Pattern formation in solidification

Abstract

Regular patterns form in many solidification processes. Examples occur during lamella and rod-like eutectic growth and when single-phase cells or dendrites are formed. The scale and regularity of the microstructure can determine the properties of the cast materials and is thus important practically. The purpose of the present paper is to show that common features occur in all processes.

Steady-state analysis indicates that a wide range of possible spacings could occur during eutectic, cellular or dendritic growth. The degree of freedom is removed by considering the mechanism determining the minimum and maximum spacing on a specimen. It is found that the minimum spacing occurs when the array first becomes stable for a lamella or rod-like eutectic, for cell growth and for some dendrites. For low temperature gradient, high-velocity dendrites, the minimum spacing is determined by thespacing when the dendrites irst become near enough to interact. The maximum spacing for eutectics andfor cells is determined by tip splitting. The maximum spacing for dendrites occurs when a tertiary arm becomes a new primary. Good agreement is obtained between theory and experiment using this approachto predict spacing limits. The average spacing on a specimen can approach either limit depending o past history. The two extreme spacings are found to span the spacing of the minimum undercooling foreutectic and cellular growth and this allows an average spacing to be estimated using a single condition.

It is concluded that three conditions are necessary to form regular structures. A mechanism must exist to eliminate members of the array when the spacing is too small. A mechanism must exist to form new members of the array when the spacing is too wide. The structure must be stable to fluctuations in the range of spacing between the two limits.

Key words:

• Solidification
• Eutectics
• Dendrites