2004 Goldschmidt Conference Abstract

Marton, F. C., and C. R. Bina, Metastable phase transitions and latent heat release, Abstracts of the 2004 Goldschmidt Conference, Copenhagen, Denmark, Geochimica et Cosmochimica Acta, 68, A92, 2004.

Exothermic phase transitions, such as olivine to wadsleyite or ringwoodite, that take place under non-equilibrium conditions can release significant amounts of latent heat to their surroundings, causing large localized temperature increases. Such temperature changes taking place within the cold interiors of subducting slabs can significantly affect the amount of metastable olivine or the generation of deep earthquakes. However, these processes are often not well understood. Calculating Gibbs free energies (G) at high pressures (P) and temperatures (T) requires integrating thermodynamic functions over both P and T from a reference state.

Calculating enthalpy (H) and entropy (S) at T is straight-forward. However, the pressure calculation typically combines both the H and S terms, as (∂H/∂P)_T = V - αVT and (∂S/∂P)_T = -αV, where α is the volume coefficient of thermal expansion and V is volume. To calculate H by itself at P and T it is therefore necessary to account for the αVT term. This pressure dependence can be quite strong. For example, a theoretical Fo₁₀₀ olivine to ringwoodite transition at 1000 K and 15 GPa would have ΔH ≈ -11.5 kJ/mol, whereas transitions at the same T but at 17.5 GPa would have ΔH ≈ -19 kJ/mol and -26 kJ/mol at 20 GPa.

As natural minerals do not typically have end-member compositions, solid solution effects must also be taken into account, through the enthalpies of non-ideal mixing. These effects result in even larger latent heat releases, especially at lower P and T. For example, ΔH for the olivine to ringwoodite transformation for a composition of Fo₉₀ ranges from -16 kJ/mol to -24 kJ/mol to -31 kJ/mol at 1000 K and 15, 17.5, and 20 GPa, respectively, increases of 39, 26, and 19% relative to Fo₁₀₀. At 800 K, however, ΔH increases by 56, 30, and 23% at the same pressures. Such effects are therefore important in the modeling of cold subducting lithosphere, but often various simplifications are used in the calculation of ΔH. These can range from ignoring the T dependence of ΔH and using a P dependence of ΔP times a constant value of ΔV to proper treatment of the T dependence but a P dependence that neglects the αVT term. The former will systematically overestimate the enthalpy changes, translating into overestimates in ΔT of tens of degrees, whereas the latter results in small T differences, but not of any systematic nature.