The role of iron in tetrahedrite and tennantite determined by Rietveld refinement of neutron powder diffraction data

Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12?xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12?xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I $ \ifmmode\expandafter\bar\else\expandafter\=\fi{4} Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12−xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12−xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I 3 m). The refinement results also confirm that M2 is a split (24g), flat-pyramidal site situated statistically on both sides of the S1−S1–S2 triangle. In tetrahedrite, this split is about 0.6 ?, in tennantite about 0.7 ?. Trends in bond lengths and magnitude of the M2 split were evaluated by means of linear regression with Fe concentration as the independent variable.     

Elasticity of single-crystal aragonite by Brillouin spectroscopy

The elastic constants of natural single-crystal aragonite (CaCO₃) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃ and C₂₃ are 171.1±1.0, 110.1±0.9, 98.4±1.2, 39.3±0.6, 24.2±0.4, 40.2±0.6, 60.3±1.0, 27.8±1.6 and 41.9±2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0±0.2, 4.2±0.2 and 7.3±0.6×10^–3 GPa^–1, respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9±1.4 and 35.8±0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies.     

A powder neutron diffraction study of the crystal structure of the fluoroperovskite NaMgF<Subscript>3</Subscript> (neighborite) from 300 to 3.6 K

The cell dimensions and crystal structures of the fluoroperovskite NaMgF₃ (neighborite), synthesized by solid state methods, have been determined by powder neutron diffraction and Rietveld refinement over the temperature range 300–3.6 K using Pt metal as an internal standard for calibration of the neutron wavelength. These data show that Pbnm NaMgF₃ does not undergo any phase transitions to structures of lower symmetry with decreasing temperature. The cell dimensions and atomic coordinates together with polyhedron volumes and distortion indices are given for Pbnm NaMgF₃ at 25 K intervals from 300 to 3.6 K. Decreases in the a and c cell dimensions reach a saturation point at 50 K, whereas the b dimension becomes saturated at 150 K. The distortion of the structure of Pbnm NaMgF₃ from the aristotype cubic structure is described in terms of the tilting of the MgF₆ octahedra according to the tilt scheme a ⁻ a ⁻ c ⁺ . With decreasing temperature the antiphase tilt (a ⁻) increases from 14.24° to 15.39°, whereas the in-phase tilt (c ⁺ ) remains effectively constant at ∼10.7°. Changes in the tilt angles are insufficient to cause changes in the coordination sphere of Na that might induce a low temperature phase transition. The structure of Pbnm NaMgF₃ is also described in terms of normal mode analysis and displacements of the condensed normal modes are compared with those of Pbnm KCaF₃.     

Elastic constants of chrome-diopside: application of resonant ultrasound spectroscopy to monoclinic single-crystals

The right-rectangular parallelepiped resonance (RPR) form of resonant ultrasound spectroscopy (RUS) is applied to monoclinic crystal symmetry to determine the 13 adiabatic elastic constants, C_ij, of single-crystal chrome-diopside Di_0.93Hd_0.03Ur_0.02X_0.02 (Di, diopside; Hd, hedenbergite; Ur, ureyite; X, other or unknown). These data represent the first published values of the elastic tensor for a monoclinic single-crystal determined by the RPR method, thus demonstrating the feasibility of this method for studying elasticity of low-symmetry crystals. The lowest 62 modal frequencies of a gem-quality specimen were measured and identified at ambient temperature and pressure. Inverting the modal frequencies results in, respectively C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃, C₂₃, C₁₅, C₂₅, C₃₅, C₄₆ values (GPa) of 228.1(1.0), 181.1(0.6), 245.4(1.3), 78.9(0.3), 68.2(0.2), 78.1(0.2), 78.8(0.5), 70.2(0.7), 61.1(0.7), 7.9(0.5), 5.9(0.5), 39.7(0.4), and 6.4(0.2), where numbers in parentheses indicate experimental uncertainty. The corresponding isotropic bulk, K_S, and shear, G, moduli are 116.5 (0.9) and 72.8(0.4) GPa, respectively. When comparing these results with other pyroxene data, we find systematic correlations between M2 site composition and C_ij values for most, but not all, moduli. Unusual compositional dependence near end-member diopside is seen for a few moduli, and is propagated to the K_S and G moduli, which should prompt a reexamination of some C_ij values of end-member diopside.     

Potential protonation sites in the Al<Subscript>2</Subscript>SiO<Subscript>5</Subscript> polymorphs based on polarized FTIR spectroscopy and properties of the electron density distribution

Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a mapping of the (3, −3) critical points displayed by their L(r) = −∇²ρ(r) distributions, are compared with polarized single-crystal FTIR spectra of kyanite and sillimanite determined earlier and with andalusite measured in this study. For andalusite, seven peaks were observed when the electric vector, E, is parallel to [100]: four intense ones at 3,440, 3,460, 3,526, and 3,597 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹. Six peaks, three intense ones at 3,440, 3,460, and 3,526 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹ when E parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of water in andalusite varies between 110 and 168 ppm by weight % H₂O. Polarized FTIR spectra indicate that the OH vector is parallel to (001) in andalusite and sillimanite and in kyanite. Examination of the L(r) (3, −3) critical points in comparison with the polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and O2 in andalusite and O2 and O4 in sillimanite which correspond to the underbonded oxygen atoms and those with the largest L(r) maxima. In kyanite, comparison of the FTIR spectrum and the critical points indicates that H will preferentially bond to the two 4-coordinated O2 and O6 atoms.     

Transmission electron microscopy on iron monosulfide varieties from the Suizhou meteorite

Transmission electron microscopy on the iron monosulfide (FeS) varieties from the Suizhou meteorite (Hubei, China) reveals the intergrowth of primary hexagonal 2C troilite and minor monoclinic 4C pyrrhotite (SG: F2/d) phases as nanometer-scale domain microstructure. In addition, anti-phase domain boundaries are found to present in the 2C troilite superstructure with the displacement vector 1/4[001]_2C, which is expected to form during the translational symmetry breaking during cooling from higher symmetry, high-temperature modification of the NiAs-type (SG: P6₃/mmc) structure. Furthermore, 60° rotation twinning about the pseudo-hexagonal c-axis is observed in the 4C pyrrhotite superstructure, which may result from rotation symmetry reduction induced by the ordered arrangements of metal vacancies through solid-state transformation during further cooling. All the above microstructural characteristics are discussed with consideration to the thermal metamorphism history experienced by the Suizhou meteorite.     

On the problem of transport species of tungsten by hydrothermal solutions

The solubility of pentatungstate of sodium (PTS) Na₂W₅O₁₆ · H₂O and sodium tungsten bronzes (STB) Na_0.16WO₃ in acid chloride solutions containing 0.026, 0.26, and 3.02m NaCl have been studied at 500°C, 1000 bar, given fO₂ (Co-CoO, Ni-NiO, PTS-STB buffers), and constant NaCl/HCl ratio (Ta₂O₅-Na₂Ta₄O₁₁ buffer). Depending on experimental conditions, the tungsten content in the solutions after experiments varied from 10⁻³ to 2 × 10⁻² mol/kg H₂O. Obtained data were used to calculate the formation constants of predominant tungsten complexes (VI, V): H₃W₃^VIO₁₂³⁻, W₃^VO₉³⁻, [W^VW₄^VIO₁₆]³⁻, for reactions

Interaction of Freshly Precipitated Silica Gel with Aqueous Silicic Acid Solutions under Ambient and Near Neutral pH-conditions: A Detailed Analysis of Linear Rate Law

Interaction of freshly precipitated silica gel with aqueous solutions was studied at laboratory batch experiments under ambient and near neutral pH-conditions. The overall process showed excellent reversibility: gel growth could be considered as an opposite process to dissolution and a linear rate law could be applied to experimental data. Depending on the used rate law form, the resulting rate constants were sensitive to errors in parameters/variables such as gel surface area, equilibrium constants, Si-fluxes, and reaction quotients. The application of an Integrated Exponential Model appeared to be the best approach for dissolution data evaluation. It yielded the rate constants k _dissol ∼ (4.50 ± 0.68) × 10⁻¹² and k _growth ∼ (2.58 ± 0.39) × 10⁻⁹ mol m⁻² s⁻¹ for zero ionic strength. In contrast, a Differential Model gave best results for growth data modeling. It yielded the rate constants k _dissol ∼ (1.14 ± 0.44) × 10⁻¹¹ and k _growth ∼ (6.08 ± 2.37) × 10⁻⁹ mol m⁻² s⁻¹ for higher ionic strength (I ∼ 0.04 to 0.11 mol L⁻¹). The found silica gel solubility at zero ionic strength was somewhat lower than the generally accepted value. Based on the and standard Gibbs free energy of silica gel formation was calculated as and −850,318 ± 20 J mol⁻¹, respectively. Activation energies for silica gel dissolution and growth were determined as and respectively. An universal value for growth of any silica polymorph, is not consistent with the value for silica gel growth, which questions the hypothesis about one unique activated complex controlling the silica polymorph growth.     

The elastic constants of monoclinic single-crystal chrome-diopside to 1,300 K

Values of the complete adiabatic elastic tensor for single-crystal chrome-diopside (a monoclinic pyroxene mineral) are presented from 298 to 1,300 K. The data were obtained using resonant ultrasound spectroscopy (RUS). They are the first published results for the temperature T dependences of the 13 individual elastic constants C _ij of any clinopyroxene mineral. Each C _ij is appropriately described by a linear function in T throughout the range of T. Values for each (∂C _ij /∂T) _P in GPa K⁻¹ are as follows: C ₁₁, −0.0291; C ₂₂, −0.0248; C ₃₃, −0.0179; C ₄₄, −0.0103; C ₅₅, −0.0077; C ₆₆, −0.0152; C ₁₂, −0.0119; C ₁₃, −0.0064; C ₂₃, 0.0000; C ₁₅, 0.0025; C ₂₅, 0.0022; C ₃₅, −0.0046; and C ₄₆, 0.0026. Values of (∂M/∂T) _P in GPa K⁻¹, where M represents an isotropic bulk property calculated from the C _ij data, are as follows: adiabatic bulk modulus K _S , −0.0123; isothermal bulk modulus K _T , −0.0178; and shear modulus G, −0.00998. Some diopside derivatives, notably (∂K _S /∂T) _P , (∂K _T /∂T) _P , and (∂V _P /∂T) _P , where V _P is the compressional wave velocity, have smaller magnitudes than all other minerals of importance in Earth’s mantle, thus, confirming predictions from systematics studies. We find several dimensionless quantities for this monoclinic mineral have normal values compared to other mantle minerals. Further, αK _T (α is the volume coefficient of thermal expansion) for diopside is approximately independent of both T and volume V at elevated temperature, so its equation of state is accurately expressed in simplified form.     

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T ₀|⁻ⁿ , where T is temperature and T ₀ is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K ₁ = (C ₁₁ +C ₁₂ +C ₁₃)/3 and K ₃ = (C ₃₃ +2C ₁₃)/3 decrease rapidly toward the transition, whereas, shear moduli C ₄₄, C _S1 = (C ₁₁ +C ₃₃ -2C ₁₃)/4 and C _S3 = (C ₁₁ -C ₁₂)/2 = C ₆₆ decrease only slightly. The shear modulus C _S3 = C ₆₆ increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.     

Elasticity of TiO2 rutile to 1800 K

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 oK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less. Received: 19 September 1997 / Revised, accepted: 27 February 1998     

Experimental study of Pd hydrolysis in aqueous solutions at 25–70°C

The hydrolysis of the Pd²⁺ ion in HClO₄ solutions was examined at 25–70°C, and the thermodynamic constants of equilibrium K ₍₁₎⁰ and K ₍₂₎⁰were determined for the reactions Pd²⁺ + H₂O = PdOH⁺ + H⁺ and Pd²⁺ + 2H₂O = Pd(OH)₂⁰ + 2H⁺, respectively. The values of log K ₍₁₎⁰ = −1.66 ± 0.5 (25°C) and −0.65 ± 0.25 (50°C) and log K ₍₂₎⁰ = −4.34 ± 0.3 (25°C) and −3.80 ± 0.3 (50°C) were derived using the solubility technique at 0.95 confidence level. The values of log K ₍₁₎⁰ = −1.9 ± 0.6 (25°C), −1.0 ± 0.4 (50°C), and −0.5 ± 0.3 (70°C) were obtained by spectrophotometric techniques. The palladium ion is significantly hydrolyzed at elevated temperatures (50–70°C) even in strongly acidic solutions (pH 1–1.5), and its hydrolysis is enhanced with increasing temperature.     

Influence of hydrogen on Fe–Mg interdiffusion in (Mg,Fe)O and implications for Earth’s lower mantle

Interdiffusion of Fe and Mg in (Mg,Fe)O has been investigated experimentally under hydrous conditions. Single crystals of MgO in contact with (Mg_0.73Fe_0.27)O were annealed hydrothermally at 300 MPa between 1,000 and 1,250°C and using a Ni–NiO buffer. After electron microprobe analyses, the dependence of the interdiffusivity on Fe concentration was determined using a Boltzmann–Matano analysis. For a water fugacity of ∼300 MPa, the Fe–Mg interdiffusion coefficient in Fe _x Mg_1−x O with 0.01 ≤ x ≤ 0.25 can be described by with and C = −80 ± 10 kJ mol⁻¹. For x = 0.1 and at 1,000°C, Fe–Mg interdiffusion is a factor of ∼4 faster under hydrous than under anhydrous conditions. This enhanced rate of interdiffusion is attributed to an increased concentration of metal vacancies resulting from the incorporation of hydrogen. Such water-induced enhancement of kinetics may have important implications for the rheological properties of the lower mantle.

The general refractivity formula applied to densified silicate glasses

Concomitant changes of refractive index (n) with density (ϱ) of isochemical series comprizing several densified silicate glasses were analyzed. The data include glasses of the systems SiO₂, TiO₂-SiO₂, Na₂O-SiO₂, and NaAlSi₃O₈-CaAl₂Si₂O₈. Extending the ideal point dipole theory, an electronic overlap parameter (b) accounting for the non-ideal behaviour of solids was refined using the general refractivity formula , where α is the molar polarizability. Statistical analyses assuming α=constant within each isochemical series showed no systematic variation of b with chemical composition. A constrained refinement of b using all data converged at b=1.3. Applying this common overlap parameter and appropriate polarizability constants, recalculated refractive index values fit excellently the experimental results within the entire n−ϱ range. Furthermore, the additivity of polarizabilities, often assumed for oxide components, is derived for TiO₂-SiO₂ glasses and for glasses of plagioclase composition.     

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

High pressure elasticity and phase transformation in brucite, Mg(OH)2

The first pressure derivatives of the second-order elastic constants have been calculated for brucite, Mg(OH)₂ from the second- and third-order elastic constants. The deformation theory and finite strain elasticity theory have been used to obtain the second- and third-order elastic constants of Mg(OH)₂ from the strain energy of the lattice. The strain energy ϕ is calculated by taking into account the interactions up to third nearest neighbors in the Mg(OH)₂ lattice. ϕ is then compared with the strain dependent lattice energy from continuum model approximation to obtain the expressions of elastic constants. The complete set of six second-order elastic constants C _IJ of brucite exhibits large anisotropy. Since C ₃₃ (= 21.6 GPa), which corresponds to the strength of the material along the c-axis direction, is less than the longitudinal mode C ₁₁ (= 156.7 GPa), the interlayer binding forces are weaker than the binding forces along the basal plane of Mg(OH)₂. The 14 nonvanishing components of the third-order elastic constants, C _IJK , of brucite have been obtained. All the C _IJK of brucite are negative except the values of C ₁₁₄ (= 230.36 GPa), C ₁₂₄ (= 75.45 GPa) and C ₁₃₄ (= 36.98 GPa). The absolute values of the C _IJK are, in general, one order of magnitude greater than the C _IJ ’s in the Mg(OH)₂ system as usually expected for a crystalline material. To our knowledge, no previous data are available to compare the pressure derivatives of brucite. The pressure derivatives of the two components viz., C ₁₄ and C ₃₃ become negative indicating an elastic instability in brucite while under pressure. This may be related to the phase transition of brucite largely involving rearrangements of H atoms revealed in the Raman spectroscopic, powder neutron diffraction and synchrotron X-ray diffraction studies.     

Elasticity of a beryllium silicate (phenacite: Be2SiO4)

The adiabatic single-crystal elastic moduli of a beryllium silicate (phenacite: Be₂SiO₄, trigonal, have been determined at atmospheric pressure and 22° C by Brillouin spectroscopy. The elastic stiffness moduli in gigapascals are: C ₁₁=341.9 C ₃₃=391.0 C ₄₄=91.4 C ₆₆= 96.9 C ₁₂=148.0 C ₁₃=136.0 C ₁₄= 0.1 C ₁₅= 3.5Overall, the elastic stiffness moduli for phenacite parallel and perpendicular to the c axis are comparable (i.e., it is almost cubic in its elastic signature). The elastic moduli can be rationalized in terms of division of the structure into two types of coordination polyhedra (1Si+2Be) with slightly different stiffnesses, which are linked to form a three dimensional framework. Values of the isothermal bulk modulus and the linear compressibilities, as determined from hydrostatic compression experiments of Hazen and Au (1986), are in good agreement with those obtained here. Combining the two studies indicates a low pressure derivative of the bulk modulus for phenacite.     

Magnesium self-diffusion in orthoenstatite

Magnesium self-diffusion coefficients were determined experimentally for diffusion parallel to each of the three crystallographic directions in natural orthoenstatite (En₈₈Fs₁₂). Experiments were conducted at 1 atm in CO-CO₂ gas mixing furnaces, which provided oxygen fugacities equivalent to the iron-wüstite buffer. Diffusion of ²⁵Mg was induced in polished samples of oriented orthoenstatite using a film of isotopically enriched ²⁵MgO as the source material. Very short (<0.15 μm) diffusional penetration profiles were measured by ion microprobe depth profiling. The diffusion coefficients determined for four temperatures (900, 850, 800, 750 °C) provide the activation energies, E _a , and frequency factors, D _o, where D = D _o exp (−E _a /RT) for Mg self-diffusion parallel to each crystallographic direction: a-axis, E _a  = 360 ± 52 kJ/mole and D _o = 1.10 × 10⁻⁴ m²/s; b-axis, E _a  = 339 ± 77 kJ/mole and D _o = 6.93 × 10⁻⁶ m²/s and c-axis, E _a  = 265 ± 66 kJ/mole and D _o = 4.34 × 10⁻⁹ m²/s. In this temperature range, any possible anisotropy of cation diffusion is very small, however the activation energy for diffusion parallel to the c-axis (001) is the lowest and the activation energies for diffusion parallel to the a-axis (100) and b-axis (010) are higher. Application of these diffusion results to the silicate phases of the Lowicz mesosiderite meteorite provides cooling rates for the silicate portion of the meteorite (4–11 °C/100 years) that are similar, although slower, to previous estimates. These silicate cooling rates are still several orders of magnitude faster than the cooling rates (0.1 °C/10⁶ years) for the metal portions. Received: 22 January 1997 / Accepted: 2 October 1997     

High-temperature elasticity of magnesioferrite spinel

The elastic moduli of magnesioferrite spinel, MgFe₂O₄, and their temperature dependence have been determined for the first time by ultrasonic measurements on a polycrystalline specimen. The measurements were carried out at 300 MPa and to 700°C in a gas-medium high-pressure apparatus. On heating, both the elastic bulk (K _S) and shear (G) moduli decrease linearly to 350°C. By combining with extant thermal-expansion data, the values for the room-temperature K _S and G, and their temperature derivatives are as follows: K ₀ = 176.3(7) GPa, G ₀ = 80.1(2) GPa, (∂K _S/∂T) _P = −0.032(3) GPa K⁻¹ and (∂G/∂T) _P = −0.012(1) GPa K⁻¹. Between 350 and 400°C, there are abrupt increases of 1.4% in both of the elastic moduli; these closely coincide with the magnetic Curie transition that was observed by thermal analyses at about 360°C.     

Elastic properties of the incommensurate phase of akermanite,Ca2MgSi2O7

The crystal structure of akermanite, Ca₂Mg-Si₂O₇, consists of mixed tetrahedral sheets formed by [MgO₄] tetrahedra and [Si₂O₇] groups interleaved along the c axis with Ca²⁺ ions in eight-fold coordination. Above 358 K, the structure is tetragonal , and below it is incommensurate with modulations parallel to [110] and . The elastic stiffness moduli, C ^ij of the incommensurate phase at room temperature were measured from wave velocities in the 20–75 MHz carrier frequency range by the ultrasonic phase comparison method using optically clear synthetic single crystal plates (3×3×2 mm) oriented parallel to (100), (001), (110) and (101) planes. The C _ij values (GPa) are: C ₁₁ 159.40, C ₃₃ 149.43, C ₄₄ 30.26, C ₆₆ 58.10, C ₁₂ 76.58 and C ₁₃ 57.80. In (010) and (001) planes, the compressional modulus, V ²(L) from the longitudinal wave, L is considerably larger than the shear moduli, V ²(T₁, T ₂) both from the in-plane and perpendicular-to-plane shear waves, T ₁ and T ₂. The relatively small values of the shear moduli indicate the ease of tetrahedral rotations in response to in-plane and perpendicular-to-plane shears and may provide preconditions for structural changes involving shear-type atomic movements.