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    • Function space theory of dynamic nucleation during solidification at high cooling rates

      S K Das

      Volume 20 Issue 5 August 1997 pp 643-650

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/boms/020/05/0643-0650

    • Keywords

       

      Function space; wave and matrix mechanics; dynamic nucleation; orthogonal set; isomorphism; solidification

    • Abstract

       

      An analytical theory is proposed to study the dynamic nucleation of crystals from melt at very high cooling rates (10−6 to 10−12 °K/sec). The mathematical framework is found to be isomorphic with the function space theory, wave and matrix mechanics, which enables application of various approximate methods of the latter disciplines. In principle, the mathematical apparatus and concepts of function space and wave mechanics can be utilized to study the time varying nucleation process. The Arrhenius law has been used to extrapolate the self-diffusion coefficient as a function of temperature above the melting point than those below. Since, applicability of Arrhenius equation at very high degrees of supercooling is not known and has to be substituted with appropriate constitutive relationship based on free volume theory of transport, the conclusion derived from the present analysis will not be unique with respect to the certainty of crystallization during the solidification process.

    • Author Affiliations

       

      S K Das1

      1. Computer Applications Division, National Metallurgical Laboratory, Jamshedpur - 831 007, India

    • Dates

       
      Published
      August 1997
      Manuscript received
      17 August 1996
      Manuscript revised
      29 April 1997

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