The elastic properties of an almandine‐spessartine garnet and elasticity in the garnet solid solution series

This paper reports the results of ultrasonic measurements of the second-order elastic constants of a single-crystal specimen of almandine-spessartine garnet as a function of pressure and temperature. The density of the sample, ρ0 = 4.2396 ± 0.0016 g/cm3, is consistent with the composition (Fe0.52, Mn0.46,Ca0.01) 3Al2Si3O12 as determined by microprobe analysis. The pertinent results, Ks = 1763.3 ± 2.3 kbar, (∂Ks/∂T)T = 4.59 ± 0.16, and (∂Ks/∂P)P = −0.172 ± 0.005 kbar/0C, where Ks is the adiabatic bulk modulus, are related systematically to other garnet results published by previous investigators. In addition to the foregoing conventional ultrasonic data we have obtained a measurement of the higher-order property (∂2Ks /∂T∂P) of 0.9±0.6×10−30C−1. The magnitude of this parameter suggests that it could significantly effect seismic velocity and density equations of state which are used commonly to model the earth's mantle. Assuming that the second-order elastic constants Cij of garnets are related linearly to the molar fraction of their constituent end-members, the present data have been combined with the work of previous investigators in order to derive the elastic properties throughout the garnet solid solution series. The relevant' results for Ks from the least squares analysis for the various end members are as follows (in kilobars); pyrope, 1658±13; almandine, 1801±7; spessartine, 1723±10; grossular, 1705±13. These data provide the basis for calculating the elastic wave velocities for any (Mg, Fe, Mn, Ca) 3Al2Si3O12 garnet.

[1]  D. Schuele,et al.  Pressure derivatives of the elastic constants of NaCl and KCl at 295°K and 195°K , 1965 .

[2]  Gerald V. Gibbs,et al.  The Crystal Chemistry of the Silicate Garnets , 1971 .

[3]  O. Anderson,et al.  Pressure Derivatives of Elastic Constants of Single‐Crystal MgO at 23° and ‐195.8°C , 1966 .

[4]  C. E. Tilley,et al.  Origin of Basalt Magmas: An Experimental Study of Natural and Synthetic Rock Systems , 1962 .

[5]  A. L. Frisillo,et al.  Measurement of single‐crystal elastic constants of bronzite as a function of pressure and temperature , 1972 .

[6]  H. J. Mcskimin,et al.  Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids , 1961 .

[7]  Z. Chang,et al.  Pressure dependence of single‐crystal elastic constants and anharmonic properties of spinel , 1973 .

[8]  G. Simmons,et al.  Elasticity of some mantle crystals structures. III - Spessartite-almandine garnet , 1974 .

[9]  Earl K. Graham.  Elasticity and Composition of the Upper Mantle , 1970 .

[10]  B. Skinner.  Physical properties of end-members of the garnet group , 1956 .

[11]  Naohiro Soga,et al.  New measurements on the sound velocity of calcium oxide and its relation to Birch's law , 1967 .

[12]  Taro Takahashi,et al.  Compression of ferromagnesian garnets and the effect of solid solutions on the bulk modulus , 1970 .

[13]  R. N. Thurston,et al.  Elastic Moduli of Quartz versus Hydrostatic Pressure at 25 and-195.8C , 1965 .

[14]  Don L. Anderson,et al.  Composition of the Mantle and Core , 1977 .

[15]  R. Verma,et al.  Elasticity of some high-density crystals , 1960 .

[16]  F. Murnaghan.  The Compressibility of Media under Extreme Pressures. , 1944, Proceedings of the National Academy of Sciences of the United States of America.

[17]  J. Forbes,et al.  Accurate Relations Determining the Volume Dependence of the Quasiharmonic Grüneisen Parameter , 1968 .

[18]  B. Mason,et al.  Pyroxene-Garnet Transformation in Coorara Meteorite , 1970, Science.

[19]  A. E. Ringwood,et al.  Phase transformations and the constitution of the mantle , 1970 .

[20]  H. J. Mcskimin.  Notes and References for the Measurement of Elastic Moduli by Means of Ultrasonic Waves , 1961 .

[21]  Naohiro Soga,et al.  Elastic constants of garnet under pressure and temperature , 1967 .

[22]  Don L. Anderson,et al.  Application of isotropic finite strain theory to ultrasonic and seismological data , 1970 .

[23]  Gene Simmons,et al.  Velocity of compressional waves in various minerals at pressures to 10 kilobars , 1964 .

[24]  F. Birch.  The variation of seismic velocities within a simplified earth model, in accordance with the theory of finite strain , 1939 .

[25]  Thomas J. Ahrens,et al.  Dynamic compression of enstatite , 1971 .

[26]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[27]  O. Anderson,et al.  Pressure Derivatives of the Sound Velocities of Polycrystalline Alumina , 1966 .