The Role of Recrystallization in Spontaneous Grain Refinement of Rapidly Solidified Ni 3 Ge
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NTRODUCTION
SPONTANEOUS grain refinement (SGR) is defined as an abrupt reduction in grain size during the solidification of deeply undercooled metallic melts. In pure metals, it is observed above a critical undercooling, DT*.[1–3] Alloys, however, often display a more complex behavior, involving two grain refinement transitions,[4–6] with SGR being observed for undercoolings below a lower critical value, DT1 ; and above an upper critical value, DT2 : Moreover, a discontinuous break in the gradient of the velocity-undercooling curve (see e.g., Reference 7) is typically observed at DT* (or DT2 in alloys systems). Below DT*, the growth velocity, v, depends upon DT according to v µ (DT)b (typically with b 2 to 3). Conversely, above DT* the dependence is approximately linear. Since it was first observed in pure Ni by Walker in 1959,[8] the origin of the phenomenon has been a subject of some controversy. Early models included shrinkage induced cavitation resulting in copious nucleation[8] or the effects of trace solute additions, particularly dissolved gasses.[9] However, these models have subsequently been discredited. A number of authors also suggested that recrystallization or recovery may play a role,[10,11] although this was difficult to reconcile with drop-tube studies, wherein it was claimed cooling rates were sufficiently high to suppress recrystallization and recovery, but in which grain refined structures were still observed.[12]
NAFISUL HAQUE, ROBERT F. COCHRANE, and ANDREW M. MULLIS are with the School of Chemical & Process Engineering, University of Leeds, Leeds LS2 9JT, U.K. Contact e-mail: [email protected] Manuscript submitted February 13, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
The ‘standard model’ for SGR is of dendritic melting and fragmentation following recalescence.[13] Whether remelting occurs or not is determined by the balance between two time scales; that for the melting of dendrite arms, sm, which in turn is a function of the characteristic length scale for growth, and that for the co-existence of the solid and liquid,ss, which depends primarily on the macroscopic cooling rate. Remelting occurs when sm < ss. The model is attractive in that it is able to explain why there is one transition in pure metals and two in alloys, this relating to the predicted dependence of the dendrite tip radius, q, upon DT, with alloy systems displaying a local minimum in q at intermediate undercoolings.[14] Despite this, there are a number of limitations in the model, not least that post-recalescence remelting cannot explain a break in the velocity-undercooling curve, which therefore needs to be ascribed to coincidence. An alternative model was therefore proposed by Mullis and Cochrane[15] which suggested that SGR was the result of a tip instability in the growing dendrite at high growth velocity, with the instability resulting in a transition in the solidification morphology from dendritic to dendritic ‘seaweed’. Subsequent remelting of the seaweed structure[16] gave rise to the grain refined microstructure. Suc
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