Changes in dimensions, stresses and gravitational energy of the Earth due to crystallization at the inner-core boundary under isochemical conditions

Abstract

Summary. If the inner-core boundary (ICB) is a phase boundary, not a chemical boundary, changes in core temperatures will lead to changes in the size of the inner core with corresponding changes in the size of the Earth. We have investigated theoretically some effects of crystallization at the ICB due to slow cooling of the core. The earth model consists of a homogeneous inner core, outer core and mantle, and the calculations are for the elastic and viscoelastic case, including self-gravitation. Complete solidification of the core is connected with a decrease of the Earth's radius by 5 km and with additional pressures in the core and mantle of the order of several kbar, under the assumption that the density change at the ICB is 1 per cent. Part of the released gravitational energy is converted into deformational energy, distributed throughout the Earth. The main part, more than 70 per cent, is converted into heat at the ICB: this is the work done by the hydrostatic pressure during contraction of the crystallizing material. It forms a part of the latent heat of crystallization that in previous estimates has been neglected. Assuming that: (1) the density change at the ICB is 1 per cent, (2) the radius (volume) of the inner core has grown to its present value in 4 x 109yr, we obtain as an estimate for this part of latent heat 5.82 x 10 (1.94~ 10) watt. This is 1.9 (0.6) per cent of the Earth's heat flux. If crystallization of the core would actually take place, the concentrated heat source at the ICB would delay cooling of the core and possibly maintain for long times temperature gradients in the outer core which are sufficient 'for thermal convection. The critical parameter for all effects studied is the (so far unknown) density change of core material upon crystallization under high pressures.