Gaussian Grooves Propagating across a Moving Curved Interface in Directional Solidification

In gratitude to Antoine Skoulios for original and illuminating insights on complex materials, and, to celebrate the emergence of his new adventures, this article is a synopsis of astonishing observations made about a decade ago on a deceptively simple material, succinonitrile, during its crystal growth from a curved phase boundary traveling in narrow channels. For a range of pulling speeds, v, vc1 < v < vc2, the flat interface transforms, first, to a curved one, then, to a cellular one by groove propagation. The shape of the lead groove is Gaussian, consistent with a linear concentration gradient across the interface, and the pattern has a well-defined wavelength. When v < vc1, the interface remains flat and when v > vc2, the pattern is time dependent. PACS: 81.30.Fb, 61.50.Cj, 05.70.Ln INTRODUCTION This article describes astonishing observations made about a decade ago [1-3] on a deceptively simple material, succinonitrile, C4H4N2: waxy isomeric crystals that melt at 57.15C, during its crystal growth from an asymmetric interface in a narrow channel. Succinonitrile is the material used to study the crystal growth processes in directional solidification (Fig. 1) because its solid-liquid interface is not facetted i.e. is “rough”, and therefore is flat in a temperature gradient [4]. Such interfaces are important as many technologically important metals and semiconductors exhibit rough interfaces. Fig. 1. Classical directional solidification where the solid-liquid phase boundary is perpendicular to a temperature gradient, G. A flat phase boundary (top) is forced to travel towards the hot contact by pulling the sample from the hot contact to the cold one (middle). Above a critical pulling speed, vcb, the flat interface develops a pattern (bottom).