The evolution of microstructure in the undercooled Zn-Sn entrained droplets
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I.
INTRODUCTION
THE
liquid entrapped in solid can undercool significantly and is often used to study the undercooling behavior of alloy melt. [1,2,3] The undercoolability in such a situation is dictated by the heterogeneous nucleation ability of the surrounding solid. This technique is, therefore, used to test the theories of heterogeneous nucleation.[a,5] Very little attention was paid to the problem of the evolution of microstructures in such droplets. The microstructure in this case will be influenced by both the nucleation and growth of solid phases in the undercooled melt and by the nature of the metastable phase diagram. Such an understanding, besides being of academic interest, may play a vital role in many practical metallurgical processes, where heterogeneous nucleation and subsequent growth of the solid in the undercooled melt control the process. Electron and laser-beam welding represent examples of such processes. The nature of metastable phase diagrams can have a dominant influence on the development of such microstructures. This is particularly so in cases where a metastable phase field or a submerged liquid miscibility gap, which can only be accessed by undercooling, exist. Several investigators have carried out experiments to determine the achievable undercooling in Zn-Sn melts in contact with zinc substrates. [4'6'71 The aim of these experiments was to understand the heterogeneous nucleation phenomenon. Although significant undercooling could be achieved in the Zn-Sn alloy melts in contact with zinc and a significant scatter in the nucleation kinetics data was observed by Boswell and Chadwick, [7] no serious attempt was made to study the microstructures of the entrained droplets. Earlier, we have shown the existence of a metastable miscibility gap in the Zn-In system, which promotes a monotectic reaction in the undercooled liquid. 18] The zinc-tin system has a very similar phase diagram, t9] and it is felt that a systematic investigation of undercooled Sn-rich Sn-Zn melt entrained in zinc matrix may provide new results, which
will enhance our understanding of the solidification of undercooled melt. II. T H E T H E O R E T I C A L C A L C U L A T I O N OF METASTABLE PHASE DIAGRAMS In order to assess the nature of the metastable phase diagram, theoretical calculations were carried out to extend the equilibrium phase diagram to the undercooled regime and ascertain the existence of a metastable miscibility gap in this system. In the simplest of these calculations, a regular solution model was used. The expression for the Gibbs energy [l~ can now be written as mix G(~,x) = RT[(1 - X) In (1 - X) + X In X]
Here, A is a constant, independent of the temperature, which scales with the critical temperature (A = 2RT,,). From this, one can obtain the binodal points from the relation -2To(1 - 2X)
METALLURGICAL TRANSACTIONS A
[21
TBin(X) =
In [ ( 1 X X ) ] The critical point T,. can be calculated from the GibbsKonovalov equation flu following a procedure suggested by Perepezko. I12]This procedure elimina
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