### 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 Fo_{100} 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 Fo_{90}
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 Fo_{100}.
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.

Copyright © 2004 The Geochemical Society

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