Garnet model

Van Westrenen et al. (2001a) present a model of lanthanide and Sc partitioning between the garnet X-site and melt. The model is a variant of the lattice strain model of clinopyroxene-melt partitioning of Wood and Blundy (1997), and is based on 160 experimental garnet-melt pairs in the pressure-temperature range 2.5-7.5 GPa and 1450-1930°C. The model includes composition-sensitive expressions for and accounts for the non-linear variation in with composition, as follows ... 

Dm (and Du) vary inversely with reciprocal temperature (Fig. 15). For mantle solidus garnets the correlation is reasonably good and can be used to make a first-order estimate of Dm- A more comprehensive model for Du and Dm, as a function of pressure, temperature and melt composition is provided by Salters et al. (2002). Their full expressions (for the molar partition coefficients, D ) are ... 

Figure 14. U-Th fractionation by garnet as a function of X-site dimension ) for 33 experimental garnet-melt pairs from the sonrees listed in the legend. r Jx) is assnmed eqnal to r (x) as given by Eqnation (22a). Note the mnch larger U-Th fractionation prodneed by garnet relative to clinopyroxene (Fig. 1). The emved line shows the prediction of the lattice strain model (at fixed temperature of 1500°C) using the Vlll-fold ionic radii in Table 2 and, as given by Equation (22b). Errors...

Table 4. Test of Salters et al. (2002) model for garnet-melt Z)u and D...

Figure 16. Electrostatic model fitted to partition coefficients for cations entering the X-site in garnet, based on the experiments of Van Westrenen et al. (1999, 2000) and Klemme et al. (2002). The curves are fits to Equation (7) and can be used to estimate and f>o(x) > which f>pa(x) can be calculated via the lattice strain model. The fit parameters are given in Table 5.

Table 5. Electrostatic model fit parameters for garnet and estimates of DpJD ...

Another evaluation of the pyroxenite hypothesis can be found in the evaluation of a suite of data from the Canaries islands (Thomas et al. 1999). These authors estimated the maximum mode of residual garnet for the 1730-1736 Lanzarote eruption modelling... 

Lassiter JC, Hauri EH (1998) Osnhum-isotope variahons in Hawaiian lavas evidence for recycled oceanic lithosphere in the Hawaiian plume. Earth Planet Sci Lett 164 483-496 LaTourrehe TZ, Kennedy AK, Wasserbuig GJ (1993) Thorium-uraiuum frachonation by garnet evidence for a deep source and rapid rise of oceanic basalts. Science 261 739-742 Liu M, Chase CG (1991) Evoluhon of Hawaiian basalts a hotspot melhng model. Earth Planet Sci Leh 104 151-165... 

In contrast to the southern volcanic zone, Parinacota volcano lies on very thick continental crust (> 70 km) in the central volcanic zone of Chile. Bourdon et al. (2000a) showed that young Parinacota lavas encompass a wide range of U-Th disequilibria. excesses were attributed to fluid addition to the mantle wedge but °Th-excesses in lavas from the same volcano are more difficult to explain. The lavas with °Th-excesses also have low ( °Th/ Th) (< 0.6) characteristic of lower continental crust characterized by low Th/U and in their preferred model. Bourdon et al. (2000a) attributed the °Th-excesses to contamination by partial melts, formed in the presence of residual garnet, of old lower crustal materials. 

If that sort of simplistic model is acceptable, the extent of fractionation hints at rather small degrees of melting in the mantle and/or the presence of a residual phase that fractionates Sm from Nd, probably garnet, o... 

Table 5.25 Parameters of the Kieflfer model for calculation of Cy and harmonic entropy for the 12 garnet end-members in the system (Mg, Fe, Ca, Mn)3(Al, Fe, Cr)2Si30i2. is the lower cutoff...

The model parameters relative to the uncommon garnet end-members were obtained by Bokreta (1992) through linear regression involving the atomistic properties of the in-... 

Figure 5A8 Enthalpy of mixing surface for aluminiferous garnets in the system (Mg,Mn,Ca,Fe)3Al2Si30i2 based on the Wohl s model parameters in table 5.28 (from Otto-nello et ah, in prep.).

Mattioli and Bishop (1984), the mixture is of regular type but has a positive bulk interaction parameter between 0.6 and 3 kcal/mole. Extension to multicomponent mixtures was attempted by Berman (1990), Ganguly (personal communication), and Ottonello et al. (in prep.). Berman (1990) applied the model of Berman and Brown (1984), originally conceived for silicate melts, to aluminiferous garnets and deduced the magnitude of ternary interaction parameters by applying... 

By applying the ionic solution model, we may express the relationship between ionic fraction and activity in the garnet phase as... 

Bokreta M. (1992). Energetics of garnets Computational model of the thermochemical and thermophysical properties. Ph.D. diss., University of Philadelphia. 

Harrison W. J. (1981). Partition coefficients for REE between garnets and liquids Implications of non-Henry s law behavior for models of basalt origin and evolution. Geochim. Cosmochim. Acta, 45 1529-1544. 

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