Melting of iron and other metals at earth’s core conditions: A simplified computational approach

In order to study melting of metals at high pressure, we propose a different method which can be thought of as a generalization of the well-known Lindemann law. One essential interesting feature is that neither the Debye temperature nor the Gr\"uneisen coefficient are used in the theory. We find that the method based on first-principles calculations can be used to model the pressure dependence of the melting properties of metals very well. Predictions of the melting along the principal Hugoniot are calculated for Cu and Ta. In the case of Fe, the melting temperature is calculated at geophysically interesting pressures.