PART XI – November 1967 - Papers - Dendritic Solidification of Aluminum-Copper Alloys

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2'3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.''' ~ohatgi' has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-