First Pressure Derivatives of Polycrystalline Elastic Moduli: Their Relation to Single-Crystal Acoustic Data and Thermodynamic Relations

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Abstract
This paper demonstrates that, for a given crystalline solid, the first pressure derivatives of polycrystalline elastic moduli can be predicted either from the corresponding derivatives of anisotropic single‐crystal elastic constants or from their single‐crystal third‐order elastic constants. Theoretical relations for the isotropic polycrystalline acoustic data in terms of their single‐crystal acoustic data are presented here for cubic, hexagonal, trigonal, and tetragonal crystals; these have been successfully applied for four cubic solids (Al, Cu, α‐Fe, and MgO) and one hexagonal metal (Mg). It is shown for these solids that the calculated isotropic acoustic data agree essentially with experimental acoustic data determined on their polycrystalline specimens, thus establishing the validity of the theoretical relations. It is concluded that the acoustic data measured on fully dense polycrystalline specimens may be as useful as the single‐crystal acoustic data in the study of the equation of state of solids, for example. And further, when anisotropic single‐crystal acoustic data are available, these can be converted into isotropic polycrystalline acoustic data so that in their applications, the use of the acoustic data becomes more practical.