New equation for the influence of pressure on melting

A new equation for the variation of melting points T_m of metals as a function of pressure p has been developed on the basis of simplified atomic considerations. The equation, [ΔT_m/T_m(0)]/βp≈ 2(γ_G − 1/3)(1 + C₂βp), is thought to be in a more convenient form for comparison with experimental data than previous relationships. In this equation, β is the compressibility, γ_G the Grüneisen parameter, and C₂ is a constant related to the anharmonicity. In checking the equation it was found that a value of C₂ = −2.9 appears to be more accurate for the ratio $a_2{\mathrm{/a}}_1^2$ than the value −2.5 reported by Slater (a₁ and a₂ are the coefficients in the expression −ΔV/V₀ = a₁p + a₂p², for the compression of a material). Obviously, the proposed equation for ΔT_m should not be applied when the compression is not well described by the relation involving a₁ and a₂.