An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique   总被引：1，自引：0，他引：1  

S. C. Elphick  P. F. Dennis  C. M. Graham 《Contributions to Mineralogy and Petrology》1986,92(3):322-330

Diffusion rates of¹⁸O tracer in quartz ( c, 1 Kb H₂O) and Amelia albite ( 001, 2 Kb H₂O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c), ,Q=98±7 KJ mol^–1 (600–825° C, 1 Kb); Amelia albite ( 001), ,Q=85±7 KJ mol^–1, (400–600° C, 2 Kb). Measured quartz¹⁸O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted.  相似文献   

Strain responses of frozen clay with thermal gradient under triaxial creep   总被引：1，自引：1，他引：0  

Xiaodong Zhao  Guoqing Zhou  Guilin Lu 《Acta Geotechnica》2017,12(1):183-193

Thermal gradient is one of the main features for the temperature distribution in artificial frozen shaft lining (FSL). The time-dependent strain responses and the corresponding heterogeneity characteristics of frozen soils with thermal gradient are of potential significance for stability assessment and prediction of FSL, especially of the FSL embedded in thick alluvium. A series of triaxial creep tests were carried out on frozen saturated clay under various thermal gradients and creep stresses. The experimental results indicated that the triaxial creep curves for frozen clay with thermal gradient exhibit viscous characteristics, and the creep rate \(\Delta \varepsilon_{\text{a}} /\Delta t\) decreases with the increase in creep time \(t\) and decrease in thermal gradient. The stress–strain curve under different \(t\) showed that the creep stress has a marked growth when axial strain \(\varepsilon_{\text{a}} \le 1\,\%\). However, when \(\varepsilon_{\text{a}} \ge 1\,\%\), the growth rate decreases gradually. The deviation between measured radial strain \(\varepsilon_{\text{r}}^{\text{m}}\) under the middle specimen section height SSH and the calculated radial strain \(\varepsilon_{\text{r}}^{\text{c}}\) from the volumetric strain increases following a unified equation with the increase in axial strain. The radial strain \(\varepsilon_{\text{r}}^{\text{f}}\) for frozen clay with thermal gradient after experiment increases with the increase in SSH, and the slope of \( \varepsilon_{\text{r}}^{\text{f}} - {\text{SSH}} \) curve is significantly dependent on the thermal gradient and creep stress. The variation of \(\varepsilon_{\text{r}}^{\text{m}} - \varepsilon_{\text{r}}^{\text{c }}\) during experiment and \(\varepsilon_{\text{r}}^{\text{f}}\) distribution after experiment are the macro-responses of internal micro-heterogeneities in frozen soils induced from thermal gradient, and are closely related to strain rate and its variation. These observations and findings provide an insight into the creep mechanism and the estimation method of creep deformation for frozen soils with thermal gradient.  相似文献   

Petrology and phase relations of the kyanite-eclogites from eastern Turkey     

A. I. Okay  M. B. Arman  M. C. Göncüoglu 《Contributions to Mineralogy and Petrology》1985,91(2):196-204

Eclogites are found as lenses or layers in the Precambrian gneiss terrain of the Bitlis Massif in eastern Turkey. Kyanite-eclogites from the region of Gablor Hill in the Bitlis Massif exhibit relatively minor alteration, and consist of garnet, omphacite, kyanite, zoisite, calcic amphibole, phengite, rutile and quartz. In terms of geological setting and mineral compositions, Gablor eclogites are very similar to eclogites from high-grade gneiss terrains. Metamorphic conditions during the eclogite crystallisation are determined as 625±35° C and 16±3 kbars. The coexistence of white mixa, omphacite and kyanite constrains between 0.4 and 1. Primary calcic amphiboles from the Gablor eclogites exhibit conflicting textures, indicating stable coexistence with, as well as growth from omphacite and garnet. This is explained by a buffering reaction between amphibole, garnet, omphacite, zoisite and kyanite during the eclogite crystallisation, whereby is controlled and buffered by the mineral assemblage.  相似文献   

Systematic study of liquidas phase relations in olivine melilitite +H2O +CO2 at high pressures and petrogenesis of an olivine melilitite magma     

G. Brey  D. H. Green 《Contributions to Mineralogy and Petrology》1977,61(2):141-162

Near-liquidus phase relationships of a spinel lherzolite-bearing olivine melilitite from Tasmania were investigated over a P, T range with varying , , and . At 30 kb under MH-buffered conditions, systematic changes of liquidus phases occur with increasing ( = CO₂/CO₂ +H₂O+olivine melilitite). Olivine is the liquidus phase in the presence of H₂O alone and is joined by clinopyroxene at low . Increasing eliminates olivine and clinopyroxene becomes the only liquidus phase. Further addition of CO₂ brings garnet+orthopyroxene onto the liquidus together with clinopyroxene, which disappears with even higher CO₂. The same systematic changes appear to hold at higher and lower pressures also, only that the phase boundaries are shifted to different . The field with olivine- +clinopyroxene becomes stable to higher with lower pressure and approaches most closely the field with garnet+orthopyroxene+clinopyroxene at about 27 kb, 1160 °C, 0.08 and 0.2 (i.e., 6–7% CO₂+ 7–8% H₂O). Olivine does not coexist with garnet+orthopyroxene+clinopyroxene under these MH-buffered conditions. Lower oxygen fugacities do not increase the stability of olivine to higher and do not change the phase relationships and liquidus temperatures drastically. Thus, it is inferred that olivine melilitite 2927 originates as a 5% melt (inferred from K_{2 O} and P₂O₅ content) from a pyrolite source at about 27kb, 1160 dg with about 6–7% CO₂ and 7–8% H₂O dissolved in the melt. The highly undersaturated character of the melt and the inability to find olivine together with garnet and orthopyroxene on the liquidus (in spite of the close approach of the respective liquidus fields) can be explained by reaction relationships of olivine and clinopyroxene with orthopyroxene, garnet and melt in the presence of CO₂.  相似文献   

Microphenocrystic pyrrhotite from dacite rocks of Satsuma-Iwojima,southwest Kyushu,Japan and the solubility of sulfur in dacite magma     

Akira Ueda  Tetsumaru Itaya 《Contributions to Mineralogy and Petrology》1981,78(1):21-26

Microphenocrystic pyrrhotites were observed in the glassy groundmass of two dacite rocks from Satsuma-Iwojima, southwest Kyushu, Japan. It suggests that the dacite magma was saturated with respect to pyrrhotite at the time of eruption, and thus the sulfur contents in the groundmass can be taken as the solubility of sulfur in the dacite magma. The solubility of sulfur in the dacite rocks thus calculated is 65 to 72 ppm sulfur at the estimated conditions of T=900±50°C, and atm.  相似文献   

The crystal structure of a triclinic roscherite     

Prof. L. Fanfani  Prof. P. F. Zanazzi  Dr. Anna Rosa Zanzari 《Mineralogy and Petrology》1977,24(3):169-178

Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group . The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula while that proposed for monoclinic roscherite is The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions.

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Die Kristallstruktur eines triklinen Roscherites

Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen.

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The effect of liquid composition on the partitioning of Ni between olivine and silicate melt     

Andrew?K.?MatzenEmail author  Michael?B.?Baker  John?R.?Beckett  Bernard?J.?Wood  Edward?M.?Stolper 《Contributions to Mineralogy and Petrology》2017,172(1):3

We report the results of experiments designed to separate the effects of temperature and pressure from liquid composition on the partitioning of Ni between olivine and liquid, \(D_{\text{Ni}}^{\text{ol/liq}}\). Experiments were performed from 1300 to 1600 °C and 1 atm to 3.0 GPa, using mid-ocean ridge basalt (MORB) glass surrounded by powdered olivine in graphite–Pt double capsules at high pressure and powdered MORB in crucibles fabricated from single crystals of San Carlos olivine at one atmosphere. In these experiments, pressure and temperature were varied in such a way that we produced a series of liquids, each with an approximately constant composition (~12, ~15, and ~21 wt% MgO). Previously, we used a similar approach to show that \(D_{\text{Ni}}^{\text{ol/liq}}\) for a liquid with ~18 wt% MgO is a strong function of temperature. Combining the new data presented here with our previous results allows us to separate the effects of temperature from composition. We fit our data based on a Ni–Mg exchange reaction, which yields \(\ln \left( {D_{\text{Ni}}^{\text{molar}} } \right) = \frac{{ -\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{RT} + \frac{{\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{R} - \ln \left( {\frac{{X_{\text{MgO}}^{\text{liq}} }}{{X_{{{\text{MgSi}}_{ 0. 5} {\text{O}}_{ 2} }}^{\text{ol}} }}} \right).\) Each subset of constant composition experiments displays roughly the same temperature dependence of \(D_{\text{Ni}}^{\text{ol/liq}}\) (i.e.,\(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\)) as previously reported for liquids with ~18 wt% MgO. Fitting new data presented here (15 experiments) in conjunction with our 13 previously published experiments (those with ~18 wt% MgO in the silicate liquid) to the above expression gives \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 3641 ± 396 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 1.597 ± 0.229. Adding data from the literature yields \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 4505 ± 196 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 2.075 ± 0.120, a set of coefficients that leads to a predictive equation for \(D_{\text{Ni}}^{\text{ol/liq}}\) applicable to a wide range of melt compositions. We use the results of our work to model the melting of peridotite beneath lithosphere of varying thickness and show that: (1) a positive correlation between NiO in magnesian olivine phenocrysts and lithospheric thickness is expected given a temperature-dependent \(D_{\text{Ni}}^{\text{ol/liq}} ,\) and (2) the magnitude of the slope for natural samples is consistent with our experimentally determined temperature dependence. Alternative processes to generate the positive correlation between NiO in magnesian olivines and lithospheric thickness, such as the melting of olivine-free pyroxenite, are possible, but they are not required to explain the observed correlation of NiO concentration in initially crystallizing olivine with lithospheric thickness.  相似文献   

Stochastic analysis of bed-thickness distribution of sediments     

S. Mizutani  I. Hattori 《Mathematical Geosciences》1972,4(2):123-146

On formation of a bed and distribution of bed thickness, A. N. Kolmogorov presented a mathematical explanation that if repetitive alternations of material accumulation and erosion form a sequence of beds, the resultant bed-thickness distribution curve takes a shape truncated by the ordinate at zero thickness. In this truncated distribution curve, its continuation and extension from positive to negative thickness represents the distribution of beds with negative thickness, that is, the depth of erosion. When a distribution curve, including both positive and negative parts, is expressed by a function f(x),the ratio \(\int_0^\infty {f(x)dx to} \int_{ - \infty }^\infty {f(x)dx} \) ,called Kolmogorov's coefficient and designated as p,is a parameter representing the degree of accumulation in the depositional environment. On the assumption that f(x)is described by the Gaussian distribution function, the coefficient pfor Permian and Pliocene sequences in central Japan was calculated. The coefficients also were obtained from published data for different types of sediments from other areas. It was determined that they are more or less different depending on their depositional environments. The calculated results are summarized as follows: $$\begin{gathered} p = 0.80 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ p = 0.65 - 0.95for{\text{ }}nearshore{\text{ }}sediments \hfill \\ p = 0.55 - 0.95for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ p = 0.90 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ In addition, a ratio \(q = \int_0^\infty {xf(x)dx/} \int_{ - \infty }^\infty {|x|f(x)dx} \) ,called Kolmogorov's ratio in this paper, is introduced for estimating a degree of total thickness actually observed in the field relative to total thickness once present in a basin. The calculated results of Kolmogorov's ratio are as follows: $$\begin{gathered} q = 0.88 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ q = 0.68 - 0.98for{\text{ }}nearshore{\text{ }}sediments \hfill \\ q = 0.55 - 0.96for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ q = 0.92 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ The sedimentological significance of these values is discussed.  相似文献   

Appraisal of groundwater quality in a crystalline aquifer: a chemometric approach     

P. D. Sreedevi  P. D. Sreekanth  S. Ahmed  D. V. Reddy 《Arabian Journal of Geosciences》2018,11(9):211

The purpose of this study is to assess the groundwater quality and identify the processes that control the groundwater chemistry in a crystalline aquifer. A total of 72 groundwater samples were collected during pre- and post-monsoon seasons in the year 2014 in a semi-arid region of Gooty Mandal, Anantapur district, Andhra Pradesh, India. The study utilized chemometric analysis like basic statistics, Pearson’s correlation coefficient (r), principal component analysis (PCA), Gibbs ratio, and index of base exchange to understand the mechanism of controlling the groundwater chemistry in the study area. The results reveal that groundwater in the study area is neutral to slightly alkaline in nature. The order of dominance of cations is Na⁺ > Ca²⁺ > Mg²⁺ > K⁺ while for anions, it is \( {\mathrm{HCO}}_3^{-}>{\mathrm{Cl}}^{-} \)>\( {\mathrm{NO}}_3^{-} \)>\( {\mathrm{SO}}_4^{2-} \)>\( {\mathrm{CO}}_3^{2-}>{\mathrm{F}}^{-} \) in both seasons. Based on the Piper classification, most of the groundwater samples are identified as of sodium bicarbonate (\( {\mathrm{Na}}^{+}-{\mathrm{HCO}}_3^{-}\Big) \) type. According to the results of the principal component analysis (PCA), three factors and two factors were identified pre and post monsoon, respectively. The present study indicates that the groundwater chemistry is mostly controlled by geogenic processes (weathering, dissolution, and ion exchange) and some extent of anthropogenic activities.  相似文献   

Relationship between fluid-bearing and fluid-absent invariant points and a petrogenetic grid for a greenschist facies assemblage in the system CaO-MgO-Al2O3-SiO2-CO2-H2O     

B. J. Watts 《Contributions to Mineralogy and Petrology》1973,40(3):225-238

In the 6 component system CaO-MgO-Al₂O₃-SiO₂-CO₂-H₂ with 9 solid phases (quartz, plagioclase, epidote, tremolite, talc, chlorite, magnesite, calcite, dolomite) and a fluid phase, all 17 possible fluid-absent reactions have been set up and balanced. Using molar entropy and volume data for the solid phases, these reactions are arranged in P-T space about the 8 possible fluid-absent invariant points after the method of Schreinemakers. Field observations in Ordovician greenschist facies basic volcanics at Sofala N.S.W., indicate that neither talc+epidote nor magnesite+calcite are stable under the conditions of metamorphism. Assuming these conditions to apply to the theoretical study here, the fluid-absent invariant points are arranged in a relative fashion with fluid-absent reactions subdividing P-T space into smaller areas.A scheme which permits a fluid of composition (i.e. a fluid containing CO₂ and H₂O together with other components), is modeled by treating H₂O as a mobile component independent of CO₂, and by allowing values that lie off the locus of binary H₂O-CO₂. Taking into account that neither talc+epidote nor magnesite +calcite is to be permitted, the fluid scheme is used to set up and balance all 39 possible fluid-bearing reactions. These are then arranged about 20 valid fluid-bearing invariant points in space after the method of Korzhinskii and Sehreinemakers.A characteristic solid phase assemblage is defined for each P-T area using chemographic relations inherent from the fluid-absent boundary reactions. The fluid-bearing invariant points that have a solid assemblage compatible with the characteristic assemblage in a particular P-T area are stable within the P-T regime of that area. When these stable fluidbearing invariant points are arranged in a relative fashion in space, they outline a fluid grid which can be used to study the possible effects of local variation in X _fluid over the particular P-T regime.Symbols Used U chemical potential - S entropy - V molar volume - n coefficient of a phase in a reaction - X mole fraction - T temperature - P pressure - F number of degrees of freedom - C number of components - p number of phases - s solid - slope of reaction - 1 quartz - 2 plagioclase - 3 epidote - 4 tremolite - 5 talc - 6 chlorite - 7 dolomite - 8 magnesite - 9 calcite  相似文献   

The generation and crystallization conditions of the Proterozoic Harney Peak Leucogranite,Black Hills,South Dakota,USA: Petrologic and geochemical constraints   总被引：1，自引：0，他引：1  

P. I. Nabelek  C. Russ-Nabelek  J. R. Denison 《Contributions to Mineralogy and Petrology》1992,110(2-3):173-191

The mineralogy, petrology and geochemistry of the Proterozoic Harney Peak Granite, Black Hills, South Dakota, were examined in view of experimentally determined phase equilibria applicable to granitic systems in order to place constraints on the progenesis of peraluminous leucogranites and commonly associated rare-element pegmatites. The granite was emplaced at 3–4 kbar as multiple sills and dikes into quartz-mica schists at the culmination of a regional high-temperature, low-pressure metamorphic event. Principally along the periphery of the main pluton and in satellite intrusions, the sills segregated into granite-pegmatite couplets. The major minerals include quartz, K-feldspar, sodic plagioclase and muscovite. Biotite-{Mg No. [Molar MgO/(MgO+FeO)]=0.32-0.38} is the predominant ferromagnesian mineral in the granite's core, whereas at the periphery of the main pluton and in the satellite intrusions tourmaline (Mg No.=0.18–0.48) is the dominant ferromagnesian phase. Almandine-spessartine garnet is also found in the outer intrusions. There is virtually a complete overlap in the wide concentration ranges of SiO₂, CaO, MgO, FeO, Sr, Zr, W of the biotite- and tourmaline-bearing granite suites with no discernable differentiation trends on Harker diagrams, precluding the derivation of one suite from the other by differentiation following emplacement. This is consistent with the oxygen isotope compositions which are 11.5 ± 0.6 for the biotite granites and 13.2 ± 0.8 for the tourmaline granites, suggesting derivation from different sources. The concentrations of TiO₂ and possibly Ba are higher and of MnO and B are lower in the biotite granites. The normative Orthoclase/Albite ratio is extremely variable ranging from 0.26 to 1.65 in the biotite granites to 0.01–1.75 in the tourmaline granites. Very few sample compositions fall near the high-pressure, watersaturated haplogranite minima-eutectic trend, indicating that the granites for the most part are not minimum melts generated under conditions with =1. Instead, most biotite granites are more potassic than the water-saturated minima and eutectics and in analogy with experimentally produced granitic melts, they are best explained by melting at 6 kbar, <1 and temperatures 800°C. Such high temperatures are also indicated by oxygen isotope equilibration among the constituent minerals (Nabelek et al. 1992). Several of the tourmaline granite samples contain virtually no K-feldspar and have oxygen isotope equilibration temperatures 716–775°C. Therefore, they must represent high-temperature accumulations of liquidus minerals crystallized under equilibrium conditions from melts more sodic than the water-saturated haplogranite minima or during fractionation of intruded melts into granite-pegmatite couplets accompanied by volatile-aided differentiation of the alkali elements. The indicated high temperatures, <1, the relatively high TiO₂ and Ba concentrations and the relatively low values of the biotite granites suggest that they were generated by high-extent, biotite-dehydration melting of an immature Archean metasedimentary source. The ascent of the hot melts may have triggered low-extent, muscovite-dehydration melting of schists higher in the crust producing the high-B, low-Ti melts comprising the periphery of the main pluton and the satellite intrusions. Alternatively, the different granite types may be the result of melting of a vertical section of the crust in response to the ascent of a thermal pulse, with the low- biotite granites generated at a deeper, hotter region and the high- tourmaline granites at a higher, cooler region of the crust. The low-Ti and high-B concentrations in the high- melts resulted in the crystallization of tourmaline rather than biotite, which promoted the observed differentiation of the melts into the granitic and pegmatitic layers found along the periphery of the main pluton and the satellite intrusions.  相似文献   

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder     

Paula M. Davidson  John Grover  Donald H. Lindsley 《Contributions to Mineralogy and Petrology》1982,80(1):88-102

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.  相似文献