# The Interrelationship of Thermodynamic Properties Obtained by the Piston-Cylinder High Pressure Experiments and RPR High Temperature Experiments for Nacl

- Murli H. Manghnani and
- Yasuhiko Syono

Published Online: 21 MAR 2013

DOI: 10.1029/GM039p0289

Copyright © 1987 by Terra Scientific Publishing Company (TERRAPUB), Tokyo.

Book Title

## High-Pressure Research in Mineral Physics: A Volume in Honor of Syun-iti Akimoto

Additional Information

#### How to Cite

Anderson, O. L. and Yamamoto, S. (1987) The Interrelationship of Thermodynamic Properties Obtained by the Piston-Cylinder High Pressure Experiments and RPR High Temperature Experiments for Nacl, in High-Pressure Research in Mineral Physics: A Volume in Honor of Syun-iti Akimoto (eds M. H. Manghnani and Y. Syono), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM039p0289

#### Publication History

- Published Online: 21 MAR 2013
- Published Print: 1 JAN 1987

#### Book Series:

#### ISBN Information

Print ISBN: 9780875900667

Online ISBN: 9781118664124

- Summary
- Chapter
- References

### Keywords:

- Mineralogy and Crystal Chemistry;
- Phase transformations;
- High Pressure-High Temperature Research

### Summary

Thermodynamic properties (e.g., *K* _{T}, (∂*K* _{T}/∂*P*)_{T}, and (∂T/∂*P*)_{s}) for compressible solids can be measured by the experimental equation of state determined by the piston-cylinder experiment. However, this experiment is more limited for relatively incompressible solids such as MgO. For incompressible solids, the rectangular parallelepiped resonance (RPR) method has been useful for finding the thermodynamic properties such as *K* _{s}, *K* _{T}, γ, δ_{s}, δ_{T}, (∂*K* _{T}/∂*P*)_{v}, and (∂γ/∂*T*)_{P} of materials at high temperatures. The measured properties derived from both types of experiments are connected by the standard thermodynamic formulas.

In this paper, we show that results from high temperature elasticity measurements, such as the RPR measurement, although having no compression information, nevertheless yield many of the piston-cylinder compression results when combined with the data of *K* _{TO}′=(∂*K* _{T}/∂*P*)_{T} versus *T* at *P*=0.

By using the high temperature elasticity data for NaCl along with *K* _{TO}′, we show that (∂*K* _{T}/∂*P*)_{V} is very close to zero at high temperatures. As a consequence many thermodynamic identities are simplified and we find: 1) the thermal pressure is independent of volume at high temperature, confirming previous conclusions (Anderson et al., 1982) about the Boehler and Kennedy NaCl data (1980); 2) the change of γ with *T* at constant *V* is negative at high *T*; 3) the variation of the parameter δ_{T} with temperature is quite small, and close in value to (∂^{2} *K* _{T}/∂*T*∂*P*) as measured by Spetzler et al. (1972).

Further simplifications are possible for NaC1 because we find that (∂α*K* _{T}/∂*T*)_{P}=0 at high *T*. This yields: 1) *q*=−(∂lnγ/∂ ln ρ)_{T} is close to unity (and thus γρ=constant) confirming several previous studies of this parameter; 2) the product α*K* _{T}=(∂*P*/∂*T*)_{V} is independent of both *P* and *T* (or *V* and *T*) as long as *T* is above the Debye temperature, θ. We further conclude that even through there is no anharmonicity in (∂*P*/∂*T*)_{V}, there is measurable anharmonicity in the temperature variation of *C* _{v} and γ(*V*=*V* _{0}); 3) the thermodynamic isothermal equation of state, derived by Brennan and Stacey (1979), is valid for NaCl because γρ = constant, and is shown to follow the pattern of shock wave experiments up to 20 GPa.

In this paper, our RPR method results were obtained to nearly 800 K. This happens to be the upper limit of the acoustic experiment measurements. Also, our elasticity data has confirmed the previous work on NaCl by Spetzler et al. (1972). Spetzler's results could have been used to find the same conclusions described above. Our emphasis on NaC1 arises from the fact that there is abundant thermodynamic data on this solid considerably above its Debye temperature, where θ=300 K. For minerals where the Debye temperature is much higher (geophysically interesting minerals, 600<θ<1000 K), the acoustic method fails to give elasticity measurements in the high temperature region. Here the RPR method succeeds, for it has been used at temperatures as high as 1300 K (Sumino et al., 1983) for MgO. The ultrasonic experiment is limited to a maximum of about 800 K because of glues and the acoustic transducer problems at high *T*.

Using the RPR experiment, the methods and equations described herein will be particularly suitable for geophysically interesting minerals with high values of θ. But the proposed method can best be illustrated by applying it to NaCl because pertinent high pressure data now exist for this solid so that exact calculations can be made in the high pressure-high temperature field (see detailed calculations of Birch, 1986).