Rhythmic Zoning and Self-organization in Silicate Solid-solution Minerals

摘要

Rhythmic zoning is ubiquitous in igneous rocks.Based on polymerization and regular solution models,a non-ideal,disequilibrium and non-linear interface equation has been estabilshed to describe the process of crystalgrowth:f=1{[1+（β/x^S)(1-x^S)exp(-W/TR)(1-2f)]}where f and x^S represent respectively the mole fraction of a component in the crystal and melt at the interface;W the total exchange energy;R the gas constant;and T the temperature:β=k B/kA,with kA and kB representing respectively the rate constants of components A and B.Results of numerical simulation of the equation demonstrate the a domain of triple valuedness exists if W/RT<-2.This model,together with the mass balance equation,explains reasonably the rhythmic phenomena in silicate solid solutions,indicating that self-organization is responible for this process during mineral growth.