A preliminary stable isotope study on Mogok Ruby, Myanmar

The primary occurrence of ruby in the Mogok area, northern Myanmar is exclusively found in marble along with spinel–forsterite-bearing marble and phlogopite–graphite marble. These marble units are enclosed within banded biotite–garnet–sillimanite–oligoclase gneisses. Samples of these marbles collected for C–O stable isotope analysis show two trends of δ¹³C–δ¹⁸O variation resulting most likely from fluid–rock interactions. Ruby-bearing marble and phlogopite–graphite marble follow a trend with coupled C–O depletion, whereas spinel–forsterite-bearing marble follows a δ¹⁸O depletion trend with relatively constant δ¹³C values. Ruby formation might have resulted from CO₂-rich fluid–rock interaction, while spinel–forsterite-bearing marble was genetically related to CO₂-poor fluid–rock interaction. Both fluids may have arisen from external sources. Based on graphite Raman spectral thermometry, the estimated temperature for phlogopite–graphite marble, and probably ruby-bearing marble, was lower than 607 °C, and for spinel–forsterite-bearing marble, lower than 710 °C. Contrasting C/O diffusion between graphite/ruby/spinel/forsterite and calcite, local variations of isotopic compositions of newly formed minerals as a result of non-pervasive fluid infiltration, and open-system isotopic disturbance during cooling may have affected C-/O-isotopic fractionations between minerals. The estimated high formation temperatures for ruby and spinel/forsterite imply that the parental fluids may have been related to nearby igneous intrusions and/or metamorphic processes. Whether these two types of fluid were genetically related is unclear based on the present data.     

Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited

Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg₂SiO₄). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg₂SiO₄ in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.     

Pressure sensitivity of olivine slip systems: first-principle calculations of generalised stacking faults

We have used a first-principle approach based on the calculation of generalised stacking faults (GSF) to study the influence of pressure on the mechanical properties of forsterite. Six cases corresponding to [100] glide over (010), (021) and (001), and [001] glide over (100), (010) and (110) have been considered. The relaxed energy barriers associated with plastic shear have been calculated by constraining the Si atoms to move perpendicular to the fault plane and allowing Mg and O atoms to move in every direction. These conditions, which preserve dilations as a relaxation process, introduce Si–O tetrahedral tilting as an additional relaxation mechanism. Relaxed GSF show little plastic anisotropy of [100] glide over different planes and confirms that [001] glide is intrinsically easier than [100] glide. The GSF are affected by the application of a 10 GPa confining pressure with a different response for each slip system that cannot be explained by sole elastic effect. In particular, [100](010) is found to harden significantly under pressure compared to [001](010). Our results give the first theoretical framework to understand the pressure-induced change of dominant slip systems observed by Couvy et al. (in Eur J Mineral 16(6):877–889, 2004) and P. Raterron et al. (in GRL, submitted). It appears necessary to account for the influence of pressure on the mechanical properties of silicates in the context of the deep Earth.     

A computational study of oxygen diffusion in olivine

Atomistic modelling techniques are used to study the rate-determining steps that limit diffusion of oxygen in forsterite. The activation energies for diffusion parallel to all three crystallographic axes by the vacancy and interstitial mechanisms are calculated. The activation energy for extrinsic vacancy diffusion is predicted to be isotropic with a barrier height of 119 kJ mol^–1. Conversely, in the interstitial case it is found to be anisotropic, with extrinsic activation energies that range between 94 and 178 kJ mol^–1. The effect of intrinsic defects and two typical impurities, iron and hydrogen, upon diffusion is also considered. We find that the migration energy is slightly higher in iron-rich fayalite compared with forsterite and that the presence of hydrogen defects will not affect the diffusion mechanism. These observations lead us to reinterpret existing experimental results on oxygen diffusion in natural olivine. We suggest that at low oxygen partial pressure the mechanism observed is a vacancy mechanism, while at high oxygen partial pressure the mechanism is interstitial. We believe that this change in mechanism is mediated by iron redox reactions. Taking this process into account, we derive activation energies in excellent agreement with those found experimentally in natural samples of olivine. The anisotropy of activation barriers and hence the change in diffusion rates with temperature could be used to distinguish between the two mechanisms in future experimental work.     

Experimental and theoretical bond critical point properties for model electron density distributions for earth materials

Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO₄-15, were also found to yield model electron density distribution values at the bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.Dedicated to Professor Robert F. Stewart of Carnegie Mellon University on his retirement for his brilliant and original work modeling electron density distributions.     

Experimental Studies on Elasticities of Forsterite-Enstatite Composites:Towards an Understanding of the Rules of Mixture

Which rule of mixture is the best for predicting the overall elastic properties of polyphase rocks based on the elastic properties and volume fractions of their constituents? In order to address this question, we sintered forsterite-enstatite polycrystalline aggregates with a varied forsterite volume fraction (0, 0.2, 0.4, 0.5, 0.6, 0.8, and 1.0). Elastic properties (shear, bulk, and Young's moduli) of these synthesized composites were measured as a function of pressure up to 3.0 GPa in a liquid-medium piston-cylinder apparatus using a high-precision ultrasonic interferometric technique. The experimental data can be much better described by the shear-lag model than by the commonly used simple models such as Voigt, Ruess and Hill averages, Hashin-Shtrikman bounds, Ravichandran bounds, Halpin-Tsai equations, and Paul's calculations. We attributed this to the fact that the elastic interaction and stress transfer between phases are neglected in all the models except for the shear-lag model. In particular, t     

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64相似文献   

Anisotropy of Mg isotopic fractionation during evaporation and Mg self-diffusion of forsterite in vacuum

Evaporation of solid materials under low-pressure conditions could play important roles in chemical and isotopic fractionations in the early solar system. We have studied anisotropy of isotopic fractionation of ²⁶Mg and ²⁵Mg during kinetic evaporation of forsterite (Mg₂SiO₄), which is potentially a powerful tool to understand thermal histories of crystals in the early solar system. Ion-microprobe depth profiling revealed that the Mg isotopic zoning profiles of forsterite evaporated at 1500-1700 °C are notably differing along the a-, b-, and c-axes, which can be attributed to anisotropy in self-diffusion coefficient of Mg (D) and an isotopic fractionation factor for evaporation of Mg (α). The D and α were obtained from zoning profiles by applying the diffusion-controlled isotopic fractionation model of Wang et al. [1999. Evaporation of single crystal forsterite: Evaporation kinetics, magnesium isotope fractionation, and implications of mass-dependent isotopic fractionation of a diffusion-controlled reservoir. Geochim. Cosmochim. Acta 63(6), 953-966.].The D is largest and smallest along the a- and c-axes, respectively. The activation energy of 560-670 kJ/mol indicates that Mg diffusion at 1500-1700 °C occurred in the intrinsic diffusion regime.The α seems to be larger along the a- or c-axes than along the b-axis. The α along the a- or c-axes show weak temperature dependence. The α along all the crystallographic orientations is closer to unity than that expected from the kinetic theory of gases. These lines of evidence suggest that surface processes such as breaking of bonds and surface diffusion are responsible for the isotopic fractionation.     

Combining ECCI and FIB milling techniques to prepare site-specific TEM samples for crystal defect analysis of deformed minerals at high pressure

Dislocation microstructures in experimentally deformed single-crystal pyrope-rich garnet, (Mg,Fe)₃(Al,Cr)₃Si₃O₁₂, and polycrystalline forsterite, Mg₂SiO₄, were investigated by using electron channeling contrast imaging (ECCI) and transmission electron microscopy (TEM) combined with a focused ion beam (FIB)-microsampling. In the orientation-optimized ECCI method, we successfully observed individual dislocations across subgrain boundaries in a low-atomic-number mineral, pyrope-rich garnet (averaged Z-numbers, AZs ～ 10). Dislocations in a deformed forsterite (iron-free olivine) were also visible in the ECCI. In the ECCI on the single-crystal garnet, deformation bands consisting of dislocations, unusual contrasts in stripes and inhomogeneous distributions of sub-micrometer-sized pores were found. Further site-specific TEM observation on the deformation band revealed a high density of partial dislocations and stacking fault ribbons. The site-specific characterizations from ECCI to TEM, with assistance of FIB, can provide a new approach to investigate dislocation microstructures of deformed materials at high pressure and high temperature.     

Pressure–volume–temperature equations of state: a comparative study based on numerical simulations

 The P–V–T equation of state (EoS) models of Birch–Murnaghan, Vinet and Poirier–Tarantola have been compared with one another and discussed in the light of their ability to reproduce thermoelastic functions and parameters by means of fitting to pressure–volume–temperature data artificially generated for spinel, corundum and forsterite. Numerical simulations relying upon semi-empirical potentials, lattice dynamics and the quasiharmonic approximation have been used to generate P–V–T data. The results obtained indicate that all the P–V–T EoSs tested predict bulk modulus at ambient conditions with errors confined, at worst, within a few percent, and reproduce correctly its dependence on temperature. The derivatives of the bulk modulus versus P and PT are less satisfactorily modelled. The bulk thermal expansion is determined by EoSs within a few percent error, but the deviations increase significantly if the approximation of linear dependence of EoS on temperature is used (linearised thermal pressure model). Received: 30 January 2001 / Accepted: 16 June 2001