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OVER the past 60 years, there has been a substantial amount of work on grain refining mechanisms in alloys,[1–3] and the factors affecting the development of grain size are now well established.[4–7] The other feature of the microstructure that is commonly observed in many castings is the secondary dendrite arm spacing (SDAS). A refined SDAS is known to improve many mechanical properties of Al-Si alloys.[8] The SDAS is also known to affect the permeability of semisolid structures during solidification[9–11] and can affect the hot tearing susceptibility of an alloy.[11–13] Hence, knowing how to manipulate or predict the SDAS of an alloy may be useful for optimizing the properties of an alloy or for designing new alloys. Equiaxed grains tend to grow dendritically for two reasons.[14] First, the thermal profile of an equiaxed grain is such that the grains are at a higher temperature than the surrounding melt. Hence, any perturbation will grow preferentially. Second, the addition of alloying elements leads to the formation of constitutional undercooling in front of the growing grain, which further increases the tendency for perturbations to grow and MARK EASTON, Program Manager, CAST Cooperative Research Centre (CRC), is with the Department of Materials Engineering, Monash University, Melbourne 3800, Australia. Contact e-mail: [email protected] CAMERON DAVIDSON, Principal Research Scientist, CAST Cooperative Research Centre (CRC), is with the Commonwealth Scientific and Industrial Research Organisation (CSIRO), Division of Process Science and Engineering, Pinjarra Hills, Queensland 4069, Australia. DAVID ST JOHN, Professor, CAST Cooperative Research Centre (CRC), is with the School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, Queensland 4072, Australia. Manuscript submitted April 20, 2009. Article published online February 23, 2010 1528—VOLUME 41A, JUNE 2010

dendrites to form. The second factor also leads to dendritic growth in columnar growth conditions. In some systems in which the grain size is small enough to satisfy the Mullins–Sekerka stability criterion, spherical growth will occur,[15] e.g., in fine-grained Mg-Zr alloys,[15,16] but in most equiaxed systems, dendritic growth occurs. It should be noted that in some systems, particularly peritectic systems such as Al-Ti, spherical grains may appear to have formed but etching techniques can reveal the dendritic structure formed during solidification of the grains.[17,18] It is well established that dendrite arms coarsen during solidification.[19,20] Factors governing arm spacing have been proposed to be a combination of competitive growth, coalescence, and ripening,[19] with ripening considered to be the dominant mechanism at low solid fractions.[14,21–23] At higher solid fractions, arm coalescence may become more influential if coarsening continues to occur.[24,25] Experimental data for the secondary SDAS, k2, are usually described by the simple empirical equation: k2 ¼ Ktnf

½1

where tf is the solidification time interval between