A mechanism for the equalisation of primary spacing during cellular and dendritic growth

The Hunt and Lu [Metall. Mater. Trans. A 27A (1996) 611] model for the sele ction of primary spacing, lambda, during cellular and dendritic growth pred icts a range of spacings falling between minimum and maximum values of lamb da (min) and lambda (max) respectively. Within the model lambda (max)/lambd a (min) will be at least 2 and may, under certain circumstances, be signifi cantly greater. In this paper we use a free boundary model of solidificatio n within an array to demonstrate that interaction between the tips of the c ells or dendrites leads to a transverse adjustment mechanism that will tend to equalise the spacing as growth proceeds. This transverse adjustment mec hanism is shown to be rapid for the spacings characteristic of cellular gro wth but much more gradual for the spacings characteristic of dendritic grow th. These findings are consistent with observations of the primary spacing of dendrites grown in alloys of the transparent casting analogue, succinoni trile. (C) 2001 Kluwer Academic Publishers.