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Phase-wise thermoelastic diagnostics of a modified rational equation of state for mantle–core pressure regimes
S. Shankar, M. Sonu, S. Gaurav, K. Shefali, Y. Nitesh and B. Arshia

A modified rational equation of state (EOS) with explicit control of the infinite-pressure bulk-modulus derivative K′ ∞ is proposed and evaluated for Earth-interior pressure windows. The formulation is presented as a phase-wise diagnostic EOS, not as a single universal mantle–core equation. Its first validation is based on the compression response P–V/V₀ , which is compared with PREM-consistent reference values and Stacey’s thermodynamically constrained EOS. since agreement in compression alone can conceal nonphysical high-pressure behaviour, the assessment is extended to derivative-sensitive quantities, including K(P), K′(P), K″(P), P/K, γ(P), q(P), and the thermoelastic derivative D_α. The Stacey/Sunil–Sharma formulation is used to test the infinite-pressure fixed-point condition (P/K)_∞ = 1/K′_∞ , the admissibility requirement K′_∞ > 5/3, and the need for finite positive limiting derivative behaviour. The EOS-derived γ(P) and q(P) trends are further connected to D_α = (V/α)(dα/dV)_S = K′ − 1 + q, for which the infinite-pressure limit is [D_α]_∞ = K_′∞ − 1. The results show that the proposed rational form is useful for compact, phase-wise fitting and for identifying where high-pressure curvature control becomes necessary. In particular, the phase-wise implementation gives physically meaningful mantle-window trends and positive D_α (P), whereas a single continuation across mantle–core regimes can produce non-monotonic stiffness behaviour. The study therefore establishes the EOS as a derivative-sensitive screening and diagnostic formulation for high-pressure extrapolation.

Keywords: equation of state; PREM; Stacey EOS; Shanker identity; K′_∞; λ_∞; Grüneisen parameter;
thermoelastic derivative; thermal expansivity; mantle; core