Shear and compressional mode measurements with GHz ultrasonic interferometry and velocity-composition systematics for the pyrope-almandine solid solution series

Successful fabrication of a high frequency (up to 600 MHz) shear transducer enables us to determine the complete sets of sound velocities for single crystal samples using GHz ultrasonic interferometry. Sound velocities for a natural pyrope and a natural almandine were measured. Re-examining the existing database, we found that velocities for the pyrope-almandine solid solution series can be modeled quantitatively with linear relationships: V-p[100]=-0.0067X(alm)+9.08 (km s(-1)) V-s[100]=-0.0041X(alm)+5.08 (km s(-1)) V-p[100]=-0.0074X(alm)+9.10 (km s(-1)) where X(alm) is the Fe/(Mg+Fe) ratio in the garnet samples. Maximum deviation of the measurement data from these linear relationships is 1%. For every 10% increase in the Fe/(Mg+Fe) ratio (almandine), the velocities decrease by about 1%. Published density data for this garnet solid solution series fit to a straight line with a maximum deviation of 1%. Thus the velocities follow linear laws with the density and such velocity-density systematics acquire the form of the Birch's law. Using these relationships, velocities of an arbitrary composition in this garnet solid solution series can be predicted. At present, measurement precision of existing data does not warrant an examination of whether bulk modulus is linear with composition. The suggested values for the P- and S-velocities for the pyrope end-member and the almandine end-member are (km s(-1)): [GRAPHICS] The technique used in monitoring the thickness of the LinbO(3) crystal during the fabrication of the shear transducer illustrates the feasibility of using samples as thin as a few micrometers in the GHz ultrasonic interferometric measurements.