Pressure dependence of the melting temperature of metals

We present a new method for the analysis of the experimental data for the pressure dependence of the melting temperature of metals. The method combines Lindemann's law, the Debye model, and a first-order equation of state with the experimental observation that the Gr\"uneisen parameter divided by the volume is constant. We observe that based on these assumptions, in the absence of phase transitions, plots of the logarithm of the normalized melting temperature T'=(Tₘ/Tₘ₀{X}²) versus the logarithm of the normalized pressure P'=1+βP are straight lines with slope 2{{γ}}₀/α;{T}ₘ₀$ is the zero-pressure melting temperature, X==(V/${V}₀)1/3, γ₀ is the Gr\"uneisen parameter at Tₘ₀, {α}==B₀'+1, {β}=={α}/B₀, where B₀ is the isothermal bulk modulus at Tₘ₀, and B₀' is the pressure derivative of B₀ at Tₘ₀. We find that the normalized-melting-temperature--versus--normalized-pressure curves accurately satisfy this linear relationship for Al, Ag, Au, Cs, Cu, K, Na, Pt, and Rb. In addition, this technique provides a sensitive tool for detecting phase transitions.