Constraints on the thermodynamic mixing properties of plagioclase feldspars

Taking account of the Cˉ1/Iˉ1 (Al/Si order/disorder) transformation at high temperatures in the albite-anorthite solid solution leads to a simple model for the mixing properties of the high structural state plagioclase feldspars. The disordered (Cˉ1) solid solution can be treated as ideal (constant activity coefficient) and, for anorthite-rich compositions, deviations from ideality can be ascribed to cation ordering. Values of the activity coefficient for anorthite in the Cˉ1 solid solution (γ _An ^Cˉ1 ) are then controlled by the free energy difference between Cˉ1 and Iˉ1 anorthite at the temperature (T) of interest according to the relation: ΔˉG _ord ^Iˉ1 ⇌Cˉ1 =RT ln γ _An ^Cˉ1 . If the Iˉ1⇌Cˉ1 transformation in pure anorthite is treated, to a first approximation, as first order and the enthalpy and entropy of ordering are taken as 3.7±0.6 kcal/mole (extrapolated from calorimetric data) and 1.4–2.2 cal/mole (using an equilibrium order/disorder temperature for An₁₀₀ of 2,000–2,250 K), a crude estimate of γ _An ^Cˉ1 for all temperatures can be made. The activity coefficient of albite in the Cˉ1 solid solution (γ _Ab ^Cˉ1 ) can be taken as 1.0. The possible importance of this model lies in its identification of the principal constraints on the mixing properties rather than in the actual values of γ _An ^Cˉ1 and γ _Ab ^Cˉ1 obtained. In particular it is recognised that γ _An ^Cˉ1 depends critically on ordering in anorthite as well as, at lower temperatures, any ordering in the Cˉ1 solid solution. A brief review of activity-composition data, from published experiments involving ranges of plagioclase compositions and from the combined heats of mixing plus Al-avoidance entropy model (Newton et al. 1980), reveals some inconsistencies. The values of γ _An ^Cˉ1 calculated using the approach of Newton et al. (1980), although consistent with Orville's (1972) ion exchange data, are slightly lower than values derived from experiments by Windom and Boettcher (1976) and Goldsmith (1982) or from ion-exchange experiments of Kotel'nikov et al. (1981). Based on the Cˉ1/Iˉ1 transformation model, values of γ _An ^Cˉ1 <1.0 are unlikely. Discrepancies between the experimental data sets are attributed to incomplete (non-equilibrium) Al/Si order attained during the experiments. It is suggested that the choice of activity coefficients remains somewhat subjective. The development of accurate mixing models would be greatly assisted by better thermodynamic data for ordering in pure anorthite and by more thorough characterisation of the state of order in plagioclase crystals used for phase equilibrium experiments.     

The thermodynamic properties of radium

The enthalpy, Gibbs free energy, and entropies of aqueous radium species and radium solids have been evaluated from empirical data, or estimated when necessary for 25°C and 1 bar. Estimates were based on such approaches as extrapolation of the thermodynamic properties of Ca, Sr, and Ba complexes and solids plotted against cationic radii and charge to radius functions, and the use of the Fuoss or electrostatic mathematical models of ion pair formation (Langmuir, 1979). Resultant log K (assoc) and ΔH⁰ (assoc) (kcal/mol) values are: for RaOH⁺ 0.5 and 1.1; RaCl⁺ ?0.10 and 0.50; RaCO⁰₃ 2.5 and 1.07; and RaSO⁰₄ 2.75 and 1.3. Log Ksp and ΔH⁰ (dissoc) (kcal/mol) values for RaCO₃(c) and RaSO₄(c) are ?8.3 and ?2.8, and ?10.26 and ?9.4, respectively.Trace Ra solid solution in salts of Pb and of the lighter alkaline earths, has been appraised based on published distribution coefficient (D) data, where D ～- (mM²⁺)(N_RaX)/(mRa²⁺)(N_MX) (m and N are the aqueous molality and mole fraction of Ra and cation M in salt X, respectively. The empirical solid solution data have been used to derive both enthalpies and Gibbs free energies of solid solution of trace Ra in sulfate and carbonate minerals up to 100°C. Results show that in every case D values decrease with increasing temperature. Among the sulfate and carbonate minerals, D values decrease for the following minerals in the order: anhydrite > celestite > anglesite > barite > aragonite > strontianite > witherite > cerussite.     

Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines

Existing data on the temperature and composition dependence of the Fe²⁺-Mg²⁺ distribution between Fe-Mg olivine and orthopyroxene, the intra-crystalline distribution of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxene, and macroscopic activity-composition relations in olivine and orthopyroxene are shown to be inconsistent with generally accepted thermodynamic formulations which assume that the non-configurational Gibbs energy of orthopyroxene is independent of the degree of long-range ordering of Fe²⁺ and Mg⁺ between M1 and M2 sites. These data are interpreted in terms of the constraints they provide on the size of Bragg-Williams type energy, entropy, and volume terms for olivine and orthopyroxene. The apparent equilibrium constant for Fe-Mg exchange between olivine and orthopyroxene is shown to be a potentially useful ‘geothermometer’ for olivine-orthopyroxene assemblages with olivines with mole fraction of Fe₂SiO₄ component less than 0.2 or greater than 0.6. A provisional calibration of this ‘geothermometer’ is presented.     

High-temperature thermodynamic properties of alkali feldspars

Recent hydrofluoric acid solution calorimetric data are used to derive standard enthalpies and Gibbs free energies of formation of low-albite, high-albite, NaAlSi₃O₈ glass, microcline, sanidine, and KAlSi₃O₈ glass. The data are presented as high-temperature functions from 298.15 to 1400° K.     

Calculated thermodynamic properties of silica polymorphs

Accurate interatomic potentials have been employed to compute the phonon density of states of αquartz, stishovite and coesite polymorphs of silica. The temperature variation of several thermodynamic properties is calculated by using the phonon density of states to describe the vibrational entropy contribution to the free energy. Results for these polymorphs are in surprisingly good agreement with available experimental data. Moreover, the microscopic origin of quantitative differences in the heat capacity behavior of low and high density polymorphs is established.     

The thermodynamic properties of reciprocal solid solutions

A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: $$\Delta G^0 = (\mu _{AX}^0 + \mu _{BY}^0 - \mu _{AY}^0 - \mu _{BX}^0 = 0$$ applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG ⁰ contributes terms of the following form to the activity coefficients of the constituent components: $$RT\ln \gamma _{AX} = - X_{B_1 } X_{Y_2 } \Delta G^0$$ (X _Ji refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the “cross-site” or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: $$\Delta G^0 \ll zn_1 RT$$ where z is the number of nearest-neighbour (X, Y) sites around A and n ₁ is the number of (A, B) sites in the formula unit. If ΔG ⁰ is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): $$\gamma _{AX} = \left( {\frac{{1 - X'_{Y_2 } }}{{1 - X_{Y_2 } }}} \right)^{zn_1 }$$ where X′_Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved.     

Fluid-mineral equilibria and thermodynamic mixing properties of fluid systems

The paper presents a review of an experimental method to quantitatively constrain thermodynamic mixing properties of fluid systems at high temperature T and pressure P. The method is based on bracketing equilibrium parameters of simple fluid-mineral reactions. Experimental data obtained with this technique for the H₂O-CO₂, H₂O-N₂, and H₂O-H₂ binary systems were utilized to calculate mixing parameters corresponding to the simplified van Laar model W ₁₂ ^VL , according to which the equation for the integral excess Gibbs free energy of a binary mixture G ^ex is G ^ex =X ₁ X ₂ W ₁₂ ^VL /(X ₁ V ₁ ⁰ + X ₂ V ₂ ⁰ ), where X _i is the mole fractions of the components, and V _i ⁰ are pure species molar volumes at given P and T (in cm³). The W ₁₂ ^VL for the three mixtures correspond to 202, 219, and 331 kJ cm³/mol. The empirical correlation $W_{H_2 O - X}^{VL}$ (kJ cm³/mol) = 887.012 Q _X ? 16.674, where Q = P _c (critical pressure, bar)/T _c (critical temperature, K) for gas X (where X = CH₄, CO, H₂S, O₂, Ar, and NH₃) is used to evaluate the van Laar parameters for a number of petrologically important water-gas mixtures. The H₂O-H₂ system is characterized by the greatest positive deviation from the ideal mixing and can thus decompose into two immiscible fluid phases under the P-T parameters typical of deep lithospheric zones. The exsolution of the H₂O-CO₂ and H₂O-N₂ systems is expected to occur only under high pressure and low temperature. This combination of parameters may be expected only in the environments of cold subduction. Salts (highly soluble simple salts and/or silicates) should significantly expand the exsolution regions in petrologically important fluids.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

冻融循环作用下黄土无侧限抗压强度和微观规律的试验研究

青海地处多年冻土地区,属于青藏高原大陆性气候带,冻融循环是路基和地基基础的一种常见破坏因素,为研究冻融循环作用对青海地区实际工程的影响,揭示冻融循环作用对其损害的机理,通过对青海西宁地区原状黄土和重塑黄土进行冻融循环试验、无侧限抗压强度试验和电镜扫描试验,分析不同冻融温度和不同冻融循环次数对原状黄土、重塑黄土无侧限抗压强度和微观结构的影响。结果表明：当黄土经历0～6次冻融循环时,原状黄土和重塑黄土的强度逐渐降低,而8～10次冻融循环后其强度先增大后趋于稳定;原状黄土的强度随冻融温度降低而降低,而重塑黄土的强度随冻融温度降低先增大后减小;从微观角度分析,冻融温度的降低和冻融循环次数的增加,均导致黄土大颗粒逐渐分解为小颗粒,颗粒的排列方式发生改变。     

The thermodynamic properties of pyrrhotite and pyrite: A re-evaluation

On a plot of log sulfur activity versus inverse absolute temperature, the variation in published pyrite/pyrrhotite curves below 500°C is larger than expected from the precision of the measurements. The precise data by Rau (1976) fall between interpretations by Scott and Barnes (1971) and by Toulmin and Barton (1964) and are recommended.Scott and Barnes calibrated sulfur fugacities in the system Fe-Zn-S, against the data of Toulmin and Barton, but this involved a double extrapolation of empirical relationships, to and from a region where fugacities in pyrrhotite are unmeasured. Regular-solution models offer no improvement. An apparent interruption in the properties of the high-temperature pyrrhotite solid solution, at the composition Fe₇S₈ (Powell, 1983) is probably due to the inclusion of metastable microdomains of monoclinic pyrrhotite in some of Rau's experimental runs, rather than to an equilibrium change of structure. Hence, the uncertainties of extrapolation are unlikely to account for the displacement of the pyrite/pyrrhotite curve of Scott and Barnes. There may be a systematic error in the composition of pyrrhotite inferred by Scott and Barnes from X-ray lattice spacings, due to the effects of preparation-dependent ordering.Other influences on pyrrhotite thermodynamics are discussed. There is a maximum in the pyrrhotite fundamental unit-cell parameter, “a,” as composition is changed. This maximum shifts towards the Fe-rich boundary of pyrrhotite as temperature is increased, so it suggests a contribution from intrinsic defects, even at low temperatures. The thermodynamic effects of pressure need recalculating to suit these unit-cell data.     

基于假三元模型的透辉石-硬玉固溶体热力学性质计算

自然界中矿物多以固溶体形式存在,据其晶体化学特征计算热力学性质是开展矿物成因理论研究的基础。本文引入描述二元矿物固溶体热力学性质的假三元模型,计算得到了透辉石-硬玉固溶体系列的热力学性质。该模型通过构造一种高度有序的中间相,同时考虑长程和短程有序效应,基于热力学平衡态矿物固溶体自由能最低的规律,可以计算特定组分下矿物的平衡自由能、焓和熵等热力学参数。本文针对透辉石-硬玉固溶体体系,取绿辉石为其中间有序态,计算了其活度-成分关系和温度-组分相图等,发现绿辉石随温度升高的有序无序相变为一级相变,相变温度为1 148±25 K,与实验研究结果一致。本文获得的透辉石-绿辉石-硬玉体系的热力学参数可用于视剖面图方法研究MORB成分的岩石的榴辉岩相变质作用过程。     

Scaling of thermodynamic mixing properties in garnet solid solutions

 The volumes and enthalpies of mixing, ΔV ^Mix and ΔH ^Mix, of binary solid-solution aluminosilicate garnets have been studied by computer simulation. The use of “average atoms” to simulate solid solution was found to give results that are considerably different from those obtained by calculating and averaging over many configurations of cations at a given composition. Although we expect mineral properties calculated from model calculations to be correct only on a qualitative rather than a quantitative scale, fair agreement with experiment was obtained where carefully tested potential parameters were used. The results show that mixing behaviour in these materials is controlled by local strain and relaxation effects resulting from the atomic size mismatch of the mixing divalent cations. In particular, ΔV ^Mix and ΔH ^Mix are shown to scale quadratically with the volume difference between the end members, and to vary essentially symmetrically with composition, with a moderate dependence on the degree and nature of cation order. We conclude that computer modelling should be useful in providing detailed qualitative information about the mixing properties of solid solutions, which can help to better constrain and interpret experimental results. Received: 8 March 2000 / Accepted: 1 October 2000