Modeling of primary and secondary dendrites in a Cu-6 Wt Pct Sn alloy
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I.
INTRODUCTION
GAS atomization is generally considered a rapid solidification process with cooling rates ranging from approximately 103 to 106 K/s.[1] Due to large cooling rates, it is possible to produce powders with a minimum of segregation and, in some cases, containing metastable phases. Much experimental work has been done on the microstructures of gas-atomized powders of binary alloys.[2–6] In these experiments, microstructures and dendrite arm spacings (DASs) have been related to the particle diameter. Often, investigations are combined with modeling of cooling of either individual droplets or several droplets of given particle-size distribution.[7,8,9] Also, experimental work has been carried out that relates cooling rate or local solidification time to the DAS. In the case of Cu-Sn alloys, a number of experiments have been carried out for Sn contents varying from 5 to 12 wt pct.[10–16] These experiments show that primary and secondary spacing are related to the square root and the cube root, respectively, of the local solidification time. The actual formation of microstructures in binary alloys, i.e., segregation and shape and spacing of cells or dendrites during solidification, has been modeled by several authors.[17–25] One of these models by Hunt[20,21,22] is a numerical model that comprises both cells and dendrites. The shape is determined by solute rejection and diffusion in the melt in a fixed temperature gradient. Cells and dendrites are assumed to grow in an array so that effects of solute rejection from neighboring dendrites are taken into account. Often, in the literature, cooling and solidification of gasatomized droplets have been treated separately and often in N. TIEDJE, formerly Postdoctoral Candidate, Risø National Laboratory, is with Georg Fischer DISA Technologies, DK-2730 Herlev, Denmark. P.N. HANSEN, formerly Associate Professor, Department of Thermal Processing of Materials, Technical University of Denmark, 2800 Lyngby, Denmark, is General Manager, Foundry Technology, with Georg Fischer DISA Technologies. A.S. PEDERSEN, Associate Professor, is with Risø National Laboratory, Roskilde, 4000, Denmark. Manuscript submitted October 19, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS A
relation to the development of models. It is the aim of the present work to combine microstructural examinations of gas-atomized Cu-6 wt pct Sn alloy powders with calculations of cooling rates and to compare these with data from Hunt’s solidification model to give a combined description of solidification and heat transfer in atomization.
II.
EXPERIMENTAL PROCEDURES
Argon-atomized Cu-6 wt pct Sn powder was made from 99.99 pct pure Cu and Sn and produced in an atomizer at Risø National Laboratory (Roskilde, Denmark), as described elsewhere.[26] The alloy was chosen because it has been used in several investigations of rapid solidification; [3,4,6,10,26] thus, it is possible to compare the results with those of other workers. The powder was fractionated using an ATM Sonic Sifter with 75-mm electroformed Ni
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