Systematics of thermodynamic data on solids: Thermochemical and pressure-volume-temperature properties of some minerals

The Helmholtz free energy of a solid may be expressed as follows F = E-st + 9/2K(0)V(0) epsilon(2)(1 - 3/2(K-0' - 4)epsilon) + 3RNT ln (h) over bar mu 0/kT + 3RNT((n=1)Sigma(infinity)(-1)(n+1)B2n/2n(2n)!((h) over bar mu 2n/kT)(2n)) where E-st is the potential of a static lattice at absolute zero (P = 0, T = 0), V-0 is the initial molar volume, K-0 the bulk modulus, K-0' the pressure derivative of K-0, epsilon the coordinate displacement (strain), R the universal gas constant, N the number of atoms in the formula unit, k the Boltzman constant, (h) over bar the Plank constant, B-2n the Bernoulli numbers, T the temperature, and mu(2n) 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) propel-ties 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 (C-v) and molar volume (V(P)) at different temperatures, we determined the complete pressure-volume-temperature data for minerals mentioned above. Copyright (C) 1997 Elsevier Science Ltd.