Mixing properties of phengitic micas and revised garnet-phengite thermobarometers

Mixing properties for muscovite–celadonite–ferroceladonite solid solutions are derived from combining available experimental phase equilibrium data with tabulated thermodynamic data for mineral end‐members. When a partially ordered solution model is assumed, the enthalpy of mixing among the end‐members muscovite–celadonite–ferroceladonite is nearly ideal, although the Gibbs energies of muscovite–celadonite and muscovite–ferroceladonite solutions are asymmetric due to an asymmetry in the entropy of mixing. Thermodynamic consistency is achieved for data on phengite compositions inassemblages with (a) pyrope+kyanite+quartz/coesite (b) almandine+kyanite+quartz/coesite (c)talc+kyanite+quartz/coesite and (d) garnet–phengite pairs equilibrated both experimentally at high temperatures and natural pairs from low‐grade schists. The muscovite–paragonite solvus has been reanalysed using the asymmetric van Laar model, and the effects of the phengite substitution into muscovite have been quantitatively addressed in order to complete the simple thermodynamic mixing model for the solid solution among the mica end‐members. Results are applied to a natural pyrope–coesite–phengite–talc rock from the Western Alps, and to investigate the conditions under which biotite‐bearing mica schists transform to whiteschist‐like biotite‐absent assemblages for average pelite bulk compositions.     

Raman spectra of silicate garnets

The single-crystal polarized Raman spectra of four natural silicate garnets with compositions close to end-members almandine, grossular, andradite, and uvarovite, and two synthetic end-members spessartine and pyrope, were measured, along with the powder spectra of synthetic pyrope-grossular and almandine-spessartine solid solutions. Mode assignments were made based on a comparison of the different end-member garnet spectra and, in the case of pyrope, based on measurements made on additional crystals synthesized with ²⁶Mg. A general order of mode frequencies, i.e. R(SiO₄)>T(metal cation)>T(SiO₄), is observed, which should also hold for most orthosilicates. The main factors controlling the changes in mode frequencies as a function of composition are intracrystalline pressure (i.e. oxygen-oxygen repulsion) for the internal SiO₄-vibrational modes and kinematic coupling of vibrations for the external modes. Low frequency vibrations of the X-site cations reflect their weak bonding and dynamic disorder in the large dodecahedral site, especially in the case of pyrope. Two mode behavior is observed for X-site cation vibrations along the pyrope-grossular binary, but not along the almandine-spessartine join. Received: 3 December 1996 / Revised, accepted: 13 April 1997     

Local structural heterogeneity in garnet solid solutions

Local heterogeneities in pyrope-almandine, almandine-grossular and pyrope-grossular solid solutions have been investigated using IR-powder absorption spectroscopy. Correlations of the wavenumber shifts and line broadening systematics with the thermodynamic mixing properties were found. Wavenumber shifts of the highest energy modes correlate closely with the Si-O bond distances and give an indirect view of the average distortions across the three solid solutions. They have a linear behaviour for Py-Alm, but show positive variations from linearity for Alm-Gr and Py-Gr systems. An effective line width (Δ_corr) of the absorption bands over a given wavenumber interval was obtained using the autocorrelation function. Line broadening is associated with local heterogeneities arising from cation substitution in the structure of samples at intermediate compositions. Non-linearities of the line broadening were found for Alm-Gr and Py-Gr and have a shape similar to the enthalpy of mixing, ΔH_mix. An empirical analysis was therefore carried out to compare ΔH_mix and Δ_corr quantitatively. Low-temperature far-IR spectra were recorded for the end-members pyrope, almandine and grossular and far-IR and mid-IR low-temperature spectra for Py₆₀Gr₄₀ in the temperature range 292–44 K. Softening of the lowest energy band with decreasing temperature was observed in the spectrum of pyrope and more enhanced in the spectrum of Py₆₀Gr₄₀. The same softening occurs by substitution of grossular component into pyrope. High energy modes of Py₆₀Gr₄₀ show the effect of saturation below 110–130 K, which correlates with the volume saturation at low temperature. This could provide an alternative explanation for the heat capacity anomaly found for Py-Gr solid solution at low-temperatures.     

Crystal field stabilization energies of almandine-pyrope and almandine-spessartine garnets determined by FTIR near infrared measurements

The band positions of three partially overlapping Fe²⁺ spin-allowed transitions located between 4000 and 9000 cm^–1 in almandine-pyrope and almandinespessartine garnets solid solutions were measured using near-infrared (NIR) spectroscopy. The crystal field stabilization energies (CFSE) along both binaries were calculated assuming a splitting of 1100 cm^–1 for the lower orbitals. The CFSE show a slight increase along the almandine-spessartine binary from 3730 to 3810 cm^–1 and a larger increase from 3730 to 3970 cm^–1 for the almandine-pyrope binary. Dodecahedral Fe²⁺-site distortion increases with an increase in spessartine component and decreases with increasing pyrope component, in agreement with average dodecahedral site distortions determined from diffraction experiments. The excess CFSE's along both joins are negative. For the almandinespessartine binary they are small, but are about 3.5 times larger in magnitude along the join almandine-pyrope, where an interaction parameter of W= -2.9 KJ/mole has been derived from a symmetric mixing model. The excess CFSE are relatively small compared to the magnitudes of the excess enthalpies of mixing that have been assigned to garnet solid solutions. Moreover, they give no indication which could support the positive and asymmetric excess enthalpies of mixing that have been proposed for almandine-pyrope solid solutions.     

Distinct local environments for Ca along the non-ideal pyrope–grossular solid solution: A new model based on crystallographic and EXAFS analysis

A multi-technique approach (based on electron microprobe analysis, structure refinement, and EXAFS analysis at the Ca K-edge) was used to characterise the local geometry of Ca in synthetic and natural garnet compositions referable to the pyrope–grossular solid solution. Multi-shell fits of the EXAFS data indicate that Ca assumes the standard [4 + 4]-fold coordination (the polyhedral shape being a triangular dodecahedron with Ca1–O = 2.30–2.31(1) and Ca2–O = 2.45–2.46(1) Å) when Ca > 1.50 atoms per formula unit (apfu), but assumes a nearly regular [8]-fold coordination with Ca–O = 2.35–2.36 (1) Å when (Mg, Fe²⁺, Mn²⁺) > 1.50 apfu. Therefore, in the pyrope-dominant structure the Ca1–O distance lengthens and the Ca2–O distance shortens to converge towards the value observed for the Mg2–O bond in pyrope. This finding is consistent with many distinct structural features observed in solid solution terms with (Mg, Fe²⁺, Mn²⁺) > 1.50 apfu or Ca > 1.50 apfu, as well as with the anomalous properties of the intermediate terms observed both in the short-range and in the long-range perspective. The presence of two distinct Ca coordinations in the pyrope (almandine, spessartine)-like and in the grossular-like structure, and thus of an isosymmetric transition at the intermediate composition, can help to explain both the strong and asymmetric non-ideality of the solid solution between pyrope (almandine) and grossular, as well as the differences in the ability to incorporate some trace elements (such as REE and actinides) which are commonly used as process-specific indicators. This feature must be taken into account when building theoretical models of the garnet solid solutions, which are at the moment the most promising approach for calculating thermodynamic properties or for interpreting and predicting trace-element behaviour in this crucial mineral phase.     

The energetics of natural garnet solid solution

Approximate mixing properties of the end-member components of the quarternary garnet solid solution, (Fe,Mg,Ca,Mn)₃Al₂Si₃O₁₂, have been derived through theoretical analysis of observational data, combined with certain experimental results and crystal chemical considerations. The results suggest that the mixing of pyrope with grossularite, spessartite, and almandine would involve significant positive excess free energies of mixing leading to the critical mixing temperatures of 694±55, 535±140, and 479±63 °C respectively. Spessartite would mix with almandine nearly ideally, and with grossularite with small positive deviation from ideality. The quarternary solution reduces essentially to a ternary mixture of pyrope, grossularite, and almandine + spessartite. The solid solubility relation, and tie line coordinates in this ternary system has been calculated as a function of temperature; the solid solution is found to be intrinsically stable for practically all ternary compositions at 600 °C.     

广西拉么Zn—Cu矿床中夕卡岩的主要矿物特点与Ca—Fe—Si—C—O体系T—lgfO2图解

用电子探针数据研究了该矿床中主要夕卡岩矿物特点及其变化规律。采用理想结晶溶液固溶体位置混合模式,计算了石榴子石和辉石矿物对中钙铁榴石和钙铁辉石的摩尔分数。在计算纯固相和流体相参加的反应抵达平衡时的边界方程中,加上理想结晶固溶体中端元组分摩尔分数的修正项后,我们便可以计算出有纯固相、流体相和理想结晶溶液固溶体参加反应的在给定T、P条件下的lgfo_2值。计算结果表明:无变度点4周围的Hed+And+Wol组合对本矿区具有重要的地质地球化学意义。     

Eclogite from serpentinite near Attunga,New South Wales

Eclogite of high‐pressure low‐temperature origin occurs within the Great Serpentine belt of New South Wales. The presence of glaucophane‐bearing rocks and other medium to high‐pressure assemblages associated with the belt is similar in many respects to the Californian and Oregon occurrences. The chemical composition of the eclogite is characterized by low K₂O values comparable to many oceanic tholeiites, although one analysis is nepheline‐normative. Ti‐Zr‐Y ratios also show affinities to ocean‐floor basalts.

The garnet contains approximately 30% grossular and is strongly zoned from almandine (Alm 56%, Py 9%) at the core towards pyrope (Alm 44%, Py 27%) at the margin. Sodic augite contains 30–33% Jd, 4–7% Ac, and 72–74% Di+He.

Distribution of Fe and Mg between co‐existing garnet and pyroxene would suggest an increasing temperature during eclogite crystallization with a possible range from 290°C to 600°C and a minimum pressure of 7–12 kb.     

Garnet-orthopyroxene-plagioclase-quartz barometry: refinement and application to the English River subprovince and the Minnesota River valley

Recent experimental, theoretical, and thermodynamic studies permit better calibration of two reactions for geobarometry: grossular+pyrope+quartz=anorthite+enstatite grossular+almandine+quartz=anorthite+ferrosilite If both reactions are applied using the same thermodynamic data and activity models they should yield the same pressure for a given garnet-pyroxene-plagioclase-quartz assemblage. Application to a variety of high-grade terrains generally yielded excellent results. However, poor results have been obtained for high-Fe rocks which can be traced to errors in activity models for garnet and/or pyroxene. Either a two-site ideal mixing model for orthopyroxene (cf. Wood and Banno 1973) underestimates enstatite activity for high-Fe orthopyroxenes or the Ganguly and Saxena (1984) model overestimates pyrope activity in low-Mg garnets. Application of both barometers to a variety of high-grade terrains gives the following average pressures:

Local structure of ferric iron-bearing garnets deduced by IR-spectroscopy

Powder IR absorption spectroscopy has been used to characterise cation substitutions in three garnet solid solutions: grossular–andradite, skiagite–andradite and skiagite–almandine. The wavenumber shift of the highest energy mode associated with tetrahedral vibrations depends on the type of cation occupying the adjacent sites in the structure. The wavenumber shifts exhibit positive deviations from linearity that correlate closely with the variations of the Si–O bond distances for all three garnet solid solutions. The autocorrelation function has been used to determine an effective line width (Δcorr) of the absorption bands over a given spectral region. Non-linear behaviour of Δcorr was found for all three solid solutions. An empirical calibration between Δcorr excess and calorimetric enthalpy of mixing data gives an estimate for the symmetric Margules parameters W_spec^H of the three solid solutions. Comparison with the systematics of aluminosilicate garnets in terms of W_spec^H vs. ΔV², where ΔV represents the difference in molar volume between the end members in a binary system, reveals that such a relationship is not generally applicable to garnet solid solutions with an octahedral cation other than Al.     

Modeling the thermodynamic parameters of six endmember garnets at ambient and high pressures from vibrational data

Raman and infrared spectroscopic data at ambient and high pressures were used to compute the lattice contribution to the heat capacities and entropies of six endmember garnets: pyrope, almandine, spessartine, grossular, andradite and uvarovite. Electronic, configurational and magnetic contributions are obtained from comparing available calorimetric data to the computed lattice contributions. For garnets with entropy in excess of the computed lattice contribution, the overwhelming majority is found in the subambient temperature regime. At room temperature, the non-lattice entropy is approximately 11.5 J/mol-K for pyrope, 49 J/mol-K for almandine, and 19 J/mol-K for andradite. The non-lattice entropy for pyrope and some for almandine cannot be accounted for by magnetic or electronic contributions and is likely to be configurational in nature. Estimates of low temperature non-lattice entropies for both spessartine and uvarovite are made in absence of calorimetric measurements and are based on low temperature calorimetry of other minerals containing the Mn²⁺ and Cr³⁺ cations as well as on solid solution garnets containing these cations. The estimate for uvarovite non-lattice entropy is approximately 18 J/mol-K, while for spessartine, approximately 45 J/mol-K. Neither of these cations is expected to provide electronic contributions to the entropy. For both iron-bearing garnets, a small electronic or magnetic entropy contribution continues above ambient temperatures. High pressure data on pyrope, grossular and andradite permit calculation of the thermodynamic parameters at high pressures, which are important for computation of processes in the Earth’s mantle. Thermal expansion coefficients of these materials were found to be 1.6, 1.5, 1.6×10⁻⁵ K⁻¹ at 298 K, respectively, using a Maxwell relation. These closely match the literature values at ambient conditions.     

Trace element incorporation into pyrope–grossular solid solutions: an atomistic simulation study

 We have performed atomistic computer simulations on trace element incorporation into the divalent dodecahedral X-sites of pyrope (Py — Mg₃Al₂Si₃O₁₂) – grossular (Gr — Ca₃Al₂Si₃O₁₂) solid solutions. An ionic model and the Mott–Littleton two-region approach to defect energies were used to calculate the energetics of substitution by a range of divalent trace-elements and of charge-balanced substitution by trivalent ions in the static limit. Results are compared with experimental high-temperature, high-pressure garnet-melt trace element partitioning data obtained for the same garnet solid solution to refine our understanding of the factors controlling element partitioning into solid solutions. Defect energies (U _def,f), relaxation (lattice strain) energies (U _rel), and solution energies (U _sol) were derived using two different approaches. One approach assumes the presence of one type of hybrid X-site with properties intermediate between pure Mg and Ca sites, and the other assumes discrete Mg and Ca X-sites, and thus two distinct cation sublattices. The hybrid model is shown to be inadequate, since it averages out local distortions in the garnet structure. The discrete model results suggest trace elements are more soluble in Py₅₀Gy₅₀ than in either end-member compound. Physically this is due to small changes in size of the X-sites and the removal of unfavourable interactions between third nearest neighbours of the same size. Surprisingly, depending on the local order, large trace element cations may substitute for Mg²⁺ and small trace elements for Ca²⁺ in Py₅₀Gr₅₀. These solubilities provide an explanation for the anomalous trace-element partitioning behaviour along the pyrope–grossular join observed experimentally. Received: 27 January 2000 / Accepted: 14 February 2003     

Garnet-cordierite-biotite equilibria in the Steinach aureole,Bavaria

Three garnet-biotite pairs and eleven garnet-cordierite-biotite triplets from the Steinach aureole (Oberpfalz, North-East Bavaria) were analyzed using an electron probe microanalyzer.The regional metamorphic muscovite-biotite schists contain garnets strongly zoned with Mn-Ca-rich centers and Fe-rich edges, the average composition being almandine 67 — spessartine 4 — pyrope 4 — grossular (+andradite) 25.The first contact garnet that is formed in mica schists of the outermost part of the aureole is small, virtually unzoned, and has an average composition of almandine 52 — spessartine 37 — pyrope 8 — grossular (+andradite) 3. With increasing metamorphic grade, there is a consistent trend to form garnets richer in Fe ending up with a composition almandine 84.5 — spessartine 5.5 — pyrope 7.5 — grossular (+andradite) 2.5. This trend is accompanied by a general increase in grain size and modal amount of garnet. Associated cordierites and biotites also become richer in Fe with increasing grade. While the garnets in the highest grade sillimanite hornfelses are poorly zoned, the transitional andalusite-sillimanite hornfelses contain garnets with distinct but variable zonation profiles.These facts can possibly be explained by the time-temperature relationships in the thermal aureole. In a phase diagram such as the Al-Fe-Mg-Mn tetrahedron, the limiting mineral compositions of a four-phase volume or a three-phase triangle are fixed by T and P (the latter remaining effectively constant within a thermal aureole). Thus, in garnet-cordierite-biotite assemblages, garnet zonation should be controlled by temperature variation rather than by a non-equilibrium depletion process. Taking into account the experimental data of Dahl (1968), a zoned garnet from a transitional andalusite-sillimanite hornfels would reflect a temperature increase of about 40° C during its growth. A hypothetical P-X diagram is proposed to show semi-quantitatively the compositional variation of garnet-cordierite pairs with varying pressures (T constant).     

接触交代夕卡岩型矿床中石榴子石和辉石成分特点及其与矿化的关系

本文对中国十四个接触交代钙夕卡岩矿床和钙-镁夕卡岩矿床中的三百多个样品的石榴子石和辉石成分进行了电子探针分析。不同矿床类型的石榴子石和辉石成分代表着钙夕卡岩矿床的十个矿种(Fe、Fe-Cu、Pb-Zn、W、Sn、Sn-Mo-Bi-W、、W-Bi-Cu-Mo、Cu-Zn、Cu-Sn、W-Zn-Cu)和钙-镁夕卡岩矿床的三个矿种(Fe-Cu、Mo、Pb-Zn)。石榴子石和辉石成分变化范围大,大多数石榴子石是含锰铝榴石+铁铝榴石+镁铝榴石小于15％(摩尔百分数)的钙铝榴石-钙铁榴石固溶体;大多数辉石是含小于5％的锰钙辉石的透辉石-钙铁辉石固溶体。有些Pb-Zn钙-镁夕卡岩矿床中的辉石显示出Mn含量有所增加。只有Sn和W钙夕卡岩矿床及Pb-Zn钙-镁夕卡岩矿床含(Sps+Alm+Pyr)总量大于15％的石榴子石。石榴子石和辉石成分与夕卡岩矿床金属矿化类型之间有某些联系。     

Garnet Types from the Cazadero Area, California

This is the third in a series of papers on glaucophane schistsfrom the Franciscan Formation near Cazadero, California. Previouspapers describe three distinct types of glaucophane-bearingFranciscan metamorphic rocks near Cazadero. The purpose of this study is to investigate the garnets presentin metamorphic types III (bedrock schists) and IV (tectonicblocks) as defined by Coleman & Lee (1963). Twenty-fourgarnet analyses are presented. Sixteen of these are from (aragonite-bearing)type III glaucophane schists, and eight are from type IV glaucophaneschists. Type IV rocks include California eclogites. Type III rocks include metabasalt, metachert, metashale, meta-ironstone,and metacarbonate that were formed under high pressure and relativelylow temperature. These rocks contain garnets that display awide range of composition, but the dominant molecules representedare consistently almandine, spessartine, and grossular. Type IV rocks are mainly metabasalts that were probably formedunder higher temperatures and pressures than type III rocks.There is a distinct difference between garnets from type IIIrocks and those from type IV (including eclogites); the lattercontainless spessartine and more pyrope, and the dominant moleculesare almandine and grossular. The four analyses of garnets fromCalifornia eclogites have an average pyrope content of aboutten molecular per cent, and they extend the range of compositionreported for eclogite garnets. Quantitative spectrographic determinations of minor elementsare listed for each of the garnets described. The values determinedfor some of the minor elements have a wide range and a capriciousdistribution over a few feet of outcrop area. As a group, both the garnets from type III rocks and those fromtype IV are pyralspites with large contents (as much as 35 molecularper cent) of ugrandite. This unusual admixture of the pyralspiteand ugrandite garnet series may have resulted in part from theconditions (high pressures and relatively low temperatures)under which the enclosing rocks were recrystallized.     

Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2

The enthalpies of solution of several synthetic garnets on the join Mg₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ (pyrope-grossular) and of several synthetic clinopyroxenes on the join CaMgSi₂O₆-CaAl₂SiO₆ (diopside-Ca-Tschermak's molecule) were measured in a melt of composition 2PbO · B₂O₃ at 970 K. The determinations were made with sufficient precision so that thermochemical characterizations of the solid solutions could be achieved.The pyrope-grossular solutions show positive enthalpies of mixing. The non-ideality in the range 0–30 mole % grossular is relatively the largest and is in good agreement with the predictions of Ganguly and Kennedy (1974) based largely on cation partitioning of natural high grade metamorphic garnets with biotite, and with the deductions of Hensenet al. (1975) based on measurement of the compositions of synthetic pyrope-rich garnets equilibrated with anorthite, Al₂SiO₅ and quartz. However, the garnets show smaller excess enthalpies at higher grossular contents. This would lead to an asymmetric solvus with a critical temperature lower than predicted by the symmetrical regular solution model of Ganguly and Kennedy (1974). The composition-dependent non-ideality can be understood by simple ionic size considerations in solid substitution and is analogous to the situations for the calcite-dolomite and enstatite-diopside solvi.The heats of solution of pyropes crystallized in the range 1000–1500°C were all the same, within the precision of measurement, and thus we have found no evidence for temperature-dependent cation disordering as a possible explanation of the high entropy of pyrope, as suggested by Charluet al. (1975). Positional disorder of dodecahedral Mg is a more probable reason.The diopside-CaTs join is also non-ideal, with the larger positive enthalpy deviations near the diopside end. The calorimetric data in the magnesian range are consistemt with the model for completely disordered tetrahedral Si and Al which results from the free energy derivations of wood (1975) based on syntheses of diopside-rich aluminous pyroxenes in the presence of anorthite and quartz. At higher Al concentrations the calorimetric data seem more consistent with the ‘local charge-balance’ model of Wood (1975).No evidence for temperature-dependent disorder was found for either the diopside or CaTs end-members.     

The genetic significance of almandine-pyrope phenocrysts in the calc-alkaline Borrowdale Volcanic Group,Northern England

A suite of garnet-bearing andesites and dacites from the Ordovician of N. W. England is described and major- and trace-element analyses of the garnet phenocrysts are presented. The garnets are of almandine-pyrope composition, with minor amounts of spessartine and grossular, and often show marked reversed zoning; the crystal becoming progressively enriched in pyrope towards the margin. Garnets from the dacites are consistently richer in almandine and spessartine than are those from the andesites.From a consideration of the chemistry of the garnet phenocrysts and host rocks, especially La and Y abundances, it is shown that garnet could not have been removed from the magma in quantities sufficient to affect the liquid composition. Consequently the magma must have evolved by some process other than crystal fractionation. It is proposed that the magma was generated by the partial melting of oceanic crust along an ancient Benioff zone, stored at depth (possibly at the crust/mantle interface) long enough for garnet to nucleate, and then transferred rapidly to the surface. Isobaric crystallisation of the garnet phenocrysts at depth could explain the reversed zoning observed.     

Effect of grossular-content in garnet on the partitioning of Fe and Mg between garnet and biotite

In contrast to Ferry (1980) (X _Ca)-values in garnet even lower than 0.1 have a significant effect on the calculated equilibrium temperature using the experimental calibration of the Fe and Mg paritioning between garnet and biotite. Garnet compositions and Mg/Fe — distribution coefficients from samples of the Eoalpine staurolite — in zone in the southern Ötztal are related by the quadratic regression equation: InK _D= -1.7500 (±0.0226) + 2.978 (±0.5317)X _Ca ^Gt -5.906(±2.359)(X _Ca ^Gt )² Temperatures derived by the Ferry and Spear (1978) calibration using chemistry — correctedK _D values are petrologically realistic.Analysis of our data supports non ideal mixing of grossular with almandine — pyrope solid solution. The derived excess mixing energies are quite small for the almandine — pyrope solution (W _FeMg= –133 cal/mole) and about +2775 cal/mole for the difference between pyrope-grossular and almandine-grossular solutions (W _MgCa —W _FeCa) at metamorphic conditions of 570° C and 5,000 bar. The mixing parameters proposed by Ganguly and Saxena (1984) are not confirmed by our data as they would result in significantly lower temperatures.     

The elastic solid solution model for minerals at high pressures and temperatures

Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order–disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.     

Metamorphic kyanite eclogites in the lufilian arc of Zambia

Eclogites formed by the Lufilian (post-Katanga) metamorphism of gabbros intruded into rocks of the Katanga System (Upper Proterozoic) occur in the Central Province of Zambia. Typical constituents of these rocks are omphacite, almandine garnet with significant contents of the pyrope and grossular components, kyanite and rutile. Eclogites from some localities display well preserved, relict ophitic texture inherited from the original gabbro. Hornblende-scapolite metagabbro and coronite metagabbro often accompany the eclogites, and metalherzolite and serpentinite occur at a few localities. The Zambian eclogites are broadly associated with a variety of relatively high-pressure, kyanite-bearing mineral assemblages some of which are possibly in the eclogite facies. It is suggested that, in addition to temperature and load pressure, fluid pressure, fluid composition (H₂O, CO₂, Cl, SO₃) and permeability of the gabbro due to deformation were important factors for the transformation of gabbro to eclogite in the environment of the Lufilian Arc.