On the use of Anderson–Grüneisen parameters in calculation of the temperature derivative of elastic moduli for cubic polycrystals

For an isotropic aggregate of cubic crystals under hydrostatic pressure, polycrystalline Anderson–Grüneisen parameters are defined. A simplified model is developed for determining their pressure dependence in terms of the isotropic elastic constants up to the fourth-order. Theoretical values of these parameters at zero pressure and room temperature are then obtained for polycrystalline noble metals (Cu, Ag, Au) by means of the extension of the Voigt–Reuss–Hill approximation to the third-order elastic constants. Finally, the results are used to calculate the temperature derivatives of the bulk, shear and young moduli, and of the Poisson ratio of the three investigated metals.