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.     

The effect of Al3+, Fe3+, and Ti4+ on the configurational heat capacities of sodium silicate liquids

The heat capacities of 29 glasses and supercooled liquids in the Na₂O-SiO₂, Na₂O-Al₂O₃-SiO₂, Na₂O-(FeO)-Fe₂O₃-SiO₂, and Na₂O-TiO₂-SiO₂ systems were measured in air from 328 to 998 K with a differential scanning calorimeter. The reproducibility of the data determined from multiple heat capacity runs on a single crystal MgO standard is within ± 1% of the accepted values at temperatures ≤ 800 K and within ± 1.5% between 800 and 1000 K. Within the resolution of the data, the heat capacities of sodium silicate and sodium aluminosilicate liquids are temperature independent. Heat capacity data in the supercooled liquid region for the sodium silicates and sodium aluminosilicates were combined and modelled assuming a linear compositional dependence. The derived values for the partial molar heat capacities of Na₂O, Al₂O₃, and SiO₂ are 112.35 ± 0.42, 153.16 ± 0.82, and 76.38 ± 0.20 J/gfw · K respectively. The partial molar heat capacities of Fe₂O₃ and TiO₂ could not be determined in the same manner because the heat capacities of the Fe₂O₃- and TiO₂-bearing sodium silicate melts showed varying degrees of negative temperature dependence. The negative temperature dependence to the configurational C _P may be related to the occurrence of sub-microscopic domains (relatively polymerized and depolymerized) that break down to a more homogeneous melt structure with increasing temperature. Such an interpretation is consistent with data from in situ Raman, Mössbauer, and X-ray absorption fine structure (XAFS) spectroscopic studies on similar melts.     

The structural role of Al2O3 and TiO2 in immiscible silicate liquids in the system SiO2-MgO-CaO-FeO-TiO2-Al2O3

The effects of the addition of Al₂O₃ on the large stable two liquid field in the SiO₂-TiO₂-CaO-MgO-FeO system were experimentally determined. The increase of Al₂O₃ content in the starting composition results in the decrease of critical temperature, phase separation and liquidus temperature of the two liquid field until it is rendered completely metastable. The shrinkage of the two liquid field indicates that Al₂O₃ is acting in the role of a network former and homogenizes the structure of the two melts. In this alkali-free system Al⁺³ utilizes the divalent cations, Ca⁺² and Mg⁺², for local charge balance with a preference for Ca⁺² over Mg⁺². Thus, AlO₄ tetrahedra combine with SiO₄ tetrahedra to form an aluminosilicate framework which polymerizes the SiO₂-poor melt and makes it structurally more similar to the SiO₂-rich melt. However, Ca⁺² and Mg⁺² are not as efficient in a charge balancing capacity as the monovalent K⁺ and Na⁺ cations. The lack of alkalis in this system limits the stability of AlO₄ tetrahedra in the highly polymerized SiO₂-rich melt and results in the preference of Al₂O₃ for the SiO₂-poor melt. The partitioning systematics of Ti are virtually identical to those of Al. It is concluded that Ti occurs in tetrahedral coordination as a network forming species in both the high — and low — SiO immiscible melts.     

Carbon in silicate liquids: the systems NaAlSi3O8-CO2, CaAl2Si2O8-CO2, and KAlSi3O8-CO2

To further our knowledge of the effects of volatile components on phase relationships in aluminosilicate systems, we determined the vapor saturated solidi of albite, anorthite, and sanidine in the presence of CO₂ vapor. The depression of the temperature of the solidus of albite by CO₂ decreases from 30° C at 10 kbar, to 10° C at 20 kbar, to about 0 at 25 kbar, suggesting that the solubility of CO₂ in NaAlSi₃O₈ liquid in equilibrium with solid albite decreases with increasing pressure and temperature. In contrast, CO₂ lowers the temperature of the solidus of anorthite by 30° C at 14 kbar, and by 70dg C at 25 kbar. This contrasting behavior of albite and anorthite is also reflected in the behavior of melting in the absence of volatile components. Whereas albite melts congruently to a liquid of NaAl-Si₃O₈ composition to pressures of 35 kbar, anorthite melts congruently to only about 10 kbar and, at higher pressures, incongruently to corundum plus a liquid that is enriched in SiO₂ and CaO and depleted in Al₂O₃ relative to CaAl₂Si₂O₈.The tendency toward incongruent melting with increasing pressure in albite and anorthite produces an increase in the activity of SiO₂ component in the liquid ( ). We predict that this increases the ratio of molecular CO₂/CO ₃ ^2– in these liquids, but the experimental results from other workers are mutually contradictory. Because of the positive dP/dT of the albite solidus and the negative dP/dT of the anorthite solidus, we propose that a negative temperature derivative of the solubility of molecular CO₂ in plagioclase liquids may partly explain the decrease in solubility of carbon with increasing pressure in near-solidus NaAlSi₃O₈ liquids, which is in contrast to that in CaAl₂Si₂O₈ liquid. Also, reaction of CO₂ with NaAlSi₃O₈ liquid to form CO ₃ ^2– that is complexed with Na⁺ must be accompanied by a change in Al³⁺ from network-former to network-modifier, as Na⁺ is no longer abailable to charge-balance Al³⁺ in a network-forming role. However, when anorthite melts incongruently to corundum plus a CaO-rich liquid, the complexing of CO ₃ ^2– with the excess Ca²⁺ in the liquid does not require a change in the structural role of aluminum, and it may be more energetically favorable.The depression of the temperature of the solidus of sanidine resulting from the addition of CO₂ increases from 50° C at 5 kbar to 170° C at 15 kbar. In marked contrast to the plagioclase feldspars, sanidine melts incongruently to leucite plus a SiO₂-rich liquid up to the singular point at 15 kbar. Above this pressure, sanidine melts congruently, resulting in a decrease in the with increasing pressure in the interval up to 15 kbar. Above this pressure, the congruent melting of sanidine results in a lower and nearly constant relative to those of albite and anorthite, and CO₂ produces a nearly constant freezing-point depression of about 170° C. Because of the low at pressures above the singular point, we infer that most of the carbon dissolves as CO ₃ ^2– , resulting in a low CO₂/ CO ₃ ^2– , but a high total carbon content.The principles derived from the studies of phase equilibria in these chemically simple systems provide some information on the structural and thermal properties of magmas. We propose that the is an important parameter in controlling the speciation of carbon in these feldspathic liquids, but it certainly is not the only factor, and it may be relatively less significant in more complex compositions. In addition, our phase-equilibria approach does not provide direct thermal and structural information as do calorimetry and spectroscopy, but the latter have been used primarily on glasses (quenched liquids) and cannot be used in situ to derive direct information on liquids at elevated pressures, as can our method. Hopefully, the results of all of these approaches can be integrated to yield useful results.Institute of Geophysics and Planetary Physics, Contribution No. 2744     

The compressibility of silicate liquids containing Fe2O3 and the effect of composition,temperature, oxygen fugacity and pressure on their redox states

Ultrasonic longitudinal acoustic velocities in oxidized silicate liquids indicate that the pressure derivative of the partial-molar volume of Fe₂O₃ is the same in iron-rich alkali-, alkaline earth- and natural silicate melt compositions at 1 bar. The dV/dP for multicomponent silicate liquids can be expressed as a linear combination of partial-molar constants plus a positive excess term for Na₂O−Al₂O₃ mixing. Partial-molar properties for FeO and Fe₂O₃ components allow extension of the empirical expression of Sack et al. (1980) to permit the calculation of Fe-redox equilibrium in a natural silicate liquid as a function of composition, temperature, fo₂ and pressure; a more formal thermodynamic expression is presented in the Appendix. The predicted equilibrium fo₂ of natural silicate melts, of fixed oxygen content, closely parallels that defined by the metastable assemblage fayalite+magnetite+β-quartz (FMQ), in pressure-temperature space. A silicate melt initially equilibrated at 3 GPa and FMQ, will remain within approximately 0.5 log₁₀ units of FMQ during its closed-system ascent. Thus, for magmas closed to oxygen, iron-redox equilibrium in crystal-poor pristine glassy lavas represents an excellent probe of the relative oxidation state of their source regions.     

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.     

Equation of state of Fe3+-bearing phase-X

We investigated the high-pressure behaviour of Fe³⁺-bearing hydrous phase-X, (K_1.307Na_0.015)(Mg_1.504Fe _0.373 ³⁺ Al_0.053Ti _0.004 ⁴⁺ )Si₂O₇H_0.36, up to 34?GPa at room temperature by synchrotron X-ray powder diffraction. The lattice parameters behave anisotropically, with the [001] direction stiffer than [100]. In the 10^?4 to 22?GPa pressure range, the axial bulk moduli are K _0a ?=?112(3) GPa and K′?=?4, and K _0c ?=?158(2) GPa and K′?=?4, and the anisotropy of the lattice parameters is β_0c :β_0a ?=?0.71:1. The cell volumes are fitted by a second-order Birch–Murnaghan equation of state giving a bulk modulus of K ₀?=?127(1) GPa and K′?=?4 in the same pressure range. After 22?GPa, a discontinuity in volume and lattice parameters can be recognized. Sample did not become amorphous up to 34?GPa. The coupled substitution K?+?Mg?=?[]?+?Fe³⁺ has only a limited influence on the bulk modulus and structural stability of phase-X.     

Heat capacity of ferrosilite, Fe2Si2O6

The heat capacity of synthetic ferrosilite, Fe₂Si₂O₆, was measured between 2 and 820 K. The physical properties measurement system (PPMS, Quantum Design^®) was used in the low-temperature region between 2 and 303 K. In the temperature region between 340 and 820 K measurements were performed using differential scanning calorimetry (DSC). The C _p data show two transitions, a sharp λ-type at 38.7 K and a small shoulder near 9 K. The λ-type transition can be related to collinear antiferromagnetic ordering of the Fe²⁺ spin moments and the shoulder at 10 K to a change from a collinear to a canted-spin structure or to a Schottky anomaly related to an electronic transition. The C _p data in the temperature region between 145 and 830 K are described by the polynomial $C_{p} {\left[ {\hbox{J\,mol}^{{ - 1}}\,{\hbox{K}}^{{ - 1}} } \right]} = 371.75 - 3219.2T^{{ - 1/2}} - 15.199 \times 10^{5} T^{{ - 2}} + 2.070 \times 10^{7} T^{{ - 3}} $ The heat content [H ₂₉₈ – H ₀] and the standard molar entropy [S ₂₉₈ – S ₀] are 28.6 ± 0.1 kJ mol^?1 and 186.5 ± 0.5 J mol^?1 K^?1, respectively. The vibrational part of the heat capacitiy was calculated using an elastic Debye temperature of 541 K. The results of the calculations are in good agreement with the maximum theoretical magnetic entropy of 26.8 J mol^?1 K^?1 as calculated from the relationship 2*Rln5.     

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     

High-Pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): Comparisons with silicate spinels

High-pressure crystal structures and compressibilities have been determined by x-ray methods for MgAl₂O₄ spinel and its isomorph magnetite, Fe₃O₄. The measured bulk moduli, K, of spinel and magnetite (assuming K′=4) are 1.94±0.06 and 1.86±0.05 Mbar, respectively, in accord with previous ultrasonic determinations. The oxygen u parameter, the only variable atomic position coordinate in the spinel structure (Fd3m, Z=8), decreases with pressure in MgAl₂O₄, thus indicating that the magnesium tetrahedron is more compressible than the aluminum octahedron. In magnetite the u parameter is unchanged, and both tetrahedron and octahedron display the 1.9 Mbar bulk modulus characteristic of the entire crystal. This behavior contrasts with that of nickel silicate spinel (γ-Ni₂SiO₄), in which the u parameter increases with pressure because the silicon tetrahedron is relatively incompressible compared to the nickel octahedron.     

Phase relations between Ca3Fe 2 3 +Si3O12-Fe 3 2 +Fe 2 3 +Si3O12 garnet and CaFeSi2O6-Fe2Si2O6 pyroxene solid solutions

Editorial responsibility: J. Hoefs     

Thermodynamic analysis of the system Fe2O3-FeTiO3

The cluster variation method, in the single prism approximation, is used to model phase relations in the system, Fe₂O₃-FeTiO₃. Ordering in FeTiO₃ is analyzed, and it is shown that the stabilization of FeTiO₃ (relative to mechanical mixing of Fe₂O₃ and Ti₂O₃) includes: (1) a contribution from the redox reaction, Fe³⁺+Ti³⁺→Fe²⁺+Ti⁴⁺ (ΔH _redox～?70kJ mole^?1); and (2) a contribution from ordering (ΔH _OD～?8kJ mole^?1). A theoretical phase diagram is presented and compared with available experimental data. Semiquantitative agreement between theory and experiment (on the location of phase boundaries) is achieved; but, owing to the paucity of experimental data on coexisting phases, these results may be fortuitous.     

Crystal chemistry of Fe3+-bearing (Mg,Fe)SiO3 perovskite: a single-crystal X-ray diffraction study

Magnesium silicate perovskite is the predominant phase in the Earth’s lower mantle, and it is well known that incorporation of iron has a strong effect on its crystal structure and physical properties. To constrain the crystal chemistry of (Mg, Fe)SiO₃ perovskite more accurately, we synthesized single crystals of Mg_0.946(17)Fe_0.056(12)Si_0.997(16)O₃ perovskite at 26 GPa and 2,073 K using a multianvil press and investigated its crystal structure, oxidation state and iron-site occupancy using single-crystal X-ray diffraction and energy-domain Synchrotron Mössbauer Source spectroscopy. Single-crystal refinements indicate that all iron (Fe²⁺ and Fe³⁺) substitutes on the A-site only, where \( {\text{Fe}}^{ 3+ } /\Upsigma {\text{Fe}}\sim 20\,\% \) based on Mössbauer spectroscopy. Charge balance likely occurs through a small number of cation vacancies on either the A- or the B-site. The octahedral tilt angle (Φ) calculated for our sample from the refined atomic coordinates is 20.3°, which is 2° higher than the value calculated from the unit-cell parameters (a = 4.7877 Å, b = 4.9480 Å, c = 6.915 Å) which assumes undistorted octahedra. A compilation of all available single-crystal data (atomic coordinates) for (Mg, Fe)(Si, Al)O₃ perovskite from the literature shows a smooth increase of Φ with composition that is independent of the nature of cation substitution (e.g., \( {\text{Mg}}^{ 2+ } - {\text{Fe}}^{ 2+ } \) or \( {\text{Mg}}^{ 2+ } {\text{Si}}^{ 4+ } - {\text{Fe}}^{ 3+ } {\text{Al}}^{ 3+ } \) substitution mechanism), contrary to previous observations based on unit-cell parameter calculations.     

High-pressure phase transformations in the MgFe2O4 and Fe2O3–MgSiO3 systems

 The crystal structure of MgFe₂O₄ was investigated by in situ X-ray diffraction at high pressure, using YAG laser annealing in a diamond anvil cell. Magnesioferrite undergoes a phase transformation at about 25 GPa, which leads to a CaMn₂O₄-type polymorph about 8% denser, as determined using Rietveld analysis. The consequences of the occurrence of this dense MgFe₂O₄ form on the high-pressure phase transformations in the (MgSi)_0.75(Fe^III)_0.5O₃ system were investigated. After laser annealing at about 20 GPa, we observe decomposition to two phases: stishovite and a spinel-derived structure with orthorhombic symmetry and probably intermediate composition between MgFe₂O₄ and Mg₂SiO₄. At pressures above 35 GPa, we observe recombination of these products to a single phase with Pbnm perovskite structure. We thus conclude for the formation of Mg₃Fe₂Si₃O₁₂ perovskite. Received: 27 March 2000 / Accepted: 1 October 2000     

Electric conductivity of Fe2SiO4–Fe3O4 spinel solid solutions

 The spinel solid solution was found to exist in the whole range between Fe₃O₄ and γ-Fe₂SiO₄ at over 10 GPa. The resistivity of Fe_{3− x} Si _x O₄ (0.0<x<0.288) was measured in the temperature range of 80∼300 K by the AC impedance method. Electron hopping between Fe³⁺ and Fe²⁺ in the octahedral site of iron-rich phases gives a large electric conductivity at room temperature. The activation energy of the electron hopping becomes larger with increasing γ-Fe₂SiO₄ component. A nonlinear change in electric conductivity is not simply caused by the statistical probability of Fe³⁺–Fe²⁺ electron hopping with increasing the total Si content. This is probably because a large number of Si⁴⁺ ions occupies the octahedral site and the adjacent Fe²⁺ keeping the local electric neutrality around Si⁴⁺ makes a cluster, which generates a local deformation by Si substitution. The temperature dependence of the conductivity of solid solutions indicates the Verwey transition temperature, which decreases from 124(±2) K at x=0 (Fe₃O₄) to 102(±5) K at x=0.288, and the electric conductivity gap at the transition temperature decreases with Si⁴⁺ substitution. Received: 15 March 2000 / Accepted: 4 September 2000     

High temperature structural investigation of Na2O·0.5Fe2O3·3SiO2 and Na2O·FeO·3SiO2 melts and glasses

The structure of glasses and melts of Na₂O· 0.5Fe₂O₃·3SiO₂ and Na₂O·FeO·3SiO₂ compositions have been measured using high temperature Raman spectroscopy. For the oxidized sample it has been demonstrated that there is a close structural relationship between melt and glass. No coordination changes of Fe³⁺ with temperature and no new anionic species have been observed in the oxidized melt. The Raman spectra of the reduced sample clearly show a decrease in the degree of polymerization, as determined by the observation of the polarization character of the spectra and the details of the change of the Raman intensities during heating in hydrogen. Mössbauer spectra suggest that Fe³⁺ is tetrahedrally coordinated in the oxidized glass and part of the Fe²⁺ is tetrahedrally coordinated in the reduced glass.     

Effect of Fe3+-bearing point defects on the UV-spectra of two natural olivines

Polarized near-UV spectra have been recorded on 20 μm diameter spots on oriented crystals of microprobe-analyzed olivines from Baikhal Rift, Fa_8.8 (I) and Seberget, Fa_9.3 (II), which have formed under different fO₂ and, therefore, are expected to contain Fe³⁺-bearing point defects in different concentrations. These should be reflected in the UV-spectra of such minerals (Cemic et al. 1986). The spectra obtained confirm these predictions: The difference in α _{Y, 26500} in both samples indicates a difference in Fe³⁺-site fractions of ΔX_Fe. = 1.78-10⁻⁴, which may be related to an fO₂ about ten times higher for the formation of olivine II compared to I.     

Temperature-dependent magnetic susceptibility behaviour of spinelloid and spinel solid solutions in the systems Fe2SiO4–Fe3O4 and (Fe,Mg)2SiO4–Fe3O4

The magnetic behaviour and Curie temperatures (T _C ) of spinelloids and spinels in the Fe₃O₄–Fe₂SiO₄ and Fe₃O₄–(Mg,Fe)₂SiO₄ systems have been determined from magnetic susceptibility (k) measurements in the temperature range –192 to 700 °C. Spinelloid II is ferrimagnetic at room temperature and the k measurements display a characteristic asymmetric hump before reaching a T _C at 190 °C. Spinelloid V from the Mg-free system is paramagnetic at room temperature and hysteresis loops at various low temperatures indicate a ferri- to superparamagnetic transition before reaching the T _{C .} The T _C shows a non-linear variation with composition between –50 and –183 °C with decreasing magnetite component (X _Fe3O₄). The substitution of Mg in spinelloid V further decreases T _C . Spinelloid III is paramagnetic over nearly the total temperature range. Ferrimagnetic models for spinelloid II and spinelloid V are proposed. The T _C of Fe₃O₄–Fe₂SiO₄ spinel solid solutions gradually decrease with increasing Si content. Spinel is ferrimagnetic at least to a composition of X _Fe3O₄=0.20, constraining a ferrimagnetic to antiferromagnetic transition to occur at a composition of X _Fe3O₄<0.20. A contribution of the studied ferrimagnetic phases for crustal anomalies on the Earth can be excluded because they lose their magnetization at relatively low temperatures. However, their relevance for magnetic anomalies on other planets (Mars?), where these high-pressure Fe-rich minerals could survive their exhumation or were formed by impacts, has to be considered.