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Contribution Oral Presentation




  • Wilfried KURZ

Primary authors


The aim of this talk is to present the evolution of the important concepts that led to the modelling of solidification, before the landmark paper by Tiller, Jackson, Rutter and Chalmers in 1953 on constitutional supercooling, and how they influenced our present-day models. Before the relevant research on solidification could start it required the development of essential basic concepts. Important theoretical contributions during the 19th century were; on contact angle, capillary pressure, heat and solute diffusion, statistical mechanics, equilibrium thermodynamics, and solidification as a free boundary value problem. The most important experimental developments were; the optical microscope and observations of solidification of transparent organics, followed by the methods of directional solidification, the discovery of X-rays and their diffraction in crystals, the electron microscope, and the microprobe. On the ground of these developments some 25 scientists, mainly during the first half of the 20th century, created the foundations of solidification science, a field that will be presented in six topics. Nucleation theories began with condensation of a supersaturated vapour and were later applied to nucleation in metals. Crystal growth was analysed and the energetics of attachment evaluated. Non-equilibrium solute distribution (segregation) was modelled. Morphological stability was described, first qualitatively and later the concept of “diffusional undercooling” developed. Observations of growth of transparent salt dendrites led to the conclusion of a parabolic tip with side branches that ripen during solidification. The diffusion equation for the tip was solved in parabolic coordinates. Eutectic growth forms were examined and growth rates of transparent organics as a function of undercooling determined. A solution of the diffusion equation for coupled eutectoid growth was given. Finally Zener presented in his highly original 1946 paper a first complete theory for single-phase (plates) and two-phase (eutectoid) structure formation using a new criterion of growth at extremum in combination with approximate solutions of the diffusion problems. Zener’s extremum criterion has been used during the following three decades before it was replaced by marginal stability. - Scientific research is done by people. The most influential authors in the field of solidification science before 1953 were, in order of the year of their contributions; Gibbs, Tammann, Volmer, Papapetrou, Scheil, Zener, Ivantsov, Turnbull. They all influenced in one or other way our modelling capabilities - the theories of Gibbs, Ivantsov and Turnbull being used still today.

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