Objective: To formulate the equation of state as well as their isothermal bulk modulus using the basic laws of thermodynamics and Identities. Method: This study has considered a relation of Eulerian finite strain having two arbitrary parameters a ∈ and b ∈ (a ∈ ,b ∈ ≤ 1). The salient feature of this equation of state is that by substituting the values of parameters, the expressions for the prominent equations of state and their bulk modulus can be obtained. Findings : Four prototype solids viz. MgO, CaO, NaCl, and Al 2 O 3 have been applied to the equation of state to test its validity and applicability. The results were compared with experimental data and other equations of state. Consequently, the proposed equation of state exhibits the same trend as prominent equations of state and provides better results. It corresponds well with the experimental curve at high pressure. Novelty: The GEOS can be used in the future for planning high-pressure experiments on the compression behavior of several materials, minerals, and solids.

The present study deals with the elastic properties at different pressure of hcp-iron have been carried out. By exerting pressure on the cubic body of n-th power of edge length, we have used a new equation of state based on Eulerian finite theory. We have computed the bulk modulus and their pressure derivative from this formulated equation of state. The results from the proposed equation of state (EOS) show the better agreement with available experimental data. Thus, the derived expressions are able to predict the elastic properties of hcp-iron under high pressures.

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