Garnets X-site

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 ... 

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...

For all ten garnets there is negligible incorporation of Nb or Ta onto the X-site, however E>Pa(X) is significant, though variable (10 " to 6 x 10 ). We conclude, as expected, that Nb and Ta predominantly enter the Y-site, while Pa enters both X and Y. 

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.

Armbruster T. and Geiger C. A. (1993). Andradite crystal chemistry Dynamic X-site disorder and structural strain in silicate garnets. Eur. J. Min., 5 59-71. 

Figure 11 Comparison of fitted values of from garnet-melt partitioning with the Hazen-Finger relationship of Equations (14) and (15). Note that the X-site is much stiffer than would be anticipated (see text).

Figure 19 Observed and predicted dependence of garnet-melt DVDxh on the radius of the X-site for 3 -h ions Solid curve was calculated from lattice strain theory and was obtained from Equation (60) ( VanWestrenen et al. (1999) Van Westrenen et al. (2000b) A La Tourrette et al. (1993) O McDade et al. (2003a) V Salters et al. (2002) Hauri et al. (1994) A Beattie (1993b) A Salters and Longhi (1999) T Landwehr et al. (2001) and Klemme et al. (2002)).

Simulated structures for pyrope, ahnandine, spessartme, and grossular were used as the basis for calculations of the energies required to introduce various trace-element defects. In every computational run, one or more defects are introduced into the crystaL e.g., for homo-valent (same-charge) substitution, one divalent cation at the X-site of a perfect garnet lattice is replaced by one trace-element divalent cation. Initial, unrelaxed defect energies were... 

Next let s take a mineral such as garnet where substitution can occur on two different groups of sites instead of one. The general formula for garnet can be written X3Y2Si30i2 (remember that this choice for the formula now fixes our choice of n in equation (15.5)). The X sites are cubic (8-coordinated) and we will assume they accept Al " and Fe ions. The Y sites are octahedral (6-fold), and let s assume they accept only Mg , Fe , and The Si site is tetrahedral (4 fold), and it can also hold AP ions. The total configurational entropy for this mineral must be the sum of the entropies on all three of these sites, or... 

In other words, n = 1 in (15.5) for the activity of the component pyrope in garnet, because this species appears once in the formula as written for garnet. To express pyrope activity in terms of the individual ions we need to use the product above and the values n = 3,2, and 3 for the X, Y, and Si sites as before, this is because the ions occur 3 times in the X sites, 2 times in the Y, and 3 times in the Si sites for the formula XsYiSisO chosen to represent garnet. Nordstrom and Munoz (1985, p. 156) give an example calculation. Keep in mind, too, that so far we are assuming ideal solutions, or ideal mixing of components. 

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