Thermochemistry of glasses along joins of pyroxene stoichiometry in the system Ca2Si2O6-Mg2Si2O6-Al4O6

Enthalpies of solution in 2PbO · B₂O₃ at 974 K have been measured for glasses along the joins Ca₂Si₂O₆ (Wo)-Mg₂Si₂O₆ (En) and Mg₂Si₂O₆-MgAl₂SiO₆ (MgTs). Heats of mixing are symmetric and negative for Wo-En with W_H = ?31.0 ± 3.6 kJ mol^?. Negative heats of mixing were also found for the En-MgTs glasses (W_H = ?33.4 ± 3.7 kJ mol^?).Enthalpies of vitrification of pyroxenes and pyroxenoids generally increase with decreasing alumina content and with decreasing basicity of the divalent cation.Heats of mixing along several glassy joins show systematic trends. When only non-tetrahedral cations mix (outside the aluminosilicate framework), small exothermic heats of mixing are seen. When both nontetrahedral and framework cations mix (on separate sublattices, presumably), the enthalpies of mixing are substantially more negative. Maximum enthalpy stabilization near compositions with Al/Si ≈ 1 is suggested.     

Thermochemistry of glasses and liquids in the systems CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAl2Si2O8-NaAlSi3O8 and SiO2-Al2O3-CaO-Na2O

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.     

A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8

Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi₂O₆ (Di)-CaAl₂Si₂O₈ (An)-NaAlSi₃O₈ (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (b_i=1,2.6, c_j=1,2..6) representing linear (e.g., b_i=1:3) and higher order, nonlinear (e.g., b_i=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of T_g for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have T_g values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.     

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 bearing of the system CaMgSi2O6CaAl2SiO6CaFeAlSiO6 on fassaitic pyroxene

The system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi₂O₆-rich portion is Cpx + An + Mel and that in the CaMgSi₂O₆-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO₆ component of the system. The Al₂O₃ content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al₂O₃ with 3.9 wt.% Fe₂O₃. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO₆ content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl₂SiO₆ and CaFeAlSiO₅ components as crystallization proceeds. These results agree with those obtained in the experimental study.     

First principles molecular dynamics simulations of diopside (CaMgSi2O6) liquid to high pressure

We use first principles molecular dynamics simulations based on density functional theory in the local density approximation to investigate CaMgSi₂O₆ liquid over the entire mantle pressure regime. We find that the liquid structure becomes much more densely packed with increasing pressure, with the mean Si-O coordination number increasing nearly linearly with volume from fourfold near ambient pressure to sixfold at the base of the mantle. Fivefold Si-O coordination environments are most abundant at intermediate compression. The properties of Mg and Si coordination environments are nearly identical to those in MgSiO₃ liquid, whereas Ca is more highly coordinated with larger mean Ca-O bond length as compared with Mg. The density increases smoothly with increasing pressure over the entire range studied. The Grüneisen parameter increases by a factor of three on twofold compression. The density contrast between diopside composition liquid and the isochemical crystalline assemblage is less than 2% at the core mantle boundary, less than that in the case of MgSiO₃. Thermodynamic properties are described in terms of a liquid-state fundamental thermodynamic relation.     

Thermochemical study of glasses in the system NaAlSi3O8-KAlSi3O8-Si4O8 and the join Na1.6Al1.6Si2.4O8-K1.6Al1.6Si2.4O8

Enthalpies of solution in 2PbO · B₂O₃ at 981 K have been measured for glasses in the system albite-orthoclase-silica and along the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈. The join KAlSi₃O₈-Si₄O₈ shows zero heat of mixing similar to that found previously for NaAlSi₃O₈-Si₄O₈ glasses. Albite-orthoclase glasses show negative heats of mixing symmetric about Ab₅₀Or₅₀ (W_n = ? 2.4 ± 0.8 kcal). Negative heats of (Na, K) mixing are also found at $\text{Si}\text{(Si + Al)}\text{= 0.6.}$ Ternary excess enthalpies of mixing in the glassy system Ab-Or-4Q are positive but rarely exceed 1 kcal mol^?1.Using earlier studies of the thermodynamic properties of the crystals, the present calorimetric data and the “two-lattice” entropy model, the albite-orthoclase phase diagram is calculated in good agreement with experimental data. Attempts to calculate albite-silica and orthoclase-silica phase diagrams reveal complexities probably related to significant (but unknown) mutual solid solubility between cristobalite and alkali feldspar and to the very small heat and entropy of fusion of SiO₂.     

Structure of mineral glasses—I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8

The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO₂ glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO₂ glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.     

An electrochemical study of Ni2+, Co2+, and Zn2+ ions in melts of composition CaMgSi2O6

Cyclic voltammetry has been done for Ni²⁺, Co²⁺, and Zn²⁺ in melts of diopside composition in the temperature range 1425 to 1575°C. Voltammetric curves for all three ions excellently match theoretical curves for uncomplicated, reversible charge transfer at the Pt electrode. This implies that the neutral metal atoms remain dissolved in the melt. The reference electrode is a form of oxygen electrode. Relative to that reference assigned a reduction potential of 0.00 volt, the values of standard reduction potential for the ions are $\text{E}{}^1\text{(}\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.32 ± .01}\text{V}$, $\text{E}{}^1\text{(}\text{Co}{}^{\mathrm{2+}}\text{Co}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.45 ± .02}\text{V}$, and $\text{E}{}^1\text{(}\text{Zn}{}^{\mathrm{2+}}\text{Zn}{}^0\text{,}\text{diopside}\text{, 1500°C) = ?0.53 ± .01}\text{V}$. The electrode reactions are rapid, with first order rate constants of the order of 10^?2 cm/sec. Diffusion coefficients were found to be 2.6 × 10^?6 cm²/sec for Ni²⁺, 3.4 × 10^?6 cm²/sec for Co²⁺, and 3.8 × 10^?6 cm²/sec for Zn²⁺ at 1500°C. The value of $\text{E1}$ ($\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0$, diopside) is a linear function of temperature over the range studied, with values of ?0.35 V at 1425°C and ?0.29 V at 1575°C. At constant temperature the value of $\text{E}{}^1\text{(}\text{Ni}{}^{\mathrm{2+}}\text{Ni}{}^0\text{, 1525°C}$) was not observed to vary with composition over the range CaO · MgO · 2SiO₂ to CaO·MgO·3SiO₂ or from 1.67 CaO·0.33MgO·2SiO₂ to 0.5 CaO·1.5MgO·2SiO₂. The value for the diffusion coefficient for Ni²⁺ decreased by an order of magnitude at 1525°C over the compositional range CaO · MgO · 1.25SiO₂ to CaO · MgO · 3SiO₂. This is consistent with a mechanism by which Ni²⁺ ions diffuse by moving from one octahedral coordination site to another in the melt, with the same Ni²⁺ species discharging at the cathode regardless of the SiO₂ concentration in the melt.     

Crystal structures of Ca-rich clinopyroxenes on the CaMgSi2O6-Mg2Si2O6 join

Summary The structural changes occurring in the clinopyroxenes with composition Di100, Di90En10 and Di80En20, due to the Ca-Mg substitution in the M2 site, have been studied. Evidence is given that with increasing Mg content a small percentage of the atoms converts from the M2 position to a new M2 position which is solely occupied by Mg. The maximum conversion of M2 to M2 found in this study is 7%. The closest parallel to the M2 geometry is found in the ZnSiO₃ pyroxene (C2/c). The presence of this new site causes significant changes in the tetrahedral configuration, because the M2 atoms are not bonded to 03. The intermediate compositions, Di90En10 and Di80En20, may be thought of as the coexistence of two structural models: diopside and ZnSiO₃ pyroxene (C2/c).

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Kristallstrukturen Ca-reicher Klinopyroxene der CaMgSi₂O₆-Mg₂Si₂O₆-Reihe

Zusammenfassung Es wurden die strukturellen Änderungen von Klinopyroxenen der Zusammensetzungen Di100, Di90En10 und Di80En20, die durch den Mg-Ersatz für Ca verursacht werden, untersucht. Es zeigt sich, daß mit steigendem Mg-Gehalt ein kleiner Teil der Atome der M2-Position zu einer neuen M2-Position wechselt; diese wird ausschließlich durch Mg besetzt. Der größte in dieser Arbeit gefundene Übergang von M2 nach M2 beträgt ca. 7%. Die stärksten Parallelen zur Geometrie um M2 werden im Pyroxen ZnSiO₃ (C2/c) gefunden. Die Besetzung dieser neuen Position verursacht bedeutende Änderungen im Tetraederverband, da die M2-Atome nicht an O3 gebunden sind. Die Pyroxenstrukturen mit den intermediären Zusammensetzungen Di90En10 und Di80En20 können als Überlagerung zweier Modelle betrachtet werden: Diopsid und ZnSiO₃-Pyroxen (C2/c).

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Abbreviations En Enstatite - Di Diopside - Hd Hedenbergite - Fs Ferrosilite - ClEn Clinoenstatite - Di100 pure diopside - Di90 Di90En10 (mol.-%) - Di80 Di80En20 - brg bridging With 6 Figures     

Water incorporation in synthetic and natural MgAl2O4 spinel

The solubility and incorporation mechanisms of water in synthetic and natural MgAl₂O₄ spinel have been investigated in a series of high-pressure/temperature annealing experiments. In contrast to most other nominally anhydrous minerals, natural spinel appears to be completely anhydrous. On the other hand, non-stoichiometric Al-rich synthetic (defect) spinel can accommodate several hundred ppm water in the form of structurally-incorporated hydrogen. Infrared (IR) spectra of hydrated defect spinel contain one main O-H stretching band at 3343-3352 cm⁻¹ and a doublet consisting of two distinct O-H bands at 3505-3517 cm⁻¹ and 3557-3566 cm⁻¹. IR spectra and structural refinements based on single-crystal X-ray data are consistent with hydrogen incorporation in defect spinel onto both octahedral and tetrahedral O-O edges. Fine structure of O-H bands in IR spectra can be explained by partial coupling of interstitial hydrogen with cation vacancies, or by the effects of Mg-Al disorder on the tetrahedral site. The concentration of cation vacancies in defect spinel is a major control on hydrogen affinity. The commercial availability of large single crystals of defect spinel coupled with high water solubility and similarities in water incorporation mechanisms between hydrous defect spinel and hydrous ringwoodite (Mg₂SiO₄) suggests that synthetic defect spinel may be a useful low-pressure analogue material for investigating the causes and consequences of water incorporation in the lower part of Earth’s mantle transition zone.     

Structure, thermodynamics, and diffusion in CaAl2Si2O8 liquid from first-principles molecular dynamics

We have performed first-principles molecular dynamics simulations of CaAl₂Si₂O₈ (anorthite) liquid at pressures up to 120 GPa and temperatures of 3000, 4000 and 6000 K. At the lowest degrees of compression the liquid is seen to accommodate changes in density through decreasing the abundance of 3- and 4-membered rings, while increases in coordination of network forming cations take effect at somewhat higher degrees of compression. Results are fit to a fundamental thermodynamic relation with 4th order finite strain and 1st order thermal variable expansions. Upon compression by a factor of two, the Grüneisen parameter (γ) is found to increase continuously from 0.35 to 1.10. Weak temperature dependence in γ is thermodynamically consistent with a slight decrease in isochoric heat capacity (C_V), for which values of between 4.4 and 5.2 Nk_B are obtained, depending on the temperature. Pressure and temperature dependence of self-diffusivities is found to be well represented by an Arrhenius relation, except at 3000 K and pressures lower than 5 GPa, where self-diffusivities of Si, Al, and O increase with pressure. Analysis of the lifetimes of individual coordination species reveals that this phenomenon arises due to the disproportionately high stability of 4-fold coordinated Si, and to a lesser extent 4-fold coordinated Al. Our results represent a marked improvement in accuracy and reliability in describing the physics of CaAl₂Si₂O₈ liquid at deep mantle pressures, pointing the way to a general thermodynamic model of melts at extreme pressures and temperatures relevant to planetary-scale magma oceans and deep mantle partial melting.     

Ca−Sr substitution in clinopyroxenes along the join CaMgSi2O6−SrMgSi2O6

Summary In order to define the limits of expansion of the M2 polyhedron in theC2/c clinopyroxenes of formulaX ^M2Mg^M1 [Si₂O₆] as the mean ionic radius in the M2 site increases, the join CaMgSi₂O₆–SrMgSi₂O₆ (Di–SrPx) has been investigated atP=1 atm and between 1090°C and 1350°C. The extent of the clinopyroxene solid solutions is limited to the compositional range Di₁₀₀–Di₇₀SrPx₃₀. Within this range the unit-cell parameters of the clinopyroxenes show a linear variation with the increase of Sr content. The comparison of the variations caused in the unit-cell dimensions by the increase of the mean ionic radius in the M2 site (Di–SrPx series) with those caused by the decrease of the mean ionic radius in M2 (Di–En series) displays a different trend ofb in the two series. This different trend ofb suggests a different mechanism of the structure deformation in the two solid solution series. The narrow extent of the Di–SrPx solid solutions atT=1200°C shows that the increase of the mean ionic radius in the M2 site is restricted to the range 1.12–1.16 Å.

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La substitution Ca–Sr dans les clinopyroxènes le long du joint CaMgSi₂O₆–SrMgSi₂O₆

Résumé Le joint CaMgSi₂O₆–SrMgSi₂O₆ (Di–SrPx) a été étudié entre 1090°C et 1350°C à 1 atm dans le but d'établir quelles sont les limites de l'expansibilité du polyhèdre M2 dans les clinopyroxènesX ^M2Mg^M1 [Si₂O₆] (group spatialC2/c) avec l'augmentation du rayon jonique moyen dans le site M2. La solution solide est limitée à l'intervalle de composition Di₁₀₀–Di₇₀ SrPx₃₀. Dans ce domaine les paramètres de la maille varient d'une façon linéaire avec la teneur croissante de Sr. Si on compare les variations de la maille, déterminées par le rayon jonique moyen croissant dans le site M2 (série Di–SrPx), avec celles causées par la diminution du rayon jonique moyen dans le site M2 (série Di–En), on observe une tendance différente du paramètreb dans les deux séries. Ceci indique un mécanisme différent de la déformation structuralle dans les deux séries de solutions solides. Puisque àT=1200°C le domaine des solutions solides Di–SrPx est étroit, l'augmentation du rayon ionique moyen dans le site M2 est bornée à l'intervalle 1.12–1.16 Å.

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With 5 Figures     

OH incorporation in nearly pure MgAl2O4 natural and synthetic spinels

Four nearly pure MgAl₂O₄ spinels, of both natural and synthetic occurrence, have been studied by means of X-ray single crystal diffraction and FTIR spectroscopy in order to detect their potential OH content. Absorption bands that can be assigned to OH incorporated in the spinel structure were only observed in spectra of a non-stoichiometric synthetic sample. The absorption intensity of two bands occurring at 3350 and 3548 cm⁻¹ indicate an OH content of 90 ppm H₂O. Based on correlations of OH vibrational frequencies and O-H?O distances, the observed absorption bands correspond to O-H?O distances of 2.77 and 2.99 Å, respectively, which is close to the values obtained by the structure refinements for ^VIO-O_unsh (2.825 Å) and ^IVO-O (3.001 Å). This indicates that one probable local position for hydrogen incorporation is the oxygens coordinating a vacant tetrahedral site. The present spectra demonstrate that the detection limit for OH in Fe-free spinels is in the range 10-20 ppm H₂O. However, at appreciable Fe²⁺ levels, the detection of OH bands becomes hampered due to overlap with strong absorption bands caused by electronic d-d transitions in Fe²⁺ in the tetrahedral position.     

Molecular H2O in armenite, BaCa2Al6Si9O30·2H2O, and epididymite, Na2Be2Si6O15·H2O: Heat capacity, entropy and local-bonding behavior of confined H2O in microporous silicates

Armenite, ideal formula BaCa₂Al₆Si₉O₃₀·2H₂O, and its dehydrated analog BaCa₂Al₆Si₉O₃₀ and epididymite, ideal formula Na₂Be₂Si₆O₁₅·H₂O, and its dehydrated analog Na₂Be₂Si₆O₁₅ were studied by low-temperature relaxation calorimetry between 5 and 300 K to determine the heat capacity, C_p, behavior of their confined H₂O. Differential thermal analysis and thermogravimetry measurements, FTIR spectroscopy, electron microprobe analysis and powder Rietveld refinements were undertaken to characterize the phases and the local environment around the H₂O molecule.The determined structural formula for armenite is Ba_0.88(0.01)Ca_1.99(0.02)Na_0.04(0.01)Al_5.89(0.03)Si_9.12(0.02)O₃₀·2H₂O and for epididymite Na_1.88(0.03)K_0.05(0.004)Na_0.01(0.004)Be_2.02(0.008)Si_6.00(0.01)O₁₅·H₂O. The infrared (IR) spectra give information on the nature of the H₂O molecules in the natural phases via their H₂O stretching and bending vibrations, which in the case of epididymite only could be assigned. The powder X-ray diffraction data show that armenite and its dehydrated analog have similar structures, whereas in the case of epididymite there are structural differences between the natural and dehydrated phases. This is also reflected in the lattice IR mode behavior, as observed for the natural phases and the H₂O-free phases. The standard entropy at 298 K for armenite is S° = 795.7 ± 6.2 J/mol K and its dehydrated analog is S° = 737.0 ± 6.2 J/mol K. For epididymite S° = 425.7 ± 4.1 J/mol K was obtained and its dehydrated analog has S° = 372.5 ± 5.0 J/mol K. The heat capacity and entropy of dehydration at 298 K are Δ = 3.4 J/mol K and ΔS^rxn = 319.1 J/mol K and Δ = −14.3 J/mol K and ΔS^rxn = 135.7 J/mol K for armenite and epididymite, respectively. The H₂O molecules in both phases appear to be ordered. They are held in place via an ion-dipole interaction between the H₂O molecule and a Ca cation in the case of armenite and a Na cation in epididymite and through hydrogen-bonding between the H₂O molecule and oxygen atoms of the respective silicate frameworks. Of the three different H₂O phases ice, liquid water and steam, the C_p behavior of confined H₂O in both armenite and epididymite is most similar to that of ice, but there are differences between the two silicates and from the C_p behavior of ice. Hydrogen-bonding behavior and its relation to the entropy of confined H₂O at 298 K is analyzed for various microporous silicates.The entropy of confined H₂O at 298 K in various silicates increases approximately linearly with increasing average wavenumber of the OH-stretching vibrations. The interpretation is that decreased hydrogen-bonding strength between a H₂O molecule and the silicate framework, as well as weak ion-dipole interactions, results in increased entropy of H₂O. This results in increased amplitudes of external H₂O vibrations, especially translations of the molecule, and they contribute strongly to the entropy of confined H₂O at T < 298 K.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts, and aqueous solutions—I. Electronic structure of H6Si2O7, H6AlSiO71−, and H6Al2O72−

As part of a study of the effect of geologically common network modifiers on polymerization in silicate melts, glasses, and silica-rich aqueous solutions, we have studied the energies, electronic structures, and inferred chemical properties of ^IVT-O-^IVT linkages in the tetrahedral dimers H₆,Si₂O₇, H₆AlSiO₇^1?, and H₆Al₂O₇^2? using semi-empirical molecular orbital theory (CNDO/2). Our results indicate that the electron donating character of the bridging oxygen, O(br), linking two tetrahedra increases with increasing T-O(br) bond length but decreases with decreasing T-O(br)-T angles and increasing O-T-O(br) angles. This increase or decrease of the donor character of O(br) coincides with an increase or decrease of the affinity of O(br) for hard acceptors. The calculated electronic structure for the H₆Si₂O₇ molecule is compared with the observed X-ray emission, absorption, and photoelectron spectra of quartz and vitreous silica; the reasonable match between calculated and observed oxygen Kα emission spectra of vitreous silica supports our assertion that non-bonded O(br) electron density energetically at the top of the valence band controls the chemical reactivity of ^IVT-O-^IVT linkages in polymerized tetrahedral environments.     

Molecular dynamics studies of CaAl2Si2O8 liquid. Part II: Equation of state and a thermodynamic model

A thermodynamic model and equation of state (EOS) is developed from the molecular dynamics simulation experiments of Spera et al. (2009) for CaAl₂Si₂O₈ liquid over the temperature range 3500-6000 K and pressure interval 0-125 GPa. The model is constructed utilizing the isothermal Universal EOS of Vinet et al. (1986) combined with an expression for the temperature-dependence of the internal energy derived from density functional theory (Rosenfeld and Tarazona, 1998). It is demonstrated that this model is more successful at reproducing the data than the temperature-dependent Universal EOS (Vinet et al., 1987) or the volume-explicit EOS of Ghiorso (2004a). Distinct parameterizations are required to model low (<20 GPa) and high (>20 GPa) pressure regimes. This result is ascribed to the affect of liquid structure on macroscopic thermodynamic properties, specifically the interdependence of average cation-oxygen coordination number on the bulk modulus. The thermodynamic transition between the high- and low-pressure parameterizations is modeled as second order, although the nature of the transition is open to question and may well be first order or lambda-like in character.Analysis of the thermodynamic model reveals a predicted region of liquid-liquid un-mixing at low-temperatures (<1624 K) and pressures (<1.257 GPa). These pressure-temperature conditions are above the glass transition temperature but within the metastable liquid region. They represent the highest temperatures yet suggested for liquid-liquid un-mixing in a silicate bulk composition. A shock wave Hugoniot curve is calculated for comparison with the experimental data of Rigden et al. (1989) and of Asimow and Ahrens (2008). The comparison suggests that the model developed in this paper underestimates the density of the liquid by roughly 10% at pressures greater than ∼20 GPa.     

Shear viscosities of CaO-Al2O3-SiO2 and MgO-Al2O3-SiO2 liquids: Implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts

The shear viscosity of 66 liquids in the systems CaO-Al₂O₃-SiO₂ (CAS) and MgO-Al₂O₃-SiO₂ (MAS) have been measured in the ranges 1-10⁴ Pa s and 10⁸-10¹² Pa s. Liquids belong to series, nominally at 50, 67, and 75 mol.% SiO₂, with atomic M²⁺/(M²⁺+2Al) typically in the range 0.60 to 0.40 for each isopleth. In the system CAS at 1600°C, viscosity passes through a maximum at all silica contents. The maxima are clearly centered in the peraluminous field, but the exact composition at which viscosity is a maximum is poorly defined. Similar features are observed at 900°C. In contrast, data for the system MAS at 1600°C show that viscosity decreases with decreasing Mg/(Mg + 2Al) at all silica contents, but that a maximum in viscosity must occur in the field where Mg/2Al >1. On the other hand, the viscosity at 850°C increases with decreasing Mg/(Mg + 2Al) and shows no sign of reaching a maximum, even for the most peraluminous composition studied. The data from both systems at 1600°C have been analysed assuming that shear viscosity is proportional to average bond strength and considering the equilibrium:

Al^[4]-(Mg,Ca)_0.5⇔(Mg,Ca)_0.5-NBO+Al_XS