Electronic and magnetic structure of pyroxenes I. Hedenbergite

The electronic and magnetic structure of the chain silicate hedenbergite (CaFe²⁺Si₂O₆) has been investigated by a number of experimental methods (neutron diffraction, Mössbauer spectroscopy, low temperature magnetic measurements), as well as by electronic structure calculations for clusters of different size in the local spin density approximation. The calculated size-converged spectroscopic data (d-d excitation energies, hyperfine parameters) are in quantitative agreement with the respective experimental values. The calculated magnetic coupling constants are about +25 cm^?1 and ?4 cm^?1 for intra-chain and inter-chain coupling, respectively. The latter value shows that weak superexchange via edges of silicon tetrahedra is well reproduced by the calculations, and it is in qualitative agreement with an observed metamagnetic transition at 4.2 K in an external magnetic field with an onset around 4 T but saturation is not achieved in fields up to 14.5 T. The large ferromagnetic intra-chain coupling is attributed to a nearly degenerate ground state. The ratio between the two magnetic coupling constants agrees with earlier estimates on similar compounds. Finally, it is demonstrated how the detailed discussion of the various exchange pathways contributes to an improved understanding of the connection between magnetic properties and the geometrical structure.     

The local structure of Ca-Na pyroxenes. II. XANES studies at the Mg and Al K edges

X-ray absorption spectra at the Mg and Al K edges have been recorded using synchrotron radiation on synthetic end member diopside (Di) and jadeite (Jd) and on a series of natural Fe-poor Ca-Na clinopyroxenes compositionally straddling the Jd-Di join. The spectra of C2/c end members and intermediate members of the solid solution series (C-omphacites) are different from those of the intermediate members having P2/n symmetry (P-omphacites). Differences can be interpreted and explained by comparing the experimental spectra with theoretical spectra calculated via the full multiple-scattering formalism, starting from the atomic positional parameters determined by single-crystal X-ray diffraction structure refinement on the same samples. Atomic clusters with at least 89 atoms, extending to more than 0.60 nm away from the Mg or Al absorbers, are needed to reproduce the experimental spectra. This shows that in the clinopyroxene systems XANES detects medium- rather than short-range order-disorder relationships. Theoretical spectra match the experimental ones well for all features in the regions from 16 to 60 eV above threshold. Experimental near-edge features in the first 16 eV are also reproduced, albeit less accurately. Certain near-edge features of C-omphacites reflect the octahedral arrangement of the back-scattering six O atoms nearest neighbours of the probed atom (Mg or Al) located at site M1 of the crystal structure, thus being indicators of short-range order. Others arise again from medium-range order. P-omphacites show more complicated spectra than C-omphacites. Their additional features reflect the increased complexity of the structure and the greater local disorder around the probed atom induced by the two alternative M1, M11 configurations of the six O atoms forming the first coordination shells. Mg and Al are confirmed to be preferentially partitioned in the M1 and M11 site of the P-omphacite crystal structure, however with a certain degree of local disorder. The relative heights of certain prominent features are directly related to sample composition in terms of Di:Jd ratio in the Al K-edge spectra, whereas they show abrupt variations in the Mg K-edge spectra. They demonstrate that XANES is directly related to composition and may be used to distinguish C- from P-omphacites. Received: 24 November 1998 / Revised, accepted: 10 June 1999     

Thermodynamics of multicomponent pyroxenes: II. Phase relations in the quadrilateral

The model for the thermodynamic properties of multicomponent pyroxenes (Part I) is calibrated for ortho- and clinopyroxenes in the quadrilateral subsystem defined by the end-member components Mg₂Si₂O₆, CaMgSi₂O₆, CaFeSi₂O₆, and Fe₂Si₂O₆. This calibration accounts for: (1) Fe-Mg partitioning relations between orthopyroxenes and augites, and between pigeonites and augites, (2) miscibility gap features along the constituent binary joins CaMgSi₂O₆-Mg₂Si₂O₆ and CaFeSi₂O₆-Fe₂Si₂O₆, (3) calorimetric data for CaMgSi₂O₆-Mg₂Si₂O₆ pyroxenes, and (4) the P-T-X systematics of both the reaction pigeonite=orthopyroxene+augite, and miscibility gap featurs, over the temperature and pressure ranges 800–1500°C and 0–30 kbar. The calibration is achieved with the simplifying assumption that all regular-solution-type parameters are constants independent of temperature. It is predicated on the assumptions that: (1) the Ca-Mg substitution is more nonideal in Pbca pyroxenes than in C2/c pyroxenes, and (2) entropies of about 3 and 6.5 J/K-mol are associated with the change of Ca from 6- to 8-fold coordination in the M2 site in magnesian and iron C2/c pyroxenes, respectively. The model predicts that Fe²⁺-Mg²⁺ M1-M2 site preferences in C2/c pyroxenes are highly dependent on Ca and Mg contents, with Fe²⁺ more strongly preferring M2 sites both in Ca-rich C2/c pyroxenes with a given Fe/(Fe+Mg) ratio, and in magnesian C2/c pyroxenes with intermediate Ca/(Ca+Fe+Mg) ratios.The proposed model is internally consistent with our previous analyses of the solution properties of spinels, rhombohedral oxides, and Fe-Mg olivines and orthpyroxenes. Results of our calibration extend an existing database to include estimates for the thermodynamic properties of the C2/c and Pbca pyroxene end-members clinoenstatite, clinoferrosilite, hedenbergite, orthodiopside, and orthohedenbergite. Phase relations within the quadrilateral and its constitutent subsystems are calculated for temperatures and pressures over the range 800–1700°C and 0–50 kbar and compare favorably with experimental constraints.     

Electronic and magnetic structure of vivianite: cluster molecular orbital calculations

The electronic and magnetic structure of the octahydrophosphate vivianite, Fe₃(PO₄)₂·8H₂O, has been investigated by cluster molecular orbital calculations in local spin density approximation. Optical and Mössbauer spectra are well reproduced by the calculations, and the differences between the two iron sites can be correlated with differences in the geometrical structure of the first coordination sphere. The spin structure within the crystallographic ac plane is derived and explained on the basis of different superexchange pathways via edges of the phosphate tetrahedra. The calculations demonstrate that quite large clusters (up to 118 atoms) are necessary to arrive at reliable results.     

The local structure of Ca-Na pyroxenes. I. XANES study at the Na K-edge

 X-ray absorption Na K-edge spectra have been recorded on synthetic endmember jadeite and on a series of natural Ca-Na pyroxenes compositionally straddling the Jd-Di join. The C2/c members of the series are systematically different from the P2/n members. Differences can be interpreted and explained by comparing the experimental spectra with theoretical spectra. These have been calculated by the multiple-scattering formalism from the atomic positional parameters determined by single-crystal X-ray diffraction structure refinement on the same samples. In the full multiple scattering region of the spectra (1075 to 1090 eV) C-pyroxenes exhibit three features which reflect the 6-2 configuration of the O back-scattering atoms around the Na absorber located at the center of the cluster (site M2 of the jadeite structure). P-pyroxenes show more complicated spectra in which at least four (possibly five) features can be recognized; they reflect the two types of configuration (6-2 and 4-2-2) of O around Na in the two independent M2 and M21 eight-fold coordinated sites of the omphacite structure. A weak, sometimes poorly resolved peak at 1079 eV is diagnostic and discriminates C- from P-pyroxenes. The Garnet Ridge C2/c impure jadeite exhibits a spectrum which is intermediate between those of jadeite and omphacite. The Hedin-Lundqvist potential proves best for these insulating materials and allows multiple-scattering calculations agreeing well with experiments. Received: July 11, 1996/Revised, accepted: October 21, 1996     

Thermodynamics of multicomponent pyroxenes: I. Formulation of a general model

A model is proposed for the thermodynamic properties of multicomponent pyroxenes in the composition space defined by the end-member component CaMgSi₂O₆ and the exchange components Fe(Mg)_-1, TiAl₂(MgSi₂)_-1, Fe³⁺(Al)_-1, Fe³⁺Al(MgSi)_-1, and Mg(Ca)_-1. It is formulated for the simplifying assumptions that: (1) a molecular mixing type approximation describes changes in the molar configurational entropy associated with the coupled exchange substitutions TiAl₂MgSi₂, Fe³⁺AlMgSi, and Al₂MgSi (and their ferroan equivalents), and (2) Fe²⁺ and Mg²⁺, and Al³⁺ and Fe³⁺ display long-range non-convergent ordering between M2 and octahedral M1 sites, and octahedral M1 and tetrahedral sites, respectively. The molar vibrational Gibbs energy is described by a Taylor expansion of second degree in seven linearly independent composition and ordering variables, which is extended to third degree to account for asymmetry in the mixing of Ca and Mg, and Ca and Fe on the M2 site, and is further modified for the assumption that the standard state properties of Ca end-member components of clinopyroxenes are linearly dependent on the coordination number of Ca²⁺ on the M2 site. The model is shown to be consistent with miscibility gap feaures of pyroxenes in the system CaMgSi₂O₆–CaTiAl₂O₆–CaAl₂SiO₆. In subsequent papers, the model is calibrated for the simplifying assumptions that: (1) all regular-solution-type parameters are constants independent of temperature, (2) Pbca and C2/c end-members have identical heat capacities and coefficients of thermal expansion and compressibility, and (3) the heat capacities and coefficients of thermal expansion and compressibility are zero for all reciprocal reactions relating Pbca and pigeonite or high-calcium pyroxene C2/c endmember components.     

Chemical etching of amphiboles and pyroxenes

Chemical etching of defect structures in pyroxenes and amphiboles has been investigated. Many features, such as very thin (～1 micrometer) exsolution lamellae not observed by transmission optical microscopy of thin sections, have been observed in reflected light after chemical etching of cleaved or polished crystal surfaces. A new feature in the microstructure of pyroxenes, not previously reported in the literature, has been revealed by one of the etchants.     

Thermodynamic analysis of quadrilateral pyroxenes

The thermodynamics of quadrilateral pyroxene solutions have been analysed with the ternary non-convergent site-disorder model developed in Part I. Solution parameters have been refined for this model with a non-linear least squares technique to fit experimentally determined phase equilibria for the assemblages orthopyroxene-clinopyroxene (opx-cpx), pigeonite-augite (pig-aug), and opx-pig-aug. Calculated phase relations agree, within error, with experiments. Predicted cation distributions and enthalpies of solution for opx are also in agreement with measurements. Predicted cation distributions for cpx are more disordered than indicated by most available measurements. Two types of pyroxene thermometers are presented: (a) a single-pyroxene (aug) thermometer, and (b), a two-pyroxene thermometer which approximates the temperature of an observed pig-aug or cpx-opx assemblage as that of its nearest model tieline. Pyroxene pairs from two granulite suites, whose compositions were projected to the ternary system by the method of Lindsley and Andersen (1983), yield temperatures that are 25° C higher by thermometers (a) and (b) than determined from Lindsley's (1983) graphical thermometer. Temperatures calculated for projected compositions of coexisting pig-aug are within 20° C of run temperatures in experiments by Grove and Bryan (1983).     

Thermochemistry of some pyroxenes and related compounds

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.     

Electronic structure of spinel

The fundamental band gap between conduction and valence bands in aluminate spinels has been found to be at least 8·1 eV; the optical reflectivity peak at this energy possibly represents the lowest-energy exciton. In crystals with non-stoichiometric Al/Mg ratios, the intensity of this first reflection peak appears to decrease with increasing Al/Mg ratio; however, the peak energies themselves are essentially independent of stoichiometry. It seems likely that spinel and olivine in spinel-structure will have electronic transport behavior similar to that of olivine in its normal structure.     

Crystallochemistry and origin of pyroxenes in komatiites

We present a detailed mineralogical and major- and trace-element study of pyroxenes in two Archean komatiitic flows in Alexo, Canada. The pyroxenes in spinifex-textured lavas commonly are zoned with cores of magnesian pigeonite and rims of augite. Concentrations of incompatible trace elements are low in pigeonite and jump to higher values in the augite mantles, a variation that can be modelled using accepted partition coefficients and assuming crystallization from komatiitic liquids. Crystallization sequences are very different in different parts of both flows. In the flow top, the sequence is olivine followed by augite: deeper in the spinifex sequence, pigeonite crystallizes after olivine, followed by augite; in lower cumulates, orthopyroxene or augite accompany olivine. In spinifex lavas, pigeonite crystallizes sooner than would be predicted on the basis of equilibrium phase relations. We propose that contrasting crystallization sequences depend on the position in the flow and on the conditions of crystal growth. In the flowtop, rapid cooling causes quench crystallization. Deeper in the spinifex layer, constrained growth in a thermal gradient, perhaps augmented by Soret differentiation, accounts for the early crystallization of pigeonite. The cumulus minerals represent a near-equilibrium assemblage. Augites in Al-undepleted Archean komatiites in various localities in Canada and Zimbabwe have high moderate to high Wo contents but their Mg# (Mg/(Mg + Fe) are lower than in augites in komatiites from Barberton, South Africa. We attribute the combination of high Wo and high Mg# in Barberton rocks to the unusually high CaO/Al₂O₃ of these Al-depleted komatiites.     

Mechanisms of exsolution in sodic pyroxenes

The free energy curves for simple binary solid solutions with limited miscibility or atomic ordering have been combined to predict the phase relations and exsolution mechanisms for a system in which both ordering and exsolution are possible. The nature of the ordering process affects which exsolution mechanisms may be used. If the ordering is second (or higher) order in character then continuous mechanisms predominate and a ‘conditional spinodal’ (Alien and Cahn, 1976) can be described which operates between ordered and disordered end members. For a first order case, the ordered phase can only precipitate a disordered phase by nucleation and growth. Microstructures in omphacites observed by transmission electron microscopy include exsolution lamellae and antiphase domains and the relations between them in selected specimens have been used to interpret the exsolution mechanisms which operated under geological conditions. It appears that most omphacites undergo cation ordering, and then remain homogeneous or exsolve a disordered pyroxene by spinodal decomposition. The predominance of continuous mechanisms has been used to indicate that the C2/c→P2/n transformation may be second (or higher) order in character. A possible phase diagram for jadeite-augite is presented. It is based on the idea that there should be limited miscibility between the disordered end members at low temperatures and that the cation ordering at intermediate compositions (omphacite) is superimposed on a solvus. It is adequate to explain many of the observed microstructures and fits with petrographic evidence of broad two phase fields between impure jadeite and omphacite and between omphacite and sodic augite. The effect of adding acmite is analogous to increasing temperature so that the phase relations for jadeite-acmite-augite can also be predicted.     

Thermochemistry of jadeite—diopside pyroxenes

The enthalpies of solution of seven synthetic clinopyroxenes on the join CaMg₂Si₂O₆ (diopside)-NaAlSi₂O₆ (jadeite), of two natural low-Fe ordered omphacites near the 1:1 composition, and of a nearly pure natural jadeite, were measured in molten Pb₂B₂O₅ at 970 K. Enthalpies of solution of the natural omphacites experimentally disordered at 1350°C and 30 kbar were also measured.The synthetic clinopyroxenes have positive excess enthalpies of mixing, which can be expressed by a symmetrical function ΔH_mix = W_HX_JdX_Di, with W_H = 7250 ±950 calories. The enthalpy of disordering of the two natural omphacites averages 1.8 kcal, which is nearly the same as the excess enthalpy of mixing of a 1:1 disordered pyroxene.The interaction parameter, W_H, can be shown to be essentially equivalent to ΔG° of the reciprocal reaction: CaMgSi₂O₆ + NaAlSi₂O₆ = CaAlSi₂O⁺₆ + NaMgSi₂O^?₆ M-site cation distribution data of natural omphacites heat-treated at 1000°C (Aldridgeet al., 1978) lead to ΔG° = 7200 cal for the above reaction, in good agreement with the calorimetric W_H. The reciprocal solution theory with ΔG° = 7200 cal predicts closely the activities of NaAlSi₂OP₆ in jadeite-diopsides found from phase equilibrium measurements at 600°C (Holland, 1979a) and is nearly equivalent to an entropically ideal two site mixing model with a (fictive) W_H of 5800 cal.Jadeite-diopside solid solutions near the 1:1 composition at temperatures of 1000–1500 K are ‘pseudoideal’; that is, they have nearly the free energies of ideal one-site mixtures (Ganguly, 1973). If the order-disorder transition is nearly first-order at about 1000 K, as suggested by Fleetet al. (1978), the pseudo-ideality holds also for ordered omphacites at least somewhat below 1000 K.     

Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation

A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si₂O₆)-jadeite (NaAlSi₂O₆) and diopside-CaTs (CaAl₂SiO₆). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other. The calculations show that the random model, in which the configurational entropy is calculated as if atoms on each crystallographic site mix randomly, is appropriate as a first approximation. The excess entropy relative to the random model behaves regularly, is always negative, and becomes more negative as temperature decreases or the ordering energies increase. The excess entropy relative to the random model can be modeled reasonably well with a simple power series, or Margules-type, formulation. In contrast, the excess entropy relative to a molecular model, in which the ideal activity is assumed to be equal to some mole fraction, is irregular, can be positive or negative, and even changes in sign with variations in temperature and composition. The configurational enthalpy is positive at high temperatures, and becomes negative with decreasing temperature or increasing ordering energy. The mixing enthalpy can have non-configurational contributions, in addition to the effective short-range configurational contributions considered explicitly. The pair approximation predicts an ordering transition from C2/c to P2₁/n for CaTs and diopside-CaTs solutions at moderate to low temperatures, respectively. A field where C2/c orders to C2 is also found. A higher order approximation, different relative ordering energies, or quantitative consideration of strain contributions is required to account for the C2/c to P2/n transition in omphacites. There is no justification for molecular models, in which the configurational entropy is calculated as if endmember “molecules” were mixing in the crystal, in either concentrated or dilute solutions. Molecular models do not represent limiting ordered states for coupled solid solutions.     

Oxygen isotope fractionations involving pyroxenes: The calibration of mineral-pair geothermometers

Oxygen isotope fractionations between wollastonite, diopside, jadeite, hedenbergite and water have been experimentally studied at high pressures (1<- PH₂O ≥ 24 kbar) and temperatures (400/dg ≤ T <- 800/dgC) using the three-isotope method (Matsuhisa et al., 1978). Initial ${}^{18}\text{O}{}^{16}\text{O}$ fractionations were made close to equilibrium and initial ${}^{17}\text{O}{}^{16}\text{O}$ ratios were well removed from equilibrium, allowing accurate determinations of the equilibrium ${}^{18}\text{O}{}^{16}\text{O}$ fractionations and of the extent of isotopic exchange. Scanning electron microscope and rate studies show that the wollastonite-water and diopside-water exchange reactions occur largely by solution-precipitation (Ostwald Ripening) mechanisms. Equilibrium ${}^{18}\text{O}{}^{16}\text{O}$ fractionations between water and the minerals wollastonite, diopside, and hedenbergite are in close agreement with one another, whereas significantly more positive fractionations are found for jadeite-water. These isotopic substitution effects can be ascribed to replacement of SiOM bonds (M is a divalent metal cation in octahedral coordination) by higher frequency SiOAl bonds. The fractionations determined in this study can be combined with quartz- and feldspar-water data of Matsuhisa et al. (1979) and revised magnetite-water data of O'NEIL (1963), to provide a coherent set of mineral-pair fractionations satisfactorily represented by straight lines through the origin on a conventional graph of In /ga versus T^?2. Mineral-water data, on the other hand, cannot readily be fitted to the simple relationship suggested by Bottinga and Javoy (1973). Coefficients “A” for the mineral-pair fractionations 1000 ln α = A × 10⁶T^?2 are:

     

16.

Luna 20 pyroxenes: exsolution and phase transformation as indicators of petrologic history     

Subrata Ghose  I.Stewart McCallum  Enrique Tidy 《Geochimica et cosmochimica acta》1973,37(4):831-839

Pyroxenes from our sample of Luna 20 soil are predominantly orthopyroxene with subordinate pigeonite. The orthopyroxenes are chromium-rich bronzites and contain submicroscopic lamellae of augite in a twinned orientation exsolved on (100). These lamellae have a composition close to the diopside-hedenbergite join. Asymmetric diffuse streaks parallel to $\text{a}{}^1$ indicate stacking faults parallel to (100) and possibly very thin (10–20 Å) lamellae of clinobronzite parallel to (100). Pigeonite crystals are very complex crystallographically and chemically, with optically visible (001) augite exsolution lamellae and two sets of chromite exsolution lamellae. In addition, there are submicroscopic (100) augite lamellae and a second generation of clinohypersthene lamellae which appear to have exsolved from the (001) augite lamellae. The clinohypersthene host, which has a large number of stacking faults parallel to (100), has partially inverted to hypersthene of the same composition. The hypersthene occurs as very fine lamellae (less than 1000 Å) parallel to the (100) plane of the clinohypersthene. X_D^Fe-Mg values for five host-lamellae pairs in pigeonite K-4 indicate a significant amount of subsolidus readjustment. We tentatively conclude that many of the bronzite and pigeonite crystals were derived from rocks crystallized from a high level magma chamber in the lunar highland crust.     

17.

Contrasting properties and behaviour of antiphase domains in pyroxenes     

Michael A. Carpenter 《Physics and Chemistry of Minerals》1979,5(2):119-131

Antiphase domains in pigeonite arise from a displacive transformation whereas in omphacite they are due to cation ordering. Their properties and behaviour are quite distinct. Domains in pigeonite are elongate, coarsen by a homogeneous and rapid mechanism and have irregular boundaries which are susceptible to the segregation of cations. In omphacite they tend to be equiaxed with smoothly curving boundaries and they coarsen extremely slowly. A heterogeneous mode of coarsening has been postulated to explain some of the observed domain distributions. A brief review of antiphase textures in other minerals, in particular the type (b) and type (c) domains in calcic plagioclase, show many of these properties to be characteristic of the transformation by which they formed, i.e., displacive or order/disorder. It is suggested that displacive type antiphase boundaries have relatively low surface energies and that their migration requires only small atomic displacements locally. In contrast, the chemical interactions associated with mistakes in the cation ordering sequence at antiphase boundaries in an ordered phase give a relatively higher excess free energy. Furthermore their movement requires the exchange of cations between sites at the boundary and hence domain coarsening is slow. The factors which control the domain size in natural specimens have been evaluated qualitatively. For the purpose of comparing thermal histories only domains with a regular size distribution in homogeneous areas of crystal which are free of defects should be used.     

18.

Subsolidus reactions in lunar pyroxenes: An electron petrographic study     

J. S. Lally  A. H. Heuer  G. L. Nord Jr.  J. M. Christie 《Contributions to Mineralogy and Petrology》1975,51(4):263-281

Zoned lunar pyroxenes have been examined by high voltage (800–1000 kV) transmission electron microscopy and electron diffraction, with the particular aim of providing information on the cooling history of individual pyroxenes. Microstructures resulting from composition discontinuities occurring during continuous crystallization, exsolution lamellae of pigeonite and augite and the development of denuded zones, and anti-phase domains (APD's) in pigeonite have been studied with respect to their scale, morphology and micro-structural evolution. These features have been further interpreted with respect to a proposed pseudobinary phase diagram of constant En/Fs.Information found to be the most useful for determining cooling rates in pyroxenes are: for quickly cooled rocks; microstructural evolution and APD size for moderately cooled rocks; and denuded zone widths and APD morphology for slowly cooled rocks.Now at U.S. Geological Survey, 959 National Center, Reston, Virginia 22092.     

19.

Fictive component model of pyroxenes and multicomponent phase equilibria     

S. K. Saxena 《Contributions to Mineralogy and Petrology》1982,78(3):345-351

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G _f ⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G ^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant     

20.

Calculation of subsolidus phase relations in carbonates and pyroxenes     

Alexandra Navrotsky  Douglas Loucks 《Physics and Chemistry of Minerals》1977,1(1):109-127

This formulation of the free energy of mixing in a binary system takes as parameters a Bragg-Williams type cooperative disordering energy and the difference in free energy between different structures for the end-members. Subsolidus phase relations in carbonate systems such as CaCO₃—MgCO₃ and CdCO₃—MgCO₃ are calculated. Similar equations also reproduce the topologies of subsolidus phase relations in pyroxenes, including orthopyroxene-clinopyroxene phase boundaries in the enstatitediopside and ferrosilite-hedenbergite systems, the pigeonite-augite solvus, and the stability field of iron-free pigeonite.     

	Ab	Jd	An	Di	Wo	Mt
Q	0.50	1.09	1.59	2.08	2.20	6.11
Ab		0.59	1.09	1.58	1.70	5.61
Jd			0.50	0.99	1.11	5.02
An				0.49	0.61	4.52
Di					0.12	4.03
Wo						3.91

Luna 20 pyroxenes: exsolution and phase transformation as indicators of petrologic history

Pyroxenes from our sample of Luna 20 soil are predominantly orthopyroxene with subordinate pigeonite. The orthopyroxenes are chromium-rich bronzites and contain submicroscopic lamellae of augite in a twinned orientation exsolved on (100). These lamellae have a composition close to the diopside-hedenbergite join. Asymmetric diffuse streaks parallel to $\text{a}{}^1$ indicate stacking faults parallel to (100) and possibly very thin (10–20 Å) lamellae of clinobronzite parallel to (100). Pigeonite crystals are very complex crystallographically and chemically, with optically visible (001) augite exsolution lamellae and two sets of chromite exsolution lamellae. In addition, there are submicroscopic (100) augite lamellae and a second generation of clinohypersthene lamellae which appear to have exsolved from the (001) augite lamellae. The clinohypersthene host, which has a large number of stacking faults parallel to (100), has partially inverted to hypersthene of the same composition. The hypersthene occurs as very fine lamellae (less than 1000 Å) parallel to the (100) plane of the clinohypersthene. X_D^Fe-Mg values for five host-lamellae pairs in pigeonite K-4 indicate a significant amount of subsolidus readjustment. We tentatively conclude that many of the bronzite and pigeonite crystals were derived from rocks crystallized from a high level magma chamber in the lunar highland crust.     

Contrasting properties and behaviour of antiphase domains in pyroxenes

Antiphase domains in pigeonite arise from a displacive transformation whereas in omphacite they are due to cation ordering. Their properties and behaviour are quite distinct. Domains in pigeonite are elongate, coarsen by a homogeneous and rapid mechanism and have irregular boundaries which are susceptible to the segregation of cations. In omphacite they tend to be equiaxed with smoothly curving boundaries and they coarsen extremely slowly. A heterogeneous mode of coarsening has been postulated to explain some of the observed domain distributions. A brief review of antiphase textures in other minerals, in particular the type (b) and type (c) domains in calcic plagioclase, show many of these properties to be characteristic of the transformation by which they formed, i.e., displacive or order/disorder. It is suggested that displacive type antiphase boundaries have relatively low surface energies and that their migration requires only small atomic displacements locally. In contrast, the chemical interactions associated with mistakes in the cation ordering sequence at antiphase boundaries in an ordered phase give a relatively higher excess free energy. Furthermore their movement requires the exchange of cations between sites at the boundary and hence domain coarsening is slow. The factors which control the domain size in natural specimens have been evaluated qualitatively. For the purpose of comparing thermal histories only domains with a regular size distribution in homogeneous areas of crystal which are free of defects should be used.     

Subsolidus reactions in lunar pyroxenes: An electron petrographic study

Zoned lunar pyroxenes have been examined by high voltage (800–1000 kV) transmission electron microscopy and electron diffraction, with the particular aim of providing information on the cooling history of individual pyroxenes. Microstructures resulting from composition discontinuities occurring during continuous crystallization, exsolution lamellae of pigeonite and augite and the development of denuded zones, and anti-phase domains (APD's) in pigeonite have been studied with respect to their scale, morphology and micro-structural evolution. These features have been further interpreted with respect to a proposed pseudobinary phase diagram of constant En/Fs.Information found to be the most useful for determining cooling rates in pyroxenes are: for quickly cooled rocks; microstructural evolution and APD size for moderately cooled rocks; and denuded zone widths and APD morphology for slowly cooled rocks.Now at U.S. Geological Survey, 959 National Center, Reston, Virginia 22092.     

Fictive component model of pyroxenes and multicomponent phase equilibria

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G _f ⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G ^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant     

Calculation of subsolidus phase relations in carbonates and pyroxenes

This formulation of the free energy of mixing in a binary system takes as parameters a Bragg-Williams type cooperative disordering energy and the difference in free energy between different structures for the end-members. Subsolidus phase relations in carbonate systems such as CaCO₃—MgCO₃ and CdCO₃—MgCO₃ are calculated. Similar equations also reproduce the topologies of subsolidus phase relations in pyroxenes, including orthopyroxene-clinopyroxene phase boundaries in the enstatitediopside and ferrosilite-hedenbergite systems, the pigeonite-augite solvus, and the stability field of iron-free pigeonite.