Elastic properties from acoustic and volume compression experiments

Abstract

Hydrostatic compression data for a number of high-pressure phases of oxides and silicates, which have been studied independently by acoustic techniques, have been analyzed by least-squares fitting of the Birch-Murnaghan equation of state to determine the zero-pressure bulk modulus K 0 and its pressure derivative K′ 0 for each material. The standard deviations of K 0 and K′ 0 so determined are generally underestimated unless the experimental errors in the measurements of volume and pressure are explicitly included. When the values of K 0 determined from the acoustic and compression techniques are consistent, test results for quartz and rutile demonstrate that constraining K 0 to be equal to the acoustic value significantly improves both the accuracy and the precision of K′ 0 obtained from the compression data. Similar analyses for high-pressure phases (e.g., pyrope garnet and silicate spinels) indicate that by combining the acoustic and P- V data, the standard deviation of K′ 0 is typically reduced by a factor of three. Thus, we conclude that this approach does allow precise determinations of K′ 0 even when neither technique alone is able to resolve this parameter. For some materials, however, the P- V and acoustic experiments do not define mutually consistent values of K 0, invalidating any combination of these data. The compression data for stishovite clearly exhibit run to run effects, and we infer that systematic errors are present in some of the P- V data which are responsible for many of the interlaboratory inconsistencies. Such systematic biases in the P- V data can at least be partially compensated for by performing several duplicate experimental runs.