R C. Pond et al/ Materials Science and Engineering A 438-440(2006)109-112 Fig. 2. Schematic view of coherently strained terraces for(a)ZrOz and(b) Ti: disconnections with the indicated b could move conservatively across these terraces. per unit length is equal(and opposite) to bcy will quench the strain parallel to y on the terrace plane as well as parallel to y on the hp in addition , r will be null since there is no residual Burgers vector content parallel to z or z. In real systems b, is generally finite, so different HP predic tions are anticipated using the PtMc and TM. However, since Fig 3. Schematic illustration of the formation of a disconnection in the ti ter- e. In the terrace coordinate frame (see Fig. 4a). the disconnections b has omponents b, and b sufficient disconnections so that the sum of b, is equal(and oppo- site)to bey will not remove all the coherency strains because the staggered array of b components remains. Pond et al. have set out the necessary procedure [1], and interested readers should refer to that work for full details. As indicated in Fig. 4(b), dis- onnections must be introduced onto the terrace with spacing A so that the residual Burgers vector components parallel to y/in b the primed HP frame(Fig. 4(b)) vanish. Residual components parallel to z produce a rotation R relative to the reference struc tures in Fig. 1, but this does not produce a long-range strain field. The spacing of the disconnections A and their step heights h determine the hP inclination 3. Congruent and disparate predictions of habit plane orientation approaches agree only when the component b or, in other words, when the inter-planar spacing of the ter race planes is the same in the parent and product, as shown Fig 4. Schematic illustrations of (a) coherency strain visualised as an aray dislocations with total Burgers vector equal to bey per unit length, (b)config in Fig 4(c). In this case, no misfit arises on disconnection risers, ration of disconnections (b, h)superimposed on the'coherency'array, bey,and and a disconnection array with spacing such that the sum of by (c)the congruent case where b,=0R.C. Pond et al. / Materials Science and Engineering A 438–440 (2006) 109–112 111 Fig. 2. Schematic view of coherently strained terraces for (a) ZrO2 and (b) Ti; disconnections with the indicated b could move conservatively across these terraces. Fig. 3. Schematic illustration of the formation of a disconnection in the Ti ter￾race. In the terrace coordinate frame (see Fig. 4a), the disconnection’s b has components by and bz. sufficient disconnections so that the sum of by is equal (and oppo￾site) to bcy will not remove all the coherency strains because the staggered array of bz components remains. Pond et al. have set out the necessary procedure [1], and interested readers should refer to that work for full details. As indicated in Fig. 4(b), dis￾connections must be introduced onto the terrace with spacing λ so that the residual Burgers vector components parallel to y in the primed HP frame (Fig. 4(b)) vanish. Residual components parallel to z produce a rotation R relative to the reference struc￾tures in Fig. 1, but this does not produce a long-range strain field. The spacing of the disconnections λ and their step heights h determine the HP inclination. 3. Congruent and disparate predictions of habit plane orientation The two approaches agree only when the component bz = 0, or, in other words, when the inter-planar spacing of the ter￾race planes is the same in the parent and product, as shown in Fig. 4(c). In this case, no misfit arises on disconnection risers, and a disconnection array with spacing such that the sum of by per unit length is equal (and opposite) to bcy will quench the strain parallel to y on the terrace plane as well as parallel to y on the HP. In addition, R will be null since there is no residual Burgers vector content parallel to z or z . In real systems bz is generally finite, so different HP predic￾tions are anticipated using the PTMC and TM. However, since Fig. 4. Schematic illustrations of (a) coherency strain visualised as an array of dislocations with total Burgers vector equal to bcy per unit length, (b) configu￾ration of disconnections (b, h) superimposed on the ‘coherency’ array, bcy, and (c) the congruent case where bz = 0