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.