An experimental study of Ostwald ripening of olivine and plagioclase in silicate melts: implications for the growth and size of crystals in magmas

We carried out an experimental study to characterize the kinetics of Ostwald ripening in the forsterite-basalt system and in the plagioclase (An₆₅)-andesite system. Eight experiments were done in each system to monitor the evolution of mean grain size and crystal size distribution (CSD) with time t; the experiments were performed in a 1-atmosphere quench furnace, at 1,250°C for plagioclase and 1,300°C for olivine. Very contrasted coarsening kinetics were observed in the two series. In the plagioclase series, the mean grain size increased as log(t), from ≈3 μm to only 8.7 μm in 336 h. The kinetic law in log(t) means that Ostwald ripening was rate-limited by surface nucleation at plagioclase-liquid interfaces. In the olivine series, the mean grain size increased as t ^1/3, from ≈3 μm to 23.2 μm in 496 h. A kinetic law in t ^1/3 is expected when Ostwald ripening is rate-limited either by diffusion in the liquid or by grain growth/dissolution controlled by a screw dislocation mechanism. The shape of olivine CSDs, in particular their positive skewness, indicates that grain coarsening in the olivine experiments was controlled by a screw dislocation mechanism, not by diffusion. As the degrees of undercooling ΔT (or supersaturation) involved in Ostwald ripening are essentially <1°C, the mechanisms of crystal growth identified in our experiments are expected to be those prevailing during the slow crystallisation of large magma chambers. We extrapolated our experimental data to geological time scales to estimate the effect of Ostwald ripening on the size of crystals in magmas. In the case of plagioclase, Ostwald ripening is only efficient for mean grain sizes of a few microns to 20 μm, even for a time scale of 10⁵ years. It can, however, result in a significant decrease of the number of small crystals per unit volume, and contribute to the development of convex upwards CSDs. For olivine, the mean grain size increases from 2–3 μm to ≈70 μm in 1 year and 700 μm in 10³ years; a mean grain size of 3 mm is reached in 10⁵ years. Accordingly, the rate of grain size-dependent processes, such as compaction of olivine-rich cumulates or melt extraction from partially molten peridotites, may significantly be enhanced by textural coarsening.     

Growth of multilayered polycrystalline reaction rims in the MgO–SiO<Subscript>2</Subscript> system,part II: modelling

Part I of this contribution (Gardés et al. in Contrib Mineral Petrol, 2010) reported time- and temperature-dependent experimental growth of polycrystalline forsterite-enstatite double layers between single crystals of periclase and quartz, and enstatite single layers between forsterite and quartz. Both double and single layers displayed growth rates decreasing with time and pronounced grain coarsening. Here, a model is presented for the growth of the layers that couples grain boundary diffusion and grain coarsening to interpret the drop of the growth rates. It results that the growth of the layers is such that (Δx)² ∝ t ^1−1/n , where Δx is the layer thickness and n the grain coarsening exponent, as experimentally observed. It is shown that component transport occurs mainly by grain boundary diffusion and that the contribution of volume diffusion is negligible. Assuming a value of 1 nm for the effective grain boundary width, the following Arrhenius laws for MgO grain boundary diffusion are derived: log D _gb,0^Fo (m²/s) = −2.71 ± 1.03 and E _gb^Fo = 329 ± 30 kJ/mol in forsterite and log D _gb,0^En (m²/s) = 0.13 ± 1.31 and E _gb^En = 417 ± 38 kJ/mol in enstatite. The different activation energies are responsible for the changes in the enstatite/forsterite thickness ratio with varying temperature. We show that significant biases are introduced if grain boundary diffusion-controlled rim growth is modelled assuming constant bulk diffusivities so that differences in activation energies of more than 100 kJ/mol may arise. It is thus important to consider grain coarsening when modelling layered reaction zones because they are usually polycrystalline and controlled by grain boundary transport.     

Thermochemistry of sulfide liquids III: Ni-bearing liquids at 1 bar

Experiments were performed in the system O–S–Fe–Ni designed to extend our understanding of the chemistry of sulfide liquids. Results indicate that adding nickel to Fe-rich sulfide liquids in equilibrium with silicate liquids extends their stability field to much higher oxygen fugacities and lower sulfur fugacities. Increasing Ni/Fe at a given temperature and sulfur and oxygen fugacity is accompanied by a significant decrease in the oxygen content of the sulfide liquid. Results of these experiments are combined with data from the literature to calibrate an associated regular solution model for O–S–Fe–Ni liquids. This model represents a complete refit of the associated regular solution model of Kress (Contrib Mineral Petrol 139:316–325, 2000). The resulting model is combined with the olivine solution model of Hirschmann (Am Mineral 76:1232–1248, 1991) to explore the effect of variations in oxygen and sulfur fugacities on the distribution of Fe and Ni between olivine and sulfide liquid. Predicted olivine–sulfide distribution trends parallel those observed by Gaetani and Grove (Geochim Cosmochim Acta 61:1829–1846, 1997), Gaetani and Grove (Earth Planet Sci Lett 169:147–163, 1999), Brenan and Caciagli (Geochim Cosmochim Acta 64:307–320, 2000) and Brenan (Geochim Cosmochim Acta 67:2663–2681, 2003), but are systematically offset toward lower predicted Ni in the sulfide. Nevertheless our results are consistent with the assertion that low K _D ^os values in magmatic ore deposits such as the J-M Reef reflect high iron contents in the sulfides combined with relatively high oxygen fugacities.

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Textural evolution of polyhedral olivine experiencing rapid cooling rates

Dynamic crystallization experiments in the CaO–MgO–Al₂O₃–SiO₂ (CMAS) system have been used to investigate the change in crystal shape when pre-existing polyhedral olivine crystals are cooled rapidly (1,639–2,182°C/h). Polyhedral olivines are crystallized initially in a first step using a slow cooling rate (2°C/h), then skeletal and dendritic overgrowths develop on the polyhedral crystals during a subsequent fast cooling event. During this second episode small dendritic olivines also nucleate within the liquid phase. Observation of the experimental sample by optical microscopy shows that the polyhedral olivine shape progressively changes to a skeletal and then to a dendritic morphology in the following sequence: polyhedral ⇒ hopper polyhedral ⇒ dendritic polyhedral. This evolutional sequence is discussed in terms of changes in the crystal growth conditions during cooling and a general relation between these olivine dynamic crystallization experiments and the integrated model of crystal growth by Sunagawa (Bull Minér 104:81–87, 1981, Morphology of crystals, Terra Scientific Publishing Company, 1987) is proposed.     

Grain growth in porous olivine aggregates

Grain growth experiments have been performed at 1 atm on fine grain size (<10 μm) synthetic olivine (Fo₉₁) aggregates at various temperatures (1200° to 1400° C), oxygen fugacities (10^-4 to 10^-11 atm) and total anneal times (10, 30, 60, 100 and 200 h). The rate of grain growth increased with increasing temperature and with increasing oxygen fugacity. The presence of a second phase (residual porosity), introduced during sample fabrication, has a significant effect on grain growth, with evolution in grain size paralleled by changes in the size and frequency of the pores. When the grain growth data were fit to a growth law G ⁿ ?G _O ⁿ =κ₀ tf ₀ ^m ₂e^?Q/RT, the growth exponents fall in the range of n=4 to 5, suggesting that grain growth may be controlled by the coalescence of the second phase. The evolution in pore size and frequency may occur either by the transport of the ionic species constituting olivine between the pores or by the movement of the pores themselves along the grain boundaries and edges. Thus, the rate of growth of the pores and grains is probably limited by diffusion of the slowest ionic species constituting olivine (magnesium, iron, silicon, or oxygen) moving along the fastest path for that species (through the lattice, along the grain boundaries, around the surface of the moving pores, or through the vapor phase in the pores). Activation energies for grain growth of Q=290 ± 20 kJ/mol and 345 ± 25 kJ/mol were calculated from our results for n=4 and 5, respectively. These activation energies preclude vapor-phase transport and iron diffusion along grain boundaries but do not otherwise permit a discrimination between the rate limiting species or path. The oxygen fugacity exponent of m ≈0.12 suggests that lattice diffusion does not control the grain growth. However, the lack of data for magnesium, iron, silicon and oxygen surface and grain boundary diffusion in olivine makes definitive determination of the mechanism controlling grain growth difficult.     

Oxygen isotope heterogeneity of the mantle beneath the Canary Islands: a discussion of the paper of Gurenko et al.

Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) report laser-assisted fluorination (LF) and secondary ionization mass spectrometry (SIMS) ¹⁸O/¹⁶O datasets for olivine grains from the Canary Islands of Gran Canaria, Tenerife, La Gomera, La Palma and El Hierro. As with prior studies of oxygen isotopes in Canary Island lavas (e.g. Thirlwall et al. Chem Geol 135:233–262, 1997; Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010), these authors find variations in δ¹⁸O_ol (~4.6–6.0 ‰) beyond that measured for mantle peridotite olivine (Mattey et al. Earth Planet Sci Lett 128:231–241, 1994) and interpret this variation to reflect contributions from pyroxenite-peridotite mantle sources. Furthermore, Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) speculate that δ¹⁸O_ol values for La Palma olivine grains measured by LF (Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) may be biased to low values due to the presence of altered silicate, possibly serpentine. The range in δ¹⁸O_ol values for Canary Island lavas are of importance for constraining their origin. Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) took a subset (39 SIMS analyses from 13 grains from a single El Hierro lava; EH4) of a more extensive dataset (321 SIMS analyses from 110 grains from 16 Canary Island lavas) to suggest that δ¹⁸O_ol is weakly correlated (R ² = 0.291) with the parameter used by Gurenko et al. (Earth Planet Sci Lett 277:514–524, 2009) to describe the estimated weight fraction of pyroxenite-derived melt (Xpx). With this relationship, end-member δ¹⁸O values for HIMU-peridotite (δ¹⁸O = 5.3 ± 0.3 ‰) and depleted pyroxenite (δ¹⁸O = 5.9 ± 0.3 ‰) were defined. Although the model proposed by Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) implicates similar pyroxenite-peridotite mantle sources to those proposed by Day et al. (Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) and Day and Hilton (Earth Planet Sci Lett 305:226–234, 2011), there are significant differences in the predicted δ¹⁸O values of end member components in the two models. In particular, Day et al. (Geochim Cosmochim Acta 74:6565–6589, 2010) proposed a mantle source for La Palma lavas with low-δ¹⁸O (<5 ‰), rather than higher-δ¹⁸O (c.f. the HIMU-peridotite composition of Gurenko et al. in Contrib Mineral Petrol 162:349–363, 2011). Here we question the approach of using weakly correlated variations in δ¹⁸O_ol and the Xpx parameter to define mantle source oxygen isotope compositions, and provide examples of why this approach appears flawed. We also provide reasons why the LF datasets previously published for Canary Island lavas remain robust and discuss why LF and SIMS data may provide complementary information on oxygen isotope variations in ocean island basalts (OIB), despite unresolved small-scale uncertainties associated with both techniques.     

Boron-isotope fractionation between tourmaline and fluid: an experimental re-investigation

The fractionation of boron isotopes between synthetic dravitic tourmaline and fluid was determined by hydrothermal experiments between 400 and 700°C at 200 MPa and at 500°C, 500 MPa. Tourmaline was crystallized from an oxide mix in presence of water that contained boron in excess. In one series of experiments, [B]_fluid/[B]_tour was 9 after the run; in another series it was 0.1. All experiments produced tourmaline as the sole boron-bearing solid, along with traces of quartz and talc. Powder XRD and Rietveld refinements revealed no significant amounts of tetrahedrally coordinated boron in tourmaline. ¹¹B always preferentially fractionated into the fluid. For experiments where [B]_fluid/[B]_tour was 9, a consistent temperature-dependent boron isotope fractionation curve resulted, approximated by Δ¹¹B_{(tour–fluid)} = −4.20 · [1,000/T (K)] + 3.52; R ² = 0.77, and valid from 400 to 700°C. No pressure dependence was observed. The fractionation (−2.7 ± 0.5‰ at 400°C; and −0.8 ± 0.5‰ at 700°C) is much lower than that previously presented by Palmer et al. (1992). Experiments where [B]_fluid/[B]_tour was 0.1 showed a significant larger apparent fractionation of up to −4.7‰. In one of these runs, the isotopic composition of handpicked tourmaline crystals of different size varied by 1.3‰. This is interpreted as resulting from fractional crystallization of boron isotopes during tourmaline growth due to the small boron reservoir of the fluid relative to tourmaline, thus indicating larger fractionation than observed at equilibrium. The effect is eliminated or minimized in experiments with very high boron excess in the fluid. We therefore suggest that values given by the above relation represent the true equilibrium fractionations.     

Dislocation recovery in fine-grained polycrystalline olivine

The rate of static dislocation recovery in Fo₉₀ olivine has been studied under conditions of high temperature and controlled atmosphere in compressively deformed polycrystals hot-pressed from synthetic (sol–gel) and natural (San Carlos) precursor powders. The sol–gel olivine, containing a small fraction of orthopyroxene, was deformed to a final strain of 19% with a maximum differential stress of 266 MPa whereas the San Carlos specimen was deformed to 15% strain and 260 MPa differential stress. Small samples cut from these deformed materials were annealed under high-temperature, controlled atmosphere conditions, for different durations to allow partial recovery of the dislocation sub-structures. Oxidative-decoration of the microstructural features, followed by backscattered electron imaging at 5 kV and image analysis, was used to determine dislocation density. The variation of dislocation density ρ with time t at absolute temperature T was fitted to a second-order rate equation, in integral form, 1/ρ(t) − 1/ρ(0) = kt with k = k ₀ exp(−E _a/RT). The activation energy E _a of the recovery process is 240 ± 43 and 355 ± 81 kJ mol⁻¹ for sol–gel and San Carlos olivine polycrystals, respectively. The measured rates are one to two orders of magnitude lower than those reported in previous studies on natural single crystal olivine. The difference may be explained by several factors such as high dislocation densities measurable from large areas at high magnification for the SEM and the technique used to estimate dislocation densities. Comparison between fine-grained sol–gel olivine and the coarser-grained San Carlos olivine aggregate did not indicate that grain boundaries play an important role in dislocation recovery, but the absence of grain boundaries might also have contributed to the high dislocation recovery rates previously measured for single crystals.     

Grain growth kinetics and the effect of crystallographic anisotropy on normal grain growth of quartz

Annealing experiments on agate were performed to investigate grain growth kinetics and the effect of crystallographic anisotropy on normal grain growth of quartz. The experiments were conducted using a piston-cylinder apparatus at 700–800°C and 0.5 GPa for 0–66 h. The grain growth rate was expressed by D ⁿ −D ₀ ⁿ  = kt with k = k ₀ exp(−H*/RT) where D ₀ is the initial grain size at t = 0, with n = 4.4 ± 0.3, and H* = 191.3 ± 11.0 kJ/mol is the activation enthalpy and logk ₀  = 19.8 ± 1.4. While the grain aspect ratios are nearly constant at ~0.7 (short/long) during grain growth, the longest axis in individual grains tends to be oriented parallel to their c-axis, indicating that a primary crystal-preferred orientation of c-axis of the agate could result in the development of a weak shape-preferred orientation during grain growth.     

A close look at dihedral angles and melt geometry in olivine-basalt aggregates: a TEM study

Olivine-basalt aggregates sintered at high P/T have been used as a simplest approximation of partially molten upper mantle peridotite. In the past, geometry of partial melt in polycrystalline olivine (and other materials) has been characterised by dihedral (wetting) angles which depend upon surface free energy. However, since olivine (like most other crystalline materials) is distinctively anisotropic, the simple surface energy balance defining the dihedral angles cos(Θ/2)=_gb/2_sl is not valid and melt geometry is more complicated than can be expressed by a single dihedral angle value. We examine in detail melt geometry in aggregates held at high temperature and pressure for very long times (240–612 h). We show the simple dihedral angle concept to be invalid via transmission electron microscope images. Olivine-basalt interfaces are frequently planar crystal faces (F-faces) which are controlled by the crystal structure rather than the surface area minimisation used in the simple dihedral angle concept. Nevertheless, the dihedral angles may provide useful insights in some situations. They may give a rough estimation of the wetting behaviour of a system, or be used to approximate the melt distribution if F-faces are not present (possibly at large grain size and very low melt fraction). Our measurements, excluding F-faces, give a range of dihedral angle values from 0 to 10° which is significantly lower than reported previously (20–50°). The nature of 0° angles (films and layers up to 1 μm in thickness) is unclear but their frequency compared to dry grain boundaries depends on grain size and melt fraction (e.g. 70% for grain size 43 μm and melt fraction 2%). Received: 13 April 1997 / Accepted: 2 October 1997     

Prediction of the thermodynamic properties of metal–arsenate and metal–arsenite aqueous complexes to high temperatures and pressures and some geological consequences

The standard thermodynamic properties at 25°C, 1 bar (ΔG _f^o, ΔH _f^o, S ^o, C _P^o, V ^o, ω) and the coefficients of the revised Helgeson–Kirkham–Flowers equations of state were evaluated for several aqueous complexes formed by dissolved metals and either arsenate or arsenite ions. The guidelines of Shock and Helgeson (Geochim Cosmochim Acta 52:2009–2036, 1988) and Sverjensky et al. (Geochim Cosmochim Acta 61:1359–1412, 1997) were followed and corroborated with alternative approaches, whenever possible. The SUPCRT92 computer code was used to generate the log K of the destruction reactions of these metal–arsenate and metal–arsenite aqueous complexes at pressures and temperatures required by the EQ3/6 software package, version 7.2b. Apart from the AlAsO₄^o and FeAsO₄^o complexes, our log K at 25°C, 1 bar are in fair agreement with those of Whiting (MS Thesis, Colorado School of Mines, Golden, CO, 1992). Moreover, the equilibrium constants evaluated in this study are in good to fair agreement with those determined experimentally for the Ca–dihydroarsenate and Ca–hydroarsenate complexes at 40°C (Mironov et al., Russ J Inorg Chem 40:1690, 1995) and for Fe(III)–hydroarsenate complex at 25°C (Raposo et al., J Sol Chem 35:79–94, 2006), whereas the disagreement with the log K measured for the Ca–arsenate complex at 40°C (Mironov et al., Russ J Inorg Chem 40:1690, 1995) might be due to uncertainties in this measured value. The implications of aqueous complexing between dissolved metals and arsenate/arsenite ions were investigated for seawater, high-temperature geothermal liquids and acid mine drainage and aqueous solutions deriving from mixing of acid mine waters and surface waters. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

High-temperature creep in a Ni2GeO4: a contribution to creep systematics in spinel

 High-temperature creep behavior in Ni₂GeO₄ spinel was investigated using synthetic polycrystalline aggregates with average grain sizes ranging from submicron to 7.4 microns. Cylindrical samples were deformed at constant load in a gas-medium apparatus at temperatures ranging from 1223 to 1523 K and stresses ranging from 40 to 320 MPa. Two deformation mechanisms were identified, characterized by the following flow laws: where σ is in MPa, d is in μm and T is in Kelvin. These flow laws suggest that deformation was accommodated by dislocation creep and grain-boundary diffusion (Coble) creep, respectively. A comparison with other spinels shows that an isomechanical group can be defined for spinels although some differences between normal and inverse spinels can be identified. When creep data for olivine and spinel are normalized and extrapolated to Earth-like conditions, spinel (ringwoodite) has a strength similar to olivine in the dislocation creep regime and is considerably stronger than olivine in the diffusion creep regime at coarse grain size. However, when grain-size reduction occurs, spinel can become weaker than olivine due to its high grain-size sensitivity (Coble creep behavior). Analysis of normalized diffusion creep data for olivine and spinel indicate that spinel is weaker than olivine at grain sizes less than 2 μm. Received: 18 June 2000 / Accepted: 3 April 2001     

New experimental determination of Li and B partition coefficients during upper mantle partial melting

Despite the growing interest for Li and B as geochemical tracers, especially for material transfer from subducting slabs to overlying peridotites, little is known about the behaviour of these two elements during partial melting of mantle sources. In particular, mineral/melt partition coefficients for B and to a lesser extent Li are still a matter of debate. In this work, we re-equilibrated a synthetic basalt doped with ~10 ppm B and ~6 ppm Li with an olivine powder from a spinel lherzolite xenolith at 1 GPa–1,330°C, and we analyzed Li and B in the run products by secondary ion mass spectrometry (SIMS). In our experiment, B behaved as a highly incompatible element with mineral/melt partition coefficients of the order of 10⁻² (D ^ol/melt = 0.008 (0.004–0.013); D ^opx/melt = 0.024 (0.015–0.033); D ^cpx/melt = 0.041 (0.021–0.061)), and Li as a moderately incompatible element (D ^ol/melt = 0.427 (0.418–0.436); D ^opx/melt = 0.211 (0.167–0.256); D ^cpx/melt = 0.246 (0.229–0.264)). Our partition coefficients for Li are in good agreement with previous determinations. In the case of B, our partition coefficients are equal within error to those reported by Brenan et al. (1998) for all the mineral phases analyzed, but are lower than other coefficients from literature for some of the phases (up to 5 times for cpx). Our measurements complement the data set of Ds for modelling partial melting of the upper mantle and basalt generation, and confirm that, in this context, B is more incompatible than previously anticipated.     

Fe–Mg diffusion in olivine II: point defect chemistry,change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27–37,1983; Phys Chem Miner 29:680–694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10⁻⁴ per atomic formula unit at 1,000–1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ∼1,100 °C and dependence on fO₂, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO₂ below 10⁻¹⁰  Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO₂ dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317–12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between −66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely ∼ 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147–162, 1998). Plots are shown for diffusion at various constant fO₂ as well as along fO₂ buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe–Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10⁻¹⁰ Pa:

Strength of single-crystal orthopyroxene under lithospheric conditions

Creep strength of oriented orthopyroxene single crystals was investigated via shear deformation experiments under lithospheric conditions [P (pressure) = 1.3 GPa and T (temperature) = 973–1,373 K]. For the A-orientation (shear direction [001] on (100) plane), the samples have transformed completely to clinoenstatite and much of the deformation occurred after transformation. In contrast, for the B-orientation (shear direction [001] on (010) plane), samples remained orthoenstatite and deformation occurred through dislocation motion in orthoenstatite. The strength of orthopyroxene with these orientations is smaller than for olivine aggregates under all experimental conditions. Flow of the B-orientation samples is described by a power-law, and the pre-exponential constant, the apparent activation energy, and the stress exponent are determined to be A = 10^−9.5 s⁻¹·MPa^−4.2, Q = 114 kJ/mol and n = 4.2. However, for the A-orientation, the results cannot be fit by a single flow law and we obtained the following: A = 10^8.9 s⁻¹·MPa^−3.0, Q = 459 kJ/mol and n = 3.0 at high temperatures (≥1,173 K), and A = 10^−27.4 s⁻¹·MPa^−14.3, Q = 296 kJ/mol and n = 14.3 at low temperatures (<1,173 K). The stress exponent for the low-temperature regime is high, suggesting that deformation involves some processes where the activation energy decreases with stress such as the Peierls mechanism. Our study shows that orthopyroxene with these orientations is significantly weaker than olivine under the lithospheric conditions suggesting that orthopyroxene may reduce the strength of the lithosphere, although the extent to which orthopyroxene weakens the lithosphere depends on its orientation and connectivity.     

Grain growth kinetics of dolomite,magnesite and calcite: a comparative study

The rates of grain growth of stoichiometric dolomite [CaMg(CO₃)₂] and magnesite (MgCO₃) have been measured at temperatures T of 700–800°C at a confining pressure P _c of 300 MPa, and compared with growth rates of calcite (CaCO₃). Dry, fine-grained aggregates of the three carbonates were synthesized from high purity powders by hot isostatic pressing (HIP); initial mean grain sizes of HIP-synthesized carbonates were 1.4, 1.1, and 17 μm, respectively, for CaMg(CO₃)₂, MgCO₃, and CaCO₃, with porosities of 2, 28, and 0.04% by volume. Grain sizes of all carbonates coarsened during subsequent isostatic annealing, with mean values reaching 3.9, 5.1, and 27 μm for CaMg(CO₃)₂, MgCO₃, and CaCO₃, respectively, in 1 week. Grain growth of dolomite is much slower than the growth rates of magnesite or calcite; assuming normal grain growth and n = 3 for all three carbonates, the rate constant K for dolomite (≃5 × 10⁻⁵ μm³/s) at T = 800°C is less than that for magnesite by a factor of ~30 and less than that for calcite by three orders of magnitude. Variations in carbonate grain growth may be affected by differences in cation composition and densities of pores at grain boundaries that decrease grain boundary mobility. However, rates of coarsening correlate best with the extent of solid solution; K is the largest for calcite with extensive Mg substitution for Ca, while K is the smallest for dolomite with negligible solid solution. Secondary phases may nucleate at advancing dolomite grain boundaries, with implications for deformation processes, rheology, and reaction kinetics of carbonates.     

Grain growth in CaTiO3-perovskite + FeO-wüstite aggregates

Grain growth kinetics in CaTiO₃-perovskite + FeO-wüstite aggregates were studied at the conditions of T = 1223–1623 K, P = 0.1 MPa and P = 200 MPa. Starting samples were fabricated by hot-pressing mechanically mixed powders of CaTiO₃ + FeO with FeO = 0%, 1%, 3%, 6%, 10%, 20% and 100% by weight in a gas-medium apparatus at 1323 K and 300 MPa for 5 h. The increase of grain size (G) of CaTiO₃ with time (t) follows a growth law: G ⁿ −G ⁿ ₀ = κ·t(κ=κ₀exp(−(Q/RT)). Two grain growth regimes are observed at T < 1523 K and T ≥ 1523 K. For T < 1523 K, the best fits of the data to the growth law yield growth exponents of n = 2.2 ± 0.2, 3.0 ± 0.3 and 3.5 ± 0.3 for samples with FeO = 0%, 3% and 10% respectively. Under these conditions the rate constants, κ, obey an Arrhenius relation with Q = 206 ± 35 kJ/mol and 385 ± 65 kJ/mol for samples with FeO = 3% and 10%. Grain growth of CaTiO₃ becomes sluggish when FeO content exceeds 6%. For T ≥ 1523 K, the best fits of the data to the growth law yield n = 2.5 ± 0.2 for both samples with FeO = 3% and 10%. The activation energies (Q ) were determined as 71 ± 30 kJ/mol and 229 ± 45 kJ/mol for samples with FeO = 3% and 10%, respectively. The TEM observations show a remarkable difference in the distribution and geometry of FeO below and above 1523 K: nanometer-sized particles of FeO were observed along CaTiO₃ grain boundaries in samples annealed at T < 1523 K. No FeO particles were detected along CaTiO₃ grain boundaries in samples annealed at T ≥ 1523 K, but large clusters of FeO particles are observed locally indicating a fast separation of FeO from CaTiO₃. Thus we conclude that the slow growth rate of CaTiO₃ at T < 1523 K is due to the pinning by FeO particles at grain boundary, and that the change of grain growth kinetics in CaTiO₃ at T ≥ 1523 K may relate to the separation of FeO from CaTiO₃, which we interpret as due to the phase transformation of CaTiO₃ at around 1523 K. Received: 19 June 1998 / Revised, accepted: 24 March 1999     

H<Subscript>2</Subscript>O storage capacity of MgSiO<Subscript>3</Subscript> clinoenstatite at 8–13 GPa, 1,100–1,400°C

We present H₂O analyses of MgSiO₃ pyroxene crystals quenched from hydrous conditions in the presence of olivine or wadsleyite at 8–13.4 GPa and 1,100–1,400°C. Raman spectroscopy shows that all pyroxenes have low clinoenstatite structure, which we infer to indicate that the crystals were high clinoenstatite (C2/c) during conditions of synthesis. H₂O analyses were performed by secondary ion mass spectrometry and confirmed by unpolarized Fourier transform infrared spectroscopy on randomly oriented crystals. Measured H₂O concentrations increase with pressure and range from 0.08 wt.% H₂O at 8 GPa and 1,300°C up to 0.67 wt.% at 13.4 GPa and 1,300°C. At fixed pressure, H₂O storage capacity diminishes with increasing temperature and the magnitude of this effect increases with pressure. This trend, which we attribute to diminishing activity of H₂O in coexisting fluids as the proportion of dissolved silicate increases, is opposite to that observed previously at low pressure. We observe clinoenstatite 1.4 GPa below the pressure stability of clinoenstatite under nominally dry conditions. This stabilization of clinoenstatite relative to orthoenstatite under hydrous conditions is likely owing to preferential substitution of H₂O into the high clinoenstatite polymorph. At 8–11 GPa and 1,200–1,400°C, observed H₂O partitioning between olivine and clinoenstatite gives values of D ^ol/CEn between 0.65 and 0.87. At 13 GPa and 1,300°C, partitioning between wadsleyite and clinoenstatite, D ^wd/CEn, gives a value of 2.8 ± 0.4.     

Octahedral cation ordering in olivine at high temperature. II: an in situ neutron powder diffraction study on synthetic MgFeSiO4 (Fa50)

 The partitioning of Fe and Mg between the M1 and M2 octahedral sites of olivine has been investigated by in situ time-of-flight neutron powder diffraction. The degree of M-cation order was determined from direct measurements of site occupancies in a synthetic sample of Fo50Fa50 heated to 1250 °C at the Fe-FeO oxygen buffer. Fe shows slight preference for M1 at temperatures below about 600 °C, progressively disordering on heating to this temperature. Above 630 °C, the temperature at which site preferences cross over (T _cr), Fe preferentially occupies M2, becoming progressively more ordered into M2 on increasing temperature. The cation-ordering behaviour is discussed in relation to the temperature dependence of the M1 and M2 site geometries, and it is suggested that vibrational entropy, crystal field effects and changes in bond characteristics play a part in the cross-over of partitioning behaviour. The temperature dependence of site ordering is modelled using a Landau expansion of the free energy of ordering of the type ΔG = −hQ + gTQ +  (T − T _c)Q ² +  Q ⁴, with a/h = 0.00406 K⁻¹, b/h = 2.3, T _c = 572 K and g/h = 0.00106 K⁻¹. These results suggest that the high-temperature ordering behaviour across the forsterite-fayalite join will have a bearing on the activity-composition relations of this important rock-forming mineral, and indicate that Fe-Mg olivine solid solutions become less ideal as temperature increases. Received: 12 August 1999 / Accepted: 25 April 2000     

Fe–Mg diffusion in olivine I: experimental determination between 700 and 1,200<Emphasis Type="Bold">°</Emphasis>C as a function of composition,crystal orientation and oxygen fugacity

We have determined Fe–Mg diffusion coefficients in olivines from different sources (Nanga Parbat, Pakistan and San Carlos, Arizona, USA) at atmospheric pressure as a function of composition, oxygen fugacity (10⁻⁵–10⁻¹² Pa) and temperature (700–1200°C) using thin films produced by pulsed laser deposition and RBS to analyze the concentration profiles. We have characterized the nano-scale structure and composition of the thin films annealed at various conditions and shown that the nature of the film (e.g. crystallinity, wetting behavior) depends strongly on the annealing conditions. If these variations are not taken into account in the form of boundary conditions for modeling the diffusion profiles, artifacts would result in the diffusion data. The diffusion coefficients obtained from 75 experiments reveal that (i) between fO₂ of 10⁻⁵ and 10⁻¹⁰ Pa, diffusion along all three principal crystallographic directions in olivine, [100], [010] and [001], are described by a constant activation energy of ∼200 kJ/mol, precluding any temperature dependence of diffusion anisotropy and change of mechanism of diffusion at temperatures between 950 and 1200°C, (ii) diffusion coefficients increase with oxygen fugacity at fO₂ > 10⁻¹⁰ Pa, with an fO₂ exponent that lies between 1/4 and 1/7, and (iii) at fO₂ below 10⁻¹⁰ Pa, and consequently at temperatures below ∼900°C, diffusion becomes weakly dependent/independent of fO₂, indicating a change of diffusion mechanism. Activation energy of diffusion at these conditions is slightly higher, ∼220 kJ/mol. The data, including the change of mechanism, are analyzed in terms of point defect chemistry in Part II of this work to derive an equation that allows calculation of diffusivities in olivine over its entire field of stability. Availability of directly measured data at temperatures down to 700°C imply that for the first time diffusion coefficients can be interpolated, rather than extrapolated, for modeling most natural systems.