Fourth‐Order Thermal Expansion for Cubic Solids. Application to Aluminum, Copper, Germanium, and Silicon

The fourth‐order anharmonic finite‐strain theory leads to a model for the volume dependence of the Grüneisen parameter and simultaneously to a Mie‐Grüneisen equation of state. These relations are used to derive the fourth‐order expressions for the thermal expansion coefficient of cubic crystals. A comparative study of the results with experimental data is given for the temperature dependence of the linear thermal expansion coefficient α of aluminum, copper, germanium, and silicon. It is shown that the theory agrees with experiment even better since the Grüneisen coefficient can be reasonably assumed to be temperature independent. Finally, an estimation of the variation of the thermal expansion coefficient with volumetric compression is given for aluminum, copper, germanium, and silicon using both, the Lagrangian and Eulerian strain measures.