In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus |
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| Authors: | G D Gwanmesia I Jackson and R C Liebermann |
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| Institution: | (1) Department of Physics and Pre-Engineering, Delaware State University, Dover, DE 19901, USA;(2) Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia;(3) Department of Geosciences, Stony Brook University, Stony Brook, NY 11794, USA |
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| Abstract: | Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg3Al2Si3O12) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated
gas-medium apparatus. The temperature derivatives of the elastic moduli (∂Ks/∂T)
P
= −19.3(4); (∂G/∂T)
P
= −10.4(2) MPa K−1] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a
DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138,
1983) method but |(∂Ks/∂T)
P
| is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth
Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this
study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂2
G/∂P∂T = 0.07(12), 0.20(14)] × 10−3 K−1 and ∂2
K
S
/∂P∂T = −0.20(24), 0.22(26)] × 10−3 K−1, both of order 10−4 K−1 and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic
measurements of precision significantly better than 1%. |
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| Keywords: | Pyrope Polycrystalline Elasticity Mixed derivative Gas-medium apparatus |
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