Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields: A test of theory with convection

Abstract

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields up to 6 T were measured using a high-speed camera. The growth velocities for undercoolings below 120 K are depressed under low magnetic fields, but are recovered progressively under high magnetic fields. This retrograde behavior arises from two competing kinds of magnetohydrodynamics in the melt and becomes indistinguishable for higher undercoolings. The measured data is used for testing of a recent theory of dendritic growth with convection. A reasonable agreement is attained by assuming magnetic field-dependent flow velocities. As is shown, the theory can 2 also account for previous data of dendritic growth kinetics in pure succinonitrile under normal gravity and microgravity conditions. These tests demonstrate the efficiency of the theory which provides a realistic description of dendritic growth kinetics of pure substances with convection.

A model for free growth of a lamellar eutectic dendrite with an incident flow

“…The flow reduces the contribution of thermal undercooling to bulk undercooling, thus increasing the growth velocity of the eutectic dendrite. This flow effect is weak compared with that observed on a pure substance dendrite [23,28]. The reason for this is that eutectic growth depends more on interdiffusion of solute atoms in the directions parallel to the solid/liquid interface than on thermal transport in the direction of tip growth.…”

“…To overcome this difficulty, experimental observations of growth velocities of eutectic dendrites under static magnetic fields may be helpful. In addition to an electromagnetic damping effect [23], the static magnetic fields can introduce localized flow due to thermoelectric magnetohydrodynamics as they do in free solidification of undercooled melts of pure metals [27,28]. Because of the large dendritic tip radius R, it may also be possible to justify the present modelling by performing in situ X-ray tomography experiments under varied flow conditions.…”

“…In free eutectic solidification, convective flow can alter the thermal gradient along the growth direction and affect thermal undercooling. Then, it may affect the tip stability of a growing eutectic dendrite and modify the eutectic growth kinetics eventually, as was unveiled for dendritic growth of pure substances [23]. In this work, a model was proposed to deal with this potential incident flow effect on free eutectic growth of a lamellar eutectic dendrite.…”

A relaxation time of secondary dendritic branches to their steady-state growth

“…For the analytical calculations of rapid solidification regimes and theoretical estimations of microstructural parameters of dendritic and eutectic crystals, different models of non-equilibrium crystallization are used, as a rule, formally developed for the steady state scenario [9][10][11]. However, the steady state approximation for conditions of rapid solidification of small samples (films, splats, droplets) is questionable and such approach is often criticized.…”

“…For instance, the experimentally measured solidification velocity has the order of 10 −1 − 10 2 m/s in droplets processed by the electromagnetic levitation facility [7,8]. As such, the total duration of primary solidification in small droplets is rather short and estimated as [8]: 10 −5 − 10 −3 s.For the analytical calculations of rapid solidification regimes and theoretical estimations of microstructural parameters of dendritic and eutectic crystals, different models of non-equilibrium crystallization are used, as a rule, formally developed for the steady state scenario [9][10][11]. However, the steady state approximation for conditions of rapid solidification of small samples (films, splats, droplets) is questionable and such approach is often criticized.…”