Kinetics of crystal growth in a terrestrial magma ocean

The problem of crystal sizes is one of the central problems of differentiation of a terrestrial magma ocean and it has been an arbitrary parameter in previous models. The crystal sizes are controlled by kinetics of nucleation and crystal growth in a convective magma ocean. In contrast with crystallization in magma chambers, volcanic lavas, dikes, and other relatively well studied systems, nucleation and crystallization of solid phases occur due to the adiabatic compression in downward moving magma (adiabatic "cooling'). This problem is solved analytically for an arbitrary crystal growth law, using the following assumptions: convection is not influenced by the kinetics, interface kinetics is the rate controlling mechanism of crystal growth, and the adiabatic cooling is sufficiently slow for the asymptotic solution to be valid. The problem of nucleation and crystal growth at constant heat flux from the system and at constant temperature drop rate are shown to be described with similar equations. -from Authors