Thermodynamic properties and hydrogen speciation from vibrational spectra of dense hydrous magnesium silicates

Infrared absorption measurements were taken from 100 to 5000 cm^?1 of a natural chondrodite and three dense hydrous magnesium silicates: phase A, phase B, and superhydrous phase B (shy-B). Raman spectra were also acquired from phase B and the chondrodite. Roughly half of the lattice modes are represented and our data are the first report of the low frequency modes. Comparison of our new spectra to symmetry analyses suggests that multiple sites for hydrogen exist for all the phases. The shy-B we examined crystallizes in P2₁ nm with two OH sites. Models for the density of states are constructed based on band assignments for the lattice modes and for the OH stretching vibrations. Heat capacity C_P and entropy S calculated using Kieffer's formulation should be accurate within 3% from 200 to 800 K. Model values for C_P at 298 K are 299.6 J/mol-K for chondrodite, 421.5 J/mol-K for phase A, 529.4 J/mol-K for shy-B, and 618.9 J/mol-K for phase B. Model values for S₂₉₈ ⁰ are 234.2 J/mol-K for chondrodite, 303.5 J/ mol-K for phase A, 377.9 J/mol-K for shy-B, and 473.3 J/mol-K for phase B. Debye temperatures are near 1000 K.     

Thermodynamic mixing properties of olivine derived from lattice vibrations

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe₂SiO₄. This semi-empirical technique is based on an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict thermodynamic mixing properties of olivine (Mg,Fe)₂SiO₄ solid solutions by using results of our previous work on the system MgO–SiO₂. Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium–iron solid solutions of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity for temperatures below 100 K.     

Vibrational spectra,lattice dynamics and chemical constitution of oxides

The relationships among lattice dynamics of oxides and their chemical constitution are discussed in terms of the concept of dynamic crystal chemistry. A new approach to the design of a dynamic model of an ionic-covalent crystal combining molecular force constants with explicit treatment of long-range electrostatic forces in a lattice is outlined and its applications exemplified. The conditions of introduction of scaled quantum chemical force constants of a suitable molecular system into the secular equation for lattice vibrations are determined rigorously. The importance of unified treatment of stability conditions and various dynamic properties of crystals including phonon spectra, macroscopic elastic and piezoelectric constants etc., is emphasized. Several results of ab initio quantum chemical SCF computations by the gradient method for molecular species containing silicon-oxygen bonds are presented and are used to explain some empirical regularities in silicate structures.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs

We use an approach based upon the Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the phonon dispersion of forsterite and the lattice dynamical behaviour of the beta-phase and spinel polymorphs of Mg₂SiO₄. The potential used (THB1) was derived largely empirically using data from simple binary oxides, and has previously been successfully used to model the infrared and Raman behaviour of forsterite. It includes ‘bond bending’ terms, that model the directionality of the Si-O bond, in addition to the pair-wise additive Coulombic and short range terms. The phonon dispersion relationships of the Mg₂SiO₄ polymorphs predicted by THB1 were used to calculate the heat capacities, entropies, thermal expansion coefficients and Gruneisen parameters of these phases. The predicted heat capacities and entropies are in outstandingly good agreement with those determined experimentally. The predicted thermodynamic data of these phases were used to construct a phase diagram for this system, which has Clausius-Clapeyron slopes in very close agreement with those found by experiment, but which has predicted transformation pressures that show less close agreement with those inferred from experiment. The overall success, however, that we have in predicting the lattice dynamical and thermodynamic properties of the Mg₂SiO₄ polymorphs shows that our potential THB1 represents a significant step towards finding the elusive quantitative link between the microscopic or atomistic behaviour of minerals and their macroscopic properties.     

Thermodynamic properties and equation of state of fcc aluminum and bcc iron, derived from a lattice vibrational method

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of the pure elements aluminum and iron in pressure–temperature space. This semi-empirical technique is based on either the Mie–Grüneisen–Debye (MGD) approach or an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity, electronic effects based on the free electron gas model, and magnetic effects based on the Calphad approach. We show that Keane’s equation of state for the static lattice is better suitable to represent thermodynamic data for aluminum from 1 bar to pressures in the multi-megabar region relative to Vinet’s universal and the Birch–Murnaghan equation of state. It appears that the MGD and Mie–Grüneisen–Kieffer approach produce similar results, but that the last one better represents heat capacity below room temperature. For iron we show that the high temperature behavior of thermal expansivity can be explained within the Calphad approach by a pressure-dependent Curie temperature with a slope between –1 and 0 K/GPa.     

Thermodynamic analysis of binary liquid silicates and prediction of ternary solution properties by modified quasichemical equations

Modified quasichemical equations, developed for the analysis of the thermodynamic properties of structurally ordered liquid solutions, are shown to be well-suited for use with molten silicates. For binary systems, these equations have been coupled with a least-squares optimization computer program to analyse simultaneously all thermodynamic data including phase diagrams, Gibbs energies and enthalpies of formation of compounds, activities, enthalpies of mixing, entropies of fusion, miscibility gaps, etc. In this manner, data for several binary systems have been analysed and represented with a small number of parameters. In the present article, results for the SiO₂-MgO, SiO₂-Na₂O and MgO-CaO systems are presented. The resulting equations represent all the binary data, including the phase diagrams, within or virtually within experimental error limits.From the modified quasichemical equations for ternary systems, ternary thermodynamic properties can be approximated solely from data from the subsidiary binary systems. Results for the SiO₂-CaO-Na₂O, SiO₂-CaO-MgO, and SiO₂-MgO-FeO systems are in excellent agreement with measured ternary data. Predictions for the quaternary system SiO₂-MgO-CaO-Na₂O are also presented.     

Lattice dynamics and Raman spectroscopy of protoenstatite Mg2Si2O6

Enstatites (Mg₂Si₂O₆) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO₆ octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg₂₊ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg₂SiO₄ and fayalite, Fe₂-SiO₄) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)_0.6Mg_1.4Si₂O₆ stable at room temperature using the 488 nm or 514.5 nm lines of an Ar⁺ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.     

Thermodynamic properties of MgSiO3 perovskite derived from large scale molecular dynamics simulations

A molecular dynamics simulation study of MgSiO₃ has been performed using a large sample containing 4096 unit cells. Thermodynamic properties have been extracted using a semiclassical approximation to the correct quantum mechanical treatment, using the calculated density of states and the quantum harmonic formalism for thermodynamic functions. Simulations performed at different temperatures and volumes have given an estimate of the relative contributions due to thermal expansion (quasi-harmonic effects) and direct anharmonic interactions. Comparison of results for mean square atomic displacements with results on smaller samples have shown the limitations of smaller sample sizes.     

Structure-composition relations and Raman spectroscopy of high-pressure sodium silicates

?-Na₂Si₂O₅, ζ-Na₂Si₂O₅, Na₂Si[Si₂O₇], and Na₆Si₃[Si₉O₂₇] have been synthesized using an MA6/8 superpress. Densification in high-pressure sodium silicates is effected largely by changes in packing. In the relaxed (1 bar) structures, cation polyhedra and thermal/displacement parameters are similar to those of low-pressure silicates, but the extra-framework cation positions are oversized. The two mixed ^[4]Si and ^[6]Si framework silicates of known structure (Na₂Si[Si₂O₇] and Na₆Si₃[Si₉O₂₇]) belong to the limited homologous series Na_2mSi_m[Si_n–mO_2n+m], with m<n. The structure-composition relationships of wadeite-type, A₂Ge₄O₉-type, and Na₆Si₃[Si₉O₂₇] silicates and germanates depend on T-O distance and size of the large extra-framework cation. Characteristic features of the SiO₄ tetrahedral units are present in micro-Raman spectra of mixed ^[4]Si and ^[6]Si framework silicates, but bands uniquely attributable to SiO₆ octahedra are weak or obscured. However, ^[6]Si has a profound indirect influence on the Raman spectra, resulting in intense and complex low-frequency bands, assigned to symmetric bending modes with coupled displacements at both bridging oxygens and nonbridging oxygens bonded to ^[6]Si, and a shift to higher frequency and reduction in intensity of the high-frequency bands assigned to symmetric ^[4]Si-O_nbr stretching vibrations. Raman spectroscopy does not appear to be a useful structural probe for small amounts of ^[6]Si in silicate glasses and melts.     

Ion dynamics studies of liquid and glassy silicates,and gas-in-liquid solutions

We give a brief review of ion dynamics studies of liquid and glassy states of SiO₂ and silicate colutions which have been carried out in recent years in this laboratory. We summarize studies on SiO₂, Na⁺ migration in Na₂O·SiO₂ in the “glassy state”, and ionic coordination in multicomponent framework silicates. We present new results on the coordination of Al³⁺ in albite as a function of pressure and show that it is consistent with results of laboratory studies on albite glasses formed at high pressure. We compare calculated PVT data for jadeite, albite and diopside and relate the behavior of the low pressure compressibility to the spinodal limit at negative pressures. Some preliminary studies of inert gas solution in jadeite and of CO₂ solution in a glass having a composition of approximately Na₂O·3SiO₂ are described.     

Bearthite,Ca2Al(PO4)2OH: stability,thermodynamic properties and phase relations

Contributions to Mineralogy and Petrology - The new phosphate bearthite, Ca2Al(PO4)2HO, found in high-pressure metamorphic rocks, has been synthesized from a stoichiometric mixture of γ-Al2O3...     

Evidence for kinks in structural and thermodynamic properties across the forsterite–fayalite binary from thin-film IR absorption spectra

Infrared absorbance spectra over ∼100 to 1,800 cm⁻¹ were collected from optically thin films of 21 samples with compositions spanning the forsterite–fayalite binary. Polarization information from previous specular reflectance data on end-members was used in tracing the peaks across the entire binary. Peak positions (ν_i) were constrained by Lorentzian decompositions. Fitting also constrained widths for singlet peaks but for doublets and triplets, variation in ν_i with composition among the constituent polarizations alters widths from intrinsic. Because film thicknesses of 0.6–1.4 μm were estimated, our band strengths are approximate; however, relative intensities should be correct. Only for a few peaks does ν_i vary smoothly across the entire binary; instead, distinct linear trends exist for Fe- and Mg-rich olivines. Discontinuities and kinks in ν_i(X) occur at X = Mg/(Fe + Mg) = 0.7 and are accompanied by a change in intensity patterns. This interesting behavior was not revealed in previous spectra of powder dispersions. The contrasting character of IR vibrations for Fe- and Mg-rich olivines is inferred to arise from structural variations because (1) frequency is related to bond length, (2) other factors affecting frequency (cation mass and probably bonding type) vary linearly across the binary, and (3) available data on unit cell parameters are consistent with distinct trends for forsterites and fayalites. Vibrational components of heat capacity (C _V) and enthalpy (H) calculated from ν_i, were found to be slightly more negative than linear interpolations between values for forsterite and fayalite. Our computations give smaller negative excesses from ideality in H than do previous calorimetric measurements, but are equal within experimental uncertainties.     

Raman spectroscopy at high pressure and high temperature. Phase transitions and thermodynamic properties of minerals

An outline of recent developments in Raman spectroscopy at high pressure, high temperature and combined high pressure and high temperature is presented. The instrumental and technical aspects of Raman spectroscopy, and coupling of diamond anvil cells and miniature furnaces to Raman microspectrometers are discussed. Some potential pitfalls, such as the thermal pressure in laser heated diamond anvil cells or the thermal radiation during high-temperature measurements, are presented. Special emphasis is given on processing of high-temperature Raman data. New recently discovered phase transformations in the SiO₂ system (quartz→ quartz II, pressure-induced amorphization of quartz) and structural changes in SiO₂ glass and melt are used to infer the capability of in-situ Raman spectroscopy for determining the microscopic behaviour of minerals, melts and glasses under extreme pressure and temperature conditions. Finally, it is shown how vibrational mode anharmonicity can be obtained from the pressure- and temperature-induced shifts of Raman modes. This anharmonicity can be introduced into the vibrational modeling of the thermodynamic properties (entropy and equation of state) of minerals. The example of calcite is briefly discussed.     

The crystal structure of Ca7Mg9(Ca,Mg)2(PO4)12

Summary The unit cell of Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂ isa=22.841(3) Å,b=9.994(1) Å,c=17.088(5) Å and =99.63(3)° at 24° C. The space-group is C2/c with four formula weights per cell. The crystal structure has been determined from 6330 X-ray reflections measured from a single crystal by a counter method and has been refined toR _w =0.044,R=0.046 (based on 4227 observed reflections and 322 of the unobserved reflections). One cation site may be occupied by Ca or Mg and gives rise to variability in composition as is reflected in the formula give above. In the sample studied, Ca and Mg occupy the site approximately equally. The direction in the unit cell is pseudo-hexagonal. The structure of Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂ is related to that of K₃Na(SO₄)₂ in that along it has columns of cations and columns of cations and anions. These columns are arranged in a K₃Na(SO₄)₂-type pseudo-cell. In the cation-anion columns, every other cation site in K₃Na(SO₄)₂ is vacant in Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂.

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Die Kristallstruktur von Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂

Zusammenfassung Die Gitterkonstanten von Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂ sind (bei 24° C)a=22,841(3) Å,b=9,994(1) Å,c=17,088(5) Å und =99,63(3)°; Raumgruppe: C2/c;Z=4. Die Kristallstruktur wurde aus 6330 Röntgendiffraktometer-Einkristalldaten bestimmt und (auf der Basis von 4227 beobachteten und 322 nicht-beobachteten Reflexen) aufR _w =0,044 undR=0,046 verfeinert. Eine Kationenlage kann von Ca oder Mg besetzt werden, was eine Variabilität der Zusammensetzung ergibt, wie sie obige Formel ausdrückt. In der untersuchten Probe besetzen Ca und Mg diese Punktlage etwa zu gleichen Teilen. Die -Richtung der Elementarzelle ist pseudo-hexagonal. Die Struktur von Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂ ist zu der von K₃Na(SO₄)₂ darin verwandt, daß sie längs Säulen von Kationen und Säulen von Anionen hat. Diese Säulen sind in einer Pseudozelle vom K₃Na(SO₄)₂-Typ angeordnet. In den Kation-Anion-Säulen ist jede zweite Kationen-Lage des K₃Na(SO₄)₂ in Ca₇Mg₉(Ca,Mg)₂(PO₄)₁₂ unbesetzt.

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With 6 Figures     

杭州湾及其邻近海域沉积物中Fe、Mn、Ca、Mg的地球化学研究

本文通过对杭州湾及其邻近海域29个站位的表层沉积物化学、粘土矿物及碎屑矿物资料的分析,详细研究了开放型海湾沉积物中Fe、Mn、Ca、Mg元素地球化学特征。研究表明,1)与同类型海湾相比,杭州湾显示高Fe、Mn、Mg低Ca的特点。表明物质来源丰富,而生物作用较弱;2)Fe、Mn主要来自长江和钱塘江径流搬运,受粘土控制。Mg主要来自粘土对海水中Mg2+的吸附,同时受上覆水盐度的影响;3)北区元素间关系明显的比南区强烈,表明南区物质来源较北区复杂;4)主断面沉积物中Mg/Ca由河口向海洋增加,并与有机碳呈明显的正相关,显示杭州湾及邻近陆架区可能发生着原始碳酸盐（钙）白云岩化的反应。     

华北地幔捕虏体Fe-Mg-Ca同位素研究进展

近年来,得益于同位素分析技术和质谱仪器性能的提高,使得铁（Fe）、镁（Mg）和钙（Ca）等非传统稳定同位素的高精度测量成为可能,并很快在地球化学、天体化学和生物地球化学等研究领域取得了丰硕的成果。本文通过对比分析来自华北克拉通不同地区不同类型地幔捕虏体的Fe、Mg和Ca位素组成特征,揭示华北克拉通岩石圈地幔Fe、Mg和Ca同位素组成不均一性的成因,并在此基础上,探讨华北大陆岩石圈地幔演化过程如部分熔融、橄榄岩-熔体反应过程、熔体的性质和来源等科学问题,为华北克拉通岩石圈的演化过程提供新证据。

     

Polarized Raman spectra of beryl and bazzite

The polarized Raman spectra of four different beryl crystals were studied at room temperature in the range from 30 to 4000 cm^-1. The spectra show significant differences between the samples studied, and corrections are proposed for the reference Raman spectra of beryl previously reported by Adams and Gardner (1974). Type II water is observed in two crystals; the corresponding symmetric Raman stretching band at 3595 cm^-1 is extremely strong for an impurity (about 20% of the strongest beryl lattice mode). Another, sharper, band of similar intensity at 3605 cm^-1 could possibly originate from a hydroxyl stretching mode. Additional weaker bands are observed around 1600 cm^-1 and 3600–3750 cm^-1. The first polarized Raman spectra of bazzite are presented and discussed.     

Experimental and thermodynamic study of the crystallization of diamond and silicates in a metal-silicate-carbon system

Silicate inclusions are widespread in natural diamonds, which also may contain rare inclusions of native iron. This suggests that some natural diamonds crystallized in metal-silicate-carbon systems. We experimentally studied the crystallization of diamond and silicate phases from the starting composition Fe_0.36Ni_0.64 + silicate glass + graphite and calculated the Fe mole fractions of the silicate phases crystallizing under these conditions. The silicates synthesized together with diamond had low Fe mole fractions [Fe/(Fe + Mg + Ca)] in spite of strong Fe predominance in the system. The Fe mole fractions of the silicates decreased in the sequence garnet-pyroxene-olivine, which is consistent with the results of our thermodynamic calculations. The Fe mole fraction of silicates under various redox conditions under which metal-carbon melts are stable drastically decreases with decreasing fo₂. The low Fe mole fractions of silicate inclusions in diamond from the Earth’s mantle can be explained by the highly reducing crystallization conditions, under which Fe was concentrated as a metallic phase of the magmatic melts and could be only insignificantly incorporated in the structures of silicates.