Primary dendrite spacing of lead dendrites in Pb-Sn and Pb-Au Alloys
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IN the past l0 to 15 years there have been several studies ~ H of steady-state directional solidification applied to dendritic growth in alloy systems. In such experiments both the growth rate, R, and the temperature gradient, G, may be independently controlled to some extent and one may evaluate the variation in dendrite spacing, ?~, with G and R. The data are generally correlated with an equation of the form ?~ = kG-aR - b where the value of k includes the composition dependence. There are some experimental difficulties in performing such experiments which have not always been appreciated. As the solid cools, coarsening occurs and the final dendrite spacing m a y be quite different than the spacing which was present at the solidification front. Experiments 2 have shown that this effect occurs for secondary dendrite arm spacing but not for primary dendrite arm spacing. A second problem involves maintaining unidirectional heat flow conditions where the latent heat flux becomes a large fraction of the total heat flux into the solid. This situation occurs at high growth rates and at low temperature gradients, and it produces two experimental difficulties. First, it leads to long initial transients prior to achieving steady-state conditions, and these transients m a y easily become longer than the sample. Secondly, it moves the solidliquid interface closer to the cooling source and often leads to lateral head transfer with consequent curved growth fronts at the base of the dendrite array or at both the base and the tip of the dendrite array. In the present experiments we have attempted to overcome these difficulties by restricting ourselves to measurement of primary dendrite a r m spacings and by maintaining high temperature gradients and a maxim u m growth rate of around 410/.tm/s. The experiments at the lowest gradients, 11 to 99 ~ employed oil bath heat transfer to maintain short transients and C. M. KLAREN, formerly with Ames Laboratory--USDOE, is currently Engineer at John Deere Waterloo Tractor Works, Waterloo, IA 50704. J. D. VERHOEVEN and R. TRIVEDI are Senior Scientists at Ames Laboratory--USDOE and Professors with the Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011. Manuscript submitted February 29, 1980.
proper unidirectional heat flow. Experiments have been carried out on a wide composition range of Pb alloys to evaluate the exponents, a and b, over a fairly wide range of G and R. EXPERIMENTAL TECHNIQUE The experiments were carried out on two lead systems, Pb-Sn and Pb-Au. Directional solidification was done in 6 m m I D (inside diameter) by 8 m m O D (outside diameter) quartz tubing whose inner surface was coated with a very thin graphite layer deposited from a graphite-methanol solution. Master alloys were intially cast to 5 m m diam from 99.999 pct pure metals. This was done by a v a c u u m / p r e s s u r e technique, casting into graphite coated 5 m m ID quartz tubes, 60 cm long. To insure uniform composition the molten alloy was thoroughly stirred with a tanta
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