Heat capacity and thermal expansion of metal crystalline materials based on dynamic thermal vibration

A novel approach based on dynamic thermal vibration is proposed to calculate the heat capacity and thermal expansion coefficient (TEC) for metal crystalline materials from 0 K to the melting point. The motion of metal atomic clusters is decomposed into structural deformation and thermal vibration. Then thermal vibration equations are established by the fourth-order Taylor expansion of Hamiltonian at the transient structural deformation position \({\bar{\mathbf {x}}}\). As a result, the thermal vibration frequencies dynamically change with the structural deformation positions and temperatures. A parameter \({\bar{\delta }} ({\bar{\mathbf {x}}}, T)\) is newly introduced to illustrate how the thermal vibration frequencies vary with the temperature T. Besides, the modified temperature-dependent Grüneisen parameter \({\bar{\gamma }} ({\bar{\mathbf {x}}}, T)\) is given. Finally, the formulae of heat capacity and TEC for metal crystalline materials are derived from the dynamic thermal vibration frequencies and \({\bar{\delta }} ({\bar{\mathbf {x}}}, T)\) as well as \({\bar{\gamma }} ({\bar{\mathbf {x}}}, T)\). The numerical results of heat capacity and TEC for metals Cu, Al, Au, Ag, Ni, Pd, Pt and Pb show a temperature dependence and agree well with the experimental data from 0 K to the melting point. This work suggests an efficient approach to calculate thermodynamic properties of metal materials for a wide range of temperatures, up to the melting point.