Applicability of three-parameter equation of state of solids: compatibility with first principles approaches and application to solids

Abstract

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

Inverted equations of state for solids under high pressures

“…It is found that some other inverted type EOS due to earlier workers [57] can also be derived from a generalized version.…”

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

“…[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…”

“…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] .…”

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

“…Thus there will be a perfect synchronization between the two approaches. However, we do not have, at the moment, an unambiguous set of bulk modulus data even for a solid as simple as NaCl [37] and as stable as Cu, as discussed later. Furthermore, the experimental uncertainty, accompanying the measured bulk modulus values, in general, is much larger than those for the measured isotherms.…”

“…An obsession of various workers with the appropriateness of the 'input' approach [17,45,46,50,70,80], over the decades, in conjunction with the paucity of the experimentally measured values of B 0 , has, in fact denied the three-parameter EOSs as much attention as the two-parameter EOSs, in respect of their utility. However, the traditionally accepted view that the inclusion of increasing number of parameters would increasingly improve the behaviour of an EOS towards experiments is not necessarily true, for reasons referred to in [37]. Sometimes the authors, viz [47], obsessed with the 'input' approach, but confronted with the problem of selection of data, picked up a measured value of B 0 of their choice, and treated B 0 as a fitting parameter to achieve the best fit to the higher-pressure EOS curves.…”