At equilibrium, the chemical composition of each phase in a rock should be uniform, unzoned. If there is compositional zoning in a mineral, the chemical diffusion that would have homogenized the mineral has not occurred or at least has not been completed. Using laboratory measurements of diffusion coefficients, it is possible to place constraints on the time-temperature history of that crystal.

For example, Figure 22 shows a gradient in the chemical composition of an olivine crystal from an andesite lava, with more Mg in the center of the crystal and less Mg at its surface. The petrologists who collected the rock and the chemical data postulated that the Mg-zoning of the olivine was caused by diffusion when the composition of the host magma was changed by magma mixing. They used diffusion modeling of the Mg-zonation to estimate how much time passed between the magma mixing and the eruption of the magma.

You can use the olivine diffusion data shown in Figure 23 and the sphere diffusion model of Figure 21 to make a rough estimate of their result. Assume that the olivine crystal is a sphere with the uniform composition of approximately Fo(81)Fa(19) at the time of mixing and that the resulting andesite had a temperature of 950°C. Assume further that there is no crystal growth or dissolution. How long would it take the olivine to completely homogenize by diffusion to the the new equilibrium composition of Fo(71)Fa(29)?

Yes. Using D = 1.61 x 10^{-18} (m^{2}/s) and a radius (**a**) of 150 µm, the homogenization time estimate from **Dt/a ^{2}** = 0.6, is 266 years. If you used the sliders in Figure 21, a radius of 0.1 mm gives a homogenization time of about 100 years and a radius of 0.2 µm gives a homogenization time of close to 500 years.

No. You can answer this question by using the result from the preceding page that **Dt/a ^{2}** >= 0.6 is needed for the homogenization of a sphere by diffusion. Get the radius (

**a**) of the sphere from Figure 22. Enter the Arrhenius equation values for Fe-Mg diffusion in olivine from Figure 23 to get D at 950°C from Figure 21. Try again.

Yes. Using D = 1.61 x 10^{-18} (m^{2}/s) and a radius (**a**) of 150 µm, the homogenization time estimate from **Dt/a ^{2}** = 0.6, is 266 years. If you used the sliders in Figure 21, a radius of 0.1 mm gives a homogenization time of about 100 years and a radius of 0.2 µm gives a homogenization time of close to 500 years.

No. Using D = 1.61 x 10^{-18} (m^{2}/s) and a radius (**a**) of 150 µm, the homogenization time estimate from **Dt/a ^{2}** = 0.6, is 266 years. If you used the sliders in Figure 21, a radius of 0.1 mm gives a homogenization time of about 100 years and a radius of 0.2 µm gives a homogenization time of close to 500 years.

**Dt/a**.

^{2}**Click on Figure 22**then

**Click on the "Show Sphere Dta2"**button. The spherical model composition profiles do not exactly match the observed profiles, but they are close. Using

**Dt/a**= 0.01 yields a time of 4 years. Using

^{2}**Dt/a**= 0.03 yields a time of 13 years.

^{2}