Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.     

Magnetic properties of the Fe2SiO4-Fe3O4 spinel solid solutions

 Magnetic measurement of Fe_{3− x} Si _x O₄ spinel solid solutions indicates that their Curie temperatures decrease gradually, but not linearly, from 851 to 12 K with increasing content of nonmagnetic ions Si⁴⁺. Magnetic hysteresis becomes more noticeable in solid solutions having a larger content of Fe₂SiO₄. Saturation magnetizations of Fe_{3− x} Si _x O₄ samples increase up to x=0.357 and they are easily saturated in the field of H=0.1 T. However, magnetization of the sample of x=0.794 does not approach saturation even at high field of H=7.0 T and has a large coercive force. The Si⁴⁺ disordered distribution is confirmed to be ^tetr[Fe³⁺ _{1− x + x t} Si⁴⁺ _{x (1− t )}] ^octa[Fe²⁺ _{1+ x} Fe³⁺ _{1− x − x t} Si⁴⁺ _{x t} ] O₄ by the spin moment, which is consistent with site occupancy obtained from X-ray crystal structure refinement. Their molecular magnetizations would be expressed as M _B={4(1+x)+10xt}μ_B as functions of composition parameter x and Si⁴⁺ ordering parameter t of the solid solution. The sample of x=0.794 is antiferromagnetic below the Néel temperature, mainly due to the octahedral cation interaction M _O–M _O, while both M _T–M _O and M _O–M _O interactions induce a ferrimagnetic property. Concerning magnetic spin configuration, in the case of x>0.42, the lowest dɛ level becomes a singlet, resulting in no orbital angular momentum. Received: 20 April 2000 / Accepted: 11 September 2000     

Olivine flotation and settling experiments on the join Mg2SiO4-Fe2SiO2

Some unusual density relations between olivine and coexisting liquid in the system fosterite-fayalite are reported. At 1 atmosphere pressure olivine floats on its coexisting liquid for intermediate compositions on this binary because of extreme partitioning of Fe into the melt phase. At 20 kilobars the usual behavior of olivine settling occurs because the partitioning of Fe in the melt is reduced, aided possibly by the dissolution of CO₂ in the melt from use of a graphite container. Olivine flotation and settling are rapid in a time period of only a few hours because viscosities are a little greater than that of paraffin oil at room temperature. Some adcumulate textures with good triple junction grain boundaries are developed. General observations of differentiated magmatic systems on a number of scales and experimental data indicate that the mechanisms by which magmas can differentiate vary considerably in the ultramafic to tholeiitic compositional range.     

Electrical conductivity measurements on olivines Mg2SiO4-Fe2SiO4 under defined thermodynamic conditions

The isobaric (P=10 kb) temperature dependence of the electrical conductivities of forsterite, fayalite and forsterite-fayalite mixed crystals was measured with special regard to the thermodynamics of point defects in these minerals. Measurements, taken at increasing and decreasing temperature, were performed on synthetic powders of the following compositions: Fo 100/Fa 0, Fo 90/Fa 10, Fo 80/Fa 20, Fo 60/Fa 40, and Fo 0/Fa100. Control of oxygen partial pressure was achieved with solid state buffers (Fa/Q/M, Fa/Q/I, and Fe/FeO). Activities of the binary components were controlled by equilibrating the sample with its neighbouring phases. All values for σ, obtained with controlled pO₂ and fixed activities of the binary components, agree well upon either heating or cooling. From the gradient of lg σ vs. 1/T plots, the following activation energies were estimated: 2,461 eV (970°–1075°C) and 0.984 eV (522°–970°C) for Fo 100/Fa 0 equilibrated with MgO; 0.777 eV and 0.683 eV for Fo 90/Fa 10 and Fo 80/Fa 20 equilibrated with enstatite and pO₂ controlled by Fe/FeO buffer; 0.622 eV, 0.528 eV, and 0.479 eV for Fo 90/Fa 10, Fo 80/Fa 20, and Fo 60/Fa 40 equilibrated with enstatite and pO₂ controlled by Fa/Q/M buffer; and 0.524 eV and 0.383 eV for Fo 0/Fa 100 equilibrated with Q/I and Q/M respectively.     

Thermodynamic properties and crystal growth behavior of the hashemite (BaSO4–BaCrO4) solid solution

Thermodynamic properties of the BaSO₄–BaCrO₄ hashemite solid solution were calculated using molecular principles. Force-field potentials and physical properties of the end member BaCrO₄ were derived using the program package GULP. Subsequently, anion–anion (SO₄²⁻–CrO₄²⁻, SO₄²⁻–SO₄²⁻, CrO₄²⁻–CrO₄²⁻) interaction energies were fitted to a number of random and ordered anion distributions, which were energy-optimized using these empirical potentials. With these interaction energies, diagrams for the enthalpy and free energy of mixing could be computed for the entire range of the hashemite solid solution between the BaSO₄ and BaCrO₄ end members and for a number of annealing temperatures. These thermodynamic data show that the solid solution is close to ideal and ordering is not observed at low temperatures for any composition. However, according to our calculations, exsolution may occur at the nanoscale due to a slight tendency of sulfate–chromate avoidance.Growth experiments of chromate-rich hashemite on barite using atomic force experiments (AFM) in a fluid cell indicate that hashemite does not show the same degree of growth anisotropy as barite. In the case of barite, this anisotropy leads to a structural self-inhibition of spiral growth. In contrast, hashemite exhibits a spatially more extended spiral growth, which can contribute more to overall volume growth than in the case of barite. This finding is confirmed by a higher growth rate of hashemite than of barite in macroscopic batch-reactor and flow-through experiments.Molecular simulations indicate that there is a less pronounced step energy difference between bounding steps of growth islands for hashemite than for barite, which may partially explain the difference in growth anisotropy of the two minerals. Differences in adsorption energies to the corners of growth islands, which are the limiting steps of growth, do not seem to be high enough to explain differences in growth anisotropies. Therefore, kinetic effects or differences in the interfacial free energies of the two minerals may serve as an additional explanation for differences in the growth behavior.     

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.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

Thermodynamic properties of strontianite-witherite solid solution (Sr,Ba)CO3

Structural parameters and thermodynamic properties of strontianite — witherite solid solutions have been studied by X-ray powder diffraction, heat flux Calvet calorimetry and cation-exchange equilibria technique. X-ray study of the synthetic samples have shown linear and quadratic (for c-parameter) composition dependencies of the lattice constants in the carbonate solid solution. The thermodynamic energy parameters demonstrate the non-ideal character of strontianite — witherite solid solutions. Enthalpies of solution of the samples have been measured in 2PbO*B₂O₃ at 973 K. The new data on the enthalpy of formation H _f,298.15 ⁰ of SrCO₃ and BaCO₃ were obtained: -1231.4±3.2 and -1209.9±5.8 kJ*mol^-1 respectively. The enthalpy of mixing of the solid solution was found to be positive and asymmetric with maximum at X_Ba (carbonate)=0.35. The composition dependence of the enthalpy of mixing may be described by two — parametric Margules model equation: H _mix=X _BaX _Sr[(4.40±3.91)X _Ba+(28.13±3.91)X _Sr] kJmol^–1 Cation-exchange reactions between carbonates and aqueous SrCl₂-BaCl₂ supercritical solutions (fluids) were carried out at 973 and 1073 K and 2 kbar. Calculated Margules model parameters of the excess free energy are: for orthorhombic carbonate solid solutions W _Sr=W _Ba=11.51±0.40 kJmol^–1 (973 K) and W _Sr=W _Ba=12.09±0.95 kJmol^– (1073 K) for trigonal carbonate solid solutions W _Sr=W _Ba=13.55±0.40 kJmol^– (1073 K).     

Single-crystal infrared reflectivity of pure Mg2SiO2 forsterite and (Mg0.86,Fe0.14)2SiO4 olivine

New polarized infrared reflectance spectra of pure synthetic forsterite and natural Fo₈₆-olivine have been recorded from 5000 to 100cm^-1. Out of the 35 expected infrared active modes, 33 have been observed (8 B_1u, 12 B_2u, 13 B_3u). The observed frequency shift from pure forsterite to Fo₈₆-olivine is consistent with the higher mass of the substituted iron. The substitution of only 14% of iron also reduces the overal far-infrared reflectivity of olivine as compared to pure forsterite. Several discrepancies associated with previous studies of forsterite are explained by our investigation. We suggest that some of the previous investigations were complicated by polarization mixing.     

Temperature-dependent magnetic susceptibility behaviour of spinelloid and spinel solid solutions in the systems Fe2SiO4–Fe3O4 and (Fe,Mg)2SiO4–Fe3O4

The magnetic behaviour and Curie temperatures (T _C ) of spinelloids and spinels in the Fe₃O₄–Fe₂SiO₄ and Fe₃O₄–(Mg,Fe)₂SiO₄ systems have been determined from magnetic susceptibility (k) measurements in the temperature range –192 to 700 °C. Spinelloid II is ferrimagnetic at room temperature and the k measurements display a characteristic asymmetric hump before reaching a T _C at 190 °C. Spinelloid V from the Mg-free system is paramagnetic at room temperature and hysteresis loops at various low temperatures indicate a ferri- to superparamagnetic transition before reaching the T _{C .} The T _C shows a non-linear variation with composition between –50 and –183 °C with decreasing magnetite component (X _Fe3O₄). The substitution of Mg in spinelloid V further decreases T _C . Spinelloid III is paramagnetic over nearly the total temperature range. Ferrimagnetic models for spinelloid II and spinelloid V are proposed. The T _C of Fe₃O₄–Fe₂SiO₄ spinel solid solutions gradually decrease with increasing Si content. Spinel is ferrimagnetic at least to a composition of X _Fe3O₄=0.20, constraining a ferrimagnetic to antiferromagnetic transition to occur at a composition of X _Fe3O₄<0.20. A contribution of the studied ferrimagnetic phases for crustal anomalies on the Earth can be excluded because they lose their magnetization at relatively low temperatures. However, their relevance for magnetic anomalies on other planets (Mars?), where these high-pressure Fe-rich minerals could survive their exhumation or were formed by impacts, has to be considered.     

Comparison of the raman microprobe spectra of (Mg,Fe)2SiO4 and Mg2GeO4 with olivine and spinel structures

Raman microprobe (RMP) spectra were produced for each of the olivine and spinel structured phases of Mg₂GeO₄ and (Mg, Fe)₂SiO₄. The assembled data show that bands due to the tetrahedra in silicate and germanate olivines shift in a way that indicates a dominant mass effect. This correspondence is difficult to make in spinels due to differences in structural type. Differences in Fe/Mg content of olivine shift the tetrahedral vibration bands only slightly, but their linear shifts could be used to indicate the composition of the phase.     

Polarized optical absorption spectra of synthetic chromium doped Mg2SiO4 (forsterite)

Polarized optical absorption measurements were carried out on three single crystals of Mg₂SiO₄ (forsterite), differently doped with Cr. Two crystals containing average 0.013 and 0.027 weight% Cr, respectively, were pulled from the melt in air, whereas one crystal containing average 0.08 weight% Cr was pulled from the melt in an argon atmosphere. The absorption spectra of the three crystals agree with each other although the intensity of single absorption bands varies significantly. In all -polarized patterns a sharp absorption line around 18000cm^-1 (550 nm) appears. Conjectures are presented to assign this line to the lasing center in Cr doped forsterite which very likely exists as Cr⁴⁺ at the fourfold coordinated Si site.     

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.     

Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress

The method of crystal static deformation, including inner strain effects, was applied to calculate the structure configuration and the elastic constants of forsterite under anisotropic and isotropic pressure. A Born type interatomic potential is used, with optimized atomic charges and repulsive radii; SiO₄ tetrahedra are approximated as rigid units. Computations were carried out in the range 1–8 GPa, with steps of 1 GPa, for the three uniaxial stresses τ₁, τ₂, τ₃ and for pressure p. By interpolation of results, interatomic distances and elastic tensor components are shown to depend quadratically on stress. A non-linear behaviour generally appears above 4 GPa; the importance of inner strain and non-linear effects is analyzed. Mg-O bond lengths and O-O edges of coordination polyhedra respond differently to anisotropic and to isotropic stresses, according to the topological features of the structure. Elastic and structural results for hydrostatic pressure are compared to experimental literature data, discussing the range of validity of the rigid body approximation for SiO₄ groups.     

Thermochemistry of (Fe2+, Mg)SiO3 orthopyroxene

Enthalpies of solution in eutectic (Li, Na)₂B₂O₄ melts at 1023 K were measured for five synthetic orthopyroxenes on the join MgSiO₃-FeSiO₃. The pyroxenes were synthesized at 1120°C and 20 kbar and thus were presumed to be highly disordered. The measurements indicate a small positive enthalpy of mixing, with W_H = 950 cal/MSiO₃.Enthalpy of solution measurements were made on a natural, well-ordered orthopyroxene near the composition En_52.5Fs_47.5 and on this material after heat-treatment at 1150°C and 20 kbar. Irreversible expansion of the unit-cell constants of the natural pyroxene after heat-treatment at various temperatures was used to characterize the degree of M-site disorder. The observed enthalpy of solution decrement of 0.85 kcal/MSiO₃ between the natural En_52.5 and the same material heated at 1150° corresponds to about half of the maximum possible disordering, or ΔX_Fe^M1? 0.25, which leads to a ΔH of 7.5 kcal/M₂Si₂O₆, for the exchange reaction: Fe(M2) + Mg(Ml) = Fe(Ml) + Mg(M2) if M-site interaction energy terms are ignored. This ΔH is larger than inferred from any of the analyses of site-occupancy data except that of Besancon (1981), who gave a very similar value. The measured ΔH of disorder and the W_H of mixing together indicate a large ΔH as great as 3.2 kcal for the reciprocal reaction: Fe₂Si₂O₆ + Mg₂Si₂O₆ = Fe(M2)Mg(M1)Si₂O₆ + Fe(M1)Mg(M2)Si₂O₆ as anticipated by Sack (1980).As a consequence of the inferred magnitudes of ΔHof the exchange and reciprocal reactions, departures from ideality of Gibbs energy of mixing of orthopyroxene are very small at 700°–1000°C. Activities of MgSiO₃ and FeSiO₃ may be replaced by their mol fractions at all temperatures in most petrologic calculations.     

High pressure phase transformations in the joins Mg2SiO4-Ca2SiO4 and MgO-CaSiO3

High pressure phase transformations for all the mineral phases along the joins Mg₂SiO₄-Ca₂-SiO₄ and MgO-CaSiO₃ in the system MgO-CaO-SiO₂ were investigated in the pressure range between 100 and 300 kbar at about 1,000 °C, by means of the technique involving a diamond-anvil press coupled with laser heating. In addition to the four end-members, there are three stable intermediate mineral components in these two joins. Phase behaviour of all the end-member components at high pressure have been reported earlier and are reviewed here. Results of this study reveal that the three intermediate components are all unstable relative to the end-members at pressures greater than 200 kbar. Ultimately, monticellite (CaMgSiO₄) decomposes into CaSiO₃ (perovskite-type)+MgO; merwinite (Ca₃MgSi₂O₈) decomposes into Ca₂SiO₄(K₂NiF₄-type)+CaSiO₃ (perovskite-type)+MgO; and akermanite (Ca₂MgSi₂O₇) decomposes into CaSiO₃ (perovskite-type)+MgO. Note that the decomposition reactions of all phases studied here result in the formation of MgO. Intermediate Ca-Mg silicates transform to pure Ca-silicates plus MgO, while pure Mg₂SiO₄ transforms to MgSiO₃+MgO.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

Thermodynamic properties of CoCr2O4: specific heat and magnetic entropy

We present the temperature dependence of the specific heat of CoCr₂O₄ between 2.08 K and 306 K in zero magnetic field. The lattice component can be described by the Komada–Westrum model with a characteristic temperature Θ_KW = 541 K. The entropy of the magnetic component amounts to 33.51 J mol^?1 K^?1 at T = 298.15 K, in good agreement with the magnetic entropy of Co²⁺ and Cr³⁺ ions with completely quenched orbital moments. We compare our results with data available in literature.     

Elastic properties of a single-crystal forsterite Mg2SiO4, up to 1,200 K

Elastic moduli of forsterite were measured between 300 and 1,200 K (? 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method. All the moduli decrease regularly with temperature. A summary of the results is as follows: