The heat capacity of two natural chlorite group minerals derived from differential scanning calorimetry

The heat capacity of natural chamosite (X_Fe=0.889) and clinochlore (X_Fe=0.116) were measured by differential scanning calorimetry (DSC). The samples were characterised by X-ray diffraction, microprobe analysis and Mössbauer spectroscopy. DSC measurements between 143 and 623?K were made following the procedure of Bosenick et?al. (1996). The fitted data for natural chamosite (CA) in J?mol^?1?K^?1 give: C _p,CA = 1224.3–10.685?×?10³?×?T ^??0.5???6.4389?× 10⁶?×T ^??2?+?8.0279?×?10⁸?×?T ^??3 and for the natural clinochlore (CE): C _p,CE = 1200.5–10.908?×?10³?×T ^??0.5?? 5.6941?×?10⁶?×?T ^??2?+?7.1166?×?10⁸?×?T ^??3. The corrected C _p-polynomial for pure end-member chamosite (Fe₅Al)[Si₃AlO₁₀](OH)₈ is C _p,CAcor = 1248.3–11.116?× 10³?×?T ^??0.5???5.1623?×?10⁶?×?T ^??2?+?7.1867?×?10⁸×T ^??3 and the corrected C _p-polynomial for pure end-member clinochlore (Mg₅Al)[Si₃AlO₁₀](OH)₈ is C _p,CEcor = 1191.3–10.665?×?10³?×?T ^??0.5???6.5136?×?10⁶?×?T ^??2?+ 7.7206?×?10⁸?×?T ^??3. The corrected C _p-polynomial for clinochlore is in excellent agreement with that in the internally consistent data sets of Berman (1988) and Holland and Powell (1998). The derived C _p-polynomial for chamosite (C _p,CAcor) leads to a 4.4% higher heat capacity, at 300?K, compared to that estimated by Holland and Powell (1998) based on a summation method. The corrected C _p-polynomial (C _p,CAcor) is, however, in excellent agreement with the computed C _p-polynomial given by Saccocia and Seyfried (1993), thus supporting the reliability of Berman and Brown's (1985) estimation method of heat capacities.     

The thermal expansion of ScAlO3 — A silicate perovskite analogue

The crystal structure of ScAlO₃ has been refined at temperatures up to 1100° C on the basis of x-ray powder diffraction data. The thermal expansion is adequately described by a Grüneisen-Debye model with the elastic Debye temperature and an effective Grüneisen parameter of 1.6. The volumetric thermal expansion of 3.0% between 10 and 1100° C, corresponding to a mean thermal expansion coefficient of 2.7 × 10⁻⁵ K⁻¹, is entirely attributable to the expansion of the AlO₆ octahedra. The interoctahedral angles, though not fixed by symmetry, do not vary significantly with temperature —indicating that the expansivities of the constituent AlO₆ and distorted ScO₈ polyhedra are well matched. Similar considerations of polyhedral expansivity suggest thermal expansion coefficients of ∼2 × 10⁻⁵K⁻¹ for cubic CaSiO₃ perovskite and a value between 2 × 10⁻⁵ K⁻¹ and 4 × 10⁻⁵ K⁻¹ for MgSiO₃ perovskite. The lower value is consistent with the reconnaissance measurements for Mg_0.9Fe_0.1SiO₃ (Knittle et al. 1986) below 350° C, with low-temperature measurements of single-crystal MgSiO₃ (Ross and Hazen 1989), and with the results of some recent calculations. The markedly greater expansivity ∼4 × 10⁻⁵ K⁻¹ measured at higher temperatures (350–570° C) by Knittle et al. is inconsistent with the simple Grüneisen-Debye quasiharmonic model and may reflect the marginal metastability of the orthorhombic perovskite phase. Under these circumstances, extrapolation of the measured expansivity is hazardous and may result in the under-estimation of lower mantle densities and the drawing of inappropriate inferences concerning the need for chemical stratification of the Earth's mantle.     

Elasticity of single-crystal MgAl2O4 spinel up to 1273 K by Brillouin spectroscopy

The adiabatic single-crystal elastic constants, C _ij , of stoichiometric magnesium aluminate spinel (MgAl₂O₄) have been measured up to 1273 K by highresolution Brillouin spectroscopy, using a 6-pass tandem Fabry-Pérot interferometer and an argon ion laser (514.5 nm). Two platelet samples were employed for probing the acoustic phonons along [100] and [110] directions by platelet and backscattering geometries. The measured temperature dependences of the elastic moduli show a distinct anomaly at 923 K in the shear modulus C _s = (C₁₁-C₁₂)/2 (along [110] direction) and the longitudinal modulus C₁₁ (along [100] direction). This anomaly is consistent with the order-disorder phase transition, resulting from the atomic exchange between Mg at the tetrahedral site and Al at the octahedral site, which has been well documented recently (Peterson et al. 1991; Millard et al. 1992) by neutron powder diffraction and ²⁷Al magic-angle spinning NMR. The values of the temperature derivatives of v _p , v _s , and K _s , in the temperature range 300–923 K, calculated by the Voigt-Reuss-Hill approximation are -0.40ms^?1 K^?1, -0.26ms^?1 K^?1, and -1.89 x 10^?2GPaK^?1.     

Laboratory simulation of meteoritic noble gases. I. Sorption of xenon on carbon: Trapping experiments

We have studied trapping of radioactive ¹²⁷Xe in three types of carbon: carbon black (lamp black  LB), pyrolyzed polyvinylidene chloride (PVDC), and pyrolyzed acridine (C₁₃H₉N). A total of 86 samples were exposed to Xe at T between 100 and 1000°C, for times between 5 min and 240 hours, at p_xe ~ 5 × 10^?7 atm. Excess gas phase and loosely sorbed Xe were pumped away and the remaining, tightly bound Xe was measured by γ-spectrometry.At 100°C,× >90% of the Xe desorbs within a few minutes' pumping but a small amount remains even after 4000 min. Distribution coefficients for this tightly bound Xe are ~1 × 10^?2, 1 and 10 ccSTP/g atm for LB, acridine and PVDC carbons. The tightly bound Xe consists of two components. One occurs over the entire range 100–1000°C, becoming less abundant at high T; it appears to be physisorbed. The other occurs only at T > 500°C and is probably due to volume diffusion. The adsorbed component in LB has an apparent ΔH between ?2.3 and ?5.7 kcal/mole. The diffused component, which occurs in LB and possibly in acridine carbon, has an activation energy Q = 27 ± 8 kcal/mole and a diffusion coefficient D = 1.3 × 10^?17 cm²/sec at 1000°C. These values are comparable to those found for other types of amorphous carbon (Morrisonet al., 1963; Nakai et al., 1960).The low-T component displays two paradoxical features: low ΔH_ads, in the range for Xe physisorbed on carbon, but exceedingly long adsorption or desorption times (~10³ min at 100–400 or 1000°C). Although these long times seem to suggest a high energy process such as chemisorption, our results are best explained by a model that invokes physisorption within a labyrinth of micropores—of atomic dimensions—known to exist in amorphous carbons. The long adsorption/desorption times reflect either the long distances (~5 cm) Xe atoms must migrate by random walk to enter or leave the labyrinth, or the long times needed for Xe atoms to traverse tight spots or constricted pores that connect interior and exterior surfaces of the carbon (activated entry). Both variants of this model predict long equilibration times for the observed ΔH_ads of ?2 to ?6 kcal/mole. Apparently, xenon can be tightly trapped in carbon without resorting to high-energy bonding or to exotic mechanisms.These results suggest that “planetary” type noble gases in meteorites, located at or near grain surfaces of amorphous carbon, may be trapped by adsorption in micropores, whereas components such as CCFXe, which are uniformly distributed in their carrier phases, may be trapped by mechanisms such as volume diffusion or ion implantation.     

An equation correlating the solubility of quartz in water from 25° to 900°C at pressures up to 10,000 bars

The solubility of quartz in water from 25° to 900°C at specific volume of the solvent ranging from about 1 to 10 and from 300° to 600°C at specific volume of the solvent ranging from about 10 to 100 is given by an empirically derived equation of the form: log m = A + B(log V) + C(log V)² where m is the molal silica concentration, V is the specific volume of pure water, and A = ?4.66206 + 0.0034063T + 2179.7T^?1 ? 1.1292 × 10⁶T^?2 + 1.3543 × 10⁸T^?3B = ?0.0014180T— 806.97T^?1C = 3.9465 × 10^?4T T is temperature in kelvins. The experimental data used in formulating the empirical relation ranged in pressure from 1 bar at 25°C to about 10,000 bars at 900°C, and the lowest pressure in the low-density steam region was about 30 bars. According to the above equation, the average difference in molality between 518 measured and calculated solubilities is ?0.016 m with a standard deviation of 0.089.     

The Mg2GeO4 olivine-spinel phase transition

Enthalpies and entropies of transition for the Mg₂GeO₄ olivine-spinel transformation have been determined from self-consistency analyses of Dachille and Roy's (1960), Hensen's (1977) and Shiota et al.'s (1981) phase boundary studies. When all three data sets are analyzed simultaneously,ΔH ₉₇₃ andΔS ₉₇₃ are constrained between ?14000 to ?15300 J mol^?1 and ?13.0 to ?14.1·J mol^?1 K^?1, respectively. High-temperature solution calorimetric experiments completed on both polymorpha yield a value of ?14046±1366 J mol^?1 forΔH ₉₇₃. Kieffer-type lattice vibrational models of Mg₂GeO₄ olivine and spinel based on newly-measured infrared and Raman spectra predict a value of ?13.3±0.6 J mol^?1 K^?1 forΔS ₁₀₀₀. The excellent agreement between these three independent determinations ofΔH andΔS suggests that the synthesis runs of Shiota et al. (1981) at high pressures and temperatures bracket equilibrium conditions. In addition, no configurational disorder of Mg and Ge was needed to obtain the consistent parameters quoted. The Raman spectrum and X-ray diffractogram show that little disorder, if any, is present in Mg₂GeO₄ spinel synthesized at 0.2 GPa and 973–1048 K.     

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     

Carbon isotopic thermometry calibrated by dolomite-calcite solvus temperatures

The temperature dependence of carbon isotopic fractionations between calcite and graphite, and between dolomite and graphite are calibrated by the calcite-dolomite solvus geothermometry using marbles collected from the contact metamorphic aureole in the Kasuga area, central Japan. The carbon isotopic fractionations (Δ¹³C_Cc-Gr and Δ¹³C_DoGr) systematically decrease with increasing metamorphic temperature. The concordant relationships between the fractionations and solvus temperatures are approximately linear with T^?2 over the temperature range. 400° to 680°C: Δ¹³C_CcGr (%.) = 5.6 × 10⁶ × T^?2 (K) ? 2.4 Δ¹³C_DoGr (%.) = 5.9 × 10⁶ × T^?2 (K) ? 1.9 These systematic relationships between fractionation and temperature suggest that carbon isotopic equilibria between carbonates and graphite were attained in many cases. The equation for the calcite-graphite system has a slope steeper than Bottinga's (1969) results. It is, however, in good agreement with that of Valley and O'Neil (1981) in the temperature range from 600° to 800°C.Because of the relatively high sensitivity to temperature, these isotopic geothermometers are useful for determining the temperatures in moderate- to high-grade metamorphosed carbonate rocks.     

The thermal expansion of anhydrite to 1000° C

The thermal expansion of anhydrite, CaSO₄, has been measured from 22° to 1,000° C by X-ray diffraction, using the Guinier-Lenné heating powder camera. The heating patterns were calibrated with Guinier-Hägg patterns at 25° C, using quartz as internal standard. Heating experiments were run on natural anhydrite (Bancroft, Ontario), which at room temperature has lattice constants in close agreement with those of synthetic material. The orthorhombic unit cell at 22° C (space group Amma) has a=7.003 (1) Å, b=6.996 (2) Å and c=6.242 (1) Å, V=305.9 (2) ų. At room temperature, the thermal expansion coefficients α and β (α in °C^?1×10⁴, β in °C^?2×10⁸) are for a, 0.10, ?0.69; for b, 0.08, 0.19; for c, 0.18, 1.60; for V, 0.37, 1.14. Second-order coefficients provide an excellent fit over the whole range to 1,000° C.     

Thermal decarboxylation of acetic acid: Implications for origin of natural gas

Laboratory experiments on the thermal decarboxylation of solutions of acetic acid at 200°C and 300°C were carried out in hydrothermal equipment allowing for on-line sampling of both the gas and liquid phases for chemical and stable-carbon-isotope analyses. The solutions had ambient pH values between 2.5 and 7.1; pH values and the concentrations of the various acetate species at the conditions of the experiments were computed using a chemical model.Results show that the concentrations of acetic acid, and not total acetate in solution, control the reaction rates which follow a first order equation based on decreasing concentrations of acetic acid with time. The decarboxylation rates at 200°C (1.81 × 10^?8 per second) and 300°C (8.17 × 10^?8 per second) and the extrapolated rates at lower temperatures are relatively high. The activation energy of decarboxylation is only 8.1 kcal/mole. These high decarboxylation rates, together with the distribution of short-chained aliphatic acid anions in formation waters, support the hypothesis that acid anions are precursors for an important portion of natural gas.Results of the δ¹³C values of CO₂, CH₄, and total acetate show a reasonably constant fractionation factor of about 20 permil between CO₂ and CH₄ at 300°C. The δ¹³C values of CO₂ and CH₄ are initially low and become higher as decarboxylation increases.     

Temperature independent thermal expansivities of calcium aluminosilicate melts between 1150 and 1973 K in the system anorthite-wollastonite-gehlenite (An-Wo-Geh): A density model

The thermal expansivities of 10 compositions from within the anorthite-wollastonite-gehlenite (An-Wo-Geh) compatibility triangle have been investigated using a combination of calorimetry and dilatometry on the glassy and liquid samples. The volumes at room temperature were derived from densities measured using the Archimedean buoyancy method. For each sample, density was measured at 298 K using glass that had a cooling-heating history of 10-10 K min⁻¹. The thermal expansion coefficient of the glass from 298 K to the glass transition interval was measured by a dilatometer and the heat capacity was measured using a differential scanning calorimeter from 298 to 1135 K. The thermal expansion coefficient and the heat flow were determined at a heating rate of 10 K min⁻¹ on glasses which were previously cooled at 10 K min⁻¹. Supercooled liquid density, molar volume and molar thermal expansivities were indirectly determined by combining differential scanning calorimetric and dilatometric measurements assuming that the kinetics of enthalpy and shear relaxation are equivalent. The data obtained on supercooled liquids were compared to high-temperature predictions from the models of (Lange, R.A., Carmichael, I.S.E., 1987. Densities of Na₂O-K₂O-CaO-MgO-FeO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂ liquids: New measurements and derived partial molar properties. Geochim. Cosmochim. Acta51, 2931-2946; Courtial, P., Dingwell, D.B., 1995. Nonlinear composition dependence of molar volume of melts in the CaO-Al₂O₃-SiO₂ system. Geochim. Cosmochim. Acta59 (18), 3685-3695; Lange, R.A., 1997. 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. Contrib. Mineral. Petrol.130, 1-11). The best linear fit combines the supercooled liquid data presented in this study and the high temperature data calculated using the Courtial and Dingwell (1995) model. This dilatometric/calorimetric method of determining supercooled liquid molar thermal expansivity greatly increases the temperature range accessible for thermal expansion. It represents a substantial increase in precision and understanding of the thermodynamics of calcium aluminosilicate melts. This enhanced precision demonstrates clearly the temperature independence of the melt expansions in the An-Wo-Geh system. This contrasts strongly with observations for neighboring system such as anorthite-diopside and raises the question of the compositional/structural origins of temperature dependence of thermal expansivity in multicomponent silicate melts.     

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ₀=3.823(1) g/cm³ . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.     

High-pressure behaviour and equation of state of calcite, CaCO3

The high-pressure response of the cell parameters of calcite, CaCO₃, has been investigated by single crystal X-ray diffraction. The unit cell parameters have been refined from 0 to 1.435?GPa, and the linear and volume compressibilities have been measured as β _a =2.62(2)?×?10^?3?GPa^?1,β _c =7.94(7)?×?10^?3?GPa^?1, β _v =13.12?×?10^?3?GPa^?1. The bulk modulus has been obtained from a fit to the Birch-Murnaghan equation of state, giving K ₀=73.46?±?0.27?GPa and V ₀=367.789 ±?0.004?ų with K′=4. Combined with earlier data for magnesite, ankerite and dolomite, these data suggest that K ₀ V ₀ is a constant for the Ca-Mg rhombohedral carbonates.     

Crystal structure, Raman and FTIR spectroscopy, and equations of state of OH-bearing MgSiO3 akimotoite

MgSiO₃ akimotoite is stable relative to majorite-garnet under low-temperature geotherms within steeply or rapidly subducting slabs. Two compositions of Mg–akimotoite were synthesized under similar conditions: Z674 (containing about 550 ppm wt H₂O) was synthesized at 22 GPa and 1,500 °C and SH1101 (nominally anhydrous) was synthesized at 22 GPa and 1,250 °C. Crystal structures of both samples differ significantly from previous studies to give slightly smaller Si sites and larger Mg sites. The bulk thermal expansion coefficients of Z674 are (153–839 K) of a ₁ = 20(3) × 10^?9 K^?2 and a ₀ = 17(2) × 10^?6 K^?1, with an average of α ₀ = 27.1(6) × 10^?6 K^?1. Compressibility at ambient temperature of Z674 was measured up to 34.6 GPa at Sector 13 (GSECARS) at Advanced Photon Source Argonne National Laboratory. The second-order Birch–Murnaghan equation of state (BM2 EoS) fitting yields: V ₀ = 263.7(2) Å³, K _T0 = 217(3) GPa (K′ fixed at 4). The anisotropies of axial thermal expansivities and compressibilities are similar: α _a  = 8.2(3) and α _c  = 10.68(9) (10^?6 K^?1); β _a  = 11.4(3) and β _c  = 15.9(3) (10^?4 GPa). Hydration increases both the bulk thermal expansivity and compressibility, but decreases the anisotropy of structural expansion and compression. Complementary Raman and Fourier transform infrared (FTIR) spectroscopy shows multiple structural hydration sites. Low-temperature and high-pressure FTIR spectroscopy (15–300 K and 0–28 GPa) confirms that the multiple sites are structurally unique, with zero-pressure intrinsic anharmonic mode parameters between ?1.02 × 10^?5 and +1.7 × 10^?5 K^?1, indicating both weak hydrogen bonds (O–H···O) and strong OH bonding due to long O···O distances.     

The thermal expansion of synthetic aluminosilicate-sodalites,M 8(Al6Si6O24)X 2

Thermal expansion data, determined by powder X-ray diffraction methods are presented for 11 members of the (Li,Na,K,Rb)₈(Al₆Si₆O₂₄)Cl₂ solid solution series, 3 members of the (Na,K)₈(Al₆Si₆O₂₄)Br₂ solid solution series and Na₈(Al₆Si₆O₂₄)I₂. Only the latter showed a discontinuity in its expansion curve at 810° C wigh a mean linear expansion coefficient of 22.0×10^?6 °C^?1 below and 7.7×10^?6 °C^?1 above the discontinuity. The mean expansion coefficients from 0° to 500° C decrease gradually over the range of room temperature cell edges from 8.4 to 8.89 Å, then increase up to a cell edge of 9.01 Å above which they decrease sharply and extrapolate to a zero coefficient at 9.4 Å. These variations may be related to the expansion characteristics of the bonds between the cavity cations and cavity anions in different sodalites. The aluminosilicate-sodalites which show a discontinuity in their thermal expansion curves are those with large cavity anions, I^? or SO ₄ ^2? ; the discontinuity is believed to occur at the point when the x-coordinate of the cavity cation becomes 0.25.     

Compositional zoning in garnet and kinetics of metamorphic crystallization

The kinetics of zoned garnet porphyroblast growth is exemplified in a sample of garnet-staurolite-biotite schist from the northern Ladoga region. The diffusion-controlled porphyroblast growth was accompanied by a decrease in the kinetic coefficient during phase reactions. Even at insignificant (1–2°C) thermal overstepping, the leading role of diffusion as a factor that controls kinetics of porphyroblast growth in medium-grade metapelites is consistent with the parameters of metamorphic crystallization: T = 500–650°C, t = 1 Ma; D _A1 ^app = 10^?14 cm²/s, L = 0.2–0.6 cm, r = 1–3 mm, ΔC _Al = 1.5 × 10^?4–1.5 × 10^?3 mol/cm³.     

The thermodynamic properties and phase relations of some minerals in the system CaO-AI2O3-SiO2-H2O

The heat capacities of lawsonite, margante, prehnite and zoisite have been measured from 5 to 350 K with an adiabatic-shield calorimeter and from 320 to 999.9 K with a differential-scanning calorimeter. At 298.15 K, their heat capacities, corrected to end-member compositions, are 66.35, 77.30, 79.13 and 83.84 cal K^?1 mol^?1; their entropies are 54.98, 63.01, 69.97 and 70.71 cal K^?1 mol^?1, respectively. Their high-temperature heat capacities are described by the following equations (in calories, K, mol): Lawsonite (298–600 K): Cp° = 66.28 + 55.95 × 10^?3T ? 15.27 × 10⁵T^?2 Margarite (298–1000 K): Cp° = 101.83 + 24.17 × 10^?3T ? 30.24 × 10⁵T^?2 Prehnite (298–800 K): Cp° = 97.04 + 29.99 × 10^?3T ? 25.02 × 10⁵T^?2 Zoisite (298–730 K): Cp° = 98.92 + 36.36 × 10^?3T ? 24.08 × 10⁵T^?2 Calculated Clapeyron slopes for univariant equilibria in the CaO-Al₂O₃-SiO₂-H₂O system compare well with experimental results in most cases. However, the reaction zoisite + quartz = anorthite + grossular + H₂O and some reactions involving prehnite or margarite show disagreements between the experimentally determined and the calculated slopes which may possibly be due to disorder in experimental run products. A phase diagram, calculated from the measured thermodynamic values in conjunction with selected experimental results places strict limits on the stabilities of prehnite and assemblages such as prehnite + aragonite, grossular + lawsonite, grossular + quartz, zoisite + quartz, and zoisite + kyanite + quartz. The presence of this last assemblage in eclogites indicates that they were formed at moderate to high water pressure.     

Ionic conductivity in sodium magnesium silicates

Na₂MgSiO₄ crystals prepared hydrothermally at 700° C and 3,000 atm are related to carnegieite with SG Pmn2₁, a=7.015(2), b=10.968(2), and c=5.260(1). Na conductivity in Na₂MgSiO₄ is 3.0×10^?5 (ohm-cm)^?1 at 300° C but can be raised to 1.1×10^?3 (ohm-cm)^?1 by creating Na vacancies in the composition Na_1.9Mg_0.9Al_0.1O₄. Na₄Mg₂Si₃O₁₀ is also a cristobalite-related carnegieite with the orthorhombic cell a=10.584(7), b=14.328(7), and c=5.233(5). The Na conductivity of Na₄Mg₂Si₃O₁₀ is 4.8×10^?3 (ohm-cm)^?1 at 300° C.     

Deviation of the arrival-time delay of pulses for the Crab pulsar from a quadratic frequency region

Our measurements of the arrival-time delays of radio pulses from the Crab pulsar, PSR B0531+21, at low frequencies 111, 63, and 44 MHz revealed additional delays compared to the usual quadratic frequency relation, Δt(v) ∝ v ^?2. These additional delays are 65 ms between 63 MHz and 111 MHz—i.e., a factor of two longer than the pulsar’s period, i.e., a factor of five longer than the pulsar period—and cannot be explained by the “twisting” of the magnetic-field lines by the rotation of the pulsar. We suggest the model in which a previously unknown high-density plasma layer with a high electron concentration is present along the line of sight in the Crab nebula, causing an additional frequency-dependent delay of the observed radio pulses at low frequencies due to the contribution of the n _e ² v ^?4 term in the dispersion-delay formula. The parameters of this inferred layer have been derived: emission measure EM ? 4 × 10⁶ pc/cm⁶, electron density n _e ? 10⁶ cm^?3, depth along the line of sight d ? 4 × 10^?6 pc, and electron temperature T _e ≥ 2 × 10⁶ K.