Abstract
In Chapter 5 the importance of formulating solute mass balances during solidification was considered from the perspective of deriving the laws of chemical macrosegregation. Specifically, the Gulliver-Scheil equations were derived from an interfacial mass balance that ignored the influences of solute transport within the solid phase. In addition, it was also found convenient to impose the condition of ‘perfectly efficient’ convective mixing in the melt, an assumption that precludes the need to consider solute transport through the melt via atomic diffusion. Efficient mixing homogenizes the melt throughout the solidification process, keeping the residual melt concentration everywhere the same at each instant of time.
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Notes
- 1.
Strictly speaking, the mathematical macrosegregation analysis shows that steady-state solidification take an ‘infinite’ amount of time and distance to be achieved. As will be demonstrated through various aspects of this analysis, practical limits can be established where the departure from the true steady-state may be ignored.
- 2.
It is worth noting that Tiller’s initial transient solution for solute macrosegregation is identical in structure to Pfann’s solute distribution derived specifically for single-pass zone refining. Cf. Eq. (5.54).
References
M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State from an and Applications, Wiley Interscience Publishers, New York, NY, 2000.
B. Chalmers, Principles of Solidification, 133, Wiley, New York, NY, 1964.
W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Metall., 1 (1953) 428.
V.G. Smith, W.A. Tiller and J.W. Rutter, Can. J. Phys., 33 (1955) 723.
W. Tiller, Liquid Metals and Solidification, ASM, Cleveland, OH, 1958, p. 276.
J.D. Verhoeven, W.N. Gill, J.A. Puszynski and R.M. Gindé, J. Cryst. Growth, 89 (1988) 189.
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Glicksman, M.E. (2011). Plane-Front Solidification. In: Principles of Solidification. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7344-3_6
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DOI: https://doi.org/10.1007/978-1-4419-7344-3_6
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