Interparticle spacings and undercoolings in Al-Si eutectic microstructures
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I.
INTRODUCTION
*C
FOR the
growth of normal eutectic microstructures the relationship between undercooling (AT), growth velocity (v), and lamellar or inter-fiber spacing (A) takes the form 1 A T = klVA + kE/A
[1]
where k~ and k2 are constants for a given eutectic alloy. The extremum condition, applied by differentiating Eq. [I], yields the two further relationships A2v = constant
[2]
A T : / v = constant
[3]
which are summarized in Figure 1. For a fixed growth velocity, the A vs AT relationship should be fixed at the point A at the minimum of the curve. This relationship has been confirmed experimentally for a wide range of normal eutectics. However, the eutectics classified as anomalous,2 of which AI-Si is a conspicuous example, generally fail to conform with this extremum condition. It has been proposed 3 that the growth behavior of the AI-Si eutectic, and probably all anomalous eutectics, should nonetheless conform to Eq. [ 1], thus falling on the curve of Figure 1, but at a point such as B, giving larger AT and A values than predicted by the extremum condition. Fisher and Kurz4 have provided experimental evidence that this is true for the camphornaphthalene eutectic, but experimental evidence for metallic eutectics is not yet available. The A1-Si eutectic exhibits the large A and AT values so predicted, but published measurements are highly variable, due to experimental difficulties, and are inadequate to test the applicability of Eq. [1 ]. This paper describes efforts to improve the accuracy of measurement and to apply Eq. [ 1] to the A1-Si eutectic system. Modification of AI-Si alloys produces a flake-fiber transition in the eutectic microstructure, in which the silicon phase changes from a "flake" or plate-like faceted morphology to a more rounded fibrous form. This is observed L. M. HOGAN is Honorary Research Associate, Department of Mining and Metallurgical Engineering, University of Queensland, St. Lucia 4067, Australia. H. SONG is with the Department of Materials Science and Engineering, Nanjing Institute of Technology, N anjing, China, and a Ph.D. Candidate with the Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931. Manuscript submitted April 30, 1986. METALLURGICALTRANSACTIONSA
AT 0.1
0.01
I
I
I0
I00 /~rn
Fig. ! - - T h e form of Eq. [l] and anticipated experimental results for A: normal lamellar or fibrous eutectics, B: anomalous eutectic growth. 4
to occur at fast freezing rates exceeding 400 to 500/xm/s 5'6 (chill modification) or at slow freezing rates after the addition of sodium or strontium (impurity modification). Flood and Hunt 3 have suggested that the flake-fiber transition coincides with a transition from faceted to nonfaceted growth of the silicon phase as undercooling increases with growth velocity. The effect of the modifier (Na or Sr) would then be to raise the faceted/nonfaceted transition temperature to very small degrees of undercooling. More recent information7'8'9 indicates that the mechanism of the flake-fiber transiti
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