The application of surface dislocation theory to the f.c.c.–b.c.c. interface

Abstract

The formal theory of surface dislocations has been applied to the f.c.c.-b.c.c, interfaces defined by (111) F II (110)B. With the Bain correspondence between the two lattices, various theoretical models and experimental results on these interfaces have been analyzed. The results of the analysis suggest that preferred interface orientations can be explained on the basis that they are those of minimum or near-minimum Burgersvector contents. This concept leads to an improved criterion for comparing the elastic component of interfacial energies. The limitations of geometrical models for predicting low-energy interfaces are discussed. IntroductionIn this paper, we describe f.c.c.-b.c.c, boundaries in terms of the formal geometrical theory of surface dislocations (Bilby, Bullough & de Grinberg, 1964), of which the 0-lattice theory (Bollmann, 1970) may be considered to be a quantized version (Christian, 1976). We also discuss the extent to which criteria such as 'best fit' are successful in predicting observed interface orientations. Particular emphasis is given to experimental results from the copper-chromium agehardening alloy system (Hall, Aaronson & Kinsman, 1972;Weatherly, Humble & Borland, 1979) for which the theory of Bollmann (1974) c, interfaceThe Burgers vector content B of an interface between two phases designated by the subscripts + and -can be defined through the formulawhere p is a vector in the interface and S+ and 5_ are the deformations carrying the reference lattice, in which B and p are expressed in the final orientations of the (+) and (-) lattices respectively. If we choose the (+) lattice to be the reference lattice, which is transformed into the (-) lattice by the deformation $, the formula becomes B = (I--S-m) p. (2)If we suppose that the misfit in the interface defined by (2) i where vx~,and v is a unit vector normal to the boundary. The form of (2) demonstrates that if p is fixed in length and none of the three eigenvalues of S is equal to unity, then the locus of all points B defined through the equation is the surface of an ellipsoid. The principal axes of the ellipsoid can be determined by application of Lagrange multipliers to the function f(p)= ~ BiB ii

Structures in irrational singular interfaces

“…[15] The irrational habit planes in different fcc/bcc alloys have also been approached by models using the energy-indicating parameters, such as the parameter R related to dislocation density, [13] and Burgers vector content. [14] Their relationships with the O-lattice approach have been discussed previously. [1,27] Since these parameters are used to seek a global minimum in the dislocation density, some D I interfaces may be explained by these parameters, if the degree of the misfit in the plane is relatively small.…”

“…A pioneer investigation was made by Hall et al, [12] who proposed a structural ledge model to account for the observed irrational habit plane in a Cu-Cr alloy. Subsequent models have approached the fcc/bcc system by addressing more or less different aspects of the interface using various terms, including a parameter related to dislocation density, [13] the Burgers vector content, [14] an unrotated plane containing an invariant line, [15] an O-line criterion [16] developed from a study of a hcp/bcc system, [17] near coincidence sites (NCS), [18] edge-to-edge matching, [19] and a topological theory [7] originally proposed by Pond. [20] Some models take a rational Orientation relationship (OR) as the input, while others derive a small misorientation with respect to the rational OR according to certain criteria.…”

A TEM study of the crystallography of lath-shaped austenite precipitates in a duplex stainless steel

“…A comparison between crystallographic features for lath-shaped austenite and those for rod-shaped austenite reported by Qiu and Zhang [13] is given in Table 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 20 austenite. As can be seen from Table 2 by Knowles and Smith [32]. It is convenient to examine the distribution of Burgers vector content in the invariant line strain condition by employing the singular value decomposition method [33] to the displacement matrix T, proposed by Gu et al [34].…”

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

“…The concept of a Burgers content ellipse suggested in this method is particularly useful for a systematic analysis of misfit distribution, and has stimulated further development along similar lines. [48][49][50] This approach can predict the shape of a single GMS cluster. However, the large dimension of a GMS cluster may or may not coincide with a row of dense GMS clusters.…”