Earl K. Graham

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

AbstractWe 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 moduliCij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineCij of fayalite are determined from three new sets of measurements. One set of our newCij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someCij 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 recommendeaCijs (GPa) and (∂Cij/∂T)p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,Ks and μ, and their temperature derivatives are:Ks=134(4) GPa; μ=50.7(0.3) GPa; (∂Ks/∂T)p=−0.024(0.005) GPa/K; and (∂μ/∂T)p=−0.013(0.001) GPa/K. An important conclusion is thatKs increases as the Fe/(Fe+Mg) ratio in olivine is increased.

Application of a simple relation for describing wave velocity as a function of pressure in rocks containing microcracks

The occurrence of microcracks and pore space reduces the P and S wave velocities in rocks from those expected for the intrinsic mineral matrix. In the low-pressure regime, before microcracks close, the elastic properties and wave velocities are characteristically nonlinear. This nonlinear behavior reflects the effects of the crack closure spectra on the P and S wave velocities. Several efforts have been made in the past to describe or model this behavior using phenomenological relations. However, success has been limited to a rather restricted pressure range. In the present study, two simple relations are considered that have a clear physical basis and are convenient to use and interpret. Both are tied to the functional form V2 = A + BP + Ce−P/τ. The fitting parameters A and B can be identified directly as second- and third-order elastic properties of the intrinsic mineral matrix of the rock specimen, and C and τ describe the nature of the microcrack distribution. The results from fitting a large number of published igneous rock data sets indicate that the relations studied yield rms errors that are (1) always within the stated accuracy of the data, (2) generally within the stated precision of the data, (3) comparable in “goodness of fit” to previously published but more complex relations over limited pressure range data sets, and (4) clearly superior over extended pressure ranges. Because of their comparative simplicity, demonstrated accuracy, and clearly defined fitting parameters, they are well suited for systematic studies of large numbers of igneous rock data sets.

The effects of annealing and aluminum substitution on the elastic behavior of alkali silicate glasses

Abstract In an effort to better understand the structural dynamics of glasses, we have measured the second-order adiabatic elastic moduli, and their pressure and temperature derivatives, of a sodium silicate and a sodium alumino-silicate glass. In both cases, we find increasing compressional and decreasing shear wave velocities with pressure. Substantial hysteresis is present in both glasses, especially in the shear-wave velocities. We also have studied the effects of annealing by measuring the elastic properties before and after annealing. We find that, in addition to previously observed increase in density and moduli, the pressure and temperature derivatives also increase, or become less negative. Comparison of the two glasses, which have nearly the same oxygen packing densities and unoccupied volumes, shows that substitution of aluminum for silicon increases the elastic moduli substantially. Shear modulus increases are accounted for by elimination of non-bonding oxygens, but bulk and Youngs modulus changes are associated either with bond strengths in the network-forming tetrahedra, or with steric hindrance effects. In contrast, aluminum substitution does not affect the pressure derivatives of the moduli. The pressure derivatives are proportional to the unoccupied volume fraction in the glass, which is a measure of ion packing efficiency. This suggests that packing efficiency alone controls moduli pressure derivatives in alumino-silicate glasses.