Search

Measurements of the effect of pressure on the elastic constants of pure and hydrogenated single crystals of V and Nb53Ta47 are reported. For both samples dC'/dP was found to decrease when hydrogen was added. The qualitative features of this behaviour can be explained by the proposal that an increase occurs in the tetragonal distortion around the H interstitial when the atomic volume decreases.

The single-crystal elastic moduli of chromium have been measured ultrasonically to 5 kbar and from 80 to 700K. In the paramagnetic phase the shear moduli are found to be approximately linear functions of pressure and temperature for pressures and temperatures above the Neel transition line. At atmospheric pressure, the compressional modulus C11 increases with temperature above TN up to a maximum at about 475K, and then decreases and becomes a linear function of T above 550K.C11 is not a linear function P for temperatures up to 473K. The results for paramagnetic chromium are combined with previous results on Ti-V and V-Cr alloys to discuss the relationship of the elastic properties to the electronic bandstructure of these alloys.

Compressional wave attenuation, Qp−1, and velocity, Vp, for an alkalic olivine basalt have been measured from 1250° to 1450°C and from 5 to 10 MHz by an ultrasonic interferometric technique. Vp shows no significant frequency or temperature dependence, and Qp−1 increases with increasing frequency and decreasing temperature. For the conditions of this study, the melt can be modeled as a viscoelastic material with a single thermally activated structural relaxation mechanism having an activation energy of 2.2 eV and a relaxation time on the order of 1 ns. The data presented here fall in the region of the relaxation spectrum where the frequency, f, is much smaller than the relaxation frequency, and the absorption coefficient is proportional to f². Analysis of the data suggests that (1) compressional wave losses will be negligible in a basalt melt at seismic frequencies, and (2) the volume viscosity of basalt melt is comparable in magnitude to shear viscosity.

The elastic constants ${C}_{\mathrm{ij}}$ of single-crystal Re and their pressure derivatives $\frac{d{C}_{\mathrm{ij}}}{\mathrm{dP}}$, measured to 4.2 kbar at 25 \ifmmode^\circ\else\textdegree\fi{}C, are, respectively; ${C}_{11}: 6177.3 \mathrm{and} 8.65$; ${C}_{33}: 6828.2 \mathrm{and} 8.45$; ${C}_{13}: 2055.7 \mathrm{and} 2.98$; ${C}_{44}: 1605.4 \mathrm{and} 1.49$; ${C}_{66}: 1714.1 \mathrm{and} 1.56$. The initial pressure derivative of the isothermal bulk modulus, ${K}_{T}^{\ensuremath{'}}={(\frac{\ensuremath{\partial}{K}_{T}}{\ensuremath{\partial}P})}_{P=0}$, calculated from the Voigt-Reuss-Hill approximation, is 5.43, which is significantly larger than the previously reported value of 2.93 based on x-ray-diffraction data. The contributions to ${K}_{T}$ and ${K}_{T}^{\ensuremath{'}}$ from long-range Fermi energy and short-range ion-core repulsive interactions (${K}_{F}$ and ${K}_{\mathrm{SR}}$, respectively) are evaluated by assuming the Born-Mayer potentials for the latter contribution. Using an empirical relationship between atomic volume and ${K}_{T}^{\ensuremath{'}} (\ensuremath{\approx}{K}_{s}^{\ensuremath{'}})$, it is found that the x-ray value for ${K}_{T}^{\ensuremath{'}}$ is probably too low. Evaluation of the Born-Mayer parameters leads to the conclusion that the short-range contribution, rather than the Fermi contribution, dominates ${K}_{T}$, and shear moduli ${C}_{44}$ and ${C}_{66}$, and their pressure derivatives, whereas the Fermi energy is a major contributory factor in the case of shear modulus ${C}_{H}=(\frac{1}{6})({C}_{11}+{C}_{12}+2{C}_{33}\ensuremath{-}4{C}_{13})$. The latter conclusion is strengthened by the nonlinearity of ${C}_{H}$ with respect to pressure, and by the anomalous variation of the superconducting temperature ${T}_{c}$ with pressure, which effect is related to the change in Fermi-surface topology. The value of the Gr\"uneisen-mode gamma ${\ensuremath{\gamma}}_{H}$ for Re, calculated from the $\frac{d{C}_{\mathrm{ij}}}{\mathrm{dP}}$, 1.83, which is significantly less than thermal gamma ${\ensuremath{\gamma}}_{\mathrm{th}} (2.39)$ at 300 \ifmmode^\circ\else\textdegree\fi{}K.

Structural transformations in pure Zr and Hf and their alloys with 5.2, 21.1, 42.9, and 71.3 at . % Hf have been investigated up to 42 GPa (1 GPa = 10 kbar) at room temperature (∼22 °C) by in situ high‐pressure x‐ray diffraction techniques, using a diamond‐anvil pressure cell. The pressure of transformation a→w increases rapidly with increasing Hf content. On extrapolation, the pressure of transformation a→w for Hf is estimated to be in the order of 60 GPa. Values of the c0/a0 ratio of the pressure‐induced w phase for Zr and its alloys are 0.621±0.002, in good agreement with those of heat‐treated w phases in the Zr‐Nb system.

Polycrystalline samples of pure Ti and Ti-V alloys containing 2.8, 7.6, 11.4, 20, 25, 35, 40 and 50 atomic percent V were investigated up to ~ 25 GPa at ambient temperature using a diamond anvil pressure cell and X-ray diffraction techniques. The X-ray data show that for alloys with less than ~ 30% V, the hexagonal ω phase is more stable under high pressure conditions than the h.c.p. α phase and the b.c.c. β phase. For alloys with higher V content (> ~ 30%), however, no ω phase was detected. The transformation pressure for the α → ω + α transition decreases gradually with increasing V content whereas for the β → ω + β transition, it increases exponentially. The pressure-induced ω phase obtained in the Ti-V system has an axial ratio c o a o of 0.6105 ± 0.0015, which is about 0.3% lower than the value (0.612) reported for thermally treated ω phases. The pressure-induced ω phase has a smaller volume than the corresponding β and a phases. Thus the relationships aω = √2 aβ and c ω = ( √3 2 ) a β , which hold very well for thermal ω phases, do not hold for the pressure-induced ω phase.

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.

The elastic moduli of single crystals of Mo‐16%Re, Mo‐29% Re, and W‐11% Re have been measured to 0.5 GPa (5 kbar) hydrostatic pressure at room temperature. The composition dependence of the pressure derivatives of the moduli follows the trends established for Nb‐Mo and Ta‐W alloys. This finding was unexpected since the shear modulus, C′ = (C11−C12)/2 has a sharp peak in its composition dependence at e/a = 6.0. The results are explained in terms of the differing effects of compression on different d‐electron subbands. Because dC′/dP decreases with increasing Re content, it is also suggested that the compositional range for stability of the bcc structure decreases with increasing pressure.

Hydrostatic pressure derivatives of the single-crystal elastic moduli, dC/sub ij//dP, have been measured ultrasonically for b.c.c. Nb--Mo and Ta--W solid solutions. The composition dependence of various electronic properties of these alloys is known to be reasonably well approximated by a rigid-electron-band filling model where e/a, the electron per atom ratio, is the primary parameter. The results indicate that the elastic moduli and their pressure derivatives may also be calculated in such a model. In particular, the dC/sub ij//dP show relatively sharp increases at e/a compositions of 5.4 for Nb--Mo and 5.7 for Ta--W. Both compositions correspond to changes in Fermi surface topology, as deduced from existing band calculations and the rigid band assumption. The results are discussed in the light of related electronic properties and possible geophysical applications. A comparison is also made between ultrasonic results and X-ray diffraction data for Nb. Using diamond-anvil pressure cell, compression of Nb was determined by X-ray diffraction up to 55 kbar in a liquid medium under purely hydrostatic conditions, and up to 175 kbar in a solid medium under nonhydrostatic conditions. The data obtained under hydrostatic conditions agree well with the ultrasonic equation of state and shock wave data, whereas the nonhydrostatic resultsmore » tend to imply either a higher bulk modulus K/sub s/ or a higher (par. deltaK/sub s//par. deltaP)/sub T/.« less

Laboratory studies have been carried out to determine the causes of velocity and attenuation anisotropy in pelagic carbonate sediments from Deep Sea Drilling Project site 288 on the Ontong-Java Plateau. Compressional velocity Vp was measured under independently controlled pore pressure and confining pressure. Velocity anisotropy for compressional waves (horizontal velocity > vertical velocity) is found to decrease with increasing effective pressure, i.e., with closure of pores. Previous studies have suggested that velocity anisotropy in pelagic carbonate sequences is due largely to preferred vertical orientation of calcite c axes. The present results indicate that preferred horizontal orientation of grain contacts and flat pores is also a significant cause of the observed anisotropy for many samples. Significant anisotropy in ultrasonic attenuation for compressional (Qp−1) and shear (Qs−1) waves is observed such that the losses are greatest for propagation modes that can generate relative motion across horizontal grain contacts or flat horizontal pores. The results are discussed in terms of the possible mechanisms of dissipation.

An interferometric technique has been developed for the purpose of measuring ultrasonic velocity and attenuation in rock melts. In essence, a long wave train is transmitted through two long buffer rods separated by a thin layer of melt. Multiple reflections in the melt layer interfere with each other and give rise to resonances for melt thicknesses equal to integral multiples of half the wavelength. The velocity and attenuation can be obtained by measuring the amplitude of the transmitted wave as a function of either the melt layer thickness or the frequency. The accuracy of the method was tested at room temperature by compressional wave measurements on water, mercury, and carbon disulfide. Velocities were found to be accurate to within 0.3%. Values of the specific dissipation factor Q/sup -1/ as low as 10/sup -3/ can be resolved for a liquid such as water with a low acoustical impedance, whereas Q/sup -1/ values as low as 10/sup -4/ can be measured for high-impedance liquids such as mercury. Q/sup -1/ values obtained on carbon disulfide agree with previous work to within better than 0.001. Experiments on a viscous organic polymer show that shear measurements can be made and that Q/sup -1/ values upmore » to at least 0.2 can be measured by this technique. The method has been successfully used to study a basalt melt to 1500/sup 0/C. Sources of error and possible improvements are discussed, and the method is compared to previously used techniques. The method has the potential of measuring velocity and attenuation in partial melts and solids.« less