Applicability of isothermal unrealistic two-parameter equations of state for solids

Abstract

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of theisothermal unrealistic two-parameter equations of state for solids (EOS), proposed atdifferent stages in the development of the EOS field, for the purposes of smoothing andinterpolation of pressure–volume data, and extraction of accurate values of the isothermalbulk 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 withour three-parameter EOS, as well as its two-parameter counterpart proposedin this work. We have applied all the EOS models, with no constraint on theparameters, to the accurate and model-independent isotherms of nine solids. Theapplicability has been assessed in terms of an unbiased composite test, comprising fittingaccuracy, agreement of the fit parameters with experiment, stability of the fitparameters with variation in the compression/pressure ranges and on the basis ofthe 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 EOSswith respect to the test parameters. A number of remarkable findings emergefrom the present study. Surprisingly, both the old EOSs, the Born–Mie and thePack–Evans–James, are significantly better in their curve-fitting capability than theBirch–Murnaghan EOS which has been widely used and continues to be used forcurve-fitting purposes as a standard EOS in the literature. The Born–Mayer as well as theWalzer–Ullmann–Pan’kov models also fit isotherms better than the Birch. Theperformance of the EOS based on the Rydberg potential—that has been rediscovered byRose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currentlyused as a standard EOS along with that of the Birch—is very poor, on a comparativescale. Furthermore, the curve-fitting capability of our original three-parameterEOS, and more importantly its two-parameter counterpart, is superior to allthe isothermal unrealistic two-parameter EOSs so far proposed in the literature.