decrease sharply as the temperature increases, while the fluctuation terms and the kinetic terms change little. As a result, the elastic constants, which are the sum of these three terms, decrease faster than the experimental data as the temperature increases. Our studies show that when the experimental zero-stress states are used as the reference states in constant volume and constant energy (NVE) simulations, the elastic constants calculated by thermal fluctuation formula are in good agreement with the experimental values.