Figure 22. Fe-Mg Zoning in Olivine Crystal from an Andesite. The forsterite content as a function of distance across a relatively equant, small olivine crystal is shown as a red line. Click on the diagram to see a larger version with more information.
Figure 23. Arrhenius fit to Fe-Mg Olivine Diffusion Data. The base 10 logarithm of the Fe-Mg interdiffusion coefficient for olivine is shown in red as a linear function of 1000/T. Click on the diagram to see a larger version with more information.
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 (m2/s) and a radius (a) of 150 µm, the homogenization time estimate from Dt/a2 = 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/a2 >= 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 (m2/s) and a radius (a) of 150 µm, the homogenization time estimate from Dt/a2 = 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 (m2/s) and a radius (a) of 150 µm, the homogenization time estimate from Dt/a2 = 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.
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/a2 = 0.01 yields a time of 4 years. Using Dt/a2 = 0.03 yields a time of 13 years.
