Olivier Jaoul

Silicon diffusion in San Carlos olivine

Abstract The diffusion of 30Si in single crystals of San Carlos olivine has been measured. To achieve diffusion experiments the olivine samples were coated with a thin Mg2SiO4 layer and then heated between 1130°C and 1530°C under controlled oxygen partial pressures in the range 10−5 to 10−1 Pa. The annealing durations ranged from 1 h 30 min to 150 h, yielding diffusion lengths of 150–425 10−10 m. Diffusion profiles were analysed using the α-RBS technics (Rutherford Backscattering Spectroscopy of α-particles). The results show that the silicon diffusion coefficient obeys the law D = D 0 ( p O 2 p 0 ) m exp (−E/RT) with E = 291 ± 15 kJ mole−1, m ∼ −0.19 ± 0.1 and ln(D0) = − 29.3 ± 1 where D is in m2 s−1, pO2 is the oxygen partial pressure, p0 the room pressure and R the gas constant. We deduce from these results that DSi ⪡ DOx ⪡ DMg, DFc in the T–pO2 domain investigated, but extrapolation towards low pO2 and temperatures suggests that it is not impossible for DSi to be larger than DOx owing to opposite pO2 dependences. The negative value of m indicates a probable interstitial mechanism for silicon diffusion. Results show that silicon diffusion in San Carlos olivine is enhanced by ∼ 30 relative to pure forsterite in the T–pO2 range studied.

FeMg interdiffusion in olivine up to 9 GPa at T = 600–900°C; experimental data and comparison with defect calculations

Abstract Interdiffusion data at high pressures are needed to provide good estimates of the closure temperatures of geothermometers based on FeMg exchange in olivine in contact with other phases and to understand the pressure dependence of high-temperature deformation in olivine. We report here measurements of the interdiffusion coefficient of Fe Mg in San Carlos olivine of mean composition Mg (Mg + Fe) = 0.90 , in the range of temperatures T = 600–900°C and pressures P = 0.5–9 GPa. The measurements were performed by preparing olivine samples covered by a thin layer of fayalite. These specimens were annealed in a uniaxial split-sphere apparatus (USSA-2000). The FeMg interdiffusion profiles were analysed by Rutherford back-scattering (RBS). The results yield a pre-exponential factor D 0 = 7.7 × 10 −8 cm 2 s −1 (7.7 × 10 −12 m 2 s −1 ), and an activation energy E ∗ = 147 ± 58 kJmol −1 (or 62 ± 58 (2 SD) kJ mol −1 if a p O 2 1 6 correction is performed), corresponding to the expression D = D 0 exp ( −E ∗ RT ) exp (ϵX Fe )exp ( −PV ∗ RT ) . Our data are fitted best with ϵ = 3; X Fe = Fe (Fe + Mg) is between zero and one (in the present experiments X Fe is around 0.1), P is the pressure and V ∗ is found to be −0.5 ± 0.6 cm 3 mol −1 (or 1 ± 0.9 cm 3 mol −1 if a p O 2 1 6 correction is performed), i.e. about zero in the P and T range investigated. Comparisons between the present results, obtained at relatively low temperature under extrinsic conditions for diffusion, with other FeMg interdiffusion data at high temperature (1125°C or more) under intrinsic conditions allow us to deduce that the migration activation volume for point defects is V M ∗ ≈ 0 whereas that for formation is V F ∗ ≈ 5.5 cm 3 mol −1 . This has important implications for the creep sensitivity to pressure. Numerical simulations involving energy minimizations and performed with the CASCADE and PARAPOCS codes confirm these conclusions: one finds V M ∗ ≈ 0 and V F ∗ ≈ 4.8 cm 3 mol −1 . The activation energy E ∗ deduced from the experiments as well as the pre-exponential factor D 0 now permit precise estimation of the closure temperatures of geothermometers based on the FeMg exchange between olivine and spinel.

High‐temperature deformation of diopside single crystal: 1. Mechanical data

Laboratory deformation experiments were carried out on diopside single crystals. Creep tests were made in a dead load apparatus at temperatures T = 1020 to 1320°C, axial compressive stresses σ = 50 to 170 MPa with strain rates ( e˙) ranging from 2×10−9 s−1 to 4×10−7 s−1. The specimens were oriented such that mechanical twinning was not possible. The experiments were designed to activate {110}1/2〈a±b〉 slip systems. Our results demonstrate that they are the major operative systems for T > 1000°C and appear to be predominant over the (100)[c] slip system. The mechanical data are fitted to a power law e˙ = A σn exp(−E*/RT). An inversion method was used to determine the parameter In (A), the activation energy E*, and the stress exponent n. Below a critical temperature Tc ≃ 1130–1140°C, E* is found to be 440 ± 30 kJ/mol associated with the {110}1/2〈a±b〉 slip systems, activated symmetrically without any contribution from the (100)[c] system (orientation [2]); E* is found equal to 740±30 kJ/mol if all three systems have the same resolved shear stresses (orientation [1]). For T > Tc, values of E* drop to 50±15 and 85±30 kJ/mol for orientations [2] and [1], respectively, so that the creep law of diopside becomes nearly temperature independent. The law derived from the orientation [2] crystals could be consistent with natural deformations. For this orientation and within the range of temperatures covered, n is 6.5±0.4. The strong decrease in the activation energy at Tc may be ascribed unambiguously to the occurrence of partial melting leading to microdroplets which pin the mobile dislocations (Ingrin et al., this issue). The high value found for the stress exponent (n) in the creep law suggests that clinopyroxene is softer than olivine at high stresses (at T = 900°C, stress σ ≥ 20 MPa and e˙≥10−15 s−1), while olivine is softer at lower stresses. This competence inversion is predicted to occur within the ranges of stresses and strain rates expected in the lower crust and upper mantle.

Calcium self-diffusion in natural diopside single crystals

We have measured the diffusion coefficient of 44Ca along and perpendicular to c direction in natural Fe-bearing (∼2 at.%) diopside single crystals. Specimens were annealed at temperatures ranging from 1000 to 1250°C, with controlled oxygen fugacity. Diffusion profiles were analysed by Rutherford Back-Scattering Spectrometry (RBS) of α-particles. The diffusion of Ca is isotropic along c and b directions. In addition, the results clearly show two distinct diffusional regimes for the natural diopside, revealed by silica precipitates occurrence in the diopside matrix when T ≥ 1150°C. In this case the oxygen partial pressure pO2 does not influence the self-diffusion coefficient which is characterized by the activation energy E = 396 ± 38 kJ/mol. For T ≤ 1100°C the diffusional process has a lower activation energy (E = 264 ± 33 kJ/mol) and varies as (pO2)−0.14±0.01 in the investigated range (from 10−16 atm to 10−6 atm). These results are consistent with previously reported results on electrical conductivity (Huebner and Voigt, 1988) and high temperature plastic deformation of natural diopside single crystals (Jaoul and Raterron, 1994). According to the point defects model, elaborated by Jaoul and Raterron (1994), the diffusional mechanism of Ca should be essentially interstitial. Furthermore, this mechanism should be the same for different diopside samples with iron content ranging from 0.4 to 2.42 at.%. Indeed, for Ca diffusion in synthetic diopside (0.4 at.% Fe) the activation enthalpy is very similar (281 ± 26 kJ/mol, Dimanov and Ingrin, 1995). On the other hand, the Fe content indoubtly influences the preexponential factor. The present paper reports Ca self-diffusion in diopside as a function of T, pO2 crystallographic orientation, and Fe content. In fact, among all diffusion coefficients previously reported in diopside, but Si, DCa is the lowest. Thereby, Ca should be a kinetically limiting species for diffusion-controlled processes such as plastic deformation and cation exchanges. For instance, Ca self-diffusion controls CaMg exchanges between pyroxenes. Then, our results could be helpful to better understand the closure behaviour (Dodson, 1973, 1976) of the Clinopyroxene-Orthopyroxene geothermometer.

Silicon self-diffusion in quartz and diopside measured by nuclear micro-analysis methods

Diffusion coefficients of silicon have been measured for synthetic quartz and natural diopside, using two micro-analysis techniques, Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis (NRA). Diffusion experiments on quartz have been performed between 1350°C and 1600°C for durations of a few days to a few minutes, at high pressure (2 GPa) in the β-quartz field, as well as at atmospheric pressure on metastable β-quartz. Both experiments give approximately the same results and no pressure effect on silicon diffusion is observed. We find the following diffusion coefficient for silicon in synthetic quartz: (cm2s−)=2.9 × 107exp−746kJ mol−1RT In the case of diopside, we have used a natural gem-quality single crystal. Annealings were performed between 1040°C and 1250°C for durations ranging from 1 month to 6 days under controlled atmosphere. From these preliminary results, we obtain (cm2s−)=2.3 × 10−10exp−211kJ mol−1RT which is not corrected for an eventual pO2 dependence. On the basis of our results, we propose an interstitial diffusion mechanism for silicon atoms in quartz based on Frenkel pairs of defects, and we suggest also the possibility of such an interstitial mechanism occurring in diopside.

High temperature deformation of diopside IV: predominance of {110} glide above 1000°C

Abstract Gem quality single crystals of diopside were deformed in orientations labelled [3] and [4] selected to promote either (100)[010] and/or (010)[100], and {110}[001], respectively. Transmission electron microscopy (TEM) investigations performed on samples deformed in orientation [3] show that (100)[010] was activated and [010] dislocations are in climb configurations. A number of 1 2 〈110〉 dislocations are also detected although the Schmid factors of {110} 1 2 〈110〉 glide systems were very low. These dislocations also lie in climb configurations. The selected thermodynamic conditions, especially the partial pressure of oxygen, allowed a large amount of partial melting to occur leading to non-intrinsic creep data. In samples deformed in orientation [4], {110}[001] glide was activated with a limited amount of partial melting. TEM investigations show that most of the dislocations are straight, and of screw character parallel to [001]. A few 1 2 〈110〉 dislocations in climb configurations are also detected. For an applied stress σ = 147 MPa and at PO2 ≈ 2.7 × 10−16 MPa the creep law for {110}[001] glide is ln ϵ = 27.33 – 518/RT ( ϵ in s −1 , R = 8.32 kJ mol −1 K −1 ). Comparison of all the data collected so far on high temperature creep of diopside indicate that the easiest glide systems above 1000°C are {110} 1 2 〈110〉 . They are followed in activity by {110}[001], then by (100)[001]. Other potential systems appear to be appreciably stronger and should remain marginal in natural deformation of diopside and similar C2 c clinopyroxenes. Climb of 1 2 〈110〉 dislocations might become relevant at temperature above 1200°C.

Oxygen and silicon self-diffusion in natural olivine at T = 1300°C

Abstract Oxygen and silicon self-diffusion in natural olivine single crystals (Mg 0.89 Fe 0.11 ) 2 SiO 4 from San Carlos, Arizona, have been measured for the first time at T = 1300°C in controlled oxygen partial pressure pO 2 ranging from 10 −4 to 10 Pa. Polished and chemically-etched specimens were heated for several hours in a gas mixture H 2 /CO 2 or H 2 /H 2 18 O. The latter gas mixture provides both the controlled pO 2 and the isotopic reservoir for the 18 O diffusion across the gas-solid interface. For 30 Si diffusion, a thin layer of isotopic forsterite Mg 2 30 SiO 4 (few hundreds of angstroms) was deposited onto the olivine surface. Diffusion profiles for oxygen and silicon were determined using the nuclear reaction 18 O(p, α ) 15 N and Rutherford back-scattering of 2 MeV α particles, respectively. The diffusion coefficients are D ox = 10 −18 ± 0.6 m 2 s −1 for oxygen and D Si = 10 −20 m 2 s −1 for silicon. We conclude from these measurements on San Carlos olivine at T = 1300°C that: (1) Si is the slowest diffusing species in natural olivine, as it is in forsterite, and (2) 30 Si and 18 O diffuse 30 to 200 times faster in olivine than in forsterite.

Surface destabilization and laboratory-induced non-stoichiometry in San Carlos olivine

Annealing experiments on natural olivine (Mg1-xFex)2SiO4 (with x≈0.11) crystals (San Carlos, Arizona, spinel-lherzolite context) have been performed between T=1,100° C and 1,500° C for oxygen partial pressures pO2=10−3 to 10−13 bar and times of 1 to 140 h in CO/CO2 or H2/H2O gas mixtures. Even specimens annealed within the T-pO2theoretical stability field (TSF) calculated for stoichiometric olivine (Nitsan 1974) show systematic alterations developed within the first few microns of the surface of the crystals. Pyroxene crystals or melt form on the original olivine surface even at T=1,100° C, with preference of pyroxene when T<1,350° C and SiO2-rich glass if T>1,350° C. This glass (rhyolite-like) can concentrate calcium from the starting olivine, and aluminum when Cr-Al spinels are present as inclusions. These observations are in contradiction with the TSF. They are obviously due to the presence of platinum used as a container of our samples, even if the contact between olivine and platinum is very weak. Rapid surficial diffusion of iron toward platinum (or via the gas phase) induces a Fe-depleted surface. According to the TSF, this more forsteritic surface should have a wider pO2 range of stability. This is not the case, just because this situation is largely out of equilibrium. This iron loss induces a departure from cationic stoichiometry: (Mg, Fe)2(1−δ), SiO4 with δ small and positive. We extended the model that Nakamura and Schmalzried (1983) (N.S.) developed for fayalite (x=1) to our natural olivine composition, under the assumption that the majority defects are magnesium vacancies, Fe3+ occupying octahedral and tetrahedral sites, and the more complex neutral defect corresponding to Coulombic attraction between neighboring Fe3+ ions. We have recalculated the olivine stability field in pO2 vs. δ space at T=1,300° C using this model for x≈0.1 (its extreme limit of validity) and conclude that olivine is stable only in a very narrow range in pO2 which depends on δ. The calculation shows also that when olivine has nearly cationic stoichiometry (δ=0) as we believe for our starting material, the pO2 range of stability is narrower than indicated by the TSF. In particular, it explains why Fe precipitates from the olivine (δ=0) (in absence of any other precipitation of SiO2-rich phases) between 10−11 and 10−13 bar at 1,300° C; this was not predicted by the TSF. Magnetite or iron precipitates also coexist with SiO2-rich exsolutions or pyroxene when pO2 is close to the upper or lower boundaries of the TSF, respectively. The N.S. model may have important implications for the interpretation of the existence of partial melting and/or the low-viscosity/low velocity zone in the upper mantle.

FeMg interdiffusion in single crystal olivine at very high pressure and controlled oxygen fugacity: technological advances and initial data at 7 GPa

Abstract The interdiffusion of iron and magnesium in natural single crystals of San Carlos olivine (Fo90) has been determined using a 2000 ton uniaxial split-sphere apparatus (USSA-2000) and Rutherford back-scattering spectrometry (RBS). Advances in the microanalysis technique made it possible to perform high-pressure experiments for short-duration runs at low temperatures in a controlled chemical and mechanical environment. Olivine crystals were coated with a thin film of fayalite, inserted in an Fe capsule and placed inside an 18 mm pyrophyllite octahedral cell assembly. After experiments at 7 GPa and 900°C for 6 h at pO2 ≈ 10−14 bar, the specimens were recovered with very few fractures and chemically unaltered. Analysis of RBS spectra from these crystals yields a value of DFeMg = 10−13.7 cm2 s−1. Comparison of this value with previous data at atmospheric pressure suggests that the activation volume for FeMg interdiffusion is V FeMg ∗ ≈ 2.2 ± 0.9 cm 3 mol −1 which, if proven correct, has important implications for electrical conductivity and creep in the upper mantle.

Early partial melting of diopside under high pressure

Abstract Early partial melting (EPM) in pyroxenes begins by the precipitation of tiny droplets (0.1 μm or less) of a molten phase highly enriched in silica. At room pressure, EPM starts at temperatures markedly lower than the pyroxene solidus temperatures approximately (250°C below). High-pressure, high-temperature experiments (up to 1.9 GPa and 1309°C) were carried out in a piston-cylinder apparatus on diopside single crystal bearing 1.2 wt.% FeO, to determine the influence of pressure on this phenomenon. The systematic transmission electron microscopy investigation of the samples annealed at high-T, high-P reveals that EPM occurs up to P ≈ 1.5 GPa above 1208°C, at pO2 ranging from 2.0 × 10−17 and 2.5 × 10−16 MPa. These T-P conditions are well below the solidus temperature of pure CaMgSi2O6 (1594°C at 1.5 GPa). For pressures above 1.7 ± 0.2 GPa, no EPM precipitates are found in sample annealed for 2 h 30 min at temperatures up to 1309°C.