Coarsening kinetics during solidification of Ni-Al-Ta dendritic monocrystals
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I. INTRODUCTION
A model for dendritic coarsening during solidification was previously developed ~and assumed: dissolution and shrinkage of smaller dendrite arms; lateral growth of larger dendrite arms; applicability of the Scheil equation to solidification and; deposition of material which solidifies during cooling on larger dendrite arms only. The kinetics were expressed as the time variation of the dendritic surface-to-volume ratio (specific dendritic surface), Sv. The model was applied to the A1-4.5 wt pet Cu alloy I and a reasonable agreement was found between calculated and measured values of S~ vs time during which solidification progressed. It was concluded that growth during solidification contributes more to the decrease of Sv than does coarsening. However, coarsening causes the disappearance of dendrite arms and, hence, enhances the effect of solidificaaion growth on Sv, since the newly solidified material is deposited on fewer arms. Directional solidification of dendritic monocrystals lends itself particularly well to studies of dendritic coarsening kinetics. By interrupting solidification through quenching of the residual liquid the specific surface or perimeter of the dendrites can be measured in the mushy zone at various distances from the dendrite tips, hence at various temperatures between the liquidus temperature and the temperature at which solidification is completed2. Thus, S~ can be plotted vs time during which solidification progressed, since the speed at which the crystal is pulled is known and distances can be transformed into times. For studies of isothermal coarsening kinetics crystal pulling can be stopped for different lengths of time before quenching the remaining liquid. S vcan then be measured at a given distance from the dendrite tips, hence at a given P. W. PETERSON and T. Z. KATTAMIS are Graduate Student and Professor, respectively, Department of Metallurgy, Institute ef Materials Science, University of Connecticut, Storrs, CT 06268. A. F. GIAMEI is Senior Staff Scientist, Pratt & Whitney Aircraft, East Hartford, CT 06108. Manuscript submitted June 14, 1979.
temperature, in specimens which were allowed to coarsen for different lengths of time. Isothermal coarsening kinetics can therefore be established. The interface between the growing dendrite and the liquid is slightly modified during quenching of the remaining liquid. 3 A certain error in measuring S v, which is inherent to all methods that involve quenching of the remaining liquid, 1,4,5is therefore introduced. This inevitable error is minimized at higher quench rates. The present investigation of coarsening kinetics of alloys in the Ni-A1-Ta system was carried out on dendritic monocrystals during solidification and aimed at: 1) extending a previous analysis I to a ternary system, and; 2) establishing the effect of composition on coarsening kinetics. II. EXPERIMENTAL PROCEDURE Dendritic monocrystals of Ni-18.7 at. pet Al-l.8 at. pet Ta, Ni-13.4 at. pct Al-I.8 at. pct Ta and Ni-13.4 at. pct A1-5.1 at. pct Ta and of other interm
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