Empirical equation of state for high compression

Mao, Nai-Hsien

doi:10.1029/jb075i035p07508

Cited by 57 publications

(8 citation statements)

References 17 publications

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“…Various forms of X and Y used in the literature have been listed by Mac Donald [31,32] and Mao [33]. If all the A i coefficients are known, then all the equations of state under the same thermodynamic conditions can be determined.…”

Section: Kumari-dass Equation Of Statementioning

confidence: 99%

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Inverted equations of state for solids under high pressures

2011

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In the present communication we have reviewed some inverted type equations of state for solids under high pressures. An inverted equation of state (EOS) gives volume as a function of pressure for a solid under isothermal conditions. We have considered various equations of state proposed by earlier workers which express volume as a function of pressure. Expressions for bulk modulus and its pressure derivatives based on such EOSs are obtained and reported here. It is emphasized here that the high pressure derivative properties are very sensitive to the forms of equations of state representing volume-pressure relationships. We have also studied the thermoelastic properties of solids based on pressure derivatives of bulk modulus. Applications have been extended in the present review article to the solids which are metals as well as non-metals including geophysical minerals present in the lower mantle and core of the Earth.

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Section: Kumari-dass Equation Of Statementioning

confidence: 99%

“…However, smaller the number of the adjustable parameters required for the highest pressure range, the better is the equation of state. It should be noted that the equation of state listed by Mao [33] and Mac Donald [31,32] may be used up to a pressure of 100 k bar (10 GPa) or so.…”

Section: Kumari-dass Equation Of Statementioning

confidence: 99%

Inverted equations of state for solids under high pressures

2011

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“…One uses the original Eulerian strain or Interatomic potential EoSs and refines their parameters in order to find a better fit to experiments [31][32][33][34] . The other approach is to find a mathematical function which gives the best fit to the experiments [35][36][37][38] .…”

Section: Empirical Eossmentioning

confidence: 99%

“…[31][32][33][34] The other approach is to find a mathematical function which gives the best fit to the experiments. [35][36][37][38] Roy and Roy 39 gave a good review and evaluate the fittings of the currently used EOSs. Their proposed 40 threeparameter empirical EOS is…”

Section: Empirical Eossmentioning

confidence: 99%

Semiempirical pressure-volume-temperature equation of state: MgSiO3 perovskite is an example

Garai

2007

Journal of Applied Physics

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Simple general formula describing the pressure-volume-temperature relationships ͑p-V-T͒ of elastic solids is constructed from theoretical considerations. The semiempirical equation of state ͑EOS͒ was tested to experiments of perovskite 0 -109 GPa and 293-2000 K. The parameters providing the best fit are B 0 = 267.5 GPa, V 0 = 24.284 cm 3 , ␣ 0 = 2.079ϫ 10 −5 K −1 , ‫ץ‬B 0 / ‫ץ‬p = 1.556, and ‫␣ץ‬ 0 / ‫ץ‬p = −1.098ϫ 10 −7 K −1 GPa −1 . The root-mean-square deviations ͑RMSDs͒ of the residuals are 0.043 cm 3 , 0.79 GPa, and 125 K for the molar volume, pressure, and temperature, respectively. These RMSD values are in the range of the uncertainty of the experiments, indicating that the five-parameter semiempirical EOS correctly describes the p-V-T relationships of perovskite. Separating the experiments into 200 K ranges the semiempirical EOS was compared to the most widely used finite strain, interatomic potential, and empirical isothermal EOSs such as the Birch-Murnaghan, the Vinet, and the Roy-Roy, respectively. Correlation coefficients, RMSDs of the residuals, and Akaike Information Criteria were used for evaluating the fitting. Based on these fitting parameters under pure isothermal conditions the semiempirical p-V EOS is slightly weaker than the Birch-Murnaghan and Vinet EOSs; however, the semiempirical p-V-T EOS is superior in every temperature range to all of the investigated conventional isothermal EOSs.

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“…The EOSs subjected to these seven tests are the three-parameter extensions of the EOS models formulated by Bridgman (1929), Murnaghan (1937), Birch (1938), Slater (1939, Davis and Gordon (1967), Macdonald (1969), Holzapfel (1991, Poirier and Tarantola (1998), and the so-called 'universal EOS' promoted by Vinet et al (1986). Also included for the inter-comparison purposes are the threeparameter EOSs proposed by Keane (1954), Mao (1970), Thomsen (1970, Huang and Chow (1974), Luban (1983, Kumari and Dass (1990), Hama andSuito (1996), and Bose Roy and Bose Roy (1999), and also the EOS based on a modified Eulerian strain as suggested by Sushil et al (2004). Interestingly, the three-parameter Mie-Gruneisen EOS, built on the…”

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confidence: 99%

Applicability of isothermal three-parameter equations of state of solids—a reappraisal

Roy¹,

Roy

2005

J. Phys.: Condens. Matter

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The objective of the present study, an extension of a recent one, is to intercompare the utility of the various isothermal three-parameter equations of state (EOSs) of solids, considered viable at different stages in the development of the EOS field, spanning over a period of about a century now. In a recent paper we have compared our isothermal three-parameter equation of state of solids with seven three-parameter isothermal EOSs-five corresponding to the regression curves of V /V 0 on P, and two to those of P on V /V 0 . In this study, we investigate the relative utility of 21, i.e., virtually all, of the viable threeparameter EOSs-for the purposes of smoothing and interpolation of pressurevolume data, and extraction of accurate values of isothermal bulk modulus and its pressure derivative-corresponding to the regression curves of P on V /V 0 . We have applied the EOSs, with no constraint on the parameters, to accurate and model-independent isotherms of nine solids, and assessed the goodness of the fitting accuracy; goodness of the stability of the fit parameters B 0 , B 0 , and B 0 with variation in the pressure/compression ranges; and goodness of the agreement of the fit parameters B 0 and B 0 with experiment. Further, an additional test of goodness of randomization of the data points about the fit curves, quantified in terms of the number of wiggles of the data deviation curves about the fits, is also applied in the present study. The EOSs subjected to these seven tests are the three-parameter extensions of the EOS models formulated by Bridgman (1929), Murnaghan (1937), Birch (1938), Slater (1939, Davis and Gordon (1967), Macdonald (1969), Holzapfel (1991, Poirier and Tarantola (1998), and the so-called 'universal EOS' promoted by Vinet et al (1986). Also included for the inter-comparison purposes are the threeparameter EOSs proposed by Keane (1954), Mao (1970), Thomsen (1970, Huang and Chow (1974), Luban (1983, Kumari and Dass (1990), Hama andSuito (1996), and Bose Roy and Bose Roy (1999), and also the EOS based on a modified Eulerian strain as suggested by Sushil et al (2004). Interestingly, the three-parameter Mie-Gruneisen EOS, built on the

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Empirical equation of state for high compression

Cited by 57 publications

References 17 publications

Inverted equations of state for solids under high pressures

Inverted equations of state for solids under high pressures

Semiempirical pressure-volume-temperature equation of state: MgSiO3 perovskite is an example

Applicability of isothermal three-parameter equations of state of solids—a reappraisal

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