The validity of the common approximate expressions for the Grüneisen parameter

Abstract

The present development of theory and experiment allows practical estimates of the Grüneisen parameter only through very approximate theories, the most common of which are known as Slater, Dugdale and MacDonald, Free‐Volume, Debye, and Acoustic formulations. While their fortune can most be traced to the capability of expressing thermodynamical properties just in terms of mechanical parameters, which in turn are the only ones directly available for the Earth's interior, no exhaustive test about their effective validity has so far been conducted. The present paper attempts to fill this gap by studying all the solids for which a set of data is available large enough to substantiate significant conclusions. The set of data analysed comprises 19 solids, i.e. five metals (Ag, Al, Au, Cu, Fe), seven alkali halides (KCl, NaCl, RbCl, KBr, RbBr, KI, RbI) and seven (synthetic) minerals (MgO, CaO, α‐Al2O3, α‐SiO2, MgF2, Mg2SiO4, Mg2Al2O4). The still poor knowledge of the second derivatives of elastic constants only allows the test to be carried out at room pressure, while the effect of temperature is studied by using data relative to both room temperature and high temperature (the highest available). The test shows that, while the traditional formulations are in general inaccurate, the Debye–Brillouin and Debye formulations, which comprise the Acoustic formulation as a particular case, provide a good agreement with experiment which holds irrespective of type solid and temperature, with probable errors between the real and the estimated values of the order of 10–15 per cent. This agreement is in fact surprising in the light of the numerous and drastic approximations made, and suggests that applications to high pressures can also possibly produce good results. Copyright © 1988, Wiley Blackwell. All rights reserved