On the Short-Time Compositional Stability of Periodic Multilayers

TL;DR

This paper analyzes the short-time stability of concentration profiles in periodic multilayers with large miscibility gaps using the Cahn-Hilliard equation, identifying conditions for stability, dissolution, and metastability.

Contribution

It provides a detailed analysis of the existence and stability limits of periodic concentration profiles in multilayers, including critical layer thicknesses and composition thresholds.

Findings

Layered structures can be metastable above a critical period length.

Minimal average composition and layer thickness for dissolution are calculated.

Thin layers show phase composition deviations from bulk phases.

Abstract

The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The limits of the existence and stability of periodic concentration profiles are discussed as a function of the average composition for given multilayer period length. The minimal average composition and the corresponding layer thickness below which artificially prepared layers dissolve at elevated temperatures are calculated as a function of the multilayer period length for a special model of the composition dependence of the Gibbs free energy. For period lengths exceeding a critical value, layered structures can exist as metastable states in a certain region of the average composition. The phase composition in very thin individual layers, comparable with the interphase boundary width, deviates from that of the corresponding bulk phase.