Dislocation-mediated melting of iron and the temperature of the Earth's core

Summary . Dislocation theories of melting provide a possibility of calculating the melting temperature, from first principles, as the temperature at which the free energy of a crystal saturated with dislocations becomes equal to that of the dislocation-free crystal. After a brief review of the physical bases of the dislocation melting theories, Ninomiya's theory is used to determine the melting temperature as well as the volume and entropy of melting and the slope of the melting curve for iron at atmospheric pressure and under conditions prevailing at the Earth's inner core boundary. The necessary parameters (elastic moduli, Grüneisen parameter) are drawn from seismological earth models. We find a melting temperature of the material of the inner core of about 6150 K, independent of shock-wave experiments but in good agreement with them and with extrapolations using Lindemann's law. With usually accepted values of the melting point depression due to light elements in solution, the temperature at the inner core boundary is found to be T _ICB≅ 5000 K. This temperature is compatible with a temperature of the outer core at the core-mantle boundary T _CMB≅ 3800 K. Dislocation melting theories can thus help constrain the temperature profile in the Earth's core.