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

Details 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 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

Mar 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007pcm....34...85g&link_type=abstract

Physics and Chemistry of Minerals, Volume 34, Issue 2, pp.85-93

Physics

2

Pyrope, Polycrystalline, Elasticity, Mixed Derivative, Gas-Medium Apparatus

Scientific paper

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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