The geochemistry of pyroxenes from the lower layered series of the Jimberlana intrusion,Western Australia

Most of the Al³⁺ entering the pyroxenes does so by substituting for tetrahedral Si⁴⁺. This creates a charge imbalance that requires the simultaneous entry of Cr³⁺, Ti⁴⁺, Fe³⁺ or Al³⁺ into octahedral sites. Cr³⁺, because of its high crystal field stabilisation energy (CFSE), is the most important of these elements to enter the early-formed pyrosenes but it is replaced by Ti⁴⁺ later in fractionation when the Cr³⁺ content of the melt becomes depleted. The dependence of Cr³⁺ and Ti⁴⁺ on charge balance controls their partition between coexisting pyroxenes and olivines. Ca-rich pyroxene which contains more Al³⁺ than Ca-poor pyroxene also has more Ti⁴⁺ and Cr³⁺ whereas olivine, which contains negligible Al³⁺, has low Cr³⁺ and Ti⁴⁺. The Al³⁺ content of pyroxenes is influenced by changes in P, T, \(a_{{\text{SiO}}_{\text{2}} }\) and \(a_{{\text{Al}}_{\text{2}} {\text{O}}_{\text{3}} }\) of the magma and by the nature of the ion providing charge balance in the octahedral site. Of these \(a_{{\text{SiO}}_{\text{2}} }\) is dominant and variations in the Al³⁺ content of the Jimberlana pyroxenes correspond closely with the expected changes in the \(a_{{\text{SiO}}_{\text{2}} }\) of the melt. The substitution of divalent ions, such as Mn²⁺ and Ni²⁺, in the pyroxene lattice is by replacement of Fe²⁺ or Mg²⁺ in the octahedral M ₃ and M ₂ sites and is therefore independent of charge balance. If there are no size restrictions, the principal factor to be considered is the CFSE the ion receives in octahedral co-ordination. Ni²⁺, which receives a high CFSE, partitions strongly between the early-formed pyroxenes and olivines and therefore becomes depleted in the magma with fractionation. Conversely Mn²⁺, which receives zero CFSE, concentrates in the magma with fractionation and becomes a more important substitute in the later-formed pyroxenes. Its geochemical behaviour is controlled by its size. The narrow miscibility gap of the Jimberlana pyroxenes and the high En content of the Ca-poor pyroxenes at the bronzite pigeonite changeover suggest that these pyroxenes crystallised at a higher temperature than pyroxenes of comparable composition from other intrusions.     

A study of Gd,Ce and Eu impurities in fluorite deposits by electron paramagnetic resonance and neutron activation analysis

In order to obtain a better understanding of fluorite deposits, rare earth impurities have been analyzed for a large number of samples taken from cross-sections of several low temperature hydrothermal veins. Two types of measurements have been used: Electron Paramagnetic Resonance (EPR) and Neutron Activation Analysis (NAA). For Gd, the ratio of spin concentrations to total concentration [Gd³⁺]/[Gd_total] is close to 1 in all the samples; on the other hand, the ratios [Eu²⁺]/[Eu_total] and [Ce³⁺ -F _? ⁱ ]/[Ce_total] exhibit large variations. The first result suggests that the major part of the lanthanides in the samples is incorporated in the crystal lattice and that clustering of lanthanides ions is not important. The behaviour of Eu and Ce is ascribed to charge state changes and symmetry state changes respectively.     

Crystal chemistry of a natural schorlomite and Ti-andradites synthesized at different oxygen fugacities

Ti-andradites were synthesized at a pressure of P(H₂O)=3 kbar and temperatures of 700–800° C. Oxygen fugacities were controlled by solid state buffers (Ni/NiO; SiO₂ + Fe/Fe₂SiO₄). The Fe²⁺-and Fe³⁺-distribution was determined by low temperature Mössbauer spectroscopy. The water content was measured by a solid's moisture analyzer. The chemical composition of the synthetic and the natural sample has been determined by electron microprobe. Ti-andradites from runs at high oxygen fugacities have Fe³⁺ on octahedral and tetrahedral sites; Ti-andradites from runs at low oxygen fugacities have tetrahedrally and octahedrally coordinated Fe²⁺ as well. These “reduced” garnets must also contain Ti³⁺ on octahedral sites. Charge balance is maintained due to substitution of O^2? by (OH)^? by two mechanisms: (SiO₄)^4? ? (O₄H₄)^4? and (Fe³⁺O₆)^9? ? (Fe²⁺O₅OH)^9?. FTIR spectra of the synthetic samples do show the presence of structurally bound (OH)^?. In a natural sample tetrahedrally and octahedrally coordinated Fe³⁺ are observed together with Fe²⁺ on all three cation sites of the garnet structure.     

The structural role of Al2O3 and TiO2 in immiscible silicate liquids in the system SiO2-MgO-CaO-FeO-TiO2-Al2O3

The effects of the addition of Al₂O₃ on the large stable two liquid field in the SiO₂-TiO₂-CaO-MgO-FeO system were experimentally determined. The increase of Al₂O₃ content in the starting composition results in the decrease of critical temperature, phase separation and liquidus temperature of the two liquid field until it is rendered completely metastable. The shrinkage of the two liquid field indicates that Al₂O₃ is acting in the role of a network former and homogenizes the structure of the two melts. In this alkali-free system Al⁺³ utilizes the divalent cations, Ca⁺² and Mg⁺², for local charge balance with a preference for Ca⁺² over Mg⁺². Thus, AlO₄ tetrahedra combine with SiO₄ tetrahedra to form an aluminosilicate framework which polymerizes the SiO₂-poor melt and makes it structurally more similar to the SiO₂-rich melt. However, Ca⁺² and Mg⁺² are not as efficient in a charge balancing capacity as the monovalent K⁺ and Na⁺ cations. The lack of alkalis in this system limits the stability of AlO₄ tetrahedra in the highly polymerized SiO₂-rich melt and results in the preference of Al₂O₃ for the SiO₂-poor melt. The partitioning systematics of Ti are virtually identical to those of Al. It is concluded that Ti occurs in tetrahedral coordination as a network forming species in both the high — and low — SiO immiscible melts.     

Isotopic composition of rain- and groundwater at Mt. Vesuvius: environmental and volcanological implications

The present work reports on the isotopic characterization of rainfall and groundwater at Mt. Vesuvius. Values of δ ¹⁸O, monthly measured on rain samples collected during the period 2002–2004 in a rain-gauge network composed of 10 stations, were compared with meteorological and DEM data. Air temperature, controlled by the local orographic structure, was identified as the main factor influencing rain isotopic composition. Another important role is played by orographic clouds, whose condensation over the top of Mt. Vesuvius is responsible for anomalously high δ ¹⁸O values recorded in rain samples from the summit area of the volcanic edifice. A spatial model of rain isotopic composition, based on a 3D distribution of temperature derived by a 1 × 1 km DEM, was implemented and used for calculating the theoretical isotopic signature of seepage, further compared with data measured in the groundwater monitoring network. The analysis evidenced the role of local meteoric recharge as the main source feeding Mt. Vesuvius aquifers. The unique exception is the Olivella drainage gallery, located on the north-eastern flank of the volcanic edifice, whose isotopic composition is slightly more positive than the one expected for its altitude, likely caused by both evaporation processes and mixing with condensed hydrothermal vapor.     

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

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.     

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.     

Calorimetric study of high-pressure polymorphs of MnSiO3

With increasing pressure, MnSiO₃ rhodonite stable at atmospheric pressure transforms to pyroxmangite, then to clinopyroxene and further to tetragonal garnet, which finally decomposes into MnO (rocksalt) plus SiO₂ (stishovite). High temperature solution calorimetry of synthetic rhodonite, clinopyroxene and garnet forms of MnSiO₃ was used to measure the enthalpies of these transitions. ΔH ₉₇₄ ⁰ for the rhodonite-clinopyroxene and ΔH ₂₉₈ ⁰ for the clinopyroxene-garnet transition are 520±490 and 8,270±590 cal/mol, respectively. The published data on the enthalpy of the rhodonite-pyroxmangite transition, phase equilibrium boundaries, compressibility and thermal expansion data are used to calculate entropy changes for the transitions. The enthalpy, entropy and volume changes are very small for all the transitions among rhodonite, pyroxmangite and clinopyroxene. The calculated boundary for the clinopyroxene-garnet transition is consistent with the published experimental results. The pyroxene-garnet transition in several materials, including MnSiO₃, is characterized by a relatively small negative entropy change and large volume decrease, resulting in a small positiveP – T slope. The disproportionation of MnSiO₃ garnet to MnO plus stishovite and of Mn₂SiO₄ olivine to garnet plus MnO are calculated to occur at about 17–18 and 14–15 GPa, respectively, at 1,000–1,500 K.     

Structural and mineralogical evaluation of an experimentally produced impact crater in granite

A crater 30 cm in diameter and 4.4 cm in depth was produced upon impact of an aluminium sphere with a homogeneous granite target. The volume excavated was 748 cm³, the mass ejected 1933 g. The crater geometry is compared with previous laboratory experiments. Mineralogical investigations revealed that shock induced, microscopic fracturing is lowest in the direction of uniaxial compression, followed by a 45° profile. Due to reflections of stress waves at the free surface, the horizontal profile displayed the highest fracture index. Kinking of biotite was very common in samples close to the crater walls (≈ 50 kb). However it faded out at a distance which corresponds to approximately 10 kb. This seems to be the lower pressure limit for the formation of kink bands under shock conditions.     

Interaction between fluorine and silica in quenched melts on the joins SiO2-AlF3 and SiO2-NaF determined by raman spectroscopy

The solubility mechanism of fluorine in quenched SiO₂-NaF and SiO₂-AlF₃ melts has been determined with Raman spectroscopy. In the fluorine abundance range of F/(F+Si) from 0.15 to 0.5, a portion of the fluorine is exchanged with bridging oxygen in the silicate network to form Si-F bonds. In individual SiO₄-tetrahedra, one oxygen per silicon is replaced in this manner to form fluorine-bearing silicate complexes in the melt. The proportion of these complexes is nearly linearly correlated with bulk melt F/(F+Si) in the system SiO₂-AlF₃, but its abundance increases at a lower rate and nonlinearly with increasing F/(F+Si) in the system SiO₂-NaF. The process results in the formation ofnonbridging oxygen (NBO), resulting in stabilization of Si₂O ₅ ^2? units as well as metal (Na⁺ or Al³⁺) fluoride complexes in the melts. Sodium fluoride complexes are significantly more stable than those of aluminum fluoride.     

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.     

Identification of the geochemical processes in groundwater by factor analysis in hard rock aquifers of Madurai District,South India

A study was carried out in the Madurai district of Tamil Nadu, India to identify the hydrogeochemical processes using factor analysis as a predictive tool. It also focuses on characterizing the samples of these factors with respect to standard geochemical plots. In order to obtain a synoptic view of the statistics and the geochemical processes, a total of 53 groundwater samples are collected representing the entire district. The major ions were analyzed; the order of ion dominance are Ca²⁺?>?Na⁺?>?Mg²⁺?>?K⁺?=?Cl^??>?HCO^? ₃?>?H₄SiO^? ₄?>?NO^? ₃?>?SO^2? ₄?>?P^3? ₄. The samples are classified according to three factors. Factor 1 shows strong positive loadings of Cl^?, Ca²⁺, Mg²⁺, and NO^? ₃ with 36.98 % of the total variance (TV); factor 2 accounts for 13.72 % of TV with high loadings of Na⁺, K⁺, and HCO^? ₃; and factor 3 shows strong positive loadings of PO^3? ₄ and SO^2? ₄ with TV of 13.1 %. In the Piper plot, few samples fall in the mix region as evidenced by the mixing proportion of two samples using AQUACHEM software. The results suggest that different hydrogeochemical processes, like weathering, ion exchange processes, and anthropogenic activities (like sewage infiltration and agriculture), has predominant impact in the study area. Thus, the study highlights the factor analysis technique as a predictive and effective tool for groundwater evolution.     

Tracing quartz through the environment

Quartz, SiO₂, a pure mineral with tight crystal structure, is widespread in rocks and soil. Cosmic rays produce¹⁰Be (t _1/2=1·5×10⁶, yr) and²⁶Al (t _1/2=7·05×10⁵ yr) in quartz exposed at or near the earth’s surface. The use of accelerator mass spectrometry permits measurement of these nuclides in samples exposed at sea level for typical periods.In situ production makes interpretation relatively straightforward. Potential applications include age determination, measurement of erosion and deposition rates, and use as a tracer for continental weathering processes.     

Carbon on surfaces of magnesium oxide and olivine single crystals. Diffusion from the bulk or surface contamination?

We have conducted detailed studies of the behavior of carbon on the surfaces of MgO and olivine single crystals using various surface analytical techniques: viz. secondary ion mass spectrometry (SIMS), Auger electron spectrometry (AES) and X-ray photoelectron spectrometry (XPS). In order to distinguish without ambiguity the effect of diffusion of carbon from the bulk to the surface and the effect of surface contamination by carbon-containing species, the experiments were conducted in ultrahigh vacuum, i.e. 10^?11–10^?9 torr. In addition to MgO and olivine single crystals, we have conducted the same studies on TiO₂, MnO, SiO₂ and Ta₂O₅ which serve as blank samples. The MgO and olivine samples were also intentionally implanted with known doses of carbon and the mobility of this particular carbon was investigated in detail. Our results show that the bulk carbon content in MgO is around 40 wt. ppm, considerably lower than the quantities quoted by Freund and co-workers in the past. We also show that the carbon in both MgO and olivine does not display any rapid diffusion behaviour leading to surface segreation in the temperature range 78–723 K, in contrast to the previous findings of Freund and co-workers.     

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

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.     

Clinopyroxene on the join CaMgSi2O6-CaFe3+AlSiO6-CaTiAl2O6 at low oxygen fugacity

Subsolidus phase relations on the join CaMgSi₂O₆-CaFe³⁺ AlSiO₆-CaTiAl₂O₆ were studied by the ordinary quenching method at \(f_{O_2 } = 10^{ - 11} \) atm and 1,100°C. Crystalline phases encountered are clinopyroxene_ss (ss:solid solution) (Cpx_ss), melilite (Mel), perovskite (Pv), spinel_ss (Sp_ss), magnetite_ss (Mt_ss) and anorthite (An). There is no Cpx_ss single phase field, and the following assemblages were found; Cpx_ss+Mel, Cpx_ss+Mel+Sp_ss, Cpx_ss+Mel+Pv, Cpx_ss+Mel+Sp_ss+Pv, Cpx_ss+Pv+Sp_ss+An, Sp_ss+Pv+Mel+An+Cpx_ss, Mel+Mt_ss+An+Sp_ss+Cpx_ss+liquid and Mel+Mt_ss+An+Sp_ss+Cpx_ss+Pv. Mössbauer spectral study revealed that Cpx_ss contains both Fe²⁺ and Fe³⁺ in the octahedral site, and it was confirmed that the CaFe³⁺ AlSiO₆ content in the Cpx_ss at low \(f_{O_2 } \) is considerably less than that in the Cpx_ss crystallized in air, whereas the CaFe²⁺Si₂O₆ component increases. The maximum solubility of CaTlAl₂O₆ component in the Cpx_ss at low \(f_{O_2 } \) is higher than that in air. The decrease of CaFe³⁺ AlSiO₆ in the Cpx_ss at low \(f_{O_2 } \) may cause increase of CaTial₂O₆ in the Cpx_ss.     

Electron paramagnetic resonance study of iron(III) and manganese(II) in the glassy and crystalline environments of synthetic fayalite and tephroite

Crystals of the olivine minerals, tephroite (Mn₂SiO₄) and fayalite (Fe₂SiO₄) containing manganese(II) and iron (II and trace of III), respectively, were synthesized. Glasses were prepared from these crystalline materials by a splat-quench technique. Measurement of electron paramagnetic resonance (EPR) of all these powdered samples at room temperature show that the g-factors of Mn²⁺ in both glassy and crystalline environments (g_eff = 2.004) are the same, although the EPR linewidths (for glass, ΔH_pp = 200 G; for crystals ΔH_pp = 287 G) suggest less clustering of paramagnetic Mn²⁺ ions in the glass. Mn²⁺ probably occupies a distorted octahedral site in the tephroite crystal structure, although a four-fold coordination is suggested from other spectroscopic investigation on this glass. The EPR parameters of Fe³⁺ in synthetic fayalite glass (g_eff = 2.01 and 6.00; ΔH_pp=150 and 1375 G, respectively, for the high and low field resonances) and powdered crystals (g_eff = 3.31 and ΔH_pp = 900 G) indicated that Fe³⁺ ion in the crystals, is probably located in a distorted tetragonal site M2 and an axial environment has been proposed in the glassy system.     

On the nonstoichiometry and point defects of olivine

This paper presents the point-defect thermodynamics for fayalite and olivine solid solutions (Fe _x Mg_1?x )₂SiO₄. By means of thermogravimetry, the metal-to-oxygen ratio of these silicates has been determined as a function of oxygen potential, compositionx and temperature. Experiments were performed in the range of 1,000° C≦T≦1,280° C and 0.2≦x≦1.0. It is found that V _Me ^″ , Fe _Me ^· and the associate {Fe′ _Si ^′ Fe _Me ^· } are the majority defects. With this knowledge it is possible to calculate the nonstoichiometry at given temperature as a function of \(p_{O_2 } \) and \(a_{SiO_2 } \) . The cation vacancy concentration shows a \(p_{O_2 }^{1/5} \) -dependence (forx≧0.2) and increases at givenT and \(p_{O_2 } \) almost exponentially with compositionx. In the composition range studied here, the silicates show an oxygen excess, and FeO is more soluble in the olivine than SiO₂.