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.     

Glass transitions and thermodynamic properties of amorphous SiO2, NaAlSinO2n+2 and KAlSi3O8

A drop calorimetric study, between 900 and 1800 K, of amorphous SiO₂, NaAlSi₃O₈, NaAlSi₂O₆, NaAlSiO₄ and KAlSi₃O₈ shows the increase in heat capacity which results from glass transitions. For these glasses, the fictive temperature has a negligible effect on the heat capacity above room temperature, but it has an important influence on the enthalpy of formation as obtained from solution calorimetry. From these results and published Cp and enthalpy of solution data, several properties have been calculated: the enthalpies of fusion of high albite, nepheline, Jadeite and high sanidine, the thermodynamic functions of amorphous NaAlSi₃O₈ and KAlSi₃O₈ between 0 and 2000 K, and some mixing properties of liquids along the join SiO₂-NaAlSi₃O₈. The latter data suggest that these liquids behave more closely as athermal solutions than as regular solutions.     

Static lattice energy calculations of mixing and ordering enthalpy in binary carbonate solid solutions

Enthalpies of mixing and ordering in the binaries of the quaternary carbonate (Ca,Mg,Fe,Mn)CO₃ solid solution have been modeled using static lattice energy minimization calculations. A set of self-consistent empirical potentials has been specially developed for this task. The calculations illustrate the importance of size mismatch in determining magnitudes of the enthalpies of mixing and ordering in the binaries. The enthalpy effects show positive correlation with the predicted temperatures of the order/disorder transitions in intermediate compounds with the dolomite structure. It is shown that the general behavior of the mixing enthalpy in high- and low-T limits can be constrained with a minimum set of sampled configurations.     

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.     

Energetics of glasses in the system diopside-anorthite-forsterite

Enthalpies of mixing in glasses in the experimentally accessible region of the system Di-An-Fo are generally less than 4 kJ/mol in magnitude. Enthalpies of mixing of liquids in this and in several other petrologically relevant melts are also small; thus, if magmas of different compositions mix isothermally, the heat released or absorbed can be neglected in any consideration of the thermal evolution of the magmas, unless melting or crystallization takes place. The enthalpy of vitrification of Mg₂SiO₄ (to form a hypothetical glass at 700°C) is estimated to be 61±4 kJ/mol, in contrast to the enthalpy of fusion at 1500°C, 89±12 kJ/mol (Navrotsky et al. 1989). This suggests an average difference in heat capacity ( C _p) between liquid and crystal of 35 J/K. mol, half that estimated by Ghiorso and Carmichael (1980, 1987).     

A thermochemical calculation of the pyroxene saturation surface in the system diopside-albite-anorthite

The pyroxene saturation surface in the system diopside-albite-anorthite may be calculated to ±10°C from thermochemical data over most of its composition range. The thermochemical data used are the experimentally determined enthalpies of mixing of the ternary liquids and the enthalpy of fusion of diopside. These are combined with a mixing model for the configurational entropy in the melt and the activity of CaMgSi₂O₆ in the clinopyroxene, which is less than unity due to departures from CaMgSi₂O₆ stoichiometry. The ‘two-lattice’ melt model appears to work satisfactorily throughout the pyroxene primary phase field but probably needs modification at more anorthite-rich compositions.     

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.     

Enthalpy of diaplectic labradorite glass

Enthalpies of solution in molten 2PbO·B₂O₃ at ～988 K have been measured for diaplectic labradorite glass from the Manicouagan impact crater and a fused glass formed from the same material. The enthalpies of solution of the diaplectic and fusion-formed glasses are 4,347 and 2,023 cal mol^?1, respectively. The more endothermic enthalpy of solution of the diaplectic glass indicates a greater relative energetic stability of about 2.3 kcal mol^?1. The data are consistent with Diemann and Arndt's (1984) structural model that suggests the diaplectic glass is more ordered than fusion-formed glass and with the presence of crystallites. Comparison of data to enthalpies of solution of crystalline labradorite (Carpenter et al. 1985) indicates a maximum percentage of crystalline relics of ～15–18%, also consistent with Diemann and Arndt's (1984) estimate of <17%. Thus the diaplectic glass is intermediate in thermochemical properties between normal glass and crystal (much closer to glass) and does not represent any state more unstable than normal fusion-formed glass.     

Effect of water on the heat capacity of polymerized aluminosilicate glasses and melts

The effect of water on heat capacity has been determined for four series of hydrated synthetic aluminosilicate glasses and supercooled liquids close to albite, phonolite, trachyte, and leucogranite compositions. Heat capacities were measured at atmospheric pressure by differential scanning calorimetry for water contents between 0 and 4.9 wt % from 300 K to about 100 K above the glass transition temperature (T_g). The partial molar heat capacity of water in polymerized aluminosilicate glasses, which can be considered as independent of composition, is (J/mol K). In liquids containing at least 1 wt % H₂O, the partial molar heat capacity of water is about 85 J/mol K. From speciation data, the effects of water as hydroxyl groups and as molecular water have tentatively been estimated, with partial molar heat capacities of 153 ± 18 and 41 ± 14 J/mol K, respectively. In all cases, water strongly increases the configurational heat capacity at T_g and exerts a marked depressing effect on T_g, in close agreement with the results of viscosity experiments on the same series of glasses. Consistent with the Adam and Gibbs theory of relaxation processes, the departure of the viscosity of hydrous melts from Arrhenian variations correlates with the magnitude of configurational heat capacities.     

A thermochemical study of glasses and crystals along the joins silica-calcium aluminate and silica-sodium aluminate

Enthalpies of solution in molten 2PbO · B₂O₃ at 985 K are reported for series of glasses xCa_0.5AlO₂-(1?x)SiO₂ (O ≤ x ≤ 0.99) and xNaAlO₂-(1?x)SiO₂ (0 ≤ x ≤ 0.56). The data are compared to values for the corresponding crystalline aluminosilicates and to preliminary data for systems containing KAlO₂ and Mg_0.5AlO₂. The enthalpies of mixing of glasses become more exothermic with increasing basicity of the mono- or divalent oxide. The tendency toward immiscibility on the silica-rich side, indicated by the shape of the heat of mixing curve between x = 0 and x = 0.4, is pronounced in the calcium aluminate system, but not in the sodium aluminate system. The shape of the heat of mixing curve, which is roughly symmetrical about x = 0.5, can be rationalized in terms of glass structure by considering essentially random substitution of Si and Al on a continuous three dimensional tetrahedral framework, with stabilization arising from electrostatic interactions between aluminum and the nonframework cation balancing the destabilizing effects arising from perturbation of the aluminosilicate framework by the nonframework cation. These trends are consistent with the variation of physical properties of aluminosilicate melts.     

High temperature heat contents and heat capacities of liquids and glasses in the system NaAlSi3O8-CaAl2Si2O8

Enthalpies and heat capacities of glasses and of stable liquids in the system NaAlSi₃O₈-CaAl₂Si₂O₈ have been measured by drop and differential scanning calorimetry. Within experimental error, values of C _p and of H _{T 300} of three intermediate compositions fall on straight line interpolations between the end members for both liquids and glasses, indicating that excesses in true and in mean heat capacities [(H _T –H ₃₀₀)/(T–300)] are small or absent. A value for the heat capacity of the An₁₀₀ liquid component can therefore be derived, and is probably a better estimate than that based on measurements on the pure substance alone. On the assumption of zero excess heat capacity in this system, heats of mixing in the stable liquids are equal to those measured in the glasses by solution calorimetry, and can be as negative as -2 kcal mol^–1.Heat capacities of solids and glasses in the Ab-An system are similar and do not vary greatly with composition. The C _P's of the liquids, however, increase strongly with An content, suggesting major structural changes take place across the binary.     

Thermochemistry and melting properties of basalt

The heat capacities of the liquid, glassy and crystalline phases of an alkali basalt have been determined from relative enthalpies measured between 400 and 1,800 K. Values given by available models of calculation generally agree to within 2% of these results. As derived from the new data and the enthalpy of vitrification measured at 973 K by oxide-melt drop solution calorimetry for the same sample, the enthalpy of fusion of this basalt increases from 15.4 kJ/mol at 1,000 K to 33.6 kJ/mol at 1,800 K. Comparisons between the enthalpies of fusion of basalt and model compositions confirm the small magnitude of the enthalpy of mixing between the molten mineral components of the liquids. Minor variations in the chemical composition have only a small effect in the heat capacity and the enthalpy of melting of basalt. The enthalpies of formation at 298 K from the oxides of the crystallized and glass phases of this alkali basalt are −112.2 and −98.5 kJ/mol, respectively, for a gram formula weight based on one mole of oxide components.     

Calorimetry of silicate melts at 1773 K: measurement of enthalpies of fusion and of mixing in the systems diopside-anorthite-albite and anorthite-forsterite

Transposed-temperature-drop calorimetry, using a Setaram HT 1500 calorimeter, was used to study directly the melting at 1773 K of mixtures of crystalline albite, anorthite, and diopside and of anorthite and forsterite. The enthalpy of albite at 1000–1773 K, starting with both crystalline and glassy samples, was also measured. The results confirm previously measured enthalpies of fusion of albite, diopside and anorthite (Stebbins et al. 1982, 1983; Richet and Bottinga 1984,1986). The new results use thermochemical cycles which completely avoid the glassy state by transforming crystals directly to melts. The enthalpy of fusion of forsterite is estimated to be 89±12 kJ/mol at 1773 K and 114±20 kJ/mol at its melting point of 2163 K. The data allow semiquantitative evaluation of heats of mixing in the molten silicates. Along the Ab-An join, enthalpies of mixing in the liquid at 773 K are the same or somewhat more negative than those in the glass at 986 K, whereas along Ab-Di and An-Di, enthalpies of mixing in the liquid are distinctly more positive than in the glass. These differences correlate with excess heat capacities in the liquids suggested by Stebbins et al. (1984).     

Calorimetric measurements of fusion enthalpies for Ni2SiO4 and Co2SiO4 olivines and application to olivine-liquid partitioning

Calorimetric measurements of fusion enthalpies for Ni₂SiO₄ and Co₂SiO₄ olivines were carried out using a high-temperature calorimeter, and Ni and Co partitioning between olivine and silicate liquid was analyzed using the measured heats of fusion. The fusion enthalpy of Co₂SiO₄ olivine measured by transposed-temperature drop calorimetry was 103 ± 15 kJ/mol at melting point (1688 K). The fusion enthalpy of Ni₂SiO₄ olivine was calculated based on the enthalpies of liquids in the system An₅₀Di₅₀-Ni₂SiO₄ measured by transposed-temperature drop calorimetry at 1773 K, and was 221 ± 26 kJ/mol at its metastable melting point (1923 K). The fusion enthalpy of Ni₂SiO₄ is the largest among those of olivine group, this is caused by the large crystal field stabilization energy of six-coordinated Ni²⁺ in olivine. The larger fusion enthalpy of Ni₂SiO₄ can account for the large and variable partition coefficient of Ni between olivine and silicate liquid. Based on the comparison between partition coefficients calculated from thermodynamic data and those observed in partition experiments, it is considered that the magnitude of partition coefficients is primarily dependent on the heats of fusion of the components. Furthermore, the activity coefficients for Ni-, Co- and Mn-bearing components in magmatic liquid are nearly of the same magnitude.     

Calorimetric study of high-pressure phase transitions among the CdGeO3 polymorphs (pyroxenoid,garnet, ilmenite,and perovskite structures)

At high pressures, CdGeO₃ pyroxenoid transforms to garnet, then to ilmenite, and finally to perovskite. Enthalpies of transition among the four phases were measured by high temperature calorimetry. The entropies of transition and slopes of the boundaries were calculated using the measured enthalpies and free energies calculated from the phase equilibrium data. Pyroxenoid and garnet are very similar energetically. However garnet is a high pressure phase because of its lower entropy and smaller volume. The pyroxenoid-garnet transition has a small positiveP-T slope. Ilmenite is intermediate in enthalpy between garnet and perovskite, but is lower in entropy than both phases. Therefore the garnet-ilmenite transition has a positivedP/dT, while a negativedP/dT is calculated for the ilmenite-perovskite transition. The thermochemical data for the CdGeO₃ phases are generally consistent with the observed high pressure phase relations. The high entropy of perovskite relative to ilmenite, observed in several ABO₃ comounds including CdGeO₃, is related to the structural features of perovskite, in which relatively small divalent cations occupy the large sites of 8–12 fold coordination. The thermochemistry of the CdGeO₃ polymorphs shows several similarities to that of the CaGeO₃ system.     

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.     

Chemical and thermal zonation in a mildly alkaline magma system Infiernito Caldera,Trans-Pecos Texas

Postcollapse lavas of the Infiernito caldera grade stratigraphically upward from nearly aphyric, high-silica rhyolite (76% SiO₂) to highly prophyritic trachyte (62% SiO₂). Plagioclase, clinopyroxene, orthopyroxene, magnetite, ilmenite, and apatite occur as phenocrysts throughout the sequence. Sanidine, biotite, and zircon are present in rocks with more than about 67% SiO₂. Major and trace elements show continuous variations from 62 to 76% SiO₂. Modeling supports fractional crystallization of the observed phenocrysts as the dominant process in generating the chemical variation.Temperatures calculated from coexisting feldspars, pyroxenes, and Fe-Ti oxides agree and indicate crystallization from slightly more than 1100° C in the most mafic trachyte to 800° C in high-silica rhyolite. The compositional zonation probably arose through crystallization against the chilled margin of the magma chamber and consequent rise of more evolved and therefore less dense liquid.Mineral compositions vary regularly with rock composition, but also suggest minor mixing and assimilation of wall rock or fluids derived from wall rock. Mixing between liquids of slightly different compositions is indicated by different compositions of individual pyroxene phenocrysts in single samples. Liquid-solid mixing is indicated by mineral compositions of glomerocrysts and some phenocrysts that apparently crystallized in generally more evolved liquids at lower temperature and higher oxygen fugacity than represented by the rocks in which they now reside. Glomerocrysts probably crystallized against the chilled margin of the magma chamber and were torn from the wall as the liquid rose during progressive stages of eruption. Assimilation is indicated by rise of oxygen fugacity relative to a buffer from more mafic to more silicic rocks.Calculation of density and viscosity from the compositional and mineralogical data indicates that the magma chamber was stably stratified; lower temperature but more evolved, thus less dense, rhyolite overlay higher temperature, less evolved, and therefore more dense, progressively more mafic liquids. The continuity in rock and mineral compositions and calculated temperature, viscosity, and density indicate that compositional gradation in the magma chamber was smoothly continuous; any compositional gaps must have been no greater than about 2% SiO₂.     

High temperature calorimetry of sulfide systems

Enthalpies of solution of synthetic pentlandite Fe_4.5Ni_4.5S₈, natural violarite (Fe_0.2941Ni_0.7059)₃S₄ from Vermillion mine, Sudbury, Ontario, synthetic pyrrhotite, FeS, synthetic high temperature NiS, synthetic vaesite, NiS₂, synthetic pyrite, FeS₂, Ni and Fe have been measured in a Ni_0.6S_0.4 melt at 1,100 K. Using these data and the standard enthalpies of formation of binary sulfides, given in literature, standard enthalpies of formation of pentlandite and violarite were calculated. The following values are reported: ΔH _f ^{o, Pent} =?837.37±14.59 kJ mol^?1 and ΔH _f ^{o, Viol} =?378.02±11.81 kJ mol^?1. While there are no thermo-chemical data for pentlandite with which our new value can be compared, an equilibrium investigation of stoichiometric violarite by Craig (1971) gives a significantly less negative enthalpy of formation. It is suggested that the difference may be due to the higher degree of order in the natural sample.     

A thermochemical study of the liquid system NaBO2 + SiO2 at 1394 K

The enthalpies of mixing in the quasi-binary liquid system NaBO₂ + SiO₂ were measured by solid-liquid calorimetry at 1394 K. Correcting for the known enthalpy of fusion of SiO₂ at this temperature we derived also the corresponding liquid-liquid enthalpies of mixing, ΔH_mix, and the enthalpy interaction parameters, ΔH_mix/N_NaBO2N_SiO2; the latter quantity changes from about −30 kj mol⁻¹ in pure NaBO₂ to about −20 kJ mol⁻¹ at N_SiO2 ≈ 0.67. From the experimentally determined curve for ΔH_mix the partial enthalpies of the two components were obtained by the method of intercepts. For n_sio2 < 0.4 values of ΔH̄_SiO2 were determined also by direct experiments. This quantity shows a sharp dependence on composition for N_SiO2 < 0.1 and for N_SiO2 ≈ 0.28. The possible significance of this is discussed in the light of reported structural information on the melts.