Analysis of the Cu-3 Wt pct Ti cellular interphase boundary by various models
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THE equilibrium precipitate phase in Cu-3 wt pct Ti has a Cu4Ti composition and occurs in two morphologies, as Widmansta¨tten plates and as lamellae in cellular colonies. The Widmansta¨tten plates are usually observed within the grain interiors, likely originating at grain boundaries, while the cellular colonies grow outward behind migrating grain boundaries. These two morphologies are characterized by the same orientation relationship (OR) between the precipitate phase ( ) and the copper matrix (␣ ).[1,2] The interphase boundary is partially coherent[1,3] and strictly adheres to a particular habit plane, leading to the observed platelike morphology of both the Widmansta¨tten plates and the cellular precipitate lamellae. The Cu4Ti precipitate phase has a Pnma orthorhombic structure with a ⫽ 0.453 nm, b ⫽ 0.434, and c ⫽ 1.293 nm.[4,5] This ordered, but slightly distorted, hexagonal closed-packed (HCP) structure is based on the Au4Zr structure and has 20 atoms per unit-cell (Figure 1). Crystalline orientations between the Cu4Ti precipitate phase, , and the fcc matrix phase, ␣, are reported[2] to have the following relationship: (111)␣ 㥋 (010) [110]␣ 㥋 [001]
[1]
[112]␣ 㥋 [100] This OR aligns the pseudohexagonal (010) plane with a
closest-packed (111) fcc plane and aligns the close-packed [001] direction along [110]␣. Following the results of Ecob et al.,[1,2] Fonda and Shiflet[6] also reported this OR in a subsequent study using electron diffraction. The interfacial structure observed between the two phases in the Cu-Ti cellular colony (at the ␣: cellular-interlamellar interface) is particularly rich in periodic defect structures.[1,3,6] What makes it possible to employ transmission electron microscopy (TEM) strain-contrast experiments to investigate interfacial structure is the development of diverse theoretical models that have facilitated the understanding of interphase ORs and interfacial structures in many alloy systems. The models applied include interfacial superposition,[7,8] the theory of ideal interfacial configurations,[9,6] Olattice,[10,8] and invariant line.[11–15] Each modeling technique can provide a unique perspective on the OR between the two phases and on the structure of the interphase boundary between them, including defects, such as, misfit dislocations and steps. The concurrent application of different modeling techniques to a particular interphase boundary can, therefore, lead to a more complete understanding of that interface. In addition, the use of any single model will be shown to be incomplete. The individual contributions of each model will be detailed emphasizing their application to the interlamellar interface between Cu and Cu4Ti. The results of these modeling techniques on this interphase boundary will be tested in the Cu-Ti system in the experimental companion article,[3] which will provide a critical test of the accepted OR (Eq. [1]). II. APPLICATION OF MODELS
R.W. FONDA, Metallurgist, is with the Naval Research Laboratory, Washington, DC 20375-5000. G.J. SHIFLET, W.G. Rey
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