On anharmonic and pressure corrections to the equilibrium isotopic constants for minerals

Abstract

Specifies of the calculations of the reduced isotopic partition function ratios (β-factor) of minerals are discussed. Comparative calculations in the framework of the fully harmonic, quasi-harmonic, and intrinsic anharmonic approximations show minor anharmonic corrections to the harmonic values of the β-factor. In the case of calcite, the difference between the fully harmonic and intrinsic anharmonic values of 10 3lnβ varies from 0.60 at 300 K to 0.37 at 1200 K and is close to typical values of the anharmonic correction in gas molecules. A new treatment for calculating isotopic effects in molar volumes of minerals and pressure effects on their β-factors is developed on the basis of the Mie-Grüneisen equation of state. There is no significant difference between the quasi-harmonic and intrinsic harmonic values of (∂lnβ/∂ P) T . For calcite, the pressure derivative of the β-factor is positive, decreases monotonically with temperature, and becomes small at T ∼ 1000 K (10 3(∂lnβ/ ∂P) T ≈ 0.1–0.15 GPa −1). These results contradict the large anharmonic and pressure effects to the β-factor of calcite calculated by Gillet et al. (1996) as well as their conclusion that the pressure correction to the β-factor of calcite is negative at higher temperatures and increases in its absolute value with increasing temperature.