Global InformationThermal equation of state of solids information
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In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V. The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
For the ideal gas at high pressure-temperature (high P-T), the soft gas is filled in a solid firm container, and the gas is restrained inside the container; while for a solid at high P-T, a solid is loaded inside the soft medium, and the solid can expands/shrinks in the soft medium when heated and compressed. Therefore, the compression/heating process of the gas could be either constant temperature (isothermal), constant pressure (isobaric) or constant volume (isochoric). Though the compression/heating process of solids can be constant temperature (isothermal), and constant pressure (isobaric), it can not be a constant volume (isochoric),
At high P-T, the pressure for the ideal gas is calculated by the force divided by the area, while the pressure for the solid is calculated from bulk modulus (K, or B) and volume at room temperature, or from Eq (1) at high P-T. A pressure gauge's bulk modulus is known, and its thermal equation of state is well known. To study a solid with unknown bulk modulus, it has to be loaded with a pressure gauge, and its pressure will be determined from its pressure gauge.
The most common pressure gauges are Au, Pt, Cu, and MgO, etc. When two or more pressure gauges are loaded together at high P-T, their pressure readings should be the same. However, large discrepancies have been reported in pressure determination using different pressure gauges or different thermal equations of state for the same pressure gauge.[1][2][3] Fig.1 is a schematic plot showing the discrepancy in paper.[4]
Out of the total pressure in Eq.(1), the first term pressures on the right side of Ag, Cu, Mo, Pd at room temperature are consistent in a wide pressure range, according to the Mao ruby scale up to 1 Mba.[5] In addition, the first term pressure of Ag, Cu, and MgO are consistent according to third-order Birch–Murnaghan equation of state.[6] Therefore, the discrepancy of the total pressure, P(V, T), should be from the second term in Eq. 1, which is the thermal pressure Pth(V, T) at high P-T.
- ^ Y. Fei, J. Li, K. Hirose, W. Minarik, J. V. Orman, C. Sanloup, W. V. Westrenen, T. Komabayashi, K. Funakosh, Physics of the Earth and Planetary Interiors 143-144, 515 (2004).
- ^ K. Hirose, S. Karato, V.F. Cormier, J.P. Brodholt, D.A. Yuen, Geophysical Research Letters 33, L12S01 (2006).
- ^ G. Fiquet, J.P. Itie, P. Richet, D. Hausermann, M. Hanfland, D. Andrault, European Journal of Mineralogy 10, 931 (1998).
- ^ Yan, Jinyuan; Yang, Shizhong (February 2022). "Pressure-Dependent Thermal Expansion Coefficient by a Diamond Anvil Cell". International Journal of Thermophysics. 43 (2): 17. Bibcode:2022IJT....43...17Y. doi:10.1007/s10765-021-02945-3. ISSN 0195-928X. OSTI 1865614. S2CID 254583807.
- ^ Mao, H. K.; Bell, P. M.; Shaner, J. W.; Steinberg, D. J. (1978-06-01). "Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R 1 fluorescence pressure gauge from 0.06 to 1 Mbar". Journal of Applied Physics. 49 (6): 3276–3283. Bibcode:1978JAP....49.3276M. doi:10.1063/1.325277. ISSN 0021-8979.
- ^ Fei, Yingwei; Ricolleau, Angele; Frank, Mark; Mibe, Kenji; Shen, Guoyin; Prakapenka, Vitali (2007-05-29). "Toward an internally consistent pressure scale". Proceedings of the National Academy of Sciences. 104 (22): 9182–9186. doi:10.1073/pnas.0609013104. ISSN 0027-8424. PMC 1890468. PMID 17483460.