Thermodynamics of the second order transitions in alpha and epsilon iron

Abstract

The presence of a second order transition in epsilon iron, the hexagonal closest packed form, is demonstrated. Two functions of the form T^*(Θ^−1/2 + A + BΘ) are proposed to model the extra heat capacity beyond what can be represented in a polynomial model in the regions 50 K below and 30 K above a lambda point. With A and B chosen so that ΔC_p/T is zero with a zero first derivative at the end points, these functions can provide an accurate and convenient representation for the thermodynamic properties of a material at temperatures and pressures near the lambda point for a second order transition. Calculations of the T/P phase diagram of iron provide a good test of the usefulness of this model since two second order transitions are present in the region of interest. This model for the thermodynamic properties of iron reconciles the static and shock wave studies on the melting point of iron at high pressures. Other forms of solid iron may be stable at the melting point above 100 GPa, but the melting point of pure iron at the inner core boundary of the Earth, 328.9 GPa, is probably within 500 K of the calculated melting point for ε′ iron at this pressure, 4 680 K.