Development and application of growth models for grain boundary allotriomorphs of a stoichiometric compound in ternary s
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I.
INTRODUCTION
GROWTHof precipitates in a multi-component alloy may be described in terms of several different stages of growth which arise due to differences in the diffusivities of the elements in the alloy. For example, both ferrite and cementite allotriomorphs in Fe-C-X alloys, where X is a substitutional alloying element, may grow in austenite without partitioning element X when the supersaturation is sufficiently large.L:'3 Such no-partition growth occurs due to the great difference between the diffusivities of C and X. Experimental evidence for the no-partition growth of ferrite allotriomorphs in many Fe-C-X alloys has been presented. 4 As the decomposition of austenite in a finite system proceeds, however, the supersaturation or the driving force for the transformation decreases and eventually reaches a point at which appreciable partitioning of the substitutional element X between the parent and product phases must occur. When isothermal decomposition of austenite is considered, an equilibrium tie-line which penetrates the point of bulk alloy composition gives the compositions of the two phases at eventual equilibrium. Since the equilibrium compositions of two coexisting phases defined by an equilibrium tie-line differ in concentrations of both C and X, partitioning of element X, as well as C, must occur before true equilibrium is established. In addition to the compositional requirements, the structure of the interface between parent and product phases must be specified for development of appropriate growth mechanisms. Cahns pointed out that there are two criteria conceming the structure of an interphase boundary to be considered in predicting growth mechanisms, namely, the diffuseness and singularity of an interphase boundary. In a diffuse boundary, the change between the two different phases is gradual and occurs over several atom planes in contrast to a sharp interface where the major property TEIICHI ANDO, formerly Research Assistant at the Colorado School of Mines, is Senior Researcher, Toyo Kohan Ltd., and is presently Visiting Scientist at the Materials Processing Center of the Massachusetts Institute of Technology, Cambridge, MA 02139. GEORGE KRAUSS is AMAX Foundation Professor, Colorado School of Mines, Golden, CO 80401. Manuscript submitted July 13, 1982.
METALLURGICALTRANSACTIONS A
change occurs within one interplanar distance. A singular interface results from a pronounced cusp in the polar surface free energy diagram. 6 Therefore, a singular interface assumes an equilibrium shape. The growth of such an interphase boundary requires steps or ledges. Conversely, a nonsingular interface can continuously advance normal to itself. Gilmour et al 7 developed a model for the growth of ferrite allotriomorphs in Fe-C-Mn ternary austenite assuming three stages: initial no-partition growth stages, which include a parabolic stage and a subsequent nonparabolic stage, and a subsequent stage in which Mn partitioning occurs. The ferrite: austenite interface was assumed to be sharp and nonsingular and ther
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