A computational study of magnesium point defects and diffusion in forsterite

We have studied the formation and migration of point defects within the magnesium sub-lattice inforsterite using a combination of empirical and quantum mechanical modelling methodologies. Empiricalmodels based on a parameterised force field coupled to a high throughput grid computing infrastructureallow rapid evaluation of a very large number of possible defect configurations. An embedded clusterapproach reveals more accurate estimates of defect energetics for the most important defect configurations. Considering all defects in their minimum energy, equilibrium positions, we find that the lowest energy intrinsic defect is the magnesium Frenkel type, where a magnesium atom moves from the M1 site to form a split interstitial defect. This defect has 2 four-co-ordinated magnesium atoms located outside opposite triangular faces of an otherwise vacant M1 octahedron. The split interstitial defect is more stable than regular interstitials where magnesium is located in either of the two structurally vacant octahedral sites in the hexagonally close packed oxygen lattice. M1 vacancies are also found to form when iron(II) oxidises to iron(III). The energy of the defects away fromthe equilibrium positions allows the energy barrier to diffusion to be calculated.Wehave considered the migration of both magnesium vacancies and interstitials and find that vacancies are more mobile. When the contribution from the formation energy of the defects is included we arrive at activation energies for vacancy diffusion that are in agreement with experiment

A computer simulation study of the effect of pressure on Mg diffusion in forsterite

Computer simulation techniques were used to investigate the effect of pressure on magnesium diffusionin forsterite between 0 and 10 GPa. We studied the diffusion path along the c crystallographic axis (we always refer to the Pbnm system) via a vacancy mechanism. Using a Mott-Littleton approach withinthe code GULP, we were able to precisely map the diffusion path of a Mg vacancy and we found theactivation energy, E = 3.97 eV at 0 GPa (with Ef = 3.35 eV for the formation energy and Em = 0.62 eV for the migration) and E = 4.46 eV at 10 GPa (Ef = 3.81 eV and Em = 0.65 eV). Preliminary results using the supercell technique gave the same saddle point coordinates and energies. This saddle point of the Mg vacancy diffusion found with GULP was then introduced in an ab initio code, confirming the values of the migration energy both at 0 and 10 GPa. We were therefore able to estimate the activation volume (V) to be around 5 cm3/mol and d(V)/dP = 0. The effect of pressure applies mostly on defect formation and little on migration

Empirical determination of diffusion coefficients and geospeedometry

International audienceGeospeedometry allows to estimate the cooling rate (sinit) of metamorphic rocks at the beginning of the cooling history using diffusion data. But the choice of a diffusion activation energy (E) and a preexponential factor (D0) from experimental results can be difficult. We propose a method to obtain E directly from the rock itself by studying the variation of the average concentration of elements or isotopes (?C?) as a function of mineral grain size (d). An appropriate value of D0 can then be estimated using an existing compensation rule, a linear relationship between log D0 and E. Consequently, uncertainties on sinit are markedly reduced. All parameters of this analytical model and their sensitivity on sinit can be estimated from ?C? of the mineral grains under study. As a test we apply our model to a study by Edwards and Valley (1998)**** on 18O/16O fractionation between diopside and calcite in Adirondacks marbles, and find a cooling rate in agreement with previous works, without choosing experimental values for E and D0

Effect of pressure on the deformation of forsterite and of iron-free enstatite

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Strength of fayalite up to 8.5 GPa

International audienceA dense polycrystalline aggregate of synthetic fayalite (Fe2SiO4) was deformed up to 8.5 GPa at room temperature in the D-DIA press installed at the European Synchrotron Radiation Facility beamline ID06. Five successive shortening-lengthening cycles were performed at different pressures and up to a final strain of approximately 25% at a typical strain rate of about 10-5 s-1. Lattice stresses were quantified from ( hkl) reflections accessible with a 55-keV monochromatic beam. Combined stress and strain data show that during each cycle, fayalite deforms elastically before yielding at an axial strain close to 2%. This yielding occurs at a macroscopic stress (taken as the average of the estimated lattice stresses) of 1.5-2 GPa, irrespective of pressure. Very moderate stress hardening takes place beyond the yield point, and the average stress becomes almost constant after a strain of 5-6%, suggesting a low-temperature plastic regime. Lattice stresses estimated with (131), (130), and (022) reflections are always higher than stresses estimated with (111) and (112) by a factor of about 1.5. In addition, the (131) lattice stress becomes progressively lower than the (130) and (022) lattice stresses with increasing pressure, which suggests a possible change in dominant slip systems around 5-6 GPa. Combining our results with data from Chen et al. (Phys Earth Planet Inter 143-144:347-356, (2004), we determined a low-temperature plasticity flow law with an activation energy of 217 ± 25 kJ mol-1 and a Peierls stress at 0 GPa, σ p0 = 3.92 ± 0.02 GPa, that is consistent with dislocation motion being limited by discrete obstacles. The pressure dependence is almost entirely accounted for by the Peierls stress, with d σ p/d P = G'/ G 0, where G' is the derivative of G 0, the shear modulus. Our results suggest that fayalite has a smaller pressure dependence of low-temperature plasticity than (Mg0.9Fe0.1)2SiO4 and that the transition between low-temperature plasticity and high-temperature creep occurs at lower temperatures and lower stresses in fayalite than in Mg-rich olivines. An increase in iron content in olivine may therefore enhance ductility and lower the effect of pressure on creep, resulting in a viscosity contrast of up to 50 between fayalite and (Mg0.9Fe0.1)2SiO4 at pressures and temperatures of the lithospheric mantle

Three water sites in upper mantle olivine and the role of titanium in the water weakening mechanism

Infrared spectroscopy on synthetic olivines has established that there are at least\ud four different mechanisms by which hydrogen is incorporated into the crystal structure.\ud Two mechanisms occur in the system MgO-SiO2-H2O associated with silicon and\ud magnesium vacancies, respectively. A third mechanism is associated with trivalent cation\ud substitution, commonly Fe3+ in natural olivine, while the fourth mechanism, which is\ud the one most prevalent in natural olivines from the spinel-peridotite facies of the Earth’s\ud upper mantle, is associated with Ti4+ [Berry et al., 2005]. Here first principles calculations\ud based on density functional theory are used to derive the structure and relative energies\ud of the two defects in the pure MgO-SiO2-H2O system, and possible hydrogen-bearing\ud and hydrogen-free point defects in Ti4+-doped forsterite. Calculated structures are used to\ud compare the predicted orientation of the O-H bonds with the experimentally determined\ud polarization. The energies are used to discuss how different regimes of chemical\ud environment, temperature (T), pressure (P), and both water content and water fugacity\ud ( fH2O), impact on which of the different hydroxyl substitution mechanisms are\ud thermodynamically stable. We find that given the presence of Ti impurities, the most\ud stable mechanism involves the formation of silicon vacancies containing two protons\ud charge balanced by a Ti4+ cation occupying an adjacent octahedral site. This mechanism\ud leads to the water-mediated formation of silicon vacancies. As silicon is known to be the\ud most slowly diffusing species in olivine, this provides a credible explanation of the\ud observed water weakening effect in olivine