In this paper, an isothermal three-parameter equation of state (EOS) of solid is presented in the form V /V 0 = f (P ). The proposed EOS uses three parameters expressible in terms of B 0 , B 0 and B 0 , denoting bulk modulus and its first and second pressure derivatives at zero pressure. The new EOS is applied to the isotherms of ionic, metallic, quantum and rare-gas solid, with pressures ranging from zero to variable maximum pressures of up to 1 TPa (= 10 Mbar). The fits are uniformly excellent, and equally excellent is the agreement of the fitted parameters B 0 and B 0 with experimental values. Deviations between data points and fits are computed and compared with the successful EOSs of similar form from the literature, and the drastic superiority of our new model is demonstrated. Further, the proposed model is applied to the isotherms of metals at ultrahigh pressures, with B 0 and B 0 constrained to experimental values. An inter-comparison of results obtained from different EOSs, including the universal formulations, shows that our new form yields a superior fit.

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

In a recent paper we have proposed a three-parameter equation of state (EOS) of solids, and applied it to a few isotherms and shown that the fits are uniformly excellent. In this paper a comprehensive comparison of the applicability of our model is made with seven existing three-parameter EOSs. We have applied our model along with seven existing three-parameter EOSs, with no constraint on the parameters, to accurate and model-independent isotherms of nine solids and studied the fitting accuracy and agreement of the fit parameters with experiment. Further, each of these nine isotherms is divided into three subsets, and the resulting subsets fitted with all the eight EOSs. The stability of the fitted stressfree bulk modulus B 0 and its pressure derivatives B 0 and B 0 with variation in the compression range is compared. Furthermore, our EOS is applied to a large number of inorganic as well as organic solids, including alloy, glasses, rubbers and plastics; of widely divergent bonding and structural characteristics, and a very good agreement is observed with the compression data. We have also studied the variation of bulk modulus with pressure, with reference to the data on NaCl and Ne, and noted a very good agreement. In addition, our model is applied, with B 0 and B 0 constrained to the theoretical values, to the five isotherms of MgO at 300, 500, 1000, 1500 and 2000 K, obtained on the basis of a first principles approach. For three of these isotherms, the fitting accuracy yielded by our model is higher than those by the three-parameter Birch and universal formulations. Further, variation of bulk modulus with pressure, and pressure with compression, is studied, and a good agreement is observed between the theoretical values and predictions. Furthermore, it is shown that our model agrees well with the theoretical isotherms of CsI and the fit parameters are in good agreement with the experimental data. In essence, the present study assesses the relative merits of the EOSs considered, in respect of applicability to the experimental isotherms with pressures ranging from low to a maximum that varies from the high to ultrahigh pressure regime; for the purposes of smoothing, interpolation and extraction of accurate values of bulk moduli. An overall inter-comparison of the calculated results for eight EOSs

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005 J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of the isothermal unrealistic two-parameter equations of state for solids (EOS), proposed at different stages in the development of the EOS field, for the purposes of smoothing and interpolation of pressure-volume data, and extraction of accurate values of the isothermal bulk modulus and its pressure derivative. To this end, 21 such EOSs are considered, formulated by/labelled as Born-Mie (1920), Born-Mayer (1932), Bardeen (1938), Slater-Morse (1939), Birch-Murnaghan (1947), Pack-Evans-James (1948), Lagrangian (1951), Davydov (1956), Davis and Gordon (1967), Onat and Vaisnys (1967), Grover-Getting-Kennedy (1973), Brennan-Stacey (1979), Walzer-Ullmann-Pan'kov (1979), Rydberg (1981), Dodson (1987), Holzapfel (1991), Parsafar-Mason (1994), Shanker-Kushwah-Kumar (1997), Poirier-Tarantola (1998), Deng-Yan (2002) and Kun-Loa-Syassen (2003). Furthermore, all these EOSs are compared with our three-parameter EOS, as well as its two-parameter counterpart proposed in this work. We have applied all the EOS models, with no constraint on the parameters, to the accurate and model-independent isotherms of nine solids. The applicability has been assessed in terms of an unbiased composite test, comprising fitting accuracy, agreement of the fit parameters with experiment, stability of the fit parameters with variation in the compression/pressure ranges and on the basis of the number of wiggles of the data deviation curves about the fit parameters. Furthermore, a rigorous method is devised to scale the relative adequacy of the EOSs with respect to the test parameters. A number of remarkable findings emerge from the present study. Surprisingly, both the old EOSs, the Born-Mie and the Pack-Evans-James, are significantly better in their curve-fitting capability than the Birch-Murnaghan EOS which has been widely used and continues to be used for curve-fitting purposes as a standard EOS in the literature. The Born-Mayer as well as the Walzer-Ullmann-Pan'kov models also fit isotherms better than the Birch. The performance of the EOS based on the Rydberg potential-that has been rediscovered by Rose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989 J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currently used as a standard EOS along with that of the Birch-is very poor, on a comparative scale. Furthermore, the curve-fitting capability of our original three-parameter EOS, and more importantly its two-parameter counterpart, is superior to all the isothermal unrealistic two-parameter EOSs so far proposed in the literature.

In this paper, an isothermal three-parameter equation of state (EOS) of solid is proposed in the form V/V 0 = f(P), with pressure P as the independent and relative volume V/V 0 as the dependent variable. The proposed EOS uses three parameters expressible in terms of B 0 , B 0 0 and B 00 0 , denoting bulk modulus and its first and second pressure derivatives at zero pressure. The new model is applied to the isotherms of ionic, metallic, quantum and rare-gas solid, with pressures ranging from zero to variable maximum pressures of up to 1 TPa. The fits are uniformly excellent. Root-meansquare deviations between data and fits are computed and compared with the three-parameter empirical EOS proposed by Kumari and Dass [J. Phys.: Condens. Matter 2, 3219 (1990)]. It is shown that our new form yields a decisively superior fit. Furthermore, it is shown that our proposed equation of state has an advantage for some close-packed materials because it allows B 0 1 ¼ ðdB s =dPÞ s (P ! 1) to be fitted, and this is where the usual standard equations fail badly.