Phase Equilibria in the Ternary Systems KBr–K2B4O7–H2O and KCl–K2B4O7–H2O at 373 K

According to the compositions of the underground gasfield brines in the west of Sichuan Basin,the phase equilibria in the ternary systems KBr-K2B4O7-H2O and KCl-K2B4O7-H2O at 373 K were studied using the isothermal dissolution equilibrium method.The solubilities of salts and the densities of saturated solutions in these ternary systems were determined.Using the experimental data,phase diagrams and density-composition diagrams were constructed.The two phase diagrams were simple co-saturation type,each having an invariant point,two univariant curves and two crystallization regions.The equilibrium solid phases in the ternary system KBr-K2B4O7-H2O are potassium bromide （KBr） and potassium tetraborate tetrahydrate （K2B4O7·4H2O）,and those in the ternary system KCl-K2B4O7-H2O are potassium chloride （KCl） and potassium tetraborate tetrahydrate （K2B4O7·4H2O）.Comparisons of the phase diagrams of the two systems at different temperatures show that there is no change in the crystallization phases,but there are changes in the size of the crystallization regions.As temperature increases,the solubility of K2B4O7·4H2O increases rapidly,so the crystallization field of K2B4O7·4H2O becomes smaller.     

Elevation of potassium content of basaltic magma by fractional crystallization: the effect of pressure

A wide range of natural quartz-normative liquids crystallizes olivine at low pressure. Addition of K₂O to the system results in expansion of the olivine primary phase field and replacement of pigeonite (stable in the K-free system) by hypersthene. Some variation in phase relations results from depression of crystallization temperature towards the temperature at which pigeonite reacts to form augite and hypersthene because of addition of K₂O. Another important influence on phase relations results from cation interactions in the liquid related to addition of K₂O. Studies of crystallization behavior of materials similar in most elements except K₂O show that K₂O content markedly alters crystallization behavior for more siliceous liquids but appears to have less effect on liquids with lower SiO₂ contents. Low-Ca pyroxenes melt congruently at P>5 kbar, so anhydrous liquids coprecipitate olivine, plagioclase, and two pyroxenes. Addition of K₂O to the liquid has the same effect as at 1 atm. Hypersthene replaces pigeonite as the Low-Ca pyroxene crystallization from liquids with >1.5% K₂O and the olivine primary phase field grows at the expense of those of pyroxenes and plagioclase. At 10 kbar, olivine may develop a reaction relationship with liquids containing >6% K₂O. At 15 kbar, however, liquids evolve to a pseudoeutectic involving alkali feldspar. The systematic variation in phase relations has important consequences for magmatic evolution in different environments. Dry mafic liquids at shallow levels in oceanic areas can crystallize olivine until the liquid is very evolved, resulting in extreme SiO₂-enrichment besides enrichment in K₂O, and producing potassic dacites. Olivine coexists with liquids with up to 54% SiO₂ if K₂O=0.6% (Grove and Baker 1984) but as much as 63% SiO₂ if K₂O3.5% (Ussler and Glazner 1989). Magmas rising beneath light continental crust may pond at the Moho and evolve to low-density liquids that can rise to the surface. Coprecipitation of olivine, plagioclase, augite, and a low-Ca pyroxene, produces enrichment in K₂O with only slight enrichment in SiO₂. This is terminated, at pressures of 6 to, possibly, 12 kbar, by development of a reaction relationship of olivine and liquid that progresses to higher K₂O contents with pressure. At pressures as high as 15 kbar, the reaction relation may not develop and only crystallization of alkali feldspar suppresses K₂O-enrichment. Any magmatic H₂O or crustal contamination may modify phase relations. The phase relations do, however, suggest that variation in K₂O:SiO₂ of evolved volcanic rocks is related to crustal thickness rather than to variation in the chemical compositions of primary magmas.     

Measurements and calculations of solid-liquid equilibria in the ternary systems NaBr–Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>–H<Subscript>2</Subscript>O and KBr–K<Subscript>2</Subscript>SO<Subscript>4</Subscript>–H<Subscript>2</Subscript>O at 348 K

According to the compositions of the underground brine resources in the west of Sichuan Basin, solubilities of the ternary systems NaBr–Na₂SO₄–H₂O and KBr–K₂SO₄–H₂O were investigated by isothermal method at 348 K. The equilibrium solid phases, solubilities of salts, and densities of the solutions were determined. On the basis of the experimental data, the phase diagrams and the density-composition diagrams were plotted. In the two ternary systems, the phase diagrams consist of two univariant curves, one invariant point and two crystallization fields. Neither solid solution nor double salts were found. The equilibrium solid phases in the ternary system NaBr–Na₂SO₄–H₂O are NaBr and Na₂SO₄, and those in the ternary system KBr–K₂SO₄–H₂O are KBr and K₂SO₄. Using the solubilities data of the two ternary subsystems at 348 K, mixing ion-interaction parameters of Pitzer’s equation θxxx, Ψxxx and Ψxxx were fitted by multiple linear regression method. Based on the chemical model of Pitzer’s electrolyte solution theory, the solubilities of phase equilibria in the two ternary systems NaBr–Na₂SO₄–H₂O and KBr–K₂SO₄–H₂O were calculated with corresponding parameters. The calculation diagrams were plotted. The results showed that the calculated values have a good agreement with experimental data.     

Silicate liquid immiscibility in magmas and in the system K2O-FeO-AI2O3-SiO2: an example of serendipity

The concept of silicate liquid immiscibility was invoked early in the history of petrology to explain certain pairs of compositionally divergent rocks, but. as a result of papers by Greig (Am. J. Sci.13, 1–44, 133–154) and Bowen (The Evolution of the Igneous Rocks), it fell into disfavor for many years. The discovery of immiscibility in geologically reasonable temperature ranges and compositions in experimental work on the system K₂O-FeO-Al₂O₃-SiO₂, and of evidence for immiscibility in a variety of lunar and terrestrial rocks, has reinstated the process.Phase equilibria in the high-silica corner of the tetrahedron representing the system K₂O- FeO-Al₂O₃-SiO₂ are presented, in the form of constant FeO sections through the tetrahedron, at 10% increments. Those sections, showing the tentative relationships of the primary phase volumes, are based on 5631 quenching runs on 519 compositions, made in metallic iron containers in pure nitrogen. Thirteen crystalline compounds are involved, of which at least six show two or more crystal modifica-tions. Two separate phase volumes, in each of which two immiscible liquids, one iron-rich and the other iron-poor, are present at the liquidus. One of these volumes is entirely within the quaternary system, astride the 1:1 K₂O:Al₂O₃ plane. No quaternary compounds as such have been found, but evidence does point toward at least partial quaternary solid solution, with rapidly lowering liquidus temperatures, from K₂O·Al₂O₃· 2SiO₂ (‘potash nepheline’, kalsilite. kaliophilite) to the isostructural compound K₂O·FeO·3SiO₂, and from K₂O·Al₂O₃·4SiO₂ (leucite) to the isostructural compound K₂O·FeO·5SiO₂, Both of these series apparently involve substitution, in tetrahedral coordination. of a ferrous iron and a silicon ion for two aluminum ions. Some of the ‘impurities’ found in analyses of the natural phases may reflect these substitutions.As a result of the geometry of the immiscibility volume located entirely within the quaternary system, compositions near it show a number of phase changes and large amounts of crystallization with small temperature changes, generally in the range 1100–1150 C. Similar low-temperature, high-alkali immiscibility was discovered in a few exploratory runs in the equivalent systems with Rb or Cs substituting for K. But not in those with Li or Na.A review of the compositions and general behavior of systems involving immiscibility, both stable and metastable, and of the evidence for natural immiscibility. indicates that it may be a much more common feature than generally thought. Several examples of natural immiscibility are detailed; most yield a felsic. alkali-aluminosilicate melt and a mafic melt. from a wide variety of generally basaltic parental magmas, both under- and over saturated. Unfortunately, the best line of evidence for immiscibility in terrestrial rocks, a sharply defined meniscus between two compositionally disparate glasses, is by its very nature self-destructing, since it is effectively eliminated by either crystallization or gravitative separation and coalescence into separate magmas. Verification of operation of the exosolutionor ‘splitting’ process on a large scale will probably require careful study of isotopic and trace element partitioning in both laboratory and field.     

Constraints on phase diagram topology for the system CaO−MgO−SiO2−CO2−H2O

Published phase diagrams for the siliceous carbonate system CaO–MgO–SiO₂–CO₂–H₂O are contradictory because of different estimates of the relative stability of magnesite. Experimental data on magnesite are too ambiguous to determine the validity of these estimates. Therefore, field evidence is used to select the correct phase diagram topology for siliceous carbonate and carbonate ultramafic rocks at pressures of about 2–5 kbar. The primary selection criterion is provided by the existence of the stable assemblage talc+dolomite+forsterite+tremolite+antigorite, which occurs in the Bergell contact aureole and Swiss Central Alps. Field evidence also is used to argue that the reaction magnesite+quartz=enstatite must occur at lower temperature than the reaction dolomite+quartz=diopside. T-X _{CO 2} and P _{CO 2}-T phase diagrams consistent with these observations are calculated from experimental and thermo-dynamic data. For antigorite ophicarbonate rocks, remarkable agreement is obtained between the spatial distribution of low variance mineral assemblages and the calculated diagrams.     

A revised model for the density and thermal expansivity of K2O-Na2O-CaO-MgO-Al2O3-SiO2 liquids from 700 to 1900 K: extension to crustal magmatic temperatures

A revised model for the volume and thermal expansivity of K₂O-Na₂O-CaO-MgO-Al₂O₃-SiO₂ liquids, which can be applied at crustal magmatic temperatures, has been derived from new low temperature (701–1092 K) density measurements on sixteen supercooled liquids, for which high temperature (1421–1896 K) liquid density data are available. These data were combined with similar measurements previously performed by the present author on eight sodium aluminosilicate samples, for which high temperature density measurements are also available. Compositions (in mol%) range from 37 to 75% SiO₂, 0 to 27% Al₂O₃, 0 to 38% MgO, 0 to 43% CaO, 0 to 33% Na₂O and 0 to 29% K₂O. The strategy employed for the low temperature density measurements is based on the assumption that the volume of a glass is equal to that of the liquid at the limiting fictive temperature, T _f ^′. The volume of the glass and liquid at T _f ^′ was obtained from the glass density at 298 K and the glass thermal expansion coefficient from 298 K to T _f ^′. The low temperature volume data were combined with the existing high temperature measurements to derive a constant thermal expansivity of each liquid over a wide temperature interval (767–1127 degrees) with a fitted 1 error of 0.5 to 5.7%. Calibration of a linear model equation leads to fitted values of Vˉ _i ±1 (cc/mol) at 1373 K for SiO₂ (26.86 ± 0.03), Al₂O₃ (37.42±0.09), MgO (10.71±0.08), CaO (15.41±0.06), Na₂O (26.57±0.06), K₂O (42.45 ± 0.09), and fitted values of dVˉ _i /dT (10⁻³ cc/mol-K) for MgO (3.27±0.17), CaO (3.74±0.12), Na₂O (7.68±0.10) and K₂O (12.08±0.20). The results indicate that neither SiO₂ nor Al₂O₃ contribute to the thermal expansivity of the liquids, and that dV/dT ^liq is independent of temperature between 701 and 1896 K over a wide range of composition. Between 59 and 78% of the thermal expansivity of the experimental liquids is derived from configurational (vs vibrational) contributions. Measured volumes and thermal expansivities can be recovered with this model with a standard deviation of 0.25% and 5.7%, respectively. Received: 2 August 1996 / Accepted: 12 June 1997     

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

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

The low temperature field of liquid immiscibility in the system K2O-Al2O3-FeO-SiO2 with special reference to the join fayalite-leucite-silica

The extent of the low temperature field of liquid immiscibility in the system K₂O-FeO-Al₂O₃-SiO₂ in the vicinity of the plane fayalite-leucite-silica has been experimentally determined. The combination of direct oxygen buffering with the use of a zirconia probe to monitor oxygen activity has allowed minimisation of K₂O-loss in the experiments while oxygen activity appropriate to the iron-wüstite buffer has been maintained. The four-phase assemblage, fayalite+tridymite+FeO-rich liquid+SiO₂-rich liquid, isobaric univariant in the quaternary system, occurs over a very small temperature range at about 1,163° C on the iron-wüstite buffer. Both liquids appear to be in a coprecipitation relationship with tridymite and fayalite although the relationships between the two liquids are more complicated. The distribution of elements between the two coexisting liquids shows an interesting concordance when plotted in a new way. The results make sense in terms of current knowledge about silicate liquid structure, including the (familiar) observation that K/Al in the SiO₂-rich liquid is always greater than in the coexisting FeO-rich liquid.     

New experimental data for the system CaO-MgO-SiO2-H2O and a synthesis of inferred phase relations

Subsolidus and vapor-saturated liquidus phase relations for a portion of the system CaO-MgO-SiO₂-H₂O, as inferred from experimental data for the composition regions CaMgSi₂O₆-Mg₂SiO₄-SiO₂-H₂O and CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈ (merwinite)-H₂O, are presented in pressure-temperature projection. Sixteen invariant points and 39 univariant reactions are defined on the basis of the 1 atm and 10 kbar (vapor-saturated) liquidus diagrams. Lack of experimental control over many of the reactions makes the depicted relations schematic in part.An invariant point involving orthoenstatite, protoenstatite, pigeonite, and diopside (all solid solutions) occurs at low pressure (probably between 1 and 2 kbar). At pressures below this invariant point, orthoenstatite breaks down at high temperature to the assemblage diopside + protoenstatite; with increasing temperature, the latter assemblage reacts to form pigeonite. At pressures above the invariant point, pigeonite forms according to the reaction diopside + orthoenstatite = pigeonite, and the assemblage diopside + protoenstatite is not stable. At 1 atm, both pigeonite and protoenstatite occur as primary liquidus phases, but at pressures above 6–7 kbar orthoenstatite is the only Ca-poor pyroxene polymorph which appears on the vapor-saturated liquidus surface.At pressures above approximately 10.8 kbar, only diopside, forsterite, and merwinite occur as primary liquidus phases in the system CaMgSi₂O₆-Mg₂SiO₄-Ca₃MgSi₂O₈-H₂O, in the presence of an aqueous vapor phase. At pressures between 1 atm and 10.2 kbar, both akermanite and monticellite also occur as primary liquidus phases. Comparison of the 1 atm and 10 kbar vapor-saturated liquidus diagrams suggests that melilite basalt bears a low pressure, or shallow depth, relationship to monticellite-bearing ultrabasites.     

An internally consistent set of thermodynamic data for twentyone CaO-Al2O3-SiO2- H2O phases by linear parametric programming

The technique of linear parametric programming has been applied to derive sets of internally consistent thermodynamic data for 21 condensed phases of the quaternary system CaO-Al₂O₃-SiO₂-H₂O (CASH) (Table 4). This was achieved by simultaneously processing:

1. calorimetric data for 16 of these phases (Table 1), and
2. experimental phase equilibria reversal brackets for 27 reactions (Table 3) involving these phases.

Calculation of equilibrium P-T curves of several arbitrarily picked reactions employing the preferred set of internally consistent thermodynamic data from Table 4 shows that the input brackets are invariably satisfied by the calculations (Fig. 2a). By contrast, the same equilibria calculated on the basis of a set of thermodynamic data derived by applying statistical methods to a large body of comparable input data (Haas et al. 1981; Hemingway et al. 1982) do not necessarily agree with the experimental reversal brackets. Prediction of some experimentally investigated phase relations not included into the linear programming input database also appears to be remarkably successful. Indications are, therefore, that the thermodynamic data listed in Table 4 may be used with confidence to predict geologic phase relations in the CASH system with considerable accuracy. For such calculated phase diagrams and their petrological implications, the reader's attention is drawn to the paper by Chatterjee et al. (1984).     

Heat capacity and phase equilibria of wadeite-type K2Si4O9

The low-temperature heat capacity (C _p) of Si-wadeite (K₂Si₄O₉) synthesized with a piston cylinder device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system. The entropy of Si-wadeite at standard temperature and pressure calculated from the measured heat capacity data is 253.8 ± 0.6 J mol⁻¹ K⁻¹, which is considerably larger than some of the previous estimated values. The calculated phase transition boundaries in the system K₂O–Al₂O₃–SiO₂ are generally consistent with previous experimental results. Together with our calculated phase boundaries, seven multi-anvil experiments at 1,400 K and 6.0–7.7 GPa suggest that no equilibrium stability field of kalsilite + coesite intervenes between the stability field of sanidine and that of coesite + kyanite + Si-wadeite, in contrast to previous predictions. First-order approximations were undertaken to calculate the phase diagram in the system K₂Si₄O₉ at lower pressure and temperature. Large discrepancies were shown between the calculated diagram compared with previously published versions, suggesting that further experimental or/and calorimetric work is needed to better constrain the low-pressure phase relations of the K₂Si₄O₉ polymorphs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Temperatures and H2O contents of low-MgO high-alumina basalts

Experimental evidence is used to estimate H₂O contents in low-MgO high-alumina basalts (HABs) (<6 wt.% MgO) and basaltic andesites (BAs) (<5 wt.% MgO) that occur worldwide in magmatic arcs. Wholerock compositions of low-MgO HABs and BAs, phenocryst assemblages, and mineral chemistry match the compositions of liquids, phase assemblages, and mineral-compositions produced in H₂O-saturated melting experiments on HABs at moderate pressure (1–2 kb). Low-MgO HABs and BAs therefore could have existed as H₂O-rich multiply-saturated liquids within the crust. Results are presented for melting experiments on two HABs and an andesite at 1 kb pressure, H₂O-saturated, with fO₂ at the NNO buffer. These data and other experimental results on HABs are used to develop a method to estimate the temperature and H₂O content of HAB or BA liquids saturated with olivine, plagioclase, and either high-Ca pyroxene or hornblende. Estimated H₂O contents of HAB liquids are variable and range from 1 to 8 wt.%. High-MgO HABs (>8wt.% MgO) could have H₂O contents reaching no more than 1–2wt.%. The more common low-MgO HABs could have existed as liquids within the crust with H₂O contents of 4 wt.% or higher at temperatures<1100°C. Magmas with these high H₂O contents will saturate with and exsolve aqueous fluid upon approaching the surface. They cannot erupt as liquids and must grow crystals at shallow depths, thus accounting for the abundant phenocrysts in low-MgO HABs and BAs.     

A new thermodynamic model for sapphirine: calculated phase equilibria in K2O–FeO–MgO–Al2O3–SiO2–H2O–TiO2–Fe2O3

The activity–composition (a–x) relations of sapphirine are re‐evaluated in the light of a recent new internally‐consistent data set of phase end‐members for use in phase equilibria modelling, particularly of ultra‐high‐temperature (UHT) rocks. This is achieved with the aid of relatively oxidized sapphirine+quartz‐bearing granulites from Wilson Lake, Canada. Calculated P–T projections and compatibility diagrams in the K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–Fe₂O₃ (KFMASHTO) system are used to illustrate sapphirine+quartz‐bearing phase equilibria in the context of UHT metamorphism. These new a–x relations for sapphirine should allow pseudosection thermobarometry in NCKFMASHTO for estimating peak P–T conditions of sapphirine‐bearing rocks.     

New density measurements on carbonate liquids and the partial molar volume of the CaCO<Subscript>3</Subscript> component

Density measurements on nine liquids in the CaCO₃–Li₂CO₃–Na₂CO₃–K₂CO₃ quaternary system were performed at 1 bar between 555 and 969 °C using the double-bob Archimedean method. Our density data on the end-member alkali carbonate liquids are in excellent agreement with the NIST standards compiled by Janz (1992). The results were fitted to a volume equation that is linear in composition and temperature; this model recovers the measured volumes within experimental error (±0.18% on average, with a maximum residual of ±0.50%). Our results indicate that the density of the CaCO₃ component in natrocarbonate liquids is 2.502 (±0.014) g/cm³ at 800 °C and 1 bar, which is within the range of silicate melts; its coefficient of thermal expansion is 1.8 (±0.5)×10^–4 K^–1 at 800 °C. Although the volumes of carbonate liquids mix linearly with respect to carbonate components, they do not mix linearly with silicate liquids. Our data are used with those in the literature to estimate the value of in alkaline silicate magmas (20 cm³/mol at 1400 °C and 20 kbar), where CO₂ is dissolved as carbonate in close association with Ca. Our volume measurements are combined with sound speed data in the literature to derive the compressibility of the end-member liquids Li₂CO₃, Na₂CO₃, and K₂CO₃. These results are combined with calorimetric data to calculate the fusion curves for Li₂CO₃, Na₂CO₃, and K₂CO₃ to 5 kbar; the calculations are in excellent agreement with experimental determinations of the respective melting reactions.Editorial responsibility: I Carmichael     

An experimental study on the partition of zinc and lead between the silicate and sulfide liquids

On the basis of experimental works in the FeS-FeO-SiO₂(-Fe₃O₄ or -Na₂O) system with synthetic ZnS or PbS, the partition of zinc and lead between silicate and sulfide liquids is shown to be affected by the oxygen content of the sulfide liquids. The partition coefficients K, metal wt. % in sulfide liquid / metal wt. % in silicate liquid, for zinc and lead go through a minimum at relatively low oxygen contents of the sulfide liquids. K_Zn and K_Pb for natural sulfide liquids in equilibrium with basic magmas near the earth's surface are estimated at 0.1–0.5 and greater than 10, respectively. Although K_Zn and K_Pb change appreciably with oxygen content of the sulfide liquids, they never become sufficiently high to concentrate zinc and lead in economic amounts in magmatic sulfide ores.     

Experimental investigations of the role of H2O in calc-alkaline differentiation and subduction zone magmatism

Phase relations of natural aphyric high-alumina basalts and their intrusive equivalents were determined through rock-melting experiments at 2 kb, H₂O-saturated with fO₂ buffered at NNO. Experimental liquids are low-MgO high-alumina basalt or basaltic andesite, and most are saturated with olivine, calcic plagioclase, and either high-calcium pyroxene or hornblende (±magnetite). Cr-spinel or magnetite appear near the liquidus of wet high-alumina basalts because H₂O lowers the appearance temperature of crystalline silicates but has a lesser effect on spinel. As a consequence, experimental liquids follow calcalkaline differentiation trends. Hornblende stability is sensitive to the Na₂O content of the bulk composition as well as to H₂O content, with the result that hornblende can form as a near liquidus mineral in wet sodic basalts, but does not appear until liquids reach andesitic compositions in moderate Na₂O basalts. Therefore, the absence of hornblende in basalts with low-to-moderate Na₂O contents is not evidence that those basalts are nearly dry. Very calcic plagioclase (>An₉₀) forms from basaltic melts with high H₂O contents but cannot form from dry melts with normal are Na₂O and CaO abundances. The presence of anorthite-rich plagioclase in high-alumina basalts indicates high magmatic H₂O contents. In sum, moderate pressure H₂O-saturated phase relations show that magmatic H₂O leads to the early crystallization of spinel, produces calcic plagioclase, and reduces the total proportion of plagioclase in the crystallizing assemblage, thereby promoting the development of the calc-alkaline differentiation trend.     

Partial molar volumes of oxide components in silicate liquids

Densities of 21 silicate liquids have been determined from 1,000 ° to 1,600 ° C. The compositions studied contain from two to eight oxide components and have the following ranges in composition (mole %): SiO₂, 35–79%; TiO₂, 4–36%; Al₂O₃, 5–25%; FeO, 11–41%; MgO, 7–28%; CaO, 7–35%; Na₂O, 5–50%; and K₂O, 4–20%. The compositions thus cover the upper range observed in magmas for each oxide. Precision for each determination of liquid density is always better than ±1%.Volumes/gfw (gram formula weight) calculated from the density measurements and the chemical compositions of the analyzed liquids have been combined with data on 96 silicate liquids reported in the literature. From this data set we derive, by using multiple linear regression, partial molar volumes of the components SiO₂, TiO₂, A1₂O₃, FeO, MgO, CaO, Na₂O, and K₂O at five temperatures. The standard deviation of the multiple regression is 1.8% of the molar volumes, which is considered about equal to the total errors due to compositional and instrumental uncertainties.These derived partial molar volumes have been used to calculate volumes/gfw of natural silicate liquids which are found to agree within 1% of the measured values. No compositional dependence of the partial molar volumes can be detected within the error considered to be typical of the measurements. This is further supported by the close agreement between the calculated volumes of CaMgSi₂O₆ and Fe₂SiO₂ liquids derived from the initial slopes of their fusion curves and their heats of fusion, and the volumes obtained by summing the respective partial molar volumes. The experimental data indicate that silicate liquids mix ideally with respect to volume, over the temperature and composition range of this data set.     

Heat capacities and entropies of silicate liquids and glasses

The heat capacities of several dozen silicate glasses and liquids composed of SiO₂, TiO₂, Al₂O₃, Fe₂O₃, FeO, MgO, CaO, BaO, Li₂O, Na₂O, K₂O, and Rb₂O have been measured by differential scanning and drop calorimetry. These results have been combined with data from the literature to fit C _pas a function of composition. A model assuming ideal mixing (linear combination) of partial molar heat capacities of oxide components (each of which is independent of composition), reproduces the glass data within error. The assumption of constancy of ¯C _p,iis less accurate for the liquids, but data are not sufficient to adequately constrain a more complex model. For liquids containing alkali metal and alkaline earth oxides, heat capacities are systematically greater in liquids with high field strength network modifying cations. Entropies of fusion (per g-atom) and changes of configurational entropy with temperature, are similarly affected by composition. Both smaller cation size and greater charge are therefore inferred to lead to greater development of new structural configurations with increasing temperature in silicate liquids.     

Modeling of the solubility of a one-component H2O or CO2 fluid in silicate liquids

The modeling of the solubility of water and carbon dioxide in silicate liquids (flash problem) is performed by assuming mechanical, thermal, and chemical equilibrium between the liquid magma and the gas phase. The liquid phase is treated as a mixture of ten silicate components + H₂O or CO₂, and the gas phase as a pure H₂O or CO₂. A general model for the solubility of a volatile component in a liquid is adopted. This requires the definition of a mixing equation for the excess Gibbs free energy of the liquid phase and an appropriate reference state for the dissolved volatile. To constrain the model parameters and identify the most appropriate form of the solubility equations for each dissolved volatile, a large number of experimental solubility determinations (640 for H₂O and 263 for CO₂) have been used. These determinations cover a large region of the P-T-composition space of interest. The resultant water and carbon dioxide solubility models differ in that the water model is regular and isometric, and the carbon dioxide model is regular and non-isometric. This difference is consistent with the different speciation modalities of the two volatiles in the silicate liquids, producing a composition-independent partial molar volume of dissolved water and a composition-dependent partial molar volume of dissolved carbon dioxide. The H₂O solubility model may be applied to natural magmas of virtually any composition in the P-T range 0.1 MPa–1 GPa and > 1000 K, whereas the CO₂ solubility model may be applied to several GPa pressures. The general consistency of the water solubility data and their relatively large number as compared to the calibrated model parameters (11) contrast with the large inconsistencies of the carbon dioxide solubility determinations and their low number with respect to the CO₂ model parameters (22). As a result, most of the solubility data in the database are reproduced within 10% of approximation in the case of water, and 30% in the case of carbon dioxide. When compared with the experimental data, the H₂O and CO₂ solubility models correctly predict many features of the saturation surface in the P-T-composition space, including the change from retrograde to prograde H₂O solubility in albitic liquids with increasing pressure, the so-called alkali effect, the increasing CO₂ solubility with increasing degree of silica undersaturation, the Henrian behavior of CO₂ in most silicate liquids up to about 30–50 MPa, and the proportionality between the fugacity in the gas phase, or the saturation activity in the liquid phase, and the square of the mole fraction of the dissolved volatile found in some unrelated silicate liquid compositions. Received: 21 August 1995 / Accepted: 8 July 1996     

Melting relations of basalt-andesile-rhyolite-H2O and a pelagic red clay at 30 kb

An olivine basalt, a tonalite (andesite), a granite (rhyolite), and a red clay (pelagic sediment) were reacted, with known quantities of water in sealed noble metal capsules, in a piston-cylinder apparatus at 30 kb pressure. For the pelagic sediment, with H₂O+=7.8% and no additional water, the liquidus temperature is 1240°C, the primary phases are garnet and kyanite. The subsolidus phase assemblage is phengite mica+garnet+clinopyroxene+coesite+kyanite. With 5 wt.% water added, the liquidus temperatures and primary phases for the calc-alkaline rocks are 1280°-1180°-1080°, garnet+clinopyroxene, garnet, and quartz respectively. Garnet and clinopyroxene occur throughout the melting interval of the olivine tholeiite for all water contents. Garnet is joined by clinopyroxene 80° below the andesite plus 5% H₂O liquidus, quartz is joined by clinopyroxene 180° below the rhyolite plus 5% H₂O liquidus. The subsolidus phase assemblage is garnet+clinopyroxene+coesite+minor kyanite for all the calc-alkaline compositions. We conclude that calc-alkaline andesites and rhyolites are not equilibrium partial melting pruducts of subducted oceanic crust consisting of olivine tholeiite basalt and siliceous sediments. Partial melting in subduction zones produces broadly acid and intermediate liquids, but these liquids lie off the calc-alkaline basalt-andesite-rhyolite join and must undergo modification at lower pressures to produce calcalkaline magmas erupted in overlying island arcs.