Aluminium diffusivity in clinoenstatite

The diffusion in high clinoenstatite down the [101]^*direction was determined to be 6 x 10^-11 cm² s^-1 at 15 GPa and 1700 °C, which is 3 – 4 orders of magnitude faster than the diffusion of the majorite component in garnet.

The reported diffusivity is a lower limit, since the exact time required before a majoritic nucleus formed is unknown. However, the measured profile used in the fit model was the longest that was found in the sample and thus probably also corresponds to one of the nucleus that formed first during the experiment. The region around the measured precipitate is relatively devoid of other precipitates, which also indicates that the

precipitate from which the profile was measured nucleated during an early stage of the experiment. Experiment S4391 (figure 6.6) was run at the same conditions, but only for 1 hour. The presence of garnet precipitates in this experiment indicate the first precipitates nucleate within the first hour. Since the run duration of experiment S4378 was 19 hours, it is thought that the error due to the uncertainty about the exact time of nucleation of the precipitates is not significant.

To project the diffusion coefficients to subduction zone conditions one needs the activation energy for diffusion of aluminium in pyroxene (or ideally high clinoenstatite). There is, however, a general lack of diffusion data on aluminium in minerals in the literature, the only data on aluminium diffusion in diopside is by Sautter et al.

(1988) and Jaoul et al. (1991) over a limited temperature range between 1000 – 1180 °C at 1 bar. They obtain an activation energy of 273 kJ mol^-1. The activation enthalpy, describing the temperature dependence, for diffusion of aluminium in high clinoenstatite will probably be higher, since the experiments in this study were conducted at a pressure of 15 GPa. Therefore a typical range of activation enthalpies have been assumed, i.e. between 275 kJ mol^-1 and 350 kJ mol^-1, corresponding to an activation volume for the diffusion of aluminium in clinoenstatite between 0 – 5 cm³ mol^-1. For the upper part of the subducting slab at a temperature of 1000 °C (Emmerson and McKenzie 2007), corresponding to the subducted oceanic crust, it gives an aluminium diffusion coefficient in the range of 5 x 10^-16 cm² s^-1 to 6 x 10^-15 cm² s^-1. For the middle to lower part of the subducting slab at 1400 °C (Emmerson and McKenzie 2007), corresponding to the subducted mantle lithosphere, the range is smaller due to a smaller temperature difference between the extrapolated temperature and the experimental condition, and is in the range between 3 x 10^-12 cm² s^-1 and 4 x 10^-12 cm² s^-1. Again this shows that diffusion of aluminium in

high clinoenstatite (in the [101]^* direction) is significantly faster than the diffusion of the majorite component in garnet, i.e. 3 – 4 orders of magnitude slower. Since the distance over which a component can diffuse can be approximated by x = √(Dt), with t the time for which the component is allowed to diffuse, one can calculate the distance over which aluminium can diffuse in pyroxene. At 1000 °C and 10 Myr, which is a typical time scale for subduction (see chapter 5), this is between 0.5 – 1.5 cm and at 1400 °C between 20 – 30 cm. If grain boundary diffusion plays a significant role, the values will be a factor 100 larger, i.e. at the meter scale at 1000 °C and at the decameter scale at 1400 °C.

Comparing the absolute values of the diffusion study by Jaoul et al. (1991) to the data presented in this study shows that our data is significantly faster, Jaoul et al. obtained a diffusivity of 3.7 x 10-17 cm² s^-1 at 1180 °C at 1 bar and our study 6 x 10^-11 cm² s^-1 at 1700 °C. This would correspond to an activation energy for diffusion of aluminium in clinopyroxene of 655 kJ mol^-1 (when the effect of pressure is neglected), which is anomalously high, or when using their activation energy for Al diffusion this corresponds to an activation volume for diffusion of aluminium in clinopyroxene of -25 cm³ mol^-1, which would mean that with increasing pressure diffusion would become faster. From this it can be concluded that there is a large difference in diffusivity between that of aluminium in HP clinoenstatite at high pressure and that of aluminium diffusion in diopside at low pressure, which possibly can be attributed to different diffusion mechanism in both clinopyroxene phases at the different conditions or a strong dependence of the diffusivity of aluminium in clinopyroxene on the calcium content.

6.6 Conclusions

• Twins and stacking faults on (100) are pervasive throughout the enstatite sample after quenching and decompression from 15 GPa and 1700 °C. The displacement vector across the stacking fault boundary was determined to be <½ ½ w>, most likely being ½ <111>. This displacement vector can be explained be the transformation of high clinoenstatite to low clinoenstatite.

• The twin boundaries and stacking faults that formed in high clinoenstatite parallel to the (100) planes during the transition from Pbca orthorombic to the C2/c high pressure phase seem to have acted as nucleation sites for majoritic garnet precipitates.

• In the case that there was a well defined long axis of the garnet precipitate in the observed TEM section, this long axis was predominantly oriented parallel to (100) and the twin planes / stacking faults in low clinoenstatite.

• There is no unique topotactic relationship between the low clinoenstatite host and the majoritic garnet precipitates. However, a dominant linear relationship was found with the <111> direction in garnet being parallel to the [001] direction in low clinoenstatite. This direction is probably controlled by the diffusivity of silicon in pyroxene and not by minimization of strain energy at the interface between the clinoenstatite host and majoritic garnet precipitates. The latter is probably due to the absence of a well defined oxygen close packing direction in garnet.

• The diffusivity of aluminium in C2/c HP-clinoenstatite in the [101]^* direction at 15 GPa and 1700 °C was determined to be at least 6 x 10^-11 cm² s^-1, which is 3 – 4 orders of magnitude faster than the diffusivity of the majorite component in garnet at the same conditions.

• There is a large difference in the diffusivity of aluminium in clinopyroxene at high pressure and the diffusivity of aluminium in clinopyroxene at room pressure, which eventually indicates a change in diffusion mechanism with pressure or a strong dependence of the diffusivity of aluminium on calcium content in clinopyroxene.

6.7 References

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Putnis, A. (1992), An Introduction to Mineral Sciences. Cambridge University Press, Cambridge Rauch, M. (2000), Der Einbau von Wasser in Pyroxene.

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Ich erkläre hiermit, dass ich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfmittel angefertigt habe. Die aus fremden Quellen direkt oder indirekt übernommenen Gedanken sind als solch kenntlich gemacht.

Die Arbeit wurde bisher weder im Inland noch im Ausland in gleicher oder ähnlicher Form als Dissertation eingereicht und ist als Ganzes auch noch nicht veröffentlicht.

Ferner erkläre ich hiermit, dass ich nicht bereits anderweitig mit oder ohne Erfolg versucht habe, eine Dissertation einzureichen oder mich der Doktorprüfung zu unterziehen.

Ulm, 29. März 2012

Willem Louis van Mierlo