The relationship betweendendrie tip characteristics and dendrite spacings in alloy directional solidification

摘要

We summarize the discuss a new theoretical mode for the direcitonal lsolidificaiton of alloys in the form of dendrtie arrays. Slender body theory is used to obtain an integral euqation for the dendrite shape in the asympototic limit of the dendrite tip radius being much smalle rhan othe solute diffusion length. This equation has a solvability condion that selects the shape anjd tip undercooling for prescribed solidification conditions and array spacings. a consequence of our results is that we obtain a unique solution to the well-known indeterminacy for the single-dendrite [2] similariyt solution by considering the interaction between individual members of an array of dendrites. Further,m the dependence of gthe solutoins on the dendrite spacing gives a family of "array solutins," in which the tip radius is related directly to thue dendrite spacing. These solutions aggree well with experimentws in parameter ranges where the slender dendrite theory is expected to be valid. Finally, we discuss how these array solutions, toigether with surface energy and stability considerations, can describe the seleciton of dendrite spacings duirng directioanl solidification.