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Unformatted text preview: T. Y. Tan 1 10. KINETICS OF PHASE CHANGES I: NUCLEATION When a homogeneous single-phase alloy is cooled or heated to a temperature range wherein some other phase or phases are stable, transformation takes place. The rate of the transformation and the form of the new phases are controlled by the associated kinetic processes, which involve atomic motions. The kinetics of phase transformation includes nucleation and growth of precipi- tates (the new phase ) in the matrix (the old phase ). For purpose of the present chapter, which discusses the nucleation process, and the next chapter, which discusses the growth process, we shall consider two kinds of model problems. The first is the transformation from a liquid to a solid for a one-component system. The second is the formation of an intermediate phase (a com- pound) from a solid solution. The choice is based on the technological importance of the prob- lems. The industrial processes of casting metals and growing single crystal semiconductor boules make use of the phase change from liquid to solid. Heat-treatment of metallic alloys and precipi- tation of impurities in semiconductor crystals involve phase changes in the solid solutions. 10.1 Processes of Nucleation and Growth In a few cases the rearrangement of atoms during phase change can take place homogene- ously throughout the alloy. An example is the somewhat idealized order-disorder transition dis- cussed in section 9.3. In general, however, this does not happen. Instead, the change begin by the formation of nuclei of the new ( ) phase in certain localities of the matrix ( ) phase. Such nu- clei then grow to ever-larger sizes by the advancement of sharp interfaces separating them from the material. Associated with this manner of the phase transformation process, there are two questions deserve immediate attention. The first is why the existence of the sharp interface be- tween the and phases? The second is why the nucleation-growth sequence of the phase- change process? The answer to both questions concerns with the minimization of the Gibbs free energy of the system. For a first order phase transformation, the new and old phases are usually having different structures or the same structure with very different lattice parameters. Since the two phases are joined together, there must be a structure transition region in between. Geometrically, such struc- ture transition regions can be either sharp, i.e., consisting of interfaces with a thickness of one to no more than a few atomic distance, for which the crystal structures on both sides of it are differ- ent, or extended over many atomic distances wherein the structures change gradually from one into another. In either case, the structure transition region is associated with a Gibbs free energy T. Y. Tan 2 that is higher than that of any one of the two bulk phases. That is, this is an energy barrier that must be overcome so that the transformation can proceed. The sharp interface is associated with must be overcome so that the transformation can proceed....
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- Fall '11