Thermodynamic mixing properties of olivine derived from lattice vibrations

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe₂SiO₄. This semi-empirical technique is based on an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict thermodynamic mixing properties of olivine (Mg,Fe)₂SiO₄ solid solutions by using results of our previous work on the system MgO–SiO₂. Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium–iron solid solutions of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity for temperatures below 100 K.     

Applications of the SW96 formulation in the thermodynamic calculation of fluid inclusions and mineral-fluid equilibria

The SW96 formulation explicit in Helmholtz free energy proposed by Span and Wagner (1996) is the most accurate multifunction equation of state of CO₂ fluid, from which all thermodynamic properties can be obtained over a wide temperature-pressure range from 216.592 to 1100 K and from 0 to 8000 bar with or close to experimental accuracy. This paper reports the applications of the SW96 formulation in fluid inclusions and mineral-fluid equilibria. A reliable and highly efficient algorithm is presented for the saturated properties of CO₂ so that the formulation can be conveniently applied in the study of fluid inclusions, such as calculation of homogenization pressures, homogenization densities (or molar volumes), volume fractions of vapor phase and isochores. Meanwhile, the univariant curves of some typical decarbonation reactions of minerals are calculated with the SW96 formulation and relevant thermodynamic models of minerals. The computer code of the SW96 formulation can be obtained from the corresponding author.     

莫尔包络线对数模型方程的建立与应用

从研究岩石破坏机理着手,结合室内相关岩石力学试验,建立莫尔包络线对数模型方程,并对其进行参数率定,得出应用范围、变化趋势和岩石的破坏机制,简化岩石破坏强度的研究,可推广到其它的岩石力学实验中。     

Equations of state of magnesium silicates anhydrous B and superhydrous B

High-pressure single crystal X-ray diffraction experiments of phase anhydrous B and superhydrous B have been carried out to 7.3 and 7.7?GPa, respectively, at room temperature. Fitting a third-order Birch-Murnaghan equation of state to the P-V data yields values of V ₀?=?838.86?±?0.04?ų, K_T,0?=?151.5?±?0.9?GPa and K′?=?5.5?±?0.3 for Anhy-B and V ₀?=?624.71?± 0.03?ų, K_T,0?=?142.6?±?0.8?GPa and K′?=?5.8?±?0.2 for Shy-B. A similar analysis of the axial compressibilities in Anhy-B reveals that the c-axis is most compressible (K_c?=?137?±?3?GPa), the b-axis is least compressible (K_b?=?175?±?4?GPa), and the a-axis is intermediate (K_a?=?148?±?1?GPa). In Shy-B, the a-axis is most compressible (K_a?=?135?±?1?GPa), followed by the b- and c-axes which have similar compressibilities (K_b?=?146?±?3?GPa; K_c?=?148?±?3?GPa). The fact that the b-axis of Shy-B is approximately 16% more compressible than Anhy-B is primarily due to differences in the O-T layer in which the H atoms are located and the linkages with the adjacent O layers. The rigid edge-sharing chains of MgO₆ and SiO₆ octahedra in the O layer control compressibility along the a- and c-axes in both structures. The net result is a reduction in the overall anisotropic compression from ～22% in Anhy-B to ～9% in Shy-B.     

P - V - T equation of state of stishovite to the mantle transition zone conditions

In-situ synchrotron X-ray diffraction experiments were conducted using the SPEED-1500 multi-anvil press of SPring-8 on stishovite SiO₂ and pressure-volume-temperature data were collected at up to 22.5 GPa and 1,073 K, which corresponds to the pressure conditions of the base of the mantle transition zone. The analysis of room-temperature data yielded V₀=46.56(1) ų, K_{T 0}=296(5) GPa and K _T =4.2(4), and these properties were consistent with the subsequent thermal equation of state (EOS) analyses. A fit of the present data to high-temperature Birch-Murnaghan EOS yielded (K_T /T) _P =–0.046(5) GPa K^–1 and = a + bT with values of a =1.26(11)×10^–5 K^–1 and b =1.29(17)×10^–8 K^–2. A fit to the thermal pressure EOS gives ₀=1.62(9)×10^–5 K^–1, ( K _T / T) _V =–0.027(4) GPa K^–1 and (²P /T ²) _V =27(5)×10^–7 GPa K^–2. The lattice dynamical approach by Mie-Grüneisen-Debye EOS yielded ₀=1.33(6), q =6.1(8) and ₀=1160(120) K. The strong volume dependence of the thermal pressure of stishovite was revealed by the analysis of present data, which was not detectable by the previous high-temperature data at lower pressures, and this yields ( K _T / T) _V 0 and q 1. The analyses for the fictive volume for a and c axes show that relative stiffness of c axis to a axis is similar both on compression and thermal expansion. Present EOS enables the accurate estimate of density of SiO₂ in the deep mantle conditions.     

An Alternative Approach to the Parameterization the Momentum Flux Over the Sea

In this study we search for the optimal wave parameters characterizing the effect of waves on the air–sea momentum flux. When an attempt using traditional statistics failed to give an unequivocal answer, we applied a neural network approach. This led to a clear choice for the optimal parameters viz. the wind speed at a level equal to the wave height and the wavelength at the peak of the spectrum. With this set we could find a dimensionally correct parameterization that gave a close fit to our stress data, obtained in the southern North Sea. A comparison with open ocean data gave comparable results, allowing a generally applicable formulation. Wave breaking could explain the remaining small differences between the two sets of stress data.     

波向对变风向的响应

由能量平衡方程导出匀质波场局地风生浪平均波向对变风向的响应。结果表明,响应的时间尺度不但取决于波能的成长速率,还取决于方向分布函数和风向与平均波向之夹角。按文圣常提出的在局地风作用下的标准风浪成长曲线,对其响应时间尺度的定量估计结果表明,本文提出的无因次响应时间尺度与无因次能量和无固次峰频率的关系,与现已提出的模式比较与实测更符合。     

First-principles simulation of high-pressure polymorphs in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>

We have used density functional theory to investigate the stability of MgAl₂O₄ polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl₂O₄ polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did not observe a stability field for a hexagonal phase or periclase + Rh₂O₃(II)-type Al₂O₃. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments. Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete optimization of a cell shape and ionic positions at high pressures in the previous calculations.     

用遗传算法优化估计Van Genuchten方程参数

描述土壤水分特征曲线的Van Genuchten方程是一个非线性复杂方程,采用传统的方法对方程参数进行估计往往因为计算复杂和人为因素的影响,而使估计结果带有较大的误差。遗传算法是当前处理一般非线性数学模型优化的一种新的优秀方法。为此,采用实数编码多子种群遗传算法对方程的参数进行优化估计。算例结果表明用遗传算法优化估计Van Genuchten方程参数具有求解速度快、计算精度和自动化程度高、人为干扰因素小、通用性强等优点。因此,遗传算法可作为计算Van Genuchten方程参数的一种新方法。