GeO2 vs SiO2: Glass transitions and thermodynamic properties of polymorphs     

Pascal Richet 《Physics and Chemistry of Minerals》1990,17(1):79-88

Relative-enthalpy measurements have been made on the hexagonal, tetragonal, glass and liquid phases of GeO₂. The glass transition is very sensitive to the impurity content, with a T _g ranging from 980 K for a pure product to 780 K for a Li-doped sample with 0.06 mol % Li. The relative C _p change at T _g of about 5% increases with the impurity content as a result of lower glass transition temperatures. Above 298 K the derived heat capacities are similar for all forms, with slightly higher values for the amorphous phases and two C _p cross-overs at 400 and 1000 K between the hexagonal and tetragonal modifications. For both GeO₂ and SiO₂ the coordination state markedly affects C _p and the entropy below 300 K, where the properties are much lower for the tetragonal than for the hexagonal modifications, i.e., S ₂₉₈ = 39.7 vs 55.3 J/mole K and 27.8 vs 41.4 J/ mole K for GeO₂ and SiO₂, respectively. The high-temperature C _p's of coesite and stishovite are likely similar to those of the low-pressure SiO₂ forms. Finally, these results, low-temperature C _p data and enthalpy-of-solution measurements have been used to derive a consistent set of thermodynamic properties for the GeO₂ modifications.  相似文献   

High-pressure phengite decomposition in the Weissenstein eclogite,Münchberger Gneiss Massif,Germany     

G. Franz  S. Thomas  D. C. Smith 《Contributions to Mineralogy and Petrology》1986,92(1):71-85

The petrography, mineral chemistry and petrogenesis of a sample from the Weissenstein eclogite, Bavaria, Germany, has been investigated. The total mineral assemblage comprises garnet, clinopyroxene_I+II, quartz, amphibole_I+II, rutile, phengite, epidote/allanite, plagioclase, biotite, apatite, pumpellyite, titanite (sphene), zircon, alkali feldspar and calcite. Textural observations combined with geothermobarometry (Fe/Mg distribution between clinopyroxene/garnet and phengite/garnet; jadeite-content of omphacite, Si-content of phengite, and An-content of plagioclase) provide indications of two different stages in the metamorphic evolution of the rock. The main phengitequartz-eclogite mineral equilibration occurred at minimum P=13–17kbar, minimum T=620±50° C; the retrograde symplectite stage (clinopyroxene_II, amphibole_II, biotite, plagioclase) occurred at P _total between 12 and 8.5 kbar. Reactions of the symplectite stage are:

1. phengite (core) + Na₂O_aq + CaO_aq=phengite (rim) + biotite + plagioclase + K₂O_aq + H₂O
2. phengite (core) + clinopyroxene_I + Na₂O_aq=phengite (rim + biotite + plagioclase + amphibole_II + SiO₂ + K₂O_aq + CaO_aq + H₂O
3. clinopyroxene_I + SiO₂ + K₂O_aq + H₂O=clinopyroxene_II + plagioclase+amphibole_II + Na₂O_aq + CaO_aq

The phengite decomposition produces H₂O, whereas the clinopyroxene decomposition consumes H₂O. The estimated P-T-conditions for the Weissenstein eclogite are in the same order of magnitude as those for other eclogite bodies from the Alps and Caledonides believed to be related to subduction processes.  相似文献   

An experimental study of the effect of Ca upon garnet-clinopyroxene Fe-Mg exchange equilibria   总被引：3，自引：1，他引：3  

D. J. Ellis  D. H. Green 《Contributions to Mineralogy and Petrology》1979,71(1):13-22

A series of basaltic compositions and compositions within the simple system CaO-MgO-FeO-Al₂O₃-SiO₂ have been crystallized to garnetclinopyroxene bearing mineral assemblages in the range 24–30 kb pressure, 750°–1,300° C temperature. Microprobe analyses of coexisting garnet and clinopyroxene show that K _D(Fe²⁺/Mg^G+/Fe²⁺/Mg^Cpx) for the Fe-Mg exchange reaction between coexisting garnet and clinopyroxene is obviously dependent upon the Ca-content and apparently independent of the Mg/(Mg+Fe) content of the clinopyroxene and garnet. The Ca-effect is believed to be due to a combination of non-ideal Ca-Mg substitutions in the garnet and clinopyroxene. Our data and interpretation reconciles previous inconsistencies in the temperature dependence of K _D ^? values determined in experimental studies of simple systems, complex basalt, grospydite and garnet peridotite compositions. Previous differences between the effect of pressure upon K _Das predicted from simple system theory (Banno, 1970), and that observed in experiments on multicomponent natural rock compositions (Råheim and Green, 1974a) can now be resolved. We have determined K _Das a function of P, T, and X _Gt ^Ca (grossular) and derived the empirical relation $$T\left( {^\circ {\text{K}}} \right) = \frac{{3104X_{{\text{Ca}}}^{{\text{Gt}}} + 3030 + 10.86P\left( {{\text{kb}}} \right)}}{{\ln K_{\text{D}} + 1.9034}}$$ . This empirical relationship has been applied to garnet-clinopyroxene bearing rocks from a wide range of geological environments. The geothermometer yields similar estimates for garnet-clinopyroxene equilibration for neighbouring rocks of different composition and different K _Dvalues. In addition, temperature estimates using the above relationship are more consistent with independent temperature estimates based on other geothermometers than previous estimates which did not correct for the Ca-effect. An alternative approach to the above empirical geothermometer was attempted using regular solution models to derive Margules parameters for various solid solutions in garnets and clinopyroxenes. The derived Margules parameters are broadly consistent with those determined from binary solution studies, but caution must be exercised in interpreting them in terms of actual thermodynamic properties of the relevant crystalline solid solutions because of the assumptions which necessarily have to be made in this approach.  相似文献   

Thermochemistry of some pyroxenes and related compounds     

Alexandra Navrotsky  William E Coons 《Geochimica et cosmochimica acta》1976,40(10):1281-1288

The enthalpies of formation of a number of crystalline silicates from the oxides at 986 K were determined by oxide melt solution calorimetry. The values of ΔH°_{f, 986}, in kcal/mol, are as follows: MgCaSi₂O₆, ? 34.3 ± 0.4; CoCaSi₂O₆, ? 26.7 ± 0.5; NiCaSi₂O₆, ? 27.1 ± 0.5; MnSiO₃, ? 6.3 ± 0.3; Mn₂SiO₄, ? 12.2 ± 0.3. In addition, for MnSiO₃ (rhodonite)→ MnSiO₃ (pyroxmangite), ΔH°₉₈₆ = + 0.06 ± 0.3₃kcal/mol and for MgCaSi₂O₆ (diopside) = MgCaSi₂O₆ (glass), ΔH°₉₈₆ = + 21.0 ± 0.3 kcal/ mol. For hedenbergite, FeCaSi₂O₆, ΔG°₁₃₅₀ = ?25.6 ± 1.5 kcal/mol. In terms of pyroxene phase equilibria and crystal chemistry, our thermochemical data support the generally accepted crystallographic arguments that (a) the C2/c clinopyroxene structure increases in stability with decreasing size of the ion occupying the Ml site in the MCaSi₂O₆ series, and (b) the energy (and enthalpy) differences between orthopyroxene, clinopyroxene, and pyroxenoid structures are generally quite small and often less than 500 cal/mol in magnitude.  相似文献   

High temperature X-ray study of single crystal stishovite synthesized with Li2WO4 as flux     

S. Endo  T. Akai  Y. Akahama  M. Wakatsuki  T. Nakamura  Y. Tomii  K. Koto  Y. Ito  M. Tokonami 《Physics and Chemistry of Minerals》1986,13(3):146-151

Single crystal stishovite with a square prismatic habit and maximum length 0.8 mm was grown from α-quartz at 120 kbar and ～1,300° C. Li₂WO₄, chosen as a result of a previous experiment in growing coesite, was also successful as flux for stishovite. Single crystal X-ray structure analysis of the crystals thus obtained has been carried out at high temperatures under ambient pressure. Lattice constant measurements give a larger thermal expansion coefficient along the a-axis than along the c-axis. The bond distances and bond angles show a decreasing distortion of the SiO₆ octahedron with increasing temperature. The increasing amplitude of thermal vibrations of oxygen atoms with increasing temperature results in increasing O-O repulsion in the basal plane, which explains the observed crystallographic changes.  相似文献   

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

Roger G. Burns  Chien-Min Sung 《Physics and Chemistry of Minerals》1978,2(4):349-364

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.  相似文献   

Energy gap and density in SiO2 polymorphs     

Sławomir Maj 《Physics and Chemistry of Minerals》1988,15(3):271-273

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.  相似文献   

An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene   总被引：1，自引：0，他引：1  

Simon L. Harley 《Contributions to Mineralogy and Petrology》1984,86(4):359-373

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.  相似文献   

The pyroxmangite-rhodonite transformation for the MnSiO3 composition     

W. V. Maresch  A. Mottana 《Contributions to Mineralogy and Petrology》1976,55(1):69-79

The polymorphic transformation between synthetic pyroxmangite and rhodonite of MnSiO₃ composition has been reversibly bracketed in the presence of water at 3 kbar (between 425 ° and 450 ° C), 6 kbar (between 475 ° and 525 ° C), 20 kbar (between 500 ° and 900 ° C), 25 kbar (between 800 ° and 900 ° C) and 30 kbar (between 900 ° and 1,000 ° C), using standard cold-seal pressure vessels and piston cylinder apparatus. Oxygen fugacities buffered by the bomb walls and piston-cylinder cell assemblies sufficed to keep manganese in the divalent state. Pyroxmangite of MnSiO₃ composition is shown to be the high-pressure, low-temperature polymorph with respect to rhodonite of the same composition. It is a stable phase at atmospheric pressure below 350–405 ° C.X-ray data for synthetic pyroxmangite are presented. The unit-cell parameters (a₀=6.717(2) Å, b₀=7.603(1)Å, c₀=17.448(5) Å, =113 °50(1), = 82 °21(2), =94 °43(1); space group P-1) give a unit-cell volume (807.5(0.3) ų) which, in accordance with other recent least squares lattice refinements of hydrothermally synthesized material, is slightly smaller than that obtained by single-crystal work on anhydrously synthesized material.Application of the present results to natural rocks is severely restricted due to the great variety and extent of cationic substitutions observed in natural pyroxenoids. The univariant polymorphic transformation determined for the MnSiO₃ composition is thus replaced in natural systems by a divariant field in which pyroxmangite and rhodonite of differing composition will stably coexist.  相似文献   

Decomposition of fayalite (Fe2SiO4) in an oxygen potential gradient at 1,418 K     

U. Brinkmann  W. Laqua 《Physics and Chemistry of Minerals》1985,12(5):283-290

The decomposition of fayalite (Fe₂SiO₄) in oxygen potential gradients is studied at T=1,418 K. The compound will be decomposed into its component oxides wüstite, Fe_1?δO, and silica, SiO₂, by the simultaneous action of two different oxygen partial pressures, exceeding a critical ratio, despite the fact that fayalite is stable at both the lower and the higher oxygen potential. A quantitative analysis of the decomposition process caused by defect fluxes within the bulk Fe₂SiO₄ is given.  相似文献   

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2     

I. Abs-Wurmbach  Prof. Dr. K. Langer 《Contributions to Mineralogy and Petrology》1975,49(1):21-38

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.  相似文献   

The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO 4 4− ion     

Michele Catti 《Physics and Chemistry of Minerals》1981,7(1):20-25

In the lattice energy expression of forsterite, based on a Born-Mayer (electrostatic+repulsive+dispersive) potential, the oxygen charge z _o, the hardness parameter ρ and the repulsive radii r _Mg and r _Si appear as unknown parameters. These were determined by calculating the first and second partial derivatives of the energy with respect to the cell edges, and equalizing them to quantities related to the crystal elastic constants; the overdetermined system of equations was solved numerically, minimizing the root-mean-square deviation. To test the results obtained, the SiO ₄ ^4? ion was assumed to move in the unit-cell, and the least-energy configuration was sought and compared with the experimental one. By combining the two methods, the optimum set of parameters was: z _o=?1.34, ρ=0.27 Å, r _Mg=0.72 Å, r _Si=0.64 Å. The values ?8565.12 and ?8927.28 kJ mol^?1 were obtained, respectively, for the lattice energy E _Land for its ionic component E _L ⁰ ,which accounts for interactions between Mg²⁺ and SiO ₄ ^4? ions only. The charge distribution calculated on the SiO ₄ ^4? ion was discussed and compared with other results. Using appropriate thermochemical cycles, the formation enthalpy and the binding energy of SiO ₄ ^4? were estimated to be: ΔH _f(SiO ₄ ^4? )=2117.6 and E(SiO ₄ ^4? )=708.6 kJ mol^?1, respectively.  相似文献   

Manganese thermometer for mantle peridotites     

J. S. Delaney  J. V. Smith  J. B. Dawson  P. H. Nixon 《Contributions to Mineralogy and Petrology》1979,71(2):157-169

The temperature dependence of the Mn-Mg distribution between garnet and clinopyroxene, originally proposed by Carswell, was confirmed by Shimizu and Allègre (1978) using ion microprobe and electron microprobe data. High precision electron microprobe analyses of a larger set of 52 Iherzolites from S. Africa and Malaita, Solomon Islands show considerable scatter in the temperature dependence of this distribution, and correlation with the CaO content of the garnet is indicated. A new distribution coefficient is based on the reaction: $$\begin{gathered} \operatorname{Mn} _{\text{2}} \operatorname{Si} _2 \operatorname{O} _6 {\text{ + }}\operatorname{CaAl} _{2/3} \operatorname{SiO} _4 {\text{ + }}\operatorname{MgAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{Mn - pyroxene grossular pyrope}} \hfill \\ {\text{ }} \rightleftharpoons \operatorname{CaMgSi} _2 \operatorname{O} _6 {\text{ + }}2\operatorname{MnAl} _{2/3} \operatorname{SiO} _4 \hfill \\ {\text{ diopside spessartine}} \hfill \\ \end{gathered} $$ It was calibrated against temperature determined from two independent thermometers (Wells pyroxene and O'Neill-Wood garnet-olivine) for Iherzolitic assemblages, and shown to to be sensitive to within + 50 °C for most specimens in the range 900 °– 1,300 ° C. This distribution coefficient appears independent of pressure within the uncertainty of the available data, and has the potential to be a third independent thermometer for use in garnet Iherzolites and possibly eclogites.  相似文献   

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

Takamitsu Yamanaka 《Physics and Chemistry of Minerals》1986,13(4):227-232

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.  相似文献   

On the Relationship between Refractive Index and Density for SiO2-polymorphs     

B. Marler 《Physics and Chemistry of Minerals》1988,16(3):286-290

Five different refraction formulas were applied to SiO₂ polymorphs in order to determine the most suitable refractive index-density relation. 13 SiO₂ polymorphs with topological different tetrahedral frameworks are used in this study including eight new low density SiO₂ polymorphs — so called “guest free porosils”. These SiO₂ polymorphs cover a density range from 1.76 to 2.92 g/cm³. The mean refractive indices (ovn) of the porosils have been determined by the immersion method, the densities (ρ) were calculated from the unit cell parameters. Assuming the polarizability (α) of all SiO₂ polymorphs to be constant the general refractivity formula $$\{ 2\overline {11} 0\} \langle 0001\rangle $$ turned out to be the most suitable for SiO₂ polymorphs. Regression analysis yields an electronic overlap parameter b=1.2(1).  相似文献   

The transition between spinel lherzolite and garnet lherzolite,and its use as a Geobarometer     

Hugh St. C. O'Neill 《Contributions to Mineralogy and Petrology》1981,77(2):185-194

The equilibrium between spinel lherzolite and garnet lherzolite has been experimentally determined in the CaO-MgO-Al₂O₃-SiO₂ system between 800° and 1,100° C. In confirmation of earlier work and predictions from thermodynamic data, it was found that theP-T slope of the reaction was close to zero, the equilibrium ranging from 16.1 kb at 800° C to 18.7 kb at 1,100° C (±0.3 kb). The addition of Cr₂O₃ to the system raised the stability field of spinel to higher pressures. It was found that the pressure at which both garnet and spinel could exist with olivine+orthopyroxene+clinopyroxene in the system CMAS ?Cr₂O₃ could best be described by the empirical relationship: $$P = P^{\text{O}} + \alpha X_{{\text{Cr}}}^{s{\text{p}}} $$ whereP ⁰ is the equilibrium pressure for the univariant reaction in the Cr₂O₃-free system,α is a constant apparently independent of temperature with a value of 27.9 kilobars, andX _Cr ^sp is the mole fraction of chromium in spinel. Use was made of the extensive literature on Mg-Fe²⁺ solid solutions to quantitatively derive the effect of Fe²⁺ on the equilibrium. The effect of other components (Fe³⁺, Na) was also considered. The equilibrium can be used as a sensitive geobarometer for rocks containing the five phases ol+opx+cpx+gt+sp, and thus provides the only independent check presently available for the more widely applicable geobarometer which uses the alumina content of orthopyroxene in equilibrium with garnet.  相似文献   

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

Michele Catti  Gabriella Ivaldi 《Physics and Chemistry of Minerals》1983,9(3-4):160-166

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.  相似文献