Interdiffusion in olivine

The diffusivity of a species in one phase depends on the composition of the phase. For example, at a given temperature, pressure, and fo, Fe-Mg interdiffusivity in olivine increases rapidly with the concentration of Fa component. Figure 3-3 7a presents some data that shows that In D is roughly linear to Xpa, although there are also data showing that the relation is curved. 

Fe-Mg interdiffusion in olivine along the c-axis (fastest diffusion direction) is... 

To treat this more quantitatively, it is necessary to know the behavior of Fe-Mg interdiffusion in olivine. Olivine crystals are usually equidimensional. The diffusion is anisotropic with Dc -- 4Da -- 5Db (Buening and Buseck, 1973), where the subscripts refer to crystallographic directions. Although the difference in diffusivity is not very large, for simplicity, diffusion in olivine is often treated to occur only along the c-axis. The Fe-Mg interdiffusivity in olivine along the c-axis at 1253-1573 K may be expressed as (Equation 3-147)... 

Jaoul O., Bertran-Alvarez Y., Eiebermann R.C., and Price G.D. (1995) Ee-Mg interdiffusion in olivine up to 9 GPa at T = 600-900°C experimental data and comparison with defect calculations. Phys. Earth Planet In. 89, 199-218. 

Figure 3-37 Compositional dependence of diffusivities. (a) Fe-Mg interdiffusivity along the c-axis in olivine as a hinction of fayalite content at P — O.l MPa and log /b2 =-6.9 0.1. Diffusion data are extracted using Boltzmann analysis. Some of the nonsmoothness is likely due to uncertainty in extracting interdiffusivity using the Boltzmann method. Data are from Chakraborty (1997). (b) Ar and CO2 diffusivity in melt as a function of H2O content. Data are from Watson (1991b) and Behrens and Zhang (2001).

Example 4.1. Suppose olivine and garnet are in contact and olivine is on the left-hand side (x<0). Ignore the anisotropic diffusion effect in olivine. Suppose Fe-Mg interdiffusion between the two minerals may be treated as one dimensional. Assume olivine is a binary solid solution between fayalite and forsterite, and garnet is a binary solid solution between almandine and pyrope. Hence, Cpe + CMg= 1 for both phases, where C is mole fraction. Let initial Fe/(Fe- -Mg) = 0.12 in olivine and 0.2 in garnet. Let Xq = (Fe/Mg)gt/ (Fe/Mg)oi = 3, >Fe-Mg,oi = 10 ° mm+s, and Dpe-Mg,gt =... 

The other major category of D values are termed interdiffusion or chemical diffusion coefficients. Experimentally, Ci does change significantly and D is a function of Ci. Diffusion of one or more chemical species is dependent on the opposing diffusion of another species in order to maintain a constant matrix volume and/or electrical neutrality. The diffusion in olivine of Mg in one direction and the complementary diffusion of Fe in the opposite direction represent one example. Rarely does this type of experiment employ the use of isotopically labeled species. However, in some cases isotopically-enriched H2O (T, D and/or O) has been used where the composition of the solid (melt) became significantly modified by incorporation of water into the structure. 

Mn Mgi )2Si04 olivine mixture obtained by Morioka (1981). The concentration profiles are symmetric, indicating that the diffusivities are independent of the concentration of the diffusing ion. On the contrary, possible asymmetry in the diffusion profiles indicate that concentration depends significantly on the diffusing cations. In this case, the interdiffusion coefficient can be obtained by the Boltzmann-Matano equation ... 

Other general cases in binary systems are referred to as interdiffusion or binary diffusion. For example, Fe-Mg diffusion between two olivine crystals of different Xpo (mole fraction of forsterite Mg2Si04) is called Fe-Mg interdiffusion. Inter-diffusivity often varies across the profile because there are major concentration changes, and diffusivity usually depends on composition. 

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