The effects of liquid immiscibility and thermal diffusion on oxygen isotopes in silicate liquids

Differences between the δ¹⁸O values of Si- and Fe-rich immiscible liquids in the system Fe₂SiO₄-KAlSi₂O₆-SiO₂ (Fa-Lc-Q) in isothermal experiments at 0.1 MPa have been determined experimentally to be 0.6 permil. The observed partition of ¹⁸O into the Si-rich liquid is consistent with previous experience with the preferential partition of ¹⁸O into Si-rich minerals in isothermal equilibrium with minerals of less polymerized structure. Crystallochemical principles affect the distribution of oxygen isotopes in coexisting isothermal liquids in the same way as they apply to isothermally coexisting crystals. The effects of Soret (thermal) diffusion on the distribution of oxygen isotopes in silicate liquids above the solvus in the system Fa-Lc-Q under conditions of an imposed temperature gradient of ca. 250 °C over 4 mm and at 2 GPa have also been investigated experimentally. Both the magnitude and the direction of separation of oxygen isotopes as a result of Soret diffusion are unexpected. For each of the silicate liquids, the cold end of the charge is enriched in ¹⁸O by up to 4.7 permil, and the highest δ¹⁸O values are associated with the most silica-poor compositions. The distribution of oxygen isotopes appears to be similar in each liquid, regardless of their chemical compositions, which is in contrast to the behaviour of cations whose distributions are compositionally dependent and characterized by strong crystallochemical effects wherein network-forming species such as Si and Al separate to the hot end and Mg, Fe and Ca are segregated preferentially to the cold end. Structural units in the melts are evidently less selective between oxygen isotopes than between cations, because oxygen redistribution over all possible sites in these units proceeds according to mass. Self-diffusion coefficients of oxygen in basaltic liquids estimated from the Soret experiments are in accord with those from other isotope tracer experiments, and comparable to those of Si. The possible effects of Soret diffusion on the oxygen isotopic composition of metasomatic veins in the mantle are examined in light of these data, and indicate that decay of the thermal gradients in the veins exceeds that of the diffusion of oxygen needed to produce variations in the δ¹⁸O values of mantle minerals. Variations in oxygen isotope ratios in most natural systems as a result of Soret effects are unlikely. Received: 6 January 1997 /  Accepted: 28 June 1998     

Magnesium isotope fractionation in silicate melts by chemical and thermal diffusion

Two types of laboratory experiments were used to quantify magnesium isotopic fractionations associated with chemical and thermal (Soret) diffusion in silicate liquids. Chemical diffusion couples juxtaposing a molten natural basalt (SUNY MORB) and a molten natural rhyolite (Lake County Obsidian) were run in a piston cylinder apparatus and used to determine the isotopic fractionation of magnesium as it diffused from molten basalt to molten rhyolite. The thermal diffusion experiments were also run in a piston cylinder apparatus but with a sample made entirely of molten SUNY MORB displaced from the hotspot of the assembly furnace so that the sample would have a temperature difference of about 100-200 °C from one end to the other. The chemical diffusion experiments showed fractionations of ²⁶Mg/²⁴Mg by as much as 7‰, which resulted in an estimate for the mass dependence of the self-diffusion coefficients of the magnesium isotopes corresponding to D_26Mg/D_24Mg=(24/26)^β with β = 0.05. The thermal diffusion experiments showed that a temperature difference of about 100 °C resulted in the MgO, CaO, and FeO components of the basalt becoming slightly enriched by about 1 wt% in the colder end while SiO₂ was enriched by several wt% in the hotter end. The temperature gradient also fractionated the magnesium isotopes. A temperature difference of about 150 °C produced an 8‰ enrichment of ²⁶Mg/²⁴Mg at the colder end relative to the hotter end. The magnesium isotopic fractionation as a function of temperature in molten basalt corresponds to 3.6 × 10⁻²‰/°C/amu.     

The behavior of noble gases in silicate liquids: Solution,diffusion, bubbles and surface effects,with applications to natural samples

Solubilities of noble gases in five natural silicate liquids as a function of temperature and partial pressure at 1 atm total pressure were determined and diffusion coefficients of the noble gases were measured in a tholeiite basalt at 1350°C. Solubilities of noble gases in silicate liquids obey Henry's law and are a strong function of composition and/or physical properties of the liquids. Solubility is greatest in less dense, more silica-rich liquids. Solubility is highest for the light gases and is related to the radius of the gas atom according to K_i = aexp (−br²_i). Temperature dependence of solubility is weak, but in general solubility increases with increasing temperature yielding positive enthalpies of solution. Diffusion coefficients in a basalt liquid at 1350°C show more or less the same linear relationship with r² as solubility and are larger than what would be expected from extrapolation of values determined at lower temperatures. A large percentage of samples of andesite composition had bubbles that contained gas which was fractionated from the gas of the experiment. Concentrations of noble gases in samples equilibrated on Pt wire loops correlate with the surface/volume ratio, suggesting that surfaces of silicate liquids can accommodate more noble gases than the liquid proper. Solubility fractionation is a valid process to account for certain patterns in marine basalts. The density of silicate liquids appears to be a good predictor of noble gas solubility in these liquids.     

Heat capacities and entropies of silicate liquids and glasses

The heat capacities of several dozen silicate glasses and liquids composed of SiO₂, TiO₂, Al₂O₃, Fe₂O₃, FeO, MgO, CaO, BaO, Li₂O, Na₂O, K₂O, and Rb₂O have been measured by differential scanning and drop calorimetry. These results have been combined with data from the literature to fit C _pas a function of composition. A model assuming ideal mixing (linear combination) of partial molar heat capacities of oxide components (each of which is independent of composition), reproduces the glass data within error. The assumption of constancy of ¯C _p,iis less accurate for the liquids, but data are not sufficient to adequately constrain a more complex model. For liquids containing alkali metal and alkaline earth oxides, heat capacities are systematically greater in liquids with high field strength network modifying cations. Entropies of fusion (per g-atom) and changes of configurational entropy with temperature, are similarly affected by composition. Both smaller cation size and greater charge are therefore inferred to lead to greater development of new structural configurations with increasing temperature in silicate liquids.     

Partial molar volumes of oxide components in silicate liquids

Densities of 21 silicate liquids have been determined from 1,000 ° to 1,600 ° C. The compositions studied contain from two to eight oxide components and have the following ranges in composition (mole %): SiO₂, 35–79%; TiO₂, 4–36%; Al₂O₃, 5–25%; FeO, 11–41%; MgO, 7–28%; CaO, 7–35%; Na₂O, 5–50%; and K₂O, 4–20%. The compositions thus cover the upper range observed in magmas for each oxide. Precision for each determination of liquid density is always better than ±1%.Volumes/gfw (gram formula weight) calculated from the density measurements and the chemical compositions of the analyzed liquids have been combined with data on 96 silicate liquids reported in the literature. From this data set we derive, by using multiple linear regression, partial molar volumes of the components SiO₂, TiO₂, A1₂O₃, FeO, MgO, CaO, Na₂O, and K₂O at five temperatures. The standard deviation of the multiple regression is 1.8% of the molar volumes, which is considered about equal to the total errors due to compositional and instrumental uncertainties.These derived partial molar volumes have been used to calculate volumes/gfw of natural silicate liquids which are found to agree within 1% of the measured values. No compositional dependence of the partial molar volumes can be detected within the error considered to be typical of the measurements. This is further supported by the close agreement between the calculated volumes of CaMgSi₂O₆ and Fe₂SiO₂ liquids derived from the initial slopes of their fusion curves and their heats of fusion, and the volumes obtained by summing the respective partial molar volumes. The experimental data indicate that silicate liquids mix ideally with respect to volume, over the temperature and composition range of this data set.     

A review and analysis of silicate mineral dissolution experiments in natural silicate melts

We present a database and a graphical analysis of published experimental results for dissolution rates of olivine, quartz plagioclase, clinopyroxene, orthopyroxene, spinel, and garnet in basaltic and andesitic melts covering a range of experimental temperatures (1100–1500°C) and pressures (10⁵ Pa-3.0 GPa). The published datasets of Donaldson (1985, 1990) and Brearly and Scarfe (1986) are the most complete. Experimental dissolution rates from all datasets are recalculated and normalized to a constant oxygen basis to allow for direct comparison of dissolution rates between different minerals. Dissolution rates (ν) range from 5·10⁻¹⁰ oxygen equivalent moles (o.e.m.) cm⁻² s⁻¹ for olivine in a basaltic melt to 1.3·10⁻⁵ o.e.m. cm⁻² s⁻¹ for garnet in a basaltic melt. Values of ln ν are Arthenian for the experiments examined and activation energies range from 118 to 1800 kJ/o.e.m. for quartz and clinopyroxene, respectively.

The relationship between calculated A/RT for the dissolution reactions, where A is the thermodynamic potential affinity, and values of ν is linear for olivine, plagioclase, and quartz. We interpret this as strong evidence in support of using calculated A as a predictor of ν for, at least, superliquidus melt conditions.     

Constraints on core formation from Pt partitioning in mafic silicate liquids at high temperatures

A new high temperature piston cylinder design has enabled the measurement of platinum solubility in mafic melts at temperatures up to 2500 °C, 2.2 GPa pressure, and under reducing conditions for 1-10 h. These high temperature and low f_O2 conditions may mimic a magma ocean during planetary core formation. Under these conditions, we measured tens to hundreds of ppm Pt in the quenched silicate glass corresponding to , 4-12 orders of magnitude lower than extrapolations from high f_O2 experiments at 1 bar and at temperatures no higher than 1550 °C. Moreover, the new experiments provide coupled textural and compositional evidence that noble metal micro-nuggets, ubiquitous in experimental studies of the highly siderophile elements, can be produced on quench: we measure equally high Pt concentrations in the rapidly quenched nugget-free peripheral margin of the silicate as we do in the more slowly quenched nugget-bearing interior region. We find that both temperature and melt composition exercise strong control on and that Pt⁰ and Pt¹⁺ may contribute significantly to the total dissolved Pt such that low f_O2 does not imply low Pt solubility. Equilibration of metal alloy with liquid silicate in a hot primitive magma might not have depleted platinum to the extent previously believed.     

Ferric-ferrous equilibria in natural silicate liquids at 1 bar

Ferric and ferrous iron concentrations have been measured in 57 silicate liquids equilibrated at temperatures (1,200°–1,330°C) above the liquidus and at oxygen fugacities close to those defined by quartz-fayalite-magnetite. The experimental results reported here span virtually the entire known compositional range of lavas. An empirical equation relating the mole fraction of Fe₂O₃ and FeO to oxygen fugacity, absolute temperature and liquid composition at 1 bar has been formulated, based on the present experimental results and published data. Extrapolating the proposed empirical relationship over several hundred degrees, for instance below the solidus of the 1965 Makaopuhi tholeiitic lava lake, yields calculated oxygen fugacities which are a little lower than those measured directly in drill holes; at 1,100°C this discrepancy is 0.4 log unit. However, the agreement between the oxygen fugacities calculated from our empirical equation and those indicated by the composition of Fe-Ti oxides in andesites and siliceous obsidians is much closer.     

The ferric-ferrous ratio of natural silicate liquids equilibrated in air

Results of chemical analyses of glasses produced in 46 melting experiments in air at 1,350° C and 1,450° C on rocks ranging in composition from nephelinite to rhyolite have been combined with other published data to obtain an empirical equation relating in \((X_{{\text{Fe}}_{\text{2}} {\text{O}}_{\text{3}} }^{{\text{liq}}} /X_{{\text{FeO}}}^{{\text{liq}}} )\) to T, \(\ln f_{{\text{O}}_{\text{2}} } \) and bulk composition. The whole set of experimental data range over 1,200–1,450° C and oxygen fugacities of 10^?9.00 to 10^?0.69 bars, respectively. The standard errors of temperature and \(\log _{10} f_{{\text{O}}_{\text{2}} } \) predictions from this equation are 52° C and 0.5 units, respectively, for 186 experiments.     

Experimental constraints on the mobility of Rhenium in silicate liquids

The volatization of Rhenium (Re) from melts of natural basalt, dacite and a synthetic composition in the CaO-MgO-Al₂O₃-SiO₂ system has been investigated at 0.1 MPa and 1250-1350 °C over a range of fO₂ conditions from log fO₂ = −10 to −0.68. Experiments were conducted using open top Pt crucibles doped with Re and Yb. Analysis of quenched glasses by laser ablation-inductively coupled plasma mass spectrometry (LA-ICP-MS) normal to the melt/gas interface showed concentration profiles for Re, to which a semi-infinite one-dimensional diffusion model could be applied to extract diffusion coefficients (D). The results show Re diffusivity in basalt at 1300 °C in air is log D_Re = −7.2 ± 0.3 cm²/s and increases to log D_Re = −6.6 ± 0.3 cm²/s when trace amounts of Cl were added to the starting material. At fO₂ conditions below the nickel-nickel oxide (NNO) buffer Re diffusivity decreases to and to in dacitic melt. In the CMAS composition, . The diffusivity of Re is comparable to Ar and CO₂ in basalt at 500 MPa favoring its release as a volatile. Our results support the contention that subaerial degassing is the cause of lower Re concentrations in arc-type and ocean island basalts compared to mid-ocean ridge basalts.     

Heat capacities of Fe2O3-bearing silicate liquids

Direct measurements of liquid heat capacity, using a Setaram HT1500 calorimeter in step-scanning mode, have been made in air on six compositions in the Na₂O-FeO-Fe₂O₃-SiO₂ system, two in the CaO-FeO-Fe₂O₃-SiO₂ system and four of natural composition (basanite, andesite, dacite, and peralkaline rhyolite). The fitted standard deviations on our heat capacity measurements range from 0.6 to 3.6%. Step-scanning calorimetry is particularly useful when applied to iron-bearing silicate liquids because: (1) measurements are made over a small temperature interval (10K) through which the ferric-ferrous ratio of the liquid remains essentially constant during a single measurement; (2) the sample is held in equilibrium with an atmosphere that can be controlled; (3) heat capacity is measured directly and not derived from the slope of enthalpy measurements with temperature. Liquid compositions in the sodic and calcic systems were chosen because they contain large concentrations of Fe₂O₃ (up to 19 mol%), and their equilibrium ferric-ferrous ratios were known at every temperature of measurement. These measurement have been combined with heat capacity (Cp) data in the literature on iron-free silicate liquids to fit Cp as a function of composition. A model assuming no excess heat capacity (linear combination of partial molar heat capacities of oxide components) reproduces the liquid data within error (±2.2% on average). The derived partial molar heat capacity of the Fe₂O₃ component is 240.9 ±7.9 J/g.f.w.-K, with a standard error reduced by more than a factor of two from that in earlier studies. The model equation, based primarily on simple, synthetic compositions, predicts the heat capacity of the four magmatic liquids within 1.8% on average.     

用BP网络求解土体的导热系数

以人工神经网络为基本工具,利用其强大的非线性映射能力,综合考虑土体的物理性质指标对其导热性能的影响,为求解土体的工程参数提供了一条新的途径。结果表明,ＢＰ网络能够充分体现土体物理指标之间的非线性关系和隐含关系,具有较高的求解能力,所求出的土体的导热系数与实测值接近,其精度远高于线性回归,且简单实用。     

The mechanisms of water diffusion in polymerized silicate melts

Diffusion of water was experimentally investigated for melts of albitic (Ab) and quartz-orthoclasic (Qz₂₉Or₇₁, in wt %) compositions with water contents in the range of 0 to 8.5 wt % at temperatures of 1100 to 1200 °C and at pressures of 1.0 and 5.0 kbar. Apparent chemical diffusion coefficients of water (D _water) were determined from concentration-distance profiles measured by FTIR microspectroscopy. Under the same P-T condition and water content the diffusivity of water in albitic, quartz-orthoclasic and haplogranitic (Qz₂₈Ab₃₈ Or₃₄, Nowak and Behrens, this issue) melts is identical within experimental error. Comparison to data published in literature indicates that anhydrous composition only has little influence on the mobility of water in polymerized melts but that the degree of polymerization has a large effect. For instance, D_water is almost identical for haplogranitic and rhyolitic melts with 0.5–3.5 wt % water at 850 °C but it is two orders of magnitude higher in basaltic than in haplogranitic melts with 0.2–0.5 wt % water at 1300 °C. Based on the new water diffusivity data, recently published in situ near-infrared spectroscopic data (Nowak 1995; Nowak and Behrens 1995), and viscosity data (Schulze et al. 1996) for hydrous haplogranitic melts current models for water diffusion in silicate melts are critically reviewed. The NIR spectroscopy has indicated isolated OH groups, pairs of OH groups and H₂O molecules as hydrous species in polymerized silicate melts. A significant contribution of isolated OH groups to the transport of water is excluded for water contents above 10 ppm by comparison of viscosity and water diffusion data and by inspection of concentration profiles from trace water diffusion. Spectroscopic measurements have indicated that the interconversion of H₂O molecules and OH pairs is relatively fast in silicate glasses and melts even at low temperature and it is inferred that this reaction is an active step for migration of water. However, direct jumps of H₂O molecules from one cavity within the silicate network to another one can not be excluded. Thus, we favour a model in which water migrates by the interconversion reaction and, possibly, small sequences of direct jumps of H₂O molecules. In this model, immobilization of water results from dissociation of the OH pairs. Assuming that the frequency of the interconversion reaction is faster than that of diffusive jumps, OH pairs and water molecules can be treated as a single diffusing species having an effective diffusion coefficient . The shape of curves of D_water versus water content implies that increases with water content. The change from linear to exponential dependence of D_water between 2 and 3 wt % water is attributed to the influence of the dissociation reaction at low water content and to the modification of the melt structure by incorporation of OH groups. Received: 26 March 1996 / Accepted: 23 August 1996     

Structural controls and mechanisms of diffusion in natural silicate melts

The diffusion properties of Na, Cs, Ba, Fe and Eu ions have been determined experimentally for a pantellerite melt and of these ions plus Li, Mn and Co in pitchstone melt, using the radiotracer residual-activity method, and narrow platinum capillaries, over the temperature range 1,200–1,400° C. In addition, Eu diffusion in a basaltic and an andesitic melt was determined. Diffusion of all cations follows an Arrhenius relationship, activation energy values being high for diffusion in the pantellerite melt (e.g. Eu: 100 kcal mol^–1) except in the case of Na (24.3 kcal mol^–1). Activation energies of diffusion in the pitchstone melt are similar to values recorded earlier for andesitic and basaltic melts.The new data are used, along with previously published data for diffusion in other composition melts, to examine the compositional and structural controls on diffusion. The range of diffusivities shows a marked change with melt composition; over two orders of magnitude for a basaltic melt, and nearly four orders for a pantellerite melt (both at 1,300° C). Diffusivity of all cations (except Li and Na) correlates positively with the proportion of network modifying cations. In the case of Li and Na the correlation is negative but the diffusivity of these ions correlates positively with the proportion of Na or of Na + K ions in the bulk melt. Diffusion behaviour in the pantellerite melt departs from the relationships shown by the data for other melt compositions, which could be partly explained by trivalent ions (such as Fe) occupying network forming positions. The diffusivity of alkali metal ions is strongly dependent on ionic radius, but this is not the case with the divalent and trivalent ions; diffusivity of these ions remains relatively constant with change in radius but decreases with increase in ionic charge.A compensation diagram shows four distinct but parallel trends for the majority of the cations in four melt types but the data for Li and Na plot on a separate trend. This and the other relationships are used to elucidate possible mechanisms of diffusion. Exchange mechanisms appear to be common, with the preservation of local charge balance. Li and Na diffuse by a distinct mechanism which involves exchange of similar or identical ions. The diffusion behaviour of the smaller alkali metal ions is sufficiently distinct from all other cations to indicate that diffusion could be an important factor in the geochemical fractionation of the alkali elements.s     

Origin of crystal-poor, differentiated magmas: insights from thermal gradient experiments

Crystal-poor, differentiated magmas are commonly erupted from shallow, thermally zoned magma chambers. In order to constrain the origin of these magmas, we have experimentally investigated crystallization, differentiation and crystal-melt separation in presence of a thermal gradient. Experiments have been designed taking advantage of the innate temperature gradient of the piston cylinder apparatus and carried out on a phonolitic system at 0.3 GPa and temperature ranging from 1,050 to 800°C. Crystallization degree and melt composition in experimental products vary as a function of the temperature gradient. In particular, melt composition differentiates from tephri-phonolite (starting material) to phonolite moving from the hotter, glassy zone (T ≤ 1,050°C) towards the cooler, heterogeneously crystallized zone (T ≤ 900°C) of the charge. The heterogeneously crystallized zone is made up of: (1) a crystal-rich, mushy region (crystallinity >30 vol%), (2) a rigid crystal framework (crystallinity ≤80 vol%) and (3) glassy belts of phonolitic glass at the top. Thermal gradient experiments picture crystallization, differentiation and crystal-melt separation processes occurring in a thermally zoned environment and reveal that relatively large volumes of crystal-poor melt (glassy belts) can originate as a consequence of the instability and collapse of the rigid crystal framework. Analogously, in thermally zoned magma chambers, the development and collapse of a solidification front may represent the controlling mechanism originating large volumes of crystal-poor, differentiated magmas.     

Calcium diffusion in a simple silicate melt to 30 kbar

Calcium-45 was used as a radiotracer to measure self-diffusion coefficients for Ca in a sodium-calcium-aluminosilicate melt (29% Na₂O, 5% CaO, 10% Al₂O₃, 56% SiO₂) at temperatures in the range 1100–1400°C and pressures to 30 kbar. Calcium diffusivity (D_Ca) was found to depend upon both temperature and pressure in a complex but systematic manner: $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?P}\text{)}{}_{\mathrm{T}}$ is always negative and has a larger absolute value at lower temperatures; $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?T}\text{)}{}_{\mathrm{P}}$ is positive and increases with increasing pressure. The overall dependence of D_Ca upon T and P is given approximately by $\text{D}{}_{\mathrm{caT.P}}\text{= [0.0025 exp(}\text{-23,107}\text{RT}\text{)] exp [P}\text{(0.7297T ? 1261.32)}\text{RT}\text{]}$. When expressed in terms of volume (V_a) and energy (E) of activation, the results are as follows: V_a ranges from 2.2 cm³/mole at 1400°C to 11.9 cm³/mole at 1100°C. and E ranges from 25.4 kcal/mole (1 kban to 49.8 kcal/mole (20 kbar).From the systematic dependence of D_Ca upon T and P, it is concluded that diffusion of Ca²⁺ in silicate melts does not take place by means of a vacant site mechanism, but is controlled instead by the amount and distribution of free volume in the melt structure.If it is assumed that the viscosity of the melt used in this study decreases with increasing pressure (Kushiro, 1976, J. Geophys. Res.81, 6351–6356) as D_Ca does, then the Stokes-Einstein inverse relation between viscosity and diffusivity is clearly violated, and its validity for silicate melts must be questioned. Thus, it appears that in silicate melts, unlike many liquids, viscous flow and diffusion are fundamentally different transport processes, involving different structural units.The effect of pressure on calcium diffusion is too small to invalidate kinetic models of upper mantle processes that have been based upon diffusivity values measured at 1 atm. Pressure may, however, induce significant reductions in the diffusion rates of large ions such as Rb⁺ or SiO^4?₄ in silicate melts.     

Oxygen diffusion in three silicate melts along the join diopside-anorthite

The self-diffusion of oxygen has been measured for three silicate melts along the join diopsideanorthite. The experiments were done by isotope exchange between an “infinite” reservoir of oxygen gas and spheres of melt. The oxygen self-diffusion coefficients for the three melts are given as: C-1(diopside): D = 1.64 × 10¹ exp(?(63.2 ± 20)(kcal/mole)/RT) cm²/sec C-2(Di₅₈An₄₂): D = 1.35 × 10^?1 exp(?(46.8 ± 9)(kcal/mole)/RT) cm²/sec C-3(Di₄₀An₆₀): D = 1.29 × 10^?2 exp(?(44.2 ± 6)(kcal/mole)/RT) cm²/secThe self-diffusion coefficients do not agree with the Eyring equation unless mean ionic jump distances (λ) considerably larger than the diameter of oxygen anion are assumed. However, the sense of variation of the actual diffusivities is as the Eyring equation predicts.Consideration of the results of this study and the bulk of previous work shows that oxygen appears to conform to the compensation law for cationic diffusion in silicate melts and glasses. The range of oxygen diffusivities was also found to encompass the field of divalent cation diffusivities in silicate melts.Those results imply that the diffusion of oxygen in silicate melts may involve a contribution from a cation-like diffusion mechanism (discrete O^2? anions) as well as contributions from the diffusion of larger structural units.     

Transport properties of olivine grain boundaries from electrical conductivity experiments

Grain boundary processes contribute significantly to electronic and ionic transports in materials within Earth’s interior. We report a novel experimental study of grain boundary conductivity in highly strained olivine aggregates that demonstrates the importance of misorientation angle between adjacent grains on aggregate transport properties. We performed electrical conductivity measurements of melt-free polycrystalline olivine (Fo₉₀) samples that had been previously deformed at 1200 °C and 0.3 GPa to shear strains up to γ?=?7.3. The electrical conductivity and anisotropy were measured at 2.8 GPa over the temperature range 700–1400 °C. We observed that (1) the electrical conductivity of samples with a small grain size (3–6 µm) and strong crystallographic preferred orientation produced by dynamic recrystallization during large-strain shear deformation is a factor of 10 or more larger than that measured on coarse-grained samples, (2) the sample deformed to the highest strain is the most conductive even though it does not have the smallest grain size, and (3) conductivity is up to a factor of ~?4 larger in the direction of shear than normal to the shear plane. Based on these results combined with electrical conductivity data for coarse-grained, polycrystalline olivine and for single crystals, we propose that the electrical conductivity of our fine-grained samples is dominated by grain boundary paths. In addition, the electrical anisotropy results from preferential alignment of higher-conductivity grain boundaries associated with the development of a strong crystallographic preferred orientation of the grains.     

Elastic properties of six silicate garnet end members from accurate ab initio simulations

The elastic properties of six silicate garnet end members, among the most important rock-forming minerals, are investigated here for the first time via accurate ab initio theoretical simulations. The Crystal program is used, which works within periodic boundary conditions and allows for all-electron basis sets to be adopted. From the computed elastic tensor, Christoffel’s equation is solved along a set of crystallographic directions in order to fully characterize the seismic wave velocity anisotropy in such materials. Polycrystalline isotropic aggregate elastic properties are derived from the computed single-crystal data via the Voigt-Reuss-Hill averaging procedure. Transferability of the elastic properties from end members to their solid solutions with different chemical compositions is also addressed.     

Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions

Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature T_r, is given by $\text{V}{}_{\mathrm{r}}\text{= ∑X}{}_{\mathrm{i}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{+ X}{}_{\mathrm{A}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$, where the summation is taken over all oxide components except A1₂O₃, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is the composition-dependent apparent partial molar volume of Al₂O₃. The thermal expansion coefficient of aluminosilicate liquids is given by $\text{α = ∑X}{}_{\mathrm{i}}\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}\text{+ X}{}_{\mathrm{A}}\text{}\text{?}\text{ga}{}_{\mathrm{A}}{}^{\mathrm{o}}$, where $\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}$ terms are constants independent of temperature and composition, and $\text{}\text{?}\text{ga}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is a composition-dependent term representing the effect of Al₂O₃ on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V(T) = V_rexp[α(T-T_r)], where T_r = 1400°C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 $\text{cc}\text{mole}$ and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is discussed in terms of several possible interpretations of the structural role of Al³⁺ in aluminosilicate melts.