Oscillatory zonation of minerals and self-organization in silicate solid-solution systems; a new nonlinear dynamic model

A new non-ideal, disequilibrium and non-linear dynamic model is presented to describe the process of crystal growth in the melt f = 1/[1 + (beta /X (super s) )exp(-W/RT)(1-2f], where f and X (super s) are, respectively, the mole fractions of a component of the crystal and melt at the interface, W the total interchange energy, R the gas constant, T temperature and beta = k (sub B) /k (sub A) , with k (sub A) and k (sub B) representing the rate constants of components A and B. Results of the numerical simulation of this model demonstrate that a domain of triple-valued compositions exists if W/RT <<<$I> -2. Together with mass-balance equations, this model explains satisfactorily the oscillatory zonation patterns in silicate solid-solution systems, indicating that self-organization is responsible for the development of such profiles during crystal growth. [Authors' abstract]