A simple relation connecting the temperature shift, the recoil-free fraction, and the force constant has been derived. The force constants for host-host and for impurity-host atoms and their ratios have been calculated from this relation. The values thus obtained are compared with the values obtained by other authors. The agreement has been found to be satisfactory and confirms the applicability of the derived relation. The results also indicate the change in the force constant for an impurity atom in a host lattice.

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Methods for determining volume changes on melting have been briefly reviewed. A new apparatus has been described which is simple in operation, accurate in measurements and is free from some of the major limitations of the apparatuses used earlier. It has been used to determine volume changes on melting of α- and β-derivatives of naphthalene (C10H7X; X = NH2, OH, COOH), as well as coefficients of cubical expansion of the solid compounds (α) and their melts (α'). The application of the apparatus has been extended to determine the densities of the compounds at any temperature both when entrapped air is present (d) and when it is completely absent (d'). An electrical method using a modified glass calorimeter has been employed for the measurement of latent heats of fusion, ΔHf. From the experimentally determined values of ΔVf/Vs,d', α and ΔHf, the molar volume of the solid compound at the melting point (V8), that of the melt at the melting point (V1), the entropy of fusion (ΔSf), the variation of the melting temperature with pressure [(∂T/∂P)v] and the compressibility coefficient of the solid compounds (β) have been calculated and the results discussed.

In the present communication we have reviewed some inverted type equations of state for solids under high pressures. An inverted equation of state (EOS) gives volume as a function of pressure for a solid under isothermal conditions. We have considered various equations of state proposed by earlier workers which express volume as a function of pressure. Expressions for bulk modulus and its pressure derivatives based on such EOSs are obtained and reported here. It is emphasized here that the high pressure derivative properties are very sensitive to the forms of equations of state representing volume-pressure relationships. We have also studied the thermoelastic properties of solids based on pressure derivatives of bulk modulus. Applications have been extended in the present review article to the solids which are metals as well as non-metals including geophysical minerals present in the lower mantle and core of the Earth.

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