The invariant line and precipitate morphology in Fcc-Bcc systems
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I.
INTRODUCTION
A L T H O U G H the importance of the invariant line in martensite transformations was first appreciated some forty years ago, t~'21 its role in diffusion-controlled phase transformations involving close-packed [hexagonal close-packed (hcp) or face-centered cubic (fcc)] and body-centered cubic (bcc) parent and product phases was only recognized thirty years later) 3:'5j With hindsight, this is somewhat surprising, as it now is clear that both types of transformation can share a common lattice correspondence (the Bain strain, B) and a similar or identical rigid body rotation, R, with the invariant line x given by x = Ax
[1]
where A = RB. However, the two types of transformation differ in two important respects. The correspondence of lattice sites in a martensitic transformation must involve a correspondence of atom positions; i.e., each atom in the parent phase is predestined to move to a unique site in the product phase as the transformation front passes. In a diffusion-controlled transformation, this clearly will not be the case. The second difference lies in the role of the lattice invariant shear. This shear is an integral part of nearly all martensitic transformations and leads to an invariant plane strain shape change for the product phase. Although there may be a lattice invariant shear in some diffusional phase transformations, t~l there is no strong evidence for one in any of the systems of interest here, viz., C u - f r , 16,7,81 Ni-Cr, t91 Fe_Cu,t~O.lll and two-phase a-T stainless steels. 112,13,141In G.C. WEATHERLY, Professor, and W.-Z. ZHANG, Postdoctoral Fellow, are with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON L8S 4M1, Canada. This article is based on a presentation made at the Pacific Rim Conference on the "Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products," held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL's Phase Transformations Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
the analysis which follows, we will assume that the matrix A in Eq. [1] is fully described by B and one (or more) rigid body rotations R. Each of the four systems, Cu-Cr, Ni-Cr, Fe-Cu, and a-3, stainless steel, has a lattice parameter ratio (a/laD close to 1.25, the value for pure Fe. They also share a number of common crystallographic and morphological features. (a) The product phase has a lath-shaped morphology. The long direction of the lath is the invariant line (x in Eq. [1]), and the lath is bounded by two or more welldeveloped facet planes. (b) The orientation relationship is close to either Nishiyama-Wasserman tt~j or Kurdjumov-Sachs. tl6l In some systems (e.g., Ni-Cr,/9j) the precipitates have a unique orientation relationship, while in others (e.g., C u - C r [6"7'81 and a-y stainless steels,H2'13'141), a range of orientation relationships has been reported. (c) For K-S-related precipitates, the invariant line x is always close to the common close-packed direction in the two p
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