Effect of solidification conditions on fractal dimension of dendrites

Abstract

Dendrites are complex, three-dimensional structures that have conventionally been characterized by measuring the secondary dendrite arm spacing or the primary spacing in a dendritic network, but these global measures do not adequately describe the branched appearance of secondary and tertiary arms. This work focuses on the integral measurement of fractal dimension, a measure of complexity relatively unexplored in dendrites, in addition to specific surface area. Measurements were made on aluminum dendrites in directionally solidified Al–Si alloys of varying composition and solidification velocity, with and without induced convection currents. Contrary to expectations, average fractal dimension was found to be relatively insensitive to changes in solidification velocity and fluid flow within the ranges observed, compared to the variation in fractal dimension measured within any individual data set. Specific surface area was found to increase linearly with solidification velocity.