Grüneisen parameter of hcp-Fe to 171 GPa

Abstract

We measured the phonon density of states (DOS) of hexagonal close-packed iron (ε-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 $\varepsilon$-Fe's total phonon DOS which, in turn, is directly related to the ambient temperature vibrational Grneisen parameter ( vib). Fitting our individual λ vib data points with λ vib = λ vib,0 (V/V 0) q, a common parameterization, we found an ambient pressure λ 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 Grneisen parameter ( D). Comparing our vib (V) and D (V), we found λ vib to be ∼10% larger than D at any given volume. Finally, applying our λ vib (V) to a Mie-Grneisen 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 ε-Fe at Earth's core pressures. Copyright 2011 by the American Geophysical Union.