The effect of crystal field stabilization on the olivine→spinel transition in the system Mg2SiO4 - Fe2SiO4

Crystal field stabilization (CFS) plays a significant role in determining equilibrium phase boundaries in olivine→spinel transformations involving transition-metal cations, including Fe²⁺ which is a major constituent of the upper mantle. Previous calculations for Fe₂SiO₄ ignored pressure and temperature dependencies of crystal field stabilization enthalpies (CFSE) and the electronic configurational entropy (S _CFS). We have calculated free energy changes (ΔG _CFS) due to differences of crystal field splittings between Fe₂SiO₄ spinel and fayalite from: ΔG _CFS=?ΔCFSE?TΔS _CFS, as functions of P and T, for different energy splittings of t _2g orbital levels of Fe²⁺ in spinel. The results indicate that ΔG _CFS is always negative, suggesting that CFS always promotes the olivine→spinel transition in Fe₂SiO₄, and expands the stability field of spinel at the expense of olivine. Because of crystal field effects, transition pressures for olivine→spinel transformations in compositions (Mg_1?x Fe _x )₂SiO₄ are lowered by approximately 50x kbar, which is equivalent to having raised the olivine→spinel boundary in the upper mantle by about 15 km.     

Electric field gradient calculation in forsterite,Mg2SiO4

The electric field gradient (EFG) in Mg₂SiO₄ is calculated on the basis of the extended point ion model, including the local term of the overlap contribution. The agreement with experimental data deduced from the quadrupole coupling constants and principal axes at the Mg sites is quite good. The results of the present calculation exhibit a small overlap contribution to the EFG at M1 and a clearly bigger one at M2, whereas the lattice contribution to the EFG at M1 and M2 is reversed. The distinct overlap effects are assumed to be due to the particular Mg₂SiO₄ crystal structure and the different point symmetry at M1 and M2. The oxygen polarizability and charge used to calculate the EFG tensor were found to be smaller than the theoretical polarizability and formal charge, respectively. The sign of the Mg quadrupole coupling constants at M1 and M2, which has not been determined experimentally, results from the EFG calculation as positive.     

Strong site preference of Co2+ in olivine,Co1.10Mg0.90SiO4

The crystal structure and site preference of Co²⁺ in a synthetic Co_1.10Mg_0.90SiO₄ olivine have been determined from single crystal X-ray diffraction data collected on an automatic diffractometer. The R factor is 0.044 for 612 reflections. The site occupancies are: Ml site: Co 0.730±0.006; Mg 0.270; M2 site: Co 0.370, Mg 0.630. The Gibbs free energy change, ΔG° for the ion-exchange reaction between M1 and M2 sites is ?4.06 kcals/mole, assuming ideal mixing at each set of sites. This energy may be called ‘site preference energy’ of Co²⁺ in olivine. The strong preference of Co²⁺ for the M1 site can be quantitatively explained by two competing forces: preference of ions larger than Mg²⁺ for the M2 site and stronger covalent bonding of transition metal ions at the M1 site. For Fe²⁺, Mg²⁺, these two effects nearly neutralize each other, explaining the lack of considerable cation-ordering in Fe-Mg olivines.     

A MEG study of the olivine and spinel forms of Mg2SiO4

In this paper we present a theoretical investigation of the structures and relative stability of the olivine and spinel phases of Mg₂SiO₄. We use both a purely ionic model, based on the Modified Electron Gas (MEG) model of intermolecular forces, and a bond polarization model, developed for low pressure silica phases, to investigate the role of covalency in these compounds. The standard MEG ionic model gives adequate structural results for the two phases but incorrectly predicts the spinel phase to be more stable at zero pressure. This is mainly because the ionic modeling of Mg₂SiO₄ only accounts for 95 percent of the lattice energy. The remainder can be attributed to covalency and many-body effects. An extension of the MEG ionic model using “many-body” pair potentials corrects the phase stability error, but predicts structures which are in poorer agreement with experiment than the standard ionic approach. In addition, calculations using these many-body pair potentials can only account for 10 percent of the missing lattice energy. This model predicts an olivine-spinel phase transition of 8 GPa, below the experimental value of 20 GPa. Therefore, in order to understand more fully the stability of these structures we must consider polarization. A two-shell bond polarization model enhances the stability of both structures, with the olivine structure being stabilized more. This model predicts a phase transition at about 80 GPa, well above the observed value. Also, the olivine and spinel structures calculated with this approach are in poorer agreement with experiment than the ionic model. Therefore, based on our investigations, to properly model covalency in Mg₂SiO₄, a treatment more sophisticated than the two-shell model is needed.     

Tracerdiffusion of the Fe-cations in olivine (Fe x Mg1−x )2SiO4 (III)

Tracerdiffusion coefficients D _Fe* (and D _Mg*) are presented for olivines of composition (Fe _x Mg_1?x )₂SiO₄ at T=1,130° C as a function of x, and oxygen activity, a _{O 2}. Since the oxygen activity dependence of D _Fe* (D _Mg*) and that of the cation vacancy concentration are almost identical, it is concluded that a vacancy diffusion mechanism is operative in the octahedrally coordinated cation sublattices. From D _Fe* and D _Mg*, the chemical diffusion coefficient \(\bar D\) can be calculated. The calculated \(\bar D\) is in agreement with \(\bar D\) -values obtained by Boltzmann-Matano analysis of interdiffusion experiments. In addition, correlation factors are evaluated from the tracerdiffusion data in order to calculate selfdiffusion coefficients.     

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

The products of the transformation of natural (Mg_0.83Fe_0.17)₂SiO₄ olivine have been prepared at various high pressures (between 25 GPa and 90 GPa), and high temperature in a laser-heated diamond-anvil cell (DAC). Studies of the high-pressure phases have been made by transmission electron microscopy (TEM), and X-ray microanalysis. The olivine/spinel boundaries exhibit all the characteristics of a diffusionless shear transition, having a finely sheared structure and a constant orientation relationship between the close-packed planes of the two structures ((100)_ol∥(111)_sp). The TEM observations of zones where olivine (or spinel) transforms into post-spinel phases show that the transformation possesses the features of an eutectoïdal decomposition, leading to a lamellar intergrowth of magnesiowüstite (Mg,Fe)O and perovskite (Mg,Fe)SiO₃. With increasing temperature and/or decreasing pressure, the grain size of the high-pressure phases increases and obeys an Arrhenius law with an activation volume equal to zero. (Mg,Fe)O grains exhibit a very high density of dislocations (higher than 10¹¹cm^?2), whereas (Mg,Fe)SiO₃ grains exhibit no dislocations but systematic twinning. The composition plane of the twins is (112) of the GdFeO₃-type perovskite, corresponding to the {110} plane of the cubic lattice of ideal perovskite.     

Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg2SiO4-Fe2SiO4-SiO2

A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg₂SiO₄-Fe₂SiO₄ and Mg₂Si₂O₆-Fe₂Si₂O₆. The formulation makes explicit provision for nonconvergent ordering of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mössbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phases-quartz,-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg₂SiO₄-Fe₂SiO₄-SiO₂ over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)₂SiO₄ olivines, (Fe, Mg)₃Al₂Si₃O₁₂ garnets, (Fe, Mg)Al₂O₄ and (Fe, Mg)Fe₂O₄ spinels, and K(Mg, Fe)₃AlSi₃O₁₀(OH)₂ biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of trace elements (Al³⁺ and Fe³⁺) to the thermodynamic formulation for orthopyroxenes.     

An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene

The partitioning of Fe and Mg between garnet and aluminous orthopyroxene has been experimentally investigated in the pressure-temperature range 5–30 kbar and 800–1,200° C in the FeO-MgO-Al₂O₃-SiO₂ (FMAS) and CaO-FeO-MgO-Al₂O₃-SiO₂ (CFMAS) systems. Within the errors of the experimental data, orthopyroxene can be regarded as macroscopically ideal. The effects of Calcium on Fe-Mg partitioning between garnet and orthopyroxene can be attributed to non-ideal Ca-Mg interactions in the garnet, described by the interaction term:W _CaMg ^ga -W _CaFe ^ga =1,400±500 cal/mol site. Reduction of the experimental data, combined with molar volume data for the end-member phases, permits the calibration of a geothermometer which is applicable to garnet peridotites and granulites: $$T(^\circ C) = \left\{ {\frac{{3,740 + 1,400X_{gr}^{ga} + 22.86P(kb)}}{{R\ln K_D + 1.96}}} \right\} - 273$$ with $$K_D = {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } \mathord{\left/ {\vphantom {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}$$ and $$X_{gr}^{ga} = (Ca/Ca + Mg + Fe)^{ga} .$$ The accuracy and precision of this geothermometer are limited by largerelative errors in the experimental and natural-rock data and by the modest absolute variation inK _D with temperature. Nevertheless, the geothermometer is shown to yield reasonable temperature estimates for a variety of natural samples.     

Single crystal growth of the modified spinel (β) and spinel (γ) phases of (Mg,Fe)2SiO4 and some geophysical implications

Single crystals of ferromagnesian orthosilicates with modified spinel (β) and spinel (γ) structure as large as 500 μm have been grown by solid state crystallization at high temperature and high pressure using an MA8-type apparatus driven in a 2,000-ton uniaxial press. This system is capable of generating pressures of 24.0 (±0.3) GPa at 2,400 (±50)°C for one hour in a sample assembly volume of 0.14 cm³. Crystals larger than 100 μm were observed to grow only at pressures within 5 percent of the phase boundary between the stability fields of the β and γ phases. Experimental determination of the phase boundaries between β or β+γ and γ phases for (Mg,Fe)₂SiO₄ has been extended to 22 GPa and 2,400°C. The effect of configurational entropy due to disordering is evaluated to be minimal on the basis of the cationic distribution in the synthesized samples; thus, we conclude that the phase boundary between β or β+γ and γ phases remains essentially linear to 2,400°C. In (Mg,Fe)₂SiO₄ solid solutions, the stability field of the γ phase shifts towards the lower pressures with increasing iron content at a rate of a 1 GPa for each 10 mole percent Fe. Assignment of the β→β+γ→γ transition to the seismic 550 km discontinuity is rejected by the present phase diagram results for (Mg_0.9Fe_0.1)₂SiO₄ and measurement of acoustic velocities for β and γ Mg₂SiO₄, but the discontinuity may be caused by a phase transition of pyroxene to a garnet-like structure.     

Charge distribution from least-energy structure in Ca - Mg orthosilicates

Calcium-olivine, γ-Ca₂SiO₄, larnite, β-Ca₂SiO₄, merwinite, Ca₃Mg(SiO₄)₂, and monticellite, CaMgSiO₄, are considered. According to a rigid oxyanion scheme, eulerian orientation angles of the SiO₄ tetrahedra and translation coordinates of Ca and Si atoms are specified as structural variables τk. All derivatives of the static energy (Born model) contain atomic charges and repulsive parameters as unknowns; the minimum energy conditions ?E _L/?τ_k=0 yield 34 equations which are solved by a least-squares method. The set of energy parameters fitting structural properties of all four phases together is: z _Ca=1.50, z _o=?1.10 e, r _Ca=1.05, ρ=0.25 Å; the Mg charge was fixed at 1.38 e, from a previous study on forsterite. An average shift of 0.04 Å is observed between experimental and least-energy calculated atomic positions. Results are compared with those of Mg₂SiO₄, where the fit was based both on thermoelastic and on structural properties. If no charge values were fixed “a priori”, just ratios between charges could be determined by fitting them to structural data only.     

Crystal structures of Ni2SiO4 and Fe2SiO4 as a function of temperature and heating duration

X-ray structure refinements of Ni₂SiO₄ and Fe₂SiO₄ spinels have been made as a function of temperature and heating duration by intensity measurements at high temperatures and room pressure. The lattice parameters of Ni₂SiO₄ spinel linearly increased with temperature up to 1,000° C. However, Fe₂SiO₄ spinel exhibited a nonlinear thermal expansion and was converted to a polycrystalline mixture of spinel and olivine by heating of less than one-hour at 800° C. The ratios between the octahedral and tetrahedral bond lengths D _oct/D _tetr and between the shared and unshared edge distances (O-O)_sh/(O-O)_unsh in Fe₂SiO₄ spinel were both much larger than those in Ni₂SiO₄. These ratios increase with temperature. The Fe₂SiO₄ spinel more readily approached a activation state which facilitated the transition to the olivine structure than the Ni₂SiO₄ spinel. The lattice parameter of Ni₂SiO₄ spinel decreased with heating period at constant temperatures of 700° C and 800° C. The parameter of the quenched sample after heating for 52 h at 700° C was smaller than that of the nonheated sample. The refinements of the site occupancies at each heating duration indicated an increase in the cation deficiency in both tetrahedral and octahedral sites. Electron microprobe analysis, however, proved no significant difference in the chemical compositions between the quenched and nonheated samples. Si and Ni atoms displaced from normally occupied spinel lattice sites are assumed to settle in vacant sites defined by the cubic close packed oxygen sublattice in a manner which preserves the electric neutrality of the bulk crystal.     

Factors effecting the stability field of Ca-poor pyroxene and the origin of the Ca-poor minimum in Ca-rich pyroxenes from tholeiitic intrusions

Ca-poor pyroxene ceases to crystallise towards the end of fractionation in tholeiitic intrusions and is usually replaced by Fe-rich olivine. Using the data of Nicholls et al. (1971), the \(a_{{\text{SiO}}_2 }\) at which olivine and pyroxene can coexist has been calculated at different temperatures and pressures. From these calculations it is clear that the Fe/Mg ratio of the last Ca-poor pyroxene to crystallise from a melt is increased by raising the temperature or pressure of crystallisation. The Ca-poor pyroxene-Fe-rich olivine relationship is also dependent on the \(a_{{\text{SiO}}_2 }\) of the melt. In magmas which crystallise Fe-rich olivine before quartz, inicreasing their \(a_{{\text{SiO}}_2 }\) will raise the Fe/Mg ratio of the last Ca-poor pyroxene to crystallise. If the \(a_{{\text{SiO}}_2 }\) of the magma is so high that SiO₂ saturation is reached before the appearance of cumulus Fe-rich olivine, any further increase in the \(a_{{\text{SiO}}_2 }\) of the melt will not influence the stability field of Ca-poor pyroxene. The replacement of Ca-poor pyroxene by Fe-rich olivine requires the magma to reach a high level of a _FeO late in its fractionation. If a magma fractionates with an FeO depletion trend, Ca-poor pyroxene is replaced by Ca-rich pyroxene. The reaction is initiated by the appearance of cumulus K-feldspar which results in a marked reduction in the amount of anorthite crystallising from the magma. This increases the a _CaO of the melt so that Ca-poor pyroxene is replaced by Ca-rich pyroxene.     

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

Annealing experiments on natural olivine (Mg_1-x Fe _x )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-pO₂ theoretical 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.     

Widespread occurrence of magnesiocummingtonite in ultramafic schists,Cima di Gagnone,Ticino, Switzerland

Abundant magnesiocummingtonite (space group P2₁/m) with Mg/(Mg+Fe) ratios between 0.85 and 0.89 occurs in lenses of schistose metaperidotite enclosed in kyanite-zone rocks of the Lepontine Alps, Ticino, Switzerland. It forms prisms and needles that extend homoaxially from cores of tremolite. Coexisting magnesian phases are olivine, orthopyroxene, talc, magnesite, and chlorite. Except for γ∶z, optical and structural properties of one example fall on extrapolations of existing determinative curves. Analogous to synthetic F-clinoamphiboles, zz∶z has a maximum at approximately 0.7 Mg/(Mg+Fe). Anthophyllite, of almost identical composition, occurs in the same region, often intergrown with cummingtonite along lamellae ‖(010) and ‖(100). Cummingtonite is believed to have partially inverted to anthophyllite during cooling.     

A thermochemical data base for phase equilibria in the system Fe-Mg-Si-O at high pressure and temperature

A thermochemical data base for phases in the system Fe-Mg-Si-O at high pressures up to 300 kbar is established by supplementing the available calorimetric data with data calculated from experimental high pressure synthesis studies. Phases included in the data base are the SiO₂ polymorphs, rock salt solid solutions (Fe-Mg-O), Fe₂O₃, Fe₃O₄, (Mg, Fe)₂SiO₄ olivine, spinel, modified spinel and (Mg, Fe)SiO₃ perovskite and pyroxene. Phases not included are the MgSiO₃-ilmenite and -garnet. Fe-Mg solution properties of olivine, spinel, perovskite and wustite (rock salt) are estimated. The wüstite solid solution has been modeled as a nonideal solution of three end members; FeO, FeO_1.5 and MgO. The new data base is made consistent with most of the available information on high pressure phase studies. The data base is useful in generating phase diagrams of various different compositions for the purpose of planning new experiments and analysing existing phase synthesis data.     

Back transformation and oxidation of (Mg,Fe)2SiO4 spinels at high temperatures

Based on the in situ and temperature-quench X-ray measurements, the back transformation in the (Mg, Fe)₂SiO₄-spinels has been characterized in terms of the transformation temperature (T _r ),mechanism and kinetics of the transformation, and of the end product(s), with specific emphasis on the effect of oxygen on this transformation. The in situ measurements were conducted to 900° C in vacuum (10^-4 to 10^-5 torr) and to 600° C in air using synchrotron radiation (SR) at Stanford Synchrotron Radiation Laboratory (SSRL). In the quench-type measurements, samples were heated in air to 1100° C, quenched and examined at ambient conditions using the conventional X-ray diffraction facilities. Important results are (1) in vacuum, all the spinels convert back into the olivine phase, with their T _r decreasing with increasing iron content; (2) the spinel olivine back transformation is a nucleation and growth type of transformation and can be described quantitatively using the Avrami equation; (3) in air, the (Mg, Fe)₂SiO₄-spinels with 0.2 mole fraction Fe or more are all oxidized, and the composition and phase of the end products depend upon the temperature and the starting composition; and (4) the oxidation of the iron-rich (Mg, Fe)₂SiO₄-spinels in air occurs at 350–400° C, which is significantly lower than its T _r ( 300° C) in vacuum.     

Infrared vibrational spectra of Beta-Phase Mg2SiO4 and Co2SiO4 to Pressures of 27 GPa

Infrared absorption spectra of the high-pressure polymorphs β-Mg₂SiO₄ and β-Co₂SiO₄ have been measured between 0 and 27 GPa at room temperature. Grüneisen parameters determined for 11 modes of β-Mg₂SiO₄ (frequencies of 300 to 1,050 cm^?1) and 5 modes of β-Co₂SiO₄ (490 to 1,050 cm^?1) range between 0.8 and 1.9. Averaging the mid-infrared spectroscopic data for β-Mg₂SiO₄ yields an average Grüneisen parameter of 1.3 (±0.1), in good agreement with the high-temperature thermodynamic value of 1.35. Similarly, we find a value of 1.05 (±0.2) for the average spectroscopic Grüneisen parameter of β-Co₂SiO₄.     

Partition of Ni between olivine and sulfide: the effect of temperature,f_{{\text{O}}_{\text{2}} } and f_{{\text{S}}_{\text{2}} }

The experimental distribution coefficient for Ni/ Fe exchange between olivine and monosulfide (K_D3) is 35.6±1.1 at 1385° C, \(f_{{\text{O}}_{\text{2}} } = 10^{ - 8.87} ,f_{{\text{S}}_{\text{2}} } = 10^{ - 1.02} \) , and olivine of composition Fo96 to Fo92. These are the physicochemical conditions appropriate to hypothesized sulfur-saturated komatiite magma. The present experiments equilibrated natural olivine grains with sulfide-oxide liquid in the presence of a (Mg, Fe)-alumino-silicate melt. By a variety of different experimental procedures, K _D3 is shown to be essentially constant at about 30 to 35 in the temperature range 900 to 1400° C, for olivine of composition Fo97 to FoO, monosulfide composition with up to 70 mol. % NiS, and a wide range of \(f_{{\text{O}}_{\text{2}} } \) and \(f_{{\text{S}}_{\text{2}} } \) .     

Elasticity of the olivine and spinel polymorphs of Ni2SiO4

The single-crystal elastic moduli, c _ij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni₂SiO₄ olivine: c ₁₁=3.40(2), c ₂₂=2.38(2), c ₃₃=2.53(2), c ₄₄=0.71(1), c ₅₅=0.87(1), c ₆₆=0.78(1), c ₁₂=1.09(2), c ₁₃=1.10(4), c ₂₃=1.13(3), Ni₂SiO₄ spinel: c ₁₁=3.66(3), c ₄₄=1.06(1), c ₁₂=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c ₁₁>c ₃₃>c ₂₂, regardless of composition. The moduli c ₅₅ and c ₆₆ are approximately equal, and greater than c ₄₄. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO₄ tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\) . When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\) , and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\) . The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni₂SiO₄ (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni₂SiO₄ are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c _ij's and shear modulus of a spinel-structure silicate to be estimated from c ₁₁ of the corresponding α phase and the bulk modulus of the γ phase.