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.     

A Raman spectroscopic study of glasses along the joins silica-calcium aluminate,silica-sodium aluminate,and silica-potassium aluminate

Aluminosilicate glasses with compositions along the joins silica-calcium aluminate, silica sodium aluminate and silica-potassium aluminate have been prepared by conventional and solar melting techniques and studied by Raman spectroscopy. The Raman spectra of crystalline calcium aluminate, anorthite and silica polymorphs are discussed in relation to their crystal structures, and compared with the spectra of the corresponding glasses. The glass and crystal spectra are generally comparable, suggesting similar vibrational structures. These crystals have structures based on tetrahedral aluminosilicate frameworks, and a similar molecular structure is suggested for the glasses, although it is noted that the Raman spectra do not directly characterize the aluminate polyhedra. Within the three glass series, our interpretation of the unresolved high-frequency bands shows the appearance of discrete bands near 1120, 1000, 930 and 890 cm^?1 as the silica content is decreased. This is compared with the behaviour of high-frequency bands in simple silicate systems, and used to suggest that the four bands in the aluminosilicate systems are due to stretching vibrations of silicate tetrahedra bound to one, two, three and four aluminium atoms. The spectra of calcium, sodium, potassium and lithium aluminosilicate glasses with similar silica contents are compared, and interpreted by the above model. This is used to construct a simple model for the effect of metal cation on aluminosilicate molecular groups in the glass structure, consistent with the results of calorimetric studies on similar systems.     

Thermochemical study of glasses in the system CaMgSi2O6-CaAl2SiO6

High temperature solution calorimetry of glasses in the system CaMgSi₂O₆ (Di)-CaAl₂SiO₆ (CaTs) show them to have negative enthalpies of mixing with a regular enthalpy parameter, W_H, of -11.4 ± 0.7 kcal. Negative heats of mixing between alumina-rich and alumina-poor glasses seem to be a general phenomenon in aluminosilicates and are not confined only to glassy systems containing anorthite as a component. The thermodynamic behavior of glasses in the system SiO₂-Ca_0.5;AlO₂-CaMgO₂ appears to vary in a smooth fashion, with small positive heats of mixing near SiO₂ and substantial negative heats of mixing for other compositions. The exothermic behavior with increasing $\text{A1}\text{(Al + Si)}$ may be related to local charge balance of M²⁺ and Al³⁺. The negative heats of mixing in MgCaSi₂O₆-CaAl₂SiO₆, MgCaSi₂O₆-CaAl₂Si₂O₈ and NaAlSi₃O₈-CaAl₂Si₂O₈ glasses are in contrast to the positive heats of mixing found in MgCaSi₂O₆-CaAl₂SiO₆ (pyroxene) and NaAlSi₃O₈-CaAl₂Si₂O₈ (high plagioclase) crystalline solid solutions.     

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.     

Effects of the degree of polymerization on the structure of sodium silicate and aluminosilicate glasses and melts: An O NMR study

Revealing the atomic structure and disorder in oxide glasses, including sodium silicates and aluminosilicates, with varying degrees of polymerization, is a challenging problem in high-temperature geochemistry as well as glass science. Here, we report ¹⁷O MAS and 3QMAS NMR spectra for binary sodium silicate and ternary sodium aluminosilicate glasses with varying degrees of polymerization (Na₂O/SiO₂ ratio and Na₂O/Al₂O₃ ratio), revealing in detail the extent of disorder (network connectivity and topological disorder) and variations of NMR parameters with the glass composition. In binary sodium silicate glasses [Na₂O-k(SiO₂)], the fraction of non-bridging oxygens (NBOs, Na-O-Si) increases with the Na₂O/SiO₂ ratio (k), as predicted from the composition. The ¹⁷O isotropic chemical shifts (¹⁷O δ_iso) for both bridging oxygen (BO) and NBO increase by about 10-15 ppm with the SiO₂ content (for k = 1-3). The quadrupolar coupling products of BOs and NBOs also increase with the SiO₂ content. These trends suggest that both NBOs and BOs strongly interact with Na; therefore, the Na distributions around BOs and NBOs are likely to be relatively homogenous for the glass compositions studied here, placing some qualitative limits on the extent of segregation of alkali channels from silica-enriched regions as suggested by modified random-network models. The peak width (in the isotropic dimension) and thus bond angle and length distributions of Si-O-Si and Na-O-Si increase with the SiO₂ content, indicating an increase in the topological disorder with the degree of polymerization. In the ternary aluminosilicate glasses [Na₂O]_x[Al₂O₃]_1−xSiO₂, the NBO fraction decreases while the Al-O-Si and Al-O-Al fractions apparently increase with increasing Al₂O₃ content. The variation of oxygen cluster populations suggests that deviation from “Al avoidance” is more apparent near the charge-balanced join (Na/Al = 1). The Si-O-Si fraction, which is closely related to the activity coefficient of silica, would decrease with increasing Al₂O₃ content at a constant mole fraction of SiO₂. Therefore, the activity of silica may decrease from depolymerized binary silicates to fully polymerized sodium aluminosilicate glasses at a constant mole fraction of SiO₂.     

Aluminum coordination in metaaluminous and peralkaline silicate melts

Incremental amounts of Na₂O and K₂O added to immiscible melts in the MgO-CaO-TiO₂-Al₂O₃ SiO₂ system cause a decrease in critical temperature, phase separation and change in the pattern of Al₂O₃ partitioning. Al₂O₃, which is concentrated in the low SiO₂ immiscible melts in the alkali-free system, is increasingly partitioned into the high-SiO₂ immiscible melt as the alkali/aluminium ratio is increased. However, K₂O is more effective than Na₂O in stabilizing Al₂O₂ in the SiO₂-rich melt. The coordination changes occurring in the aluminosilicate melts upon the addition of the alkali oxides are described by CaAl₂O₄+2SiOK=2KAlO₂+SiOCaOSi where K (or Na) displaces Ca as the charge-balancing cation for the networkforming AlO₄ tetrahedra. The increased stability of the AlO₄ species in the highly polymerized SiO₂-rich melt and the consequent shrinkage of the miscibility gap is ascribed to positive configurational entropy and negative enthalpy changes associated with the formation of K, Na-AlO₄ species. Element partition systematics indicate that (Na, K)AlO₂ species favor the more polymerized, CaAl₂O₄ and TiO₂ species, the less polymerized silicate structure in the melt.     

Natrolite,part II: Determination of deformation electron densities by the X-X method

A single crystal of natrolite, Na₂Al₂Si₃O₁₀ ·2H₂O (space group Fdd2), was studied by X-ray diffraction methods at room temperature. The intensities were measured in a complete sphere of reflection up to sinΘ/ λ=0.903 Å^?1. A refinement of high-order diffraction data yielded residuals of R/(F)=0.9%, R_w(F)=0.8%, GoF=1.40 for 1856 high-angle reflections (0.7≤sinΘ/ λ≤0.903 Å^?1) and R(F)=1.0%, R_w(F)=1.2%, GoF=3.07 for all 3471 independent reflections in the complete sphere of reflection. The X-X method was used to calculate deformation electron densities (DED) in natrolite. Within all tetrahedra, residual electron density-was found in the T-O bond directions indicating a considerable covalent contribution to the chemical bond. The range of the interatomic peak heights was from 0.19 to 0.34 e/ų in the SiO₄ tetrahedra and from 0.11 to 0.23 e/ų in the AlO₄ tetrahedron. The ionic contribution to the chemical bond manifests itself in the displacement of the peaks towards the oxygen atoms. Charge displacement due to interaction of nonframework cations with framework oxygen atoms as well as electron densities attributable to the lone pair orbitals in the water molecule have been observed.     

The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure,thermodynamics, and physical properties

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups. Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO₂-M ₁ ^n/n+ AlO₂ and SiO₂-M ⁿ⁺O _n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.     

PbO-SiO2 melts: structure and thermodynamics of mixing

Thermodynamic properties of PbO-SiO₂ melts, obtained from published data and calculated from freezing point depressions, reflect the gradual polymerization of silicate anions in the melt as the $\text{SiO}{}_2\text{PbO}$ ratio is increased. The free energy of mixing curve at 1000°C has a minimum at 40 mole % SiO₂ and is convex-upward between 72 and 98 mole % SiO₂. The latter is an indication of metastable liquid immiscibility. The free energy minimum is correlated with the maximum in the distribution of nonbridging oxygens in the melt. In SiO₂-poor melts, the activities of PbO and SiO₂ (pure liquid standard states) show sharp negative deviations from ideality. The PbO activity reflects the paucity of free oxygen species in the melt whereas the SiO₂ activity reflects the depolymerized state of the silicate anions. In more SiO₂-rich melts, the activity of SiO₂ shows a positive deviation from ideality which is qualitatively correlated to a polymerization parameter. The heat of mixing term has a minimum of ?2000 cal at 35 mole % SiO₂ and a maximum of +200 cal at 90 mole % SiO₂. The minimum is associated with the exothermic heat effect obtained during the reaction (O⁰) + (O^2?) = 2(O^?), whereas the maximum corresponds to the endothermic heat effect obtained when coordination polyhedra of oxygens form around the Pb cation. The entropy of mixing curve has the same form but is systematically smaller than a theoretical curve calculated on the assumption of random mixing of oxygen species. The discrepancy is due to the entropy loss obtained by the clustering of oxygen species to form complex silicate species.     

Disorder and the extent of polymerization in calcium silicate and aluminosilicate glasses: O-17 NMR results and quantum chemical molecular orbital calculations

Estimation of the framework connectivity and the atomic structure of depolymerized silicate melts and glasses (NBO/T > 0) remains a difficult question in high-temperature geochemistry relevant to magmatic processes and glass science. Here, we explore the extent of disorder and the nature of polymerization in binary Ca-silicate and ternary Ca-aluminosilicate glasses with varying NBO/T (from 0 to 2.67) using O-17 NMR at two different magnetic fields of 9.4 and 14.1 T in conjunction with quantum chemical calculations. Non-random distributions among framework cations (Si and Al) are demonstrated in the variation of relative populations of oxygen sites with NBO/T. The proportion of non-bridging oxygen (NBO, Ca-O-Si) in the binary and ternary aluminosilicate glasses increases with NBO/T. While the trend is consistent with predictions from composition, the detailed fractions apparently deviate from the predicted values, suggesting further complications in the nature of polymerization. The proportion of each bridging oxygen in the glasses also varies with NBO/T. The fractions of Al-O-Si and Al-O-Al increase with increasing polymerization as CaO is replaced with Al₂O₃, while that of Si-O-Si seems to decrease, implying that activity of silica may decrease from calcium silicate to polymerized aluminosilicates (X_SiO2=constant). Quantum chemical molecular orbital calculations based on density functional theory show that a silicate chain with Al-NBO (Ca-O-Al) has an energy penalty (calculated cluster energy difference) of about 108 kJ/mol compared with the cluster with Ca-O-Si, consistent with preferential depolymerization of Si-networks, reported in an earlier O-17 NMR study [Allwardt, J., Lee, S.K., Stebbins, J.F., 2003. Bonding preferences of non-bridging oxygens in calcium aluminosilicate glass: Evidence from O-17 MAS and 3QMAS NMR on calcium aluminate glass. Am. Mineral.88, 949-954]. These prominent types of non-randomness in the distributions suggest significant chemical order in silicate glasses that leads to a decrease in silica activity coefficient and will be useful in modeling transport properties of melts.     

Aluminum speciation, vibrational entropy and short-range order in calcium aluminosilicate glasses

The heat capacity and vibrational entropy of a calcium aluminate and three peraluminous calcium aluminosilicate glasses have been determined from 2 to 300 K by heat-pulse relaxation calorimetry. Together with previous adiabatic data for six other glasses in the system CaO-Al₂O₃-SiO₂, these results have been used to determine partial molar heat capacities and entropies for five species namely, SiO₂, CaO and three different sorts of Al₂O₃ in which Al is 4-, 5- and 6-fold coordinated by oxygen. Given the determining role of oxygen coordination on low-temperature heat capacity, the composition independent entropies found for SiO₂ and CaO indicate that short-range order around Si and Ca is not sensitive to aluminum speciation up to the highest fraction of 25% observed for ^VAl by NMR spectroscopy. Because of the higher room-temperature vibrational entropy of ^IVAl₂O₃ (72.8 J/mol K) compared to ^VAl₂O₃ (48.5 J/mol K), temperature-induced changes from ^IVAl to ^VAl give rise to a small negative contribution of the order of 1 J/mol K to the partial molar configurational heat capacity of Al₂O₃ in melts. Near 0 K, pure SiO₂ glass distinguishes itself by the importance of the calorimetric boson peak. On a g atom basis, the maximum of this peak varies with the composition of calcium aluminosilicate glasses by a factor of about 2. It does not show smooth variations, however, either as a function of SiO₂ content, at constant CaO/Al₂O₃ ratio, or as a function of Al₂O₃ content, at constant SiO₂ content.     

Composition dependence of elasticity in aluminosilicate glasses

The elastic properties of two types of aluminosilicate (basaltic and rhyolitic) glasses have been studied using both Brillouin and Raman spectroscopy at ambient conditions. It has been found that the elastic moduli of the basaltic glasses decrease with increasing SiO₂ concentration. The shear moduli displayed the least dependence on SiO₂ content. The bulk moduli of the basaltic glasses strongly depend on the sum of the Q ³ and Q ⁴ anionic units. Among the modifiers, iron cations showed the strongest effect on the elastic properties of the rhyolitic glasses. For the elastic moduli of rhyolitic glasses, the major effect of alkaline earth cations is on shear modulus; however, both iron and alkali cations showed stronger effects on bulk modulus and similar relative contribution between bulk and shear moduli (based on the equivalent M⁺ cation). The dependences of elastic moduli on bulk NBO/T observed in both types of glasses suggest that the elastic modulus of an aluminosilicate glass depends on the concentration of effective modifying cations rather than the apparent concentration of all non-network-forming cations. An analysis of data also indicated that the ideal molar mixing model is failed in prediction of the elastic properties of the present multicomponent glasses by using the known parameters.     

Water and magmas; a mixing model

A model for the mixing of H₂O and silicate melts has been derived from the experimentally determined effects of H₂O on the viscosity (fluidity), volumes, electrical conductivities, and especially the thermodynamic properties of hydrous aluminosilicate melts. It involves primarily the reaction of H₂O with those O^?2 ions of the melt that are shared (bridging) between adjacent (Al, Si)O₄ tetrahedra to produce OH^? ions. However, in those melts that contain trivalent ions in tetrahedral coordination, such as the Al³⁺ ion in feldspathic melts, the model further involves exchange of a proton from H₂O with a non-tetrahedrally coordinated cation that must be present to balance the net charge on the AlO₄ group. This cation exchange reaction, which goes essentially to completion, results in dissociation of the H₂O and is limited only by the availability of H₂O and the number of exchangeable cations per mole of aluminosilicate.In the system NaAlSi₃O₈-H₂O, upon which this thermodynamic model is based, there is 1 mole of exchangeable cations (Na⁺) per mole (GFW) of NaAlSi₃O₈, consequently ion exchange occurs for H₂O contents up to a 1:1 mole ratio (X^m_w = mole fraction H₂O = 0.5). For mole fractions of H₂O greater than 0.5, no further exchange can occur and the reaction with additional bridging oxygens of the melt produces 2 moles of associated OH^? ions per mole of H₂O dissolved. These reactions lead to a linear dependence of the thermodynamic activity of H₂O (a^m_w) on the square of its mole fraction (X^m_w) for values of X^m_w, up to 0.5 and an exponential dependence on X^m_w at higher H₂O contents. Thus, for values of $\text{X}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{? 0.5, a}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{= k(X}{}^{\mathrm{m}}{}_{\mathrm{w}}\text{)}{}^2$, where k is a Henry's law constant for the dissociated solute.Extension of the thermodynamic model for NaAlSi₃O₈-H₂O to predict H₂O solubilities and other behavior of compositionally more complex aluminosilicate melts (magmas) requires placing these melts on an equimolal basis with NaAlSi₃O₈. This is readily accomplished using chemical analyses of quenched glasses by normalizing to the stoichiometric requirements of NaAlSi₃O₈, first in terms of equal numbers of exchangeable cations for mole fractions of H₂O up to 0.5 and secondly in terms of 8 moles of oxygen for higher H₂O contents. Chemical analyses of three igneous-rock glasses, ranging in composition from tholeiitic basalt to lithium-rich pegmatite, were thus recast and the experimental H₂O solubilities were computed on this equimolal basis. The resulting equimolal solubilities are all the same, within experimental error, as the solubility of H₂O in NaAlSi₃O₈ melt calculated from the thermodynamic relations.The equivalence of equimolal solubilities implies that the Henry's law constant (k), which is a function of temperature and pressure, is independent of aluminosilicate composition over a wide range. Moreover, as a consequence of the Gibbs-Duhem relation and the properties of exact differentials, it is clear that the silicate components of the melt, properly defined, mix ideally. Thus, a relatively simple mixing model for H₂O in silicate melts has led to a quantitative thermodynamic model for magmas that has far-reaching consequences in igneous petrogenesis.     

Water solubility in a calcium aluminosilicate melt

We have measured the water solubility between 1 atmosphere and 5 kilobars for a calcium aluminosilicate melt of molar composition CaO 0.28, Al₂O₃ 0.06, SiO₂ 0.66 (An₉Wo₃₈Qz₅₃). The water contents were measured via thermogravimetric analysis of isobarically quenched glasses, and range from 0.121 wt% H₂O near 1 aim to 9.25 wt% H₂O at 5 kilobars. The molar water solubility lies between those of SiO₂ and albite melts below around three kilobars, and crosses the albite solubility curve above this pressure. The present results are compared with data in the literature on related calcium aluminosilicate melts. There seems to be little variation of water solubility with composition for calcium aluminosilicate melts, unlike analogous alkali aluminosilicate compositions. Examination of the data suggests that there may be a maximum in molar water solubility along the albite-anorthite join.     

Application of infrared spectroscopy to studies of silicate glass structure: Examples from the melilite glasses and the systems Na2O-SiO2 and Na2O-Al2O3-SiO2

Infrared (IR) and Raman spectroscopic methods are important complementary techniques in structural studies of aluminosilicate glasses. Both techniques are sensitive to small-scale (<15 Å) structural features that amount to units of several SiO₄ tetrahedra. Application of IR spectroscopy has, however, been limited by the more complex nature of the IR spectrum compared with the Raman spectrum, particularly at higher frequencies (1200–800 cm^?1) where strong antisymmetric Si-O and Si-O-Si absorptions predominate in the former. At lower frequencies, IR spectra contain bands that have substantial contributions from ‘cage-like’ motions of cations in their oxygen co-ordination polyhedra. In aluminosilicates these bands can provide information on the structural environment of Al that is not obtainable directly from Raman studies. A middle frequency envelope centred near 700 cm^?1 is indicative of network-substituted AlO₄ polyhedra in glasses with Al/(Al+Si)>0·25 and a band at 520–620cm^?1 is shown to be associated with AlO₆ polyhedra in both crystals and glasses. The IR spectra of melilite and melilite-analogue glasses and crystals show various degrees of band localization that correlate with the extent of Al, Si tetrahedral site ordering. An important conclusion is that differences in Al, Si ordering may lead to very different vibrational spectra in crystals and glasses of otherwise gross chemical similarity.     

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.     

Ab initio calculation of H, O, Al and Si NMR parameters, vibrational frequencies and bonding energetics in hydrous silica and Na-aluminosilicate glasses

Ab initio, molecular orbital (MO) calculations were performed on model systems of SiO₂, NaAlSi₃O₈ (albite), H₂O-SiO₂ and H₂O-NaAlSi₃O₈ glasses. Model nuclear magnetic resonance (NMR) isotropic chemical shifts (δ_iso) for ¹H, ¹⁷O, ²⁷Al and ²⁹Si are consistent with experimental data for the SiO₂, NaAlSi₃O₈, H₂O-SiO₂ systems where structural interpretations of the NMR peak assignments are accepted. For H₂O-NaSi₃AlO₈ glass, controversy has surrounded the interpretation of NMR and infrared (IR) spectra. Calculated δ_iso¹H, δ_iso¹⁷O, δ_iso²⁷Al and δ_iso²⁹Si are consistent with the interpretation of Kohn et al. (1992) that Si-(OH)-Al linkages are responsible for the observed peaks in hydrous Na-aluminosilicate glasses. In addition, a theoretical vibrational frequency associated with the Kohn et al. (1992) model agrees well with the observed shoulder near 900 cm⁻¹ in the IR and Raman spectra of hydrous albite glasses. MO calculations suggest that breaking this Si-(OH)-Al linkage requires ∼+56 to +82 kJ/mol which is comparable to the activation energies for viscous flow in hydrous aluminosilicate melts.     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

Oxide solution mechanisms in silicate melts: Systematic variations in the activity coefficient of SiO2

Phase equilibria and spectroscopic data are used to develop a simple model for the interaction of various oxide components and molten SiO₂. Network modifying oxides, M_xO_y produce nonbridging oxygens thereby depolymerizing the SiO₂ network. The energetics of nonbridging oxygen formation are least favorable when the field strength of the metal cation is high. This produces relatively strong M-O and Si-O-Si bridging bonds at the expense of weaker Si-O-M bonds (De Jonget al., 1980). This relationship is manifested by an increase in positive deviations from ideality with increasing cation field strength in M_xO_y-SiO₂ systems; the activity coefficient of SiO₂ is inversely correlated with Si-O-M bond strength. Network forming oxides (aluminates, phosphates, titanates. zirconates, etc.) may copolymerize with the SiO₂ network. Mixing on the same quasi-lattice produces solutions which approach ideality. Deviations from ideality in such solutions can be linked to distortions in the SiO₂ network. Discrete anion formers (phosphates, titanates, chromates, zirconates) complex with metal oxides other than SiO₂ to form discrete structural units which do not copolymerize with SiO₂. The SiO₂ network is essentially shielded from the high charge density cations in such systems and unmixing is common. As a result, the relative deviations from ideality in such melts are high. It is important to recognize that oxides such as P₂O₅, TiO₂ and ZrO₂ may act as either network-formers or discrete anion formers depending upon melt composition, and are probably distributed between these two “sites” in most geologically important liquids. The latter structural role is favored in more basic compositions.     

Molecular orbital calculations of vibrations in three-membered aluminosilicate rings

Ab initio, molecular orbital calculations at the 3–21G^* level were carried out on H₆Si₃O₉, [H₆Si₂AlO₂]^1?, [H₆SiAl₂O₉]^2?, and [H₆A1₃O₉]^3? cyclic molecules in order to determine their structures and vibrational frequencies. These three-membered rings were found to have minima in their potential energy surfaces indicating stability of the species. The H₆Si₃O₉ ring was found to be slightly non-planar, but the [H₆SiAl₂O₉]^2? and [H₆Al₃3O₉]^3? configurations are more planar. Vibrational frequencies of the Raman-active, bridging oxygen “breathing” modes increase with Si⁴⁺ content. Galeener's (1982a, b) assignment of the D₂ peak (606 cm^?1) in the Raman spectrum of vitreous silica to an oxygen breathing mode in rings of three SiO₄ tetrahedra is reconfirmed. Correlation of the ring breathing mode frequencies as a function of (AI/AI + Si) with Raman peaks in the SiO₂-NaAlSiO₄ system is high. Three-membered aluminosilicate rings are likely to exist and give rise to Raman peaks between 540 and 600 cm_?1 in fully-polymerized aluminosilicate glasses.