The dependence of the melting temperatures of iron

Summary. The melting curve (melting temperature versus pressure) of iron is fundamental to an understanding of the physics of the Earth’s core. Since experimental data are available for pressures a few orders of magnitude smaller than the core pressures, the problem is to find the correct ways of extrapolating them. Here we employ Ross ’ melting criterion, a reformulation of Lindemann’s law in the framework of statistical mechanics, because all the proposed empirical melting laws can be deduced from it; it also allows us to take into account the interatomic potential and the various crystal structures which iron may possess. The results of our calculations lead us to the conclusion that the melting temperatures of iron at the core pressures are extremely uncertain since no definite choice among possible potential functions is allowed. The melting temperature at the mantle-core boundary may range between 3500 and 4300 K, while at the inner core-outer core boundary it may range between 4500 and 7000K. The average melting temperature gradient is shown to be between 0.6 and 1.1 deg/km. The problem of establishing if the core is made of fcc or hcp iron is definitely secondary to that of the choice of the potential function