A hydrofluoric acid solution calorimetric investigation of glasses in the systems NaAlSi3O8-KAlSi3O8 and NaAlSi3O8-Si4O8

Glasses in the systems NaAlSi₃O₈-KAlSi₃O₈ and NaAlSi₃O₈-Si₄O₈ have been studied by means of hydrofluoric acid solution calorimetry at 50°C. Results indicate small negative enthalpies of mixing in the former system and small positive departures from ideality in the latter.     

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.     

The mixing properties of melts and glasses in the system NaAlSi3O8-KAlSi3O8: Comparison of experimental data obtained by knudsen cell mass spectrometry and solution calorimetry

The apparent differences between heats of mixing determined by solution calorimetric measurements on quenched samples in the system NaAlSi₃O₈-KAlSi₃O₈ and heats of mixing determined at high temperatures by Knudsen cell mass spectrometry are caused by thermal effects related to the glass transition. When these effects are allowed for, the calorimetric data and Knudsen cell measurements are in good agreement.     

Determination of activities in silicate melts by Knudsen cell mass spectrometry—I. The system NaAlSi3O8-KAlSi3O8

The mixing properties of aluminosilicate melts in the pseudobinary system NaAlSi₃O₈-KAlSi ₃O₈ have been determined by measuring the compositions of their saturated vapours by hightemperature Knudsen cell mass spectrometry. The melts mix close to ideally over most of the composition range with small positive deviations from ideality for K-rich compositions. These may be related to incipient partial ordering of melt constituents into leucite-like and SiO₂-like structures above the feldspar liquidus.     

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.     

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.     

Structure of mineral glasses—III. NaAlSi3O8 supercooled liquid at 805°C and the effects of thermal history

The distribution of interatomic distances in amorphous NaAlSi₃O₈ has been determined at 805°C by X-ray radial distribution analysis to investigate structural differences between the glass (T < 763°C) and the supercooled liquid (763°C < T < 1118°C). Except for slight differences attributable to thermal expansion, no significant changes were observed. The sample crystallized during the course of the experiment, but at least one crystal-free data set was obtained. The transition from the inferred six-membered ring structure of the supercooled liquid to the four-membered ring structure of the crystal was clearly visible in radial distribution function (RDF's) determined before and after crystallization.RDF's were also determined at 25°C for two NaAlSi₃O₈ glasses with different histories. The first was derived from a melt that had been cooled slowly from 1600 to 32°C above the melting point (T_f = 1118°C) to detect possible repolymerization to a more ‘crystal-like’ structure as the melt approached T_f. The second glass was prepared by holding a single crystal of Amelia albite at 50°C above T_f to see if the crystalline four-membered ring structure was preserved in melts at temperatures just above the liquidus. No significant differences were observed between these two RDF's and one obtained from a glass quenched from 1800°C. These results suggest that in addition to the destruction of formation of a periodic structure, melting and crystallization in NaAlSi₃O₈ also involves a repolymerization of tetrahedra. This would explain the observed kinetic barrier to melting and crystallization in the anhydrous system and the catalytic effect of small amounts of water or alkali oxide.     

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 synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6

Enthalpies of solution of synthetic clinopyroxenes on the join CaMgSi₂O₆-Mg₂Si₂O₆ have been measured in a melt of composition Pb₂B₂O₅ at 970 K. Most of the measurements were made on samples crystallized at 1600°–1700°C and 30 kbar pressure, which covered the range 0–78 mole per cent Mg₂Si₂O₆, and whose X-ray patterns could be satisfactorily indexed on the diopside (C2/c) structure. For the reaction: Mg₂Si₂O₆→-Mg₂Si₂O₆ enstatite diopside the present data, in conjunction with previous and new measurements on Mg₂Si₂O₆ enstatite, determine ΔH° ~ 2 kcal and W_H (regular solution parameter) ~ 7 kcal. These values are in good agreement with those deduced by Saxena and Nehru (1975) from a study of high temperature, high pressure phase equilibrium data under the assumption that the excess entropy of mixing is small, but, in light of the recent theoretical treatment of Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), the meanings of these parameters may be ambiguous.Heat of solution measurements on Ca-rich binary diopsides made by annealing glasses at 1358°C in air gave slighter higher values than the higher temperature high pressure samples. This may be evidence for some (Ca, Mg) disorder of the sort postulated by Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), although no differences in heat of solution dependent on synthesis temperature in the range 1350°–1700°C could be found in stoichiometric CaMgSi₂O₆.     

Enthalpy of formation of Fe3Al2Si3O12 (almandine) by high temperature alkali borate solution calorimetry

A high-temperature solution calorimetric method suitable for thermochemical studies of anhydrous minerals containing Fe²⁺ ions has been developed. The method is based on an oxide melt solvent with 52 wt% LiBO₂ and 48 wt% NaBO₂ maintained at a temperature of 750°C. In a first application of this method the enthalpies of solution of synthetic almandine, fayalite, a mixture of fayalite plus quartz on FeSiO₃ composition, and natural quartz were measured. For the reaction:

the enthalpy change at 1023 K is ?3.82 ± 0.87 kcal, based on fayalite, quartz, corundum and almandine, and ?5.96 ± 0.90 kcal based on the fayalite plus quartz mixture, corundum, and almandine. These values lead to standard molar enthalpies of formation of almandine from the oxides at 1023 K of ?14.10 ± 1.22 kcal and ?16.24 ± 1.74 kcal, respectively. The measured enthalpy of formation of almandine is less negative by several kilocalories than values derived from analysis of the phase equilibrium work of Hsu (1968), but in closer agreement with the phase equilibrium study of O'Neill and Wood (1979) and similar to the phase equilibrium deduction of Froese (1973).The agreement of the present almandine enthalpy of formation with O'Neill and Wood (1979) and Froese (1973) suggests that almandine entropies at 298 K to be obtained from their studies, in the range 79–81 cal/K, are more nearly correct than the several estimates based on oxide sum and volume-entropy systematics, most of which are much lower.     

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.     

Solubility of grossular, Ca3Al2Si3O12, in H2O-NaCl solutions at 800 °C and 10 kbar, and the stability of garnet in the system CaSiO3-Al2O3-H2O-NaCl

The solubility and stability of synthetic grossular were determined at 800 °C and 10 kbar in NaCl-H₂O solutions over a large range of salinity. The measurements were made by evaluating the weight losses of grossular, corundum, and wollastonite crystals equilibrated with fluid for up to one week in Pt capsules and a piston-cylinder apparatus. Grossular dissolves congruently over the entire salinity range and displays a large solubility increase of 0.0053 to 0.132 molal Ca₃Al₂Si₃O₁₂ with increasing NaCl mole fraction (X_NaCl) from 0 to 0.4. There is thus a solubility enhancement 25 times the pure H₂O value over the investigated range, indicating strong solute interaction with NaCl. The Ca₃Al₂Si₃O₁₂ mole fraction versus NaCl mole fraction curve has a broad plateau between X_NaCl = 0.2 and 0.4, indicating that the solute products are hydrous; the enhancement effect of NaCl interaction is eventually overtaken by the destabilizing effect of lowering H₂O activity. In this respect, the solubility behavior of grossular in NaCl solutions is similar to that of corundum and wollastonite. There is a substantial field of stability of grossular at 800 °C and 10 kbar in the system CaSiO₃-Al₂O₃-H₂O-NaCl. At high Al₂O₃/CaSiO₃ bulk compositions the grossular + fluid field is limited by the appearance of corundum. Zoisite appears metastably with corundum in initially pure H₂O, but disappears once grossular is nucleated. At X_NaCl = 0.3, however, zoisite is stable with corundum and fluid; this is the only departure from the quaternary system encountered in this study. Corundum solubility is very high in solutions containing both NaCl and CaSiO₃: Al₂O₃ molality increases from 0.0013 in initially pure H₂O to near 0.15 at X_NaCl = 0.4 in CaSiO₃-saturated solutions, a >100-fold enhancement. In contrast, addition of Al₂O₃ to wollastonite-saturated NaCl solutions increases CaSiO₃ molality by only 12%. This suggests that at high pH (quench pH is 11-12), the stability of solute Ca chloride and Na-Al ± Si complexes account for high Al₂O₃ solubility, and that Ca-Al ± Si complexes are minor. The high solubility and basic dissolution reaction of grossular suggest that Al may be a very mobile component in calcareous rocks in the deep crust and upper mantle when migrating saline solutions are present.     

Phosphoinnelite, Ba4Na3Ti3Si4O14(PO4,SO4)2(O,F)3, a new mineral species from peralkaline pegmatite of the Kovdor pluton, Kola Peninsula

Phosphoinnelite, an analogue of innelite with P > S, has been found in a peralkaline pegmatite vein crosscutting calcite carbonatite at the phlogopite deposit, Kovdor pluton, Kola Peninsula. Cancrinite (partly replaced with thomsonite-Ca), orthoclase, aegirine-augite, pectolite, magnesioarfvedsonite, golyshevite, and fluorapatite are associated minerals. Phosphoinnelite occurs as lath-shaped crystals up to 0.2 × 1 × 6 mm in size, which are combined typically in bunch-, sheaf-, and rosettelike segregations. The color is yellow-brown, with vitreous luster on crystal faces and greasy luster on broken surfaces. The mineral is transparent. The streak is pale yellowish. Phosphoinnelite is brittle, with perfect cleavage parallel to the {010} and good cleavage parallel to the {100}; the fracture is stepped. The Mohs hardness is 4.5 to 5. Density is 3.82 g/cm³ (meas.) and 3.92 g/cm³ (calc.). Phosphoinnelite is biaxial (+), α = 1.730, β = 1.745, and γ = 1.764, 2V (meas.) is close to 90°. Optical orientation is Z^c ∼ 5°. Chemical composition determined by electron microprobe is as follows (wt %): 6.06 Na₂O, 0.04 K₂O, 0.15 CaO, 0.99 SrO, 41.60 BaO, 0.64 MgO, 1.07 MnO, 1.55 Fe₂O₃, 0.27 Al₂O₃, 17.83 SiO₂, 16.88 TiO₂, 0.74 Nb₂O₅, 5.93 P₂O₅, 5.29 SO₃, 0.14 F, −O=F₂ = −0.06, total is 99.12. The empirical formula calculated on the basis of (Si,Al)₄O₁₄ is (Ba_3.59Sr_0.13K_0.01)_Σ3.73(Na_2.59Mg_0.21Ca_0.04)_Σ3.04(Ti_2.80Fe _0.26 ³⁺ Nb_0.07)_Σ3.13[(Si_3.93Al_0.07)_Σ4O₁₄(P_1.11S_0.87)_Σ1.98O_7.96](O_2.975F_0.10)_Σ3.075. The simplified formula is Ba₄Na₃Ti₃Si₄O₁₄(PO₄,SO₄)₂(O,F)₃. The mineral is triclinic, space group P or P1. The unit cell dimensions are a = 5.38, b = 7.10, c = 14.76 ?; α = 99.00°, β = 94.94°, γ = 90.14°; and V = 555 ?³, Z = 1. The strongest lines of the X-ray powder pattern [d, ? in (I)(hkl)] are: 14.5(100)(001), 3.455(40)(103), 3.382(35)(0 2), 2.921(35)(005), 2.810(40)(1 4), 2.683(90)(200, 01), 2.133(80)( 2), 2.059(40)(204, 1 3, 221), 1.772(30)(0 1, 1 7, 2 2, 2 3). The infrared spectrum is demonstrated. An admixture of P substituting S has been detected in the innelite samples from the Inagli pluton (South Yakutia, Russia). An innelite-phosphoinnelite series with a variable S/P ratio has been discovered. The type material of phosphoinnelite has been deposited at the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow. Original Russian Text ? I.V. Pekov, N.V. Chukanov, I.M. Kulikova, D.I. Belakovsky, 2006, published in Zapiski Rossiiskogo Mineralogicheskogo Obshchestva, 2006, No. 3, pp. 52–60. Considered and recommended by the Commission on New Minerals and Mineral Names, Russian Mineralogical Society, May 9, 2005. Approved by the Commission on New Minerals and Mineral Names, International Mineralogical Association, July 4, 2005 (proposal 2005-022).     

Structure vs. composition: A solid-state H and Si NMR study of quenched glasses along the Na2O-SiO2-H2O join

A suite of six hydrous (7 wt.% H₂O) sodium silicate glasses spanning sodium octasilicate to sodium disilicate in composition were analyzed using ²⁹Si single pulse (SP) magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, ¹H-²⁹Si cross polarization (CP) MAS NMR, and fast MAS ¹H-NMR. From the ²⁹Si SPMAS data it is observed that at low sodium compositions dissolved water significantly depolymerizes the silicate network. At higher sodium contents, however, dissolved H₂O does not affect a significant increase in depolymerization over that predicted based on the Na/Si ratio alone. The fast MAS ¹H-NMR data reveal considerable complexity in proton environments in each of the glasses studied. The fast MAS ¹H-NMR spectra of the highest sodium concentration glasses do not exhibit evidence of signficantly greater fractions of dissolved water as molecular H₂O than the lower sodium concentration glasses requiring that the decrease in polymerization at high sodium contents involves a change in sodium solution mechanism. Variable contact time ¹H-²⁹Si cross polarization (CP) MAS NMR data reveal an increase in the rotating frame spin lattice relaxation rate constant (T_1ρ*) for various Qⁿ species with increasing sodium content that correlates with a reduction in the average ¹H-²⁹Si coupling strength. At the highest sodium concentration, however, T_1ρ* drops significantly, consistent with a change in the Na₂O solution mechanism.     

Mineral-solution equilibria—III. The system Na2OAl2O3SiO2H2OHCl

Chemical equilibrium between sodium-aluminum silicate minerals and chloride bearing fluid has been experimentally determined in the range 500–700°C at 1 kbar, using rapid-quench hydrothermal methods and two modifications of the Ag + AgCl acid buffer technique. The temperature dependence of the thermodynamic equilibrium constant (K) for the reaction $\text{NaAlSi}{}_3\text{O}{}_8\text{+ HCl}{}^{\mathrm{o}}\text{= NaCl}{}^{\mathrm{o}}\text{+}\text{1}\text{2Al}{}_2\text{SiO}{}_5\text{, +}\text{5}\text{2SiO}{}_2\text{+}\text{1}\text{2H}{}_2\text{O}$ Albite Andalusite Qtz. can be described by the following equation: log k = ?4.437 + 5205.6/T(K) The data from this study are consistent with experimental results reported by Montoya and Hemley (1975) for lower temperature equilibria defined by the assemblages albite + paragonite + quartz + fluid and paragonite + andalusite + quartz + fluid. Values of the equilibrium constants for the above reactions were used to estimate the difference in Gibbs free energy of formation between NaCl^o and HCl^o in the range 400–700°C and 1–2 kbar. Similar calculations using data from phase equilibrium studies reported in the literature were made to determine the difference in Gibbs free energy of formation between KCl^o and HCl^o. These data permit modelling of the chemical interaction between muscovite + kspar + paragonite + albite + quartz assemblages and chloride-bearing hydrothermal fluids.     

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.     

The MgO-Al2O3-SiO2 system: free energy of pyrope and Al2O3-enstatite

Using the model of fictive ideal components, Gibbs free energies of formation of pyrope and Al₂O₃-enstatite have been determined from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range of 1200–1600 K. The negative free energies in kJ/mol are:

     

TK	1200	1300	1400	1500	1600
Pyrope	4869.92	4747.05	4614.26	4462.63	4311.00
Al2O3-enstatite	1257.25	1244.28	1191.93	1158.67	1125.64