SHEAR AND COMPRESSIONAL MODE MEASUREMENTS WITH GHZ ULTRASONIC INTERFEROMETRY AND VELOCITY-COMPOSITION SYSTEMATICS FOR THE PYROPE-ALMANDINE SOLID-SOLUTION SERIES
Gl. Chen et al., SHEAR AND COMPRESSIONAL MODE MEASUREMENTS WITH GHZ ULTRASONIC INTERFEROMETRY AND VELOCITY-COMPOSITION SYSTEMATICS FOR THE PYROPE-ALMANDINE SOLID-SOLUTION SERIES, Physics of the earth and planetary interiors, 99(3-4), 1997, pp. 273-287
Successful fabrication of a high frequency (up to 600 MHz) shear trans
ducer enables us to determine the complete sets of sound velocities fo
r single crystal samples using GHz ultrasonic interferometry. Sound ve
locities for a natural pyrope and a natural almandine were measured. R
e-examining the existing database, we found that velocities for the py
rope-almandine solid solution series can be modeled quantitatively wit
h 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 d
eviation of the measurement data from these linear relationships is 1%
. For every 10% increase in the Fe/(Mg+Fe) ratio (almandine), the velo
cities decrease by about 1%. Published density data for this garnet so
lid 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. Usin
g 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-m
ember 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 f
ew micrometers in the GHz ultrasonic interferometric measurements.