Estimation of Cooling Rates During Close-Coupled Gas Atomization Using Secondary Dendrite Arm Spacing Measurement
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INTRODUCTION
CLOSE-COUPLED gas atomization (CCGA) is an important technique for the commercial production of fine, spherical metal powders. Such powders have a variety of uses, such as for pigments, catalysts, metal injection molding (MIM) feedstock, solder pastes for ‘‘flip-chip’’-type circuit board fabrication and solid rocket propellant. One of the advantages of gas-atomized powders over the conventionally cast materials is the high cooling rates experienced by the metal during solidification in flight.[1,2] This leads to many preferable properties including a decrease in segregation, higher solid solubility, and a finer microstructure which in turn gives better chemical homogeneity, a more corrosionresistant end product and more favorable hot- and coldworking properties. Moreover, high cooling rates and the subdivision of the melt into fine droplets can also give rise to significant undercooling in the melt,[3] allowing for access to metastable phases that, under close to equilibrium processing conditions, would be inaccessible. Despite the importance of rapid cooling to the performance of gas-atomized metal powders, the range of cooling rates quoted for these varies considerably. At the lower end of this spectrum, Zeoli et al.[4] and Shulka et al.[5] quote 102 to 104 K s1 while much higher rates of 105 to 108 K s1 are quoted by He et al.[6] and ANDREW M. MULLIS, Professor, LEANE FARRELL, Student, and ROBERT F. COCHRANE, Senior Lecturer, are with the Institute for Materials Research, University of Leeds, Leeds LS2-9JT, UK. Contact e-mail: [email protected] NICHOLAS J. ADKINS, Researcher, is with the IRC in Materials Processing, The University of Birmingham, Edgbaston, Birmingham B15-2TT. Manuscript submitted February 1, 2013. Article published online April 26, 2013. 992—VOLUME 44B, AUGUST 2013
intermediate values up to 105 K s1 are given by Kearns[2] and by Kellie.[7] These differences may in part be explained by the fact that the values are quoted for a range of different particle sizes, atomization pressures, atomizing gases (including air, Argon, and Helium), and atomizer configurations. However, this cannot account for the entire discrepancy, suggesting that there is still considerable uncertainty regarding the cooling rates that may be encountered during the gas atomization of liquid metals. Estimates of the cooling rate during gas atomization are generally made either on the basis of theoretical models[4,6] or by measuring the secondary dendrite arm spacing (SDAS) in the resulting powder product.[5] The starting point for modeling the cooling rate is the balance of heat fluxes for a given droplet, which can be expressed as dTp df cl ð1 fÞ þ cs f L dt dt ½1 6h 6erb 4 ðTp Tg Þ þ ¼ ðTp T4R Þ; qd qd where Tp is the instantaneous temperature of the particle, cl and cs are the specific heats of the metal in the liquid and solid states, respectively, f is the solid fraction, h is the heat-transfer coefficient, q is the density of the metal, d is the diameter of the droplet, e is the emissivity of the drop
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