Murli H. Manghnani

Effects of pore and differential pressure on compressional wave velocity and quality factor in Berea and Michigan sandstones

Compressional‐wave velocity (VP) and quality factor (QP) have been measured in Berea and Michigan sandstones as a function of confining pressure (Pc) to 55 MPa and pore pressure (Pp) to 35 MPa. VP values are lower in the poorly cemented, finer grained, and microcracked Berea sandstone. QP values are affected to a lesser extent by the microstructural differences. A directional dependence of QP is observed in both sandstones and can be related to pore alignment with pressure. VP anisotropy is observed only in Berea sandstone. VP and QP increase with both increasing differential pressure (Pd=Pc-Pp) and increasing Pp. The effect of Pp on QP is greater at higher Pd. The results suggest that the effective stress coefficient, a measure of pore space deformation, for both VP and QP is less than 1 and decreases with increasing Pd.

Pressure derivatives of the elastic moduli of BCC Ti-V-Cr, Nb-Mo and Ta-W alloys

The single-crystal elastic moduli Cij and their pressure derivatives dCij/dP have been measured ultrasonically at 25 degrees C for six Ti-V-Cr, eight Nb-Mo and seven Ta-W solid solutions. The rigid-band model for the alloy electronic structure is known to work fairly well for these BCC metals in predicting the density of states at the Fermi energy and related properties. The results of this study show that changes in the composition dependence of the Cij and dCij/dP appear to be related to specific topological changes in the Fermi surface which occur as the electron population varies in the rigid-band model. The relationship between the bandstructure and the Cij is discussed and a qualitative explanation is given for the correlations between the moduli and the Fermi surface and for some of the differences between the three alloy series.

Isothermal compression of bcc transition metals to 100 kbar

Pressure‐volume relationships for the bcc transition metals in the groups VB (V, Nb, and Ta) and VIB (Cr, Mo, and W) were determined under hydrostatic pressure to 100 kbar at room temperature by means of x‐ray diffraction, employing diamond‐anvil pressure cell and the ruby (R1 line) fluorescence calibration technique. Using the measured ultrasonic K′0 values, where K0 is the bulk modulus at ambient pressure, for five metals and the deduced shock‐wave K′0 value for Cr, the values of K0 for V, Nb, Ta, Mo, W, and Cr are calculated to be 1.54, 1.71, 1.94, 2.67, 3.07, and 1.93 Mbar, respectively, by least‐squares fit of the experimental P‐V data to the Birch‐Murnaghan equation. The K0 values thus determined are in good agreement with the ultrasonic and shock‐wave values for V, Nb, Ta, Mo, and W. For Cr, the K0 value (1.93 Mbar) is in agreement with the shock‐wave value (1.92 Mbar) but not with the ultrasonic value (1.65 Mbar). This discrepancy can be explained in view of the paramagnetic→antiferromagnetic tran...

Temperature dependence of the elastic constants of single-crystal rutile between 4° and 583°K*

Abstract Measurements of all the six principal elastic constants of single-crystal rutile were made in the temperature range of 298–583°K. The temperature derivatives (in kb/deg) at 298°K are: dC11/dT = − 0·510, dC33/dT = − 0·900, dC44/dT = − 0·220, dC66dT = − 0·458, dC12/dT = − 0·580, and dC13/dT = − 0·330. Measurements of the four modes, C11, C′ = (C11 — C12)/2, C66, and C110L = (C11 + C12 + 2C66)/2, were extended to 4°K. Two features related to the temperature and volume dependences of the lattice vibrational frequencies are revealed: first, all the measured dClj/dT except dC′/dT become less negative with increasing temperature above 100°K. Second, dC′/dT is positive at all temperatures but decreases with increasing temperature at temperatures > 300°K. Indirectly shown is that (∂C′/∂P)T having a value of − 1·32 at 298°K, decreases with decreasing temperatures. The significance of this latter fact is discussed in light of the computation of Gruneisen mode γs from the acoustic (∂Cij/∂P)T values, and the results are compared with the γ (αv) values obtained by Kirby from thermal expansion data. It is concluded that the large increase in γ(αv) at low temperatures cannot be ascribed to a large temperature dependence of (∂C′/∂P)T. Therefore, Kirbys explanation, that the large increase in γ(αv) is caused by the large volume dependence of the acoustical mode frequencies, is not substantiated.

Electrical conductivity of ultramafic rocks to 1820 kelvin

Abstract Electrical conductivity, σ, of six ultramafic rocks (garnet-bearing peridotites and an eclogite) has been investigated in the temperature range 670–1820 K under known ƒ O 2 environment. Between 670 and ∼1320 K σ increases with 1/T monotonically, first slowly, by 1–1.5 orders of magnitude. Above 1320 K σ increases sharply; an increase of 3–4 orders of magnitude is observed between 1320 and 1670 K. In the same temperature range the σ values for all the six rocks fall within 1.5 orders of magnitude, the lowest conductivity being for a spinel lherzolite. The range of σ values is narrowed at higher temperatures. The differences in σ values above 1470 K may be explained on the basis of varying degrees of partial melting in the rocks. Over the entire range of temperature, the σ values for the ultramafic rocks are lower than those reported for basalts but higher (by 1–2 orders of magnitude) than those for single-crystal olivines.

Infrared absorption spectra of sodium silicate glasses at high pressures

Infrared absorption spectra of 12 sodium silicate glasses of varying composition (10 to 45 mole% Na2O) are examined at varying pressures to 58.8 kbar. The pressure dependences of all the infrared absorption frequencies studied are found to be positive. Gruneisen γs are evaluated from the pressure dependence of the infrared vibrations and elastic parameters. The results are compared with those obtained from previous high‐pressure studies of α‐quartz and several other silicate glasses.

Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry

Using a Fizeau interferometry technique, we have measured the coefficients of linear thermal expansion of single-crystal forsterite (Mg2SiO4) along three axial directions to 1023 K during heating and cooling cycles. Overall, the present data are consistent in magnitude (within 1 to 2%) with those previously reported but have less scatter. We used the Grüneisen statistical mechanical approach in analzying the data. The least-squares method was applied to evaluate thermal parameters (ϑ, Q0, k and a) in two cases. The expansion coefficients in wider temperature ranges were extrapolated by using the parameters of solution 2 (i.e., solution by fixing ϑ and k). In contrast to earlier findings, our results show that for forsterite the Grüneisen parameter decreases with temperature, implying that it does not behave too differently from fayalite (Fe2SiO4) and periclase (MgO).

Elastic properties of diopside, anorthite, and grossular glasses and liquids: A Brillouin scattering study up to 1400 K

The compressional Vpand shear Vs wave velocities of diopside (CaMgSi2O6), anorthite (CaAl2Si2O8), and grossular (Ca3Al2Si3O12) glasses and liquids have been measured by high-resolution Brillouin spectroscopy up to 1200 or 1400 K. For all three materials, marked breaks in the wave velocity-temperature relationships are observed at temperatures consistent with the glass transition temperatures observed in viscosity and calorimetry experiments. From comparisons between high-temperature ultrasonic (relaxed Vp) data and extrapolated Brillouin (unrelaxed Vp and Vs) values, the configurational compressibility of diopside and anorthite liquids has been determined. The relative importance of vibrational and configurational contributions can be markedly different for the compressibility and heat capacity of silicate melts.

Ultrasonic measurements of Vp and Qp: relaxation spectrum of complex modulus on basalt melts

Abstract Ultrasonic compressional wave velocity V p and quality factor Q p have been measured in alkali basalt, olivine basalt and basic andesite melts in the frequency range of 3.4–22 MHz and in the temperature range of 1100–1400°C. Velocity and attenuation of the melts depend on frequency and temperature, showing that there are relaxation mechanisms in the melts. Complex moduli are calculated from the ultrasonic data. The results fit well a complex modulus of Arrhenius temperature dependence with log-normal Gaussian distribution in relaxation times of attenuation. The analysis yields average relaxation time, its activation energy, relaxed modulus, unrelaxed modulus and width of Gaussian distribution in relaxation times. Relaxed modulus is smaller (17.5 GPa) for basic andesite melt of high silica and high alumina contents than for the other two basalt melts (18.1–18.4 GPa). The most probable relaxation times decrease from ∼ 3 × 10 −10 s for basic andesite to ∼ 10 −11 s for alkali basalt at 1400°C. Activation energies of attenuation, ranging from 270 to 340 kJ mol −1 in the three melts, are highest in basic andesite. Longitudinal viscosity values and their temperature dependences are also calculated from V p and Q p data. The volume viscosity values are estimated from the data using the shear viscosity values. Longitudinal, volume and shear viscosities and their activation energies are highest in the basic andesite melt of the most polymerized structure.

Elasticity of single-crystal MgAl2O4 spinel up to 1273 K by Brillouin spectroscopy

The adiabatic single-crystal elastic constants, Cij, of stoichiometric magnesium aluminate spinel (MgAl2O4) have been measured up to 1273 K by highresolution Brillouin spectroscopy, using a 6-pass tandem Fabry-Pérot interferometer and an argon ion laser (514.5 nm). Two platelet samples were employed for probing the acoustic phonons along [100] and [110] directions by platelet and backscattering geometries. The measured temperature dependences of the elastic moduli show a distinct anomaly at 923 K in the shear modulus Cs = (C11-C12)/2 (along [110] direction) and the longitudinal modulus C11 (along [100] direction). This anomaly is consistent with the order-disorder phase transition, resulting from the atomic exchange between Mg at the tetrahedral site and Al at the octahedral site, which has been well documented recently (Peterson et al. 1991; Millard et al. 1992) by neutron powder diffraction and 27Al magic-angle spinning NMR. The values of the temperature derivatives of vp, vs, and Ks, in the temperature range 300–923 K, calculated by the Voigt-Reuss-Hill approximation are -0.40ms−1 K−1, -0.26ms−1 K−1, and -1.89 x 10−2GPaK−1.