Mid-concentration distance

For a given garnet crystal, Wang et al. (1996) found that the mid-concentration distance in the rim is about 150/im (garnet radius is 2.1mm). Suppose the magma temperature was 1173 K, at which Dout is about 8 /im /s. Hence, the time required for garnet to ascend from mantle to the surface is... 

Next we turn to the inference of cooling history. The length of the concentration profile in each phase is a rough indication of (jDdf) = (Dot), where Do is calculated using Tq estimated from the thermometry calculation. If can be estimated, then x, Xc and cooling rate q may be estimated. However, because the interface concentration varies with time (due to the dependence of the equilibrium constants between the two phases, and a, on temperature), the concentration profile in each phase is not a simple error function, and often may not have an analytical solution. Suppose the surface concentration is a linear function of time, the diffusion profile would be an integrated error function i erfc[x/(4/Ddf) ] (Appendix A3.2.3b). Then the mid-concentration distance would occur at... 

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