The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

Temperature dependence of the polarized electronic absorption spectra of olivines. Part I – fayalite

 Polarized electronic absorption spectra of orthorhombic fayalite, Fe₂SiO₄, [E || a(|| Z),E || b(|| X), E || c(|| Y)], space group Pbnm, have been studied in the temperature range 293 ≤T/K ≤ 1273. The spectra were analysed into component bands originating from spin-allowed dd transitions of iron(II) at the different sites, M1 and M2, in the structure. The assignments of bands, made on the basis of the polarization dependence of the spectra and considerations of transition energies, were confirmed by the analysis of the temperature-dependent spectra. The temperature dependencies of integral intensities, half band widths and energy positions of absorptions bands caused by Fe²⁺ on the different octahedral sites, M1 and M2, were evaluated for the individual transitions. Independent of the site symmetry, absorption bands shift to lower energies and half band widths increase on rising temperature. The temperature dependence of band intensities depends on site symmetry. The integral intensities are found to increase with temperature for the transition metal ion on a centrosymmetric site, or remain constant when the site is missing an inversion centre. This is consistent with the general conclusion of Taran et al. (1994). Received: 11 October 2001 / Accepted: 17 January 2002     

接近于铁橄榄石端员组份的铁橄榄石集合体的发现及其初步研究

铁橄榄石集合体为无根岩石。外观呈铁黑色,风化面呈亮栗褐色。本文对铁橄榄石集合体的形态特征、物理性质和化学成分进行了研究。通过化学式的计算,其化学式为:(Mg_(0.0168)Fe_(0.9802)Mn_(0.003))_2[SiO_4],证明其为铁橄榄石的端员组份。此外,还对其进行了穆斯堡尔谱分析、X射线粉晶衍射分析和红外光谱分析。其穆斯斑堡尔谱分析结果与人工合成的铁橄榄石数据相近,它的衍射数据及计算的晶胞参数也与JCPDS所提供的标准数据非常接近,这些进一步证明了铁橄榄石集合体的成分接近于铁橄榄石端员组份。     

铁橄榄石高温高压流变性的实验研究

通过高温高压实验研究了铁橄榄石集合体的流变性.首先,利用高精度的Paterson气体介质变形装置对铁橄榄石集合体Fe2SiO4进行了高温三轴压缩蠕变试验.变形试验条件为:温度1273～1423K,围压300MPa,差应力10～250MPa,应变率10-7～10-4s-1,试件的最大变形量不超过20%.利用三维非线性拟合方法对蠕变试验数据进行分析,得到铁橄榄石集合体的微观变形机制为扩散域和位错域,扩散域的应力指数为1左右.位错蠕变域中,干燥铁橄榄石集合体的应力指数为5.4.活化能为781kJ/mol;含水铁橄榄石集合体的应力指数为3.4,活化能为516kJ/mol.实验结果表明,含水时铁橄榄石的流变强度比干燥时小一个数量级.将实验结果与铁橄榄石单晶的强度进行对比,发现铁橄榄石集合体的流变强度比铁橄榄石单晶的强度高.从而得到了铁橄榄石集合体高温高压流变性(强度)的初步试验结果.     

A temperature-dependent single-crystal Raman spectroscopic study of fayalite: evidence for phonon-magnetic excitation coupling

The polarized single-crystal Raman spectrum of synthetic fayalite, Fe₂SiO₄, was recorded between 5 and 773 K in order to investigate its lattice dynamic behavior. A broad absorption envelope is observed at wavenumbers between 800 and 960 cm^–1 and it contains two intense bands at 816 and 840 cm^–1 at 293 K in the (cc) spectrum. The integral area of the envelope decreases upon cooling from 293 K and reaches a minimum around 55 K. It then increases again with a further decrease in temperature down to 5 K. It is proposed that the envelope in the (cc) spectra consists of seven different modes, some of which are symmetry-forbidden, that arise from combination scattering of nonsymmetric internal SiO₄-stretching modes of B_ig symmetry (i = 1, 2, 3) and low-energy excitations. The individual modes can be observed under different polarizations and agree in number and wavenumber with those obtained by fitting the broad envelope with Lorentzians. An analysis of the Raman spectrum as a function of temperature, using the known magnetic properties of fayalite, allows the assignment of the low-energy excitations to short-range magnetic interactions. Modulation of the Fe²⁺(1)–Fe²⁺(2) exchange energy leads to phonon-magnetic excitation coupling and the main role in the Fe²⁺(1)–Fe²⁺(2) magnetic interaction occurs via superexchange through the oxygens. The magnetic excitations are not magnons in the usual sense, that is as quasiparticles having a long wavelength in an ordered system. The degree of observed broadening of the SiO₄-stretching modes is consonant with a Fe²⁺(1)–Fe²⁺(2) exchange energy of 4.7 cm^–1 presented by Schmidt et al. (1992). At temperatures above 300 K the line width of the mode at 840 cm^–1 decreases slightly, whereas those of low energy lattice modes increase. This suggests that a decrease in mode broadening due to weakened magnetic interactions compensates any thermally related broadening. Complete Fe²⁺ spin disorder may not be reached until at least 530 K. Results from this study show that estimates of third-law entropies for silicates using simple crystal-chemical considerations that do not account for magnetic properties cannot give accurate values for many transition-metal-containing phases.     

A Raman spectroscopic study of Fe–Mg olivines

End-member synthetic fayalite and forsterite and a natural solid-solution crystal of composition (Mg_1.80,Fe_0.20)SiO₄ were investigated using Raman spectroscopy. Polarized single-crystal spectra were measured as a function of temperature. In addition, polycrystalline forsterite and fayalite, isotopically enriched in ²⁶Mg and ⁵⁷Fe, respectively, were synthesized and their powder spectra measured. The high-wavenumber modes in olivine consist of internal SiO₄ vibrations that show little variation upon isotopic substitution. This confirms conclusions from previous spectroscopic studies that showed that the internal SiO₄ vibrations have minimal coupling with the lower-wavenumber lattice modes. The lowest wavenumber modes in both forsterite and fayalite shift in energy following isotopic substitution, but with energies less than that which would be associated with pure Mg and Fe translations. The low-wavenumber Raman modes in olivine are best described as lattice modes consisting to a large degree of mixed vibrations of M(2) cation translations and external vibrations of the SiO₄ tetrahedra. The single-crystal spectra of forsterite and Fo₉₀Fa₁₀ were recorded at a number of temperatures from room temperature to about 1200 °C. From these data the microscopic Grüneisen parameters for three different A_g modes for both compositions were calculated, and also the structural state of the solid solution crystal was investigated. Small discontinuities observed in the wavenumber behavior of a low-energy mixed Mg/T(SiO₄) mode between 700 and 1000 °C may be related to minor variations in the Fe–Mg intracrystalline partitioning state in the Fo₉₀Fa₁₀ crystal, but further spectroscopic work is needed to clarify and quantify this issue. The mode wavenumber and intensity behavior of internal SiO₄ vibrations as a function of temperature are discussed in terms of crystal field and dynamic splitting and also ₁ and ₃ coupling. Crystal-field splitting increases only very slightly with temperature, whereas dynamical-field splitting is temperature dependent. The degree of ₁–₃ coupling decreases with increasing temperature.