17.10 Mantle convection with phase changes 297
fields of geodynamic modelling in terms of both technical and conceptual pro-
gresses (e.g., Yuen et al., 2000). Realistic modelling of terrestrial and planetary
convection is a challenging topic (e.g., Hansen and Yuen, 1988; Larsen et al.,
1995; Yuen et al., 2000; Zhong et al., 2007; Tackley, 2008) and requires the appli-
cation of sophisticated 3D numerical codes working with spherical geometries at
high grid resolution which can almost exclusively only be preformed by parallel
computing on ‘big machines’. Indeed, one important aspect of modelling mantle
convection, which is of interest for this chapter, is the incorporation of solid-state
phase transitions into such numerical models.
Solid-state phase transitions are crucial phenomena in the Earth’s mantle. Major
phase transitions include olivine–spinel at 410 km depth and spinel–perovskite
at 670 km depth. These transitions are associated with significant changes in
mantle density and seismic wave speeds (Turcotte and Schubert, 2002). It was
also suggested recently, that the so-called D
(D-double-prime) discontinuity near
the core–mantle boundary is related to perovskite–post-perovskite phase transition
(Oganov and Ono, 2004; Murakami et al., 2004). Phase transitions affect the
dynamics of mantle convection due to (1) density changes and (2) latent heating
(Richter, 1973; Schubert et al., 1975; Christensen and Yuen, 1985; Tackley, 1993;
Zhong and Gurnis, 1994).
Phase changes are traditionally included in mantle convection models (e.g.,
Richter, 1973; Schubert et al., 1975; Christensen and Yuen, 1985; Tackley, 1993;
Zhong and Gurnis, 1994) by programming each transition individually (i.e. sim-
ilarly to what we did with melting reactions in the previous example). However,
for realistic mantle compositions, the amount of various phase transitions is larger
than only three (Fig. 17.10) and these phase transitions involve several minerals
of variable composition (so called solid solutions, Table 17.3) which makes the
traditional approach quite inconvenient. An alternative method has been developed
recently based on Gibbs free energy minimisation (Chapter 2). This method was
initially applied for crustal- and lithospheric-scale thermal (Petrini et al., 2001;
Gerya et al., 2001; Kaus et al., 2005) and thermomechanical (Gerya et al., 2004c,
2006; Yamato et al., 2008) models and then expanded to mantle convection models
(Tackley, 2008).
The idea of this petrological-thermomechanical method is relatively simple
(Gerya et al., 2004c; 2006): (i) phase diagrams (P–T pseudosections) and related
density (ρ) and enthalpy (H) maps (see programming exercise 2.3; Chapter 2) are
first computed for the necessary rock compositions in a relevant range of P–T
conditions and (ii) these maps are then used in thermomechanical experiments for
computing density (ρ), effective heat capacity incorporating latent heat (C
Peff
)and
energetic effects (both adiabatic and latent heating) for isothermal (de)compression
(H
P
) for material points (markers) based on standard thermodynamic formulas and