Formation of regular structures in the process of phase separation

TL;DR

This paper investigates how directional quenching in a Cahn-Hilliard model leads to the formation of periodic stripe patterns during phase separation, with pattern wavelength depending on quench velocity, offering insights for nanostructure design.

Contribution

It provides analytical and numerical analysis of pattern formation during phase separation under directional quenching, highlighting the control of pattern wavelength via quench velocity.

Findings

Periodic stripe patterns form behind the quench front.

Pattern wavelength is uniquely determined by quench interface velocity.

Numerical results agree with analytical predictions.

Abstract

Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front. Their wavelength is uniquely defined by the velocity of the quench interface in a wide range. Numerical simulations match perfectly analytical results obtained in the limit of small and large velocities of the quench interface. Additional periodic modulation of the quench interface may lead to cellular patterns. The quenching protocols analyzed in this paper are expected to be an effective tool in technological applications to design nanostructured materials.