A numerical and experimental study of the rate of transformation in three directionally grown peritectic systems
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I. INTRODUCTION
A PERITECTIC phase diagram is shown in Figure 1. As a mixture of the primary phase, a, and liquid, L, is cooled below the peritectic temperature, TP, liquid and a should react together to give b. L1a→b
[1]
At equilibrium, the phases remaining after completion depend only on the composition of the alloy and on the phase diagram. In practice, it is generally not possible to get equilibrium quantities of the different phases during cooling because solid-state diffusion is slow. There have been a number of investigations of peritectics.[1–5] It is generally proposed that b phase is produced by one of three mechanisms. (1) Initially, b will be formed around the primary a phase and this will occur where a, b, and liquid are in contact. It will be formed quickly because diffusion is rapid in the liquid phase. This is often defined as b formed by the peritectic reaction.[2] (2) Once the primary a phase is covered, further transformation can take place by solid-state diffusion through the b phase. This is often termed b formed by the peritectic transformation.[2] It should be noted that diffusion through the b phase leads to the formation of b at both the a-b and the b-liquid interfaces (Figure 2(b)). (3) The b phase can also be formed by solidification (precipitation) from the liquid. This b is deposited because of the need for the liquid phase to change composition on cooling and does not depend on the presence of the a phase. Generally, the amount of b phase formed is assumed to depend mainly on the extent of the peritectic transformation (mechanism 2) and on the amount of solidification (mechanism 3). This is because even though the peritectic reaction
H.P. HA, Dr., formerly with the Department of Materials, University of Oxford, is with the Division of Metals, Korea Institute of Science and Technology, 39-1 Hawolgok, Seongbook, Seoul, Korea. J.D. HUNT, Professor, is with the Department of Materials, University of Oxford, Oxford OX1 3PH, England. Manuscript submitted November 16, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
(mechanism 1) is rapid, the amount of b formed is generally a small fraction of the total. Using this approach, the rate of the peritectic transformation has been examined by a number of authors.[6–10] Titchener and Spittle[6] investigated several binary systems and found that under isothermal conditions the thickness, W, of the b phase varied with time, t, according to a power relationship of the type W 5 Ktn where the n is approximately 0.5. From these results, they concluded that the peritectic transformation is diffusion controlled. They proposed an analytical solution of the diffusional growth of the peritectic phase using equations derived by Wagner[10] for corrosion. Titchener and Spittle and St John and Hogan[8] pointed out that the rapid formation of the b during a peritectic transformation will occur if the composition gap between the a and b and between the b and liquid are small and when the range of composition across the b phase is large. The first two compositi
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