Bj. Spencer et He. Huppert, ON THE SOLIDIFICATION OF DENDRITIC ARRAYS - AN ASYMPTOTIC THEORY FOR THE DIRECTIONAL SOLIDIFICATION OF SLENDER NEEDLE CRYSTALS, Acta materialia, 45(4), 1997, pp. 1535-1549
Citations number
18
Categorie Soggetti
Material Science","Metallurgy & Metallurigical Engineering
We consider a mathematical model for directional solidification of a b
inary alloy as a periodic array of three-dimensional needle crystals.
Arguing from an analysis of published experimental data for dendritic
growth, we identify a natural separation of characteristic length scal
es;br dendrites. We use these observed disparities in length scales to
define a small parameter for dendritic growth and identify scalings f
or all the process parameters in terms of this small parameter. We the
n solve the resulting free boundary problem using matched asymptotic e
xpansions. Our analysis results in an Integral equation for the shape
of the needle crystal. We suggest that the integral equation contains
a mechanism for the unique selection of the tip radius of the needle c
rystal independent of surface energy. This is in sharp contrast to pre
vious studies regarding determination of the tip radius of an isolated
, single-component, isothermal dendrite. Our results suggest that sele
ction of the tip radius is linked to the spacing of the array. (C) 199
7 Acta Metallurgica Inc.