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

• Published in: Physics and chemistry of minerals 2007-03, Vol.34 (2), p.85-93
• Main Authors: Gwanmesia, G. D., Jackson, I., Liebermann, R. C.
• Format: Article
• Language: English
• Subjects: Acoustic measurement; Data analysis; Derivatives; Earth; Elastic waves; Interferometry; Magnesium aluminum silicates; Modulus of elasticity; Parallelepipeds; Phase comparison; Planets; Polycrystals; Single crystals; Theoretical density; Ultrasonic testing; Wave velocity
• ISSN: 0342-1791; 1432-2021
• DOI: 10.1007/s00269-006-0130-x

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 ∂2G/∂P∂T = [0.07(12), 0.20(14)] × 10−3 K−1 and ∂2KS/∂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%.