Array of doublets: A branch of cellular solutions in directional solidification

Abstract

In directional solidification of alloys, the interface pattern assumes a cellular structure, with a periodic array of cells, when the velocity is increased beyond the threshold of planar interface instability. A detailed experimental study in the succinonitrile-acetone system has revealed a branch of cellular structure in which the interface pattern consists of a periodic array of coupled cells or doublets. This doublet interface evolves with two characteristic length scales at the advancing front: a small intraspacing between the cells in a doublet, whose selection is sharp, and a larger interspacing corresponding to the distance between cells in adjoining doublets, whose selection is weak. The dynamics of the time-dependent evolution of a doublet interface is investigated by statistical analysis of tip spacings, by using a Fourier transform of the interface shape and through the study of the variation of shape parameters with time. These dynamical studies have confirmed the selection of doublet interface as a stable solution of the cellular pattern formation. A range of stable regime for an array with doublets is determined and the key factor that controls the formation of regular cells or doublets in an array is discussed. When doublets are unstable, time dependency may follow due to a source mechanism at grain boundaries, which induces strong spatiotemporal chaos.