Separation of Scales for Growth of an Alloy Needle Crystal
R F. Sekerka, Sam R. Coriell, Geoffrey B. McFadden
We reexamine the problem of a needle crystal (a model for a dendrite primary stalk) having the shape of a paraboloid of revolution growing at constant velocity from a supercooled binary alloy with given bulk concentration and far-field temperature. The coupled problem of thermal and solutal diffision has been studied by a number of authors, includingIvantsov, Bolling & Tiller, Langer, and Lipton, Glicksman, & Kurz. We discuss the form of the analytical relation between the growth rate and the undercooling. For typical material properties in a metallic system, there is an obvious separation of scales of thermal and solutal effects, and this relation has the form of a doubly sigmoidal function, with a nearly flat intermediate region where the two sigmoids join. To the left of this nearly flat region, the dendrites are 'solutal' with negligible contributions from the thermal field, whereas to the right of this region, they are 'thermal' with the solutal contribution fixed at its value for unit supersaturation.
Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science
, Coriell, S.
and McFadden, G.
Separation of Scales for Growth of an Alloy Needle Crystal, Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science
(Accessed February 22, 2024)