We measured the phonon density of states (DOS) of hexagonal close-packed iron (ɛ-Fe) with high statistical quality using nuclear resonant inelastic X-ray scattering and in situ X-ray diffraction experiments between pressures of 30 GPa and 171 GPa and at 300 K, with a neon pressure medium up to 69 GPa. The shape of the phonon DOS remained similar at all compression points, while the maximum (cutoff) energy increased regularly with decreasing volume. As a result, we present a generalized scaling law to describe the volume dependence of ɛ-Fe's total phonon DOS which, in turn, is directly related to the ambient temperature vibrational Grüneisen parameter (γ_(vib)). Fitting our individual γ_(vib) data points with γ_(vib) = γ_(vib),0(V/V0)^q, a common parameterization, we found an ambient pressure γ_(vib,0) = 2.0 ± 0.1 for the range q = 0.8 to 1.2. We also determined the Debye sound velocity (v_D) from the low-energy region of the phonon DOS and our in situ measured volumes, and used the volume dependence of v_D to determine the commonly discussed Debye Grüneisen parameter (γ_D). Comparing our γ_(vib)(V) and γ_D(V), we found γ_(vib) to be ∼10% larger than γ_D at any given volume. Finally, applying our γ_(vib)(V) to a Mie-Grüneisen type relationship and an approximate form of the empirical Lindemann melting criterion, we predict the vibrational thermal pressure and estimate the high-pressure melting behavior of ɛ-Fe at Earth's core pressures
