SYSTEMATICS OF THERMODYNAMIC DATA ON SOLIDS: THERMOCHEMICAL AND PRESSURE-VOLUME-TEMPERATURE PROPERTIES OF SOME MINERALS

Abstract

The Helmholtz free energy of a solid may be expressed as follows where Est is the potential of a static lattice at absolute zero (P = 0, T = 0), Vo is the initial molar volume, K0 the bulk modulus, K'0 the pressure derivative of K0, # the coordinate displacement (strain), R the universal gas constant, N the number of atoms in the formula unit, k the Boltzman constant, # the Plank constant, B2n the Bernoulli numbers, T the temperature, and μ2n the spectral frequency moments. By suitably differentiating the above equation, one may write expressions for all the thermochemical (e.g., heat capacity) and thermophysical (e.g., thermal expansion, bulk modulus) properties of a solid. The frequency moments and their derivatives have been determined for several solids (periclase MgO, forsterite Mg2SiO4, lime CaO, and corundum Al2O3). From the heat capacity at zero pressure (Cv) and molar volume (V(P)) at different temperatures, we determined the complete pressure-volume-temperature data for minerals mentioned above.