Garnets coefficients

The molecular extinction coefficients (at various wavelengths) of the four main components of the irradiation are shown in Table 5. The absorption of light above 300 nm is favored by tachysterol. A yield of 83% of the previtamin at 95% conversion of 7-dehydrocholesterol can be obtained by irradiation first at 254 nm, followed by reirradiation at 350 nm with a yttrium aluminum garnet (YAG) laser to convert tachysterol to previtamin D. A similar approach with laser irradiation at 248 nm (KrF) and 337 nm (N2) has also been described (76). 

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 15. Variation in Dxh for garnet versns reciprocal temperature for experimental data sources listed in Table lb at a variety of pressures n = 33). A distinction is made between mantle solidus partition coefficients (Salters and Longhi 1999 Salters et al. 2002 McDade et al. 2003a,b) and the rest. Note the strong temperatnre dependence, which is qnalitatively similar to that incorporated in Equation (25b). The scatter is due to additional compositional controls.

Perhaps the biggest challenge in estimating U-series partition coefficients is the case of protactinium partitioning into garnet. The difficulty arises because the ionic radius of... 

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.

Green TH, Blundy JD, Adam J, Yaxley GM (2000) SIMS determination of trace element partition coefficients between garnet clinopyroxene and hydrous basaltic liquids at 2-7.5 GPa and 1080-1200°C. Lithos 53 165-187... 

Table 2. Experimentally determined mineral/melt partition coefficients (x 10 ) for U, Th, and Ba in clinopyroxene and garnet and calculated bulk partition coefficients (xlO ) for a garnet peridotite source.

D s were calculated assuming 60% cpx, 40% garnet and no rutile using values from Keppler (1996) and gamet/melt cpx/melt partition coefficients to estimate gamet/fluid partitioning. ... 

Figure 4.11 Monte-Carlo simulation (100 trials) of error propagation for La/Yb fractionation in residual melts by clinopyroxene-garnet removal from a basaltic parent magma (see text for parameter description and distributions used). Top mineral-liquid partition coefficients for La and Yb. Bottom variations of the La/Yb ratio as a function of the fraction F of residual melt.

Figure 5,65 Garnet-clinopyroxene geothermometric exchange (Fe +-Mg +). Thermodynamic constant K is compared with distribution coefficient K the difference between the two terms represents the effect of interactions in mixtures. Reprinted from J. Ganguly, Geochimica et Cosmochimica Acta, 43, 1021-1029, copyright 1979, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Chakraborty S. and Ganguly J. (1992). Cation diffusion in aluminosilicate garnets Experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contrib. Mineral Petrol, 111 74-86. 

Ganguly J. (1979). Garnet and clinopyroxene solid solutions and geothermometry based on Fe-Mg distribution coefficient. Geochim. Cosmochim. Acta, 43 1021-1029. 

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. 

Oka Y. and Matsumoto T. (1974). Study on the compositional dependence of the apparent partitioning coefficient of iron and magnesium between coexisting garnet and clinopyro-xene solid solutions. Contrib. Mineral. Petrol, 48 115-121. 

Raheim A. and Green D. H. (1974). Experimental determination of the temperature and pressure dependence of the Ee-Mg partition coefficient for coexisting garnet and clinopyro-xene. Contrib. Mineral Petrol, 48 179-203. 

If the diffusion medium is isotropic in terms of diffusion, meaning that diffusion coefficient does not depend on direction in the medium, it is called diffusion in an isotropic medium. Otherwise, it is referred to as diffusion in an anisotropic medium. Isotropic diffusion medium includes gas, liquid (such as aqueous solution and silicate melts), glass, and crystalline phases with isometric symmetry (such as spinel and garnet). Anisotropic diffusion medium includes crystalline phases with lower than isometric symmetry. That is, most minerals are diffu-sionally anisotropic. An isotropic medium in terms of diffusion may not be an isotropic medium in terms of other properties. For example, cubic crystals are not isotropic in terms of elastic properties. The diffusion equations that have been presented so far (Equations 3-7 to 3-10) are all for isotropic diffusion medium. 

Figure 3-5 MnO partition between and diffusion in two minerals, olivine and garnet. Diffusional anisotropy of olivine is ignored. Initially, MnO in both phases were 0.2 wt%. As the two minerals come into contact, there will be diffusion to try to reach the equilibrium state. The partition coefficient (Mn)oiiv/(Mn)gt is assumed to be 0.59. The diffusivity in olivine is assumed to be 10 times that in garnet, resulting in a wider diffusion profile with a smaller slope in olivine.

Loomis T.P., Ganguly J., and Elphick S.C. (1985) Experimental determination of cation diffusivities in aluminosilicate garnets, II multicomponent simulation and tracer diffusion coefficients. Contrib. Mineral. Petrol. 90, 45-51. 

The distribution coefficients of the parent and daughter nuclides are important in U-series disequilibria. If the parent has a higher distribution coefficient than the daughter, its extraction from the matrix is retarded and the daughter/parent activity ratio in the melt can be greater than 1. Experiments have shown that Dy > Dj for garnet peridotites but Du spinel peridotites at low pressures. Due to experimental difficulties, Dro and Dpa are not directly known but are inferred to be very small. Therefore, it is reasonable to assume Dj, >Di and Du > Dp for both garnet peridotites and spinel peridotites. 

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