Different routes towards oscillatory zoning in the growth of solid solutions

TL;DR

This paper presents a theoretical analysis of oscillatory zoning in solid solutions, introducing a 1D model that accounts for nonideality and asymmetry, and identifies conditions leading to oscillations.

Contribution

It develops a new 1D model incorporating nonideality and asymmetry to explain oscillatory zoning in solid solutions, supported by stability analysis and simulations.

Findings

Oscillatory zoning can occur even in ideal solutions with high asymmetry.

Linear stability analysis identifies parameter regions for oscillations.

Numerical simulations reveal the nature of limit cycles in the system.

Abstract

Oscillatory zoning, i.e. self-formation of spatial quasi-periodic oscillations in the composition of solid growing from aqueous solution, is analyzed theoretically. Keeping in mind systems like (Ba,Sr)SO4 we propose a 1D model that takes into account the nonideality of the solid solution and the system asymmetry, in particular, reflecting itself in different solubilities for such systems. Based on a linear stability analysis different parameter regions can be identified. Even an ideal solution solution with a sufficiently large asymmetry can display oscillatory zoning. Numerical simulations complement the linear stability analysis as well as the qualitative consideration of the instability development and reveal the nature of the limit cycles.