X Ma, R.C. Pond Materials Science and Engineering A 481-482(2008)404-408 l0/100l4 口■△。口■ [101l 口■△C 口■△D口■ l2h[01]a t(a) t(?) Schematic illustration of the coherent dichromatic pattern; the b of ca ions, joining sites of opposite colour, and LID, joining sites of ne colour are also shown 3. 2. Stage 2; interfacial defects The elastic strain defined above is relieved plastically by incorporation into the interface of admissible interfacial t(a)t(r) defects. Their Burgers vectors and step heights are conveniently illustrated in the coherent dichromatic pattern, Fig 3. Slip dislo- cations of the martensite have b corresponding to black-to-black translation vectors, t(a), for example b= 1/2[11 l ]a; this dis- location do not exhibit step character when embedded in the terrace plane Disconnections have b corresponding to black- Fig 4 Schematic illustration of a(a)b=l-I and(b)b=23/-2disconnections in to-white vectors, t(y)-t(o), in a dichromatic pattern, and two the coherent reference interface examples are depicted in Fig 3 and their parameters are listed in Table 1. One is designated bD-i to indicate that its step goes For this stage, the small components b: of the disconnections are downwards into the(lower)martensite crystal by one(111)y suppressed temporarily Solutions can then be found using the and one(01 1)a plane, and the other, having a step twice this Frank-Bilby equation either as in expression (3) for the NW Or, height is b a schematic illustration of these discon- or alternative natural reference states with finite values of o. The nections, viewed along [1o1Jy/ 1]a, is shown in Fig. 4. spacing of the disconnections, d, and LID, dl,and their line their /-l and b=2/-2 are glissile in the terrace directions, sD and EL, are treated as variable quantities in order plane despite their components bz. Intersections of disconnec tions b=l/- and b=2)-2 with slip dislocations are glissile if the two arrays are present it is possible to choose a probe vector b of the latter is not perpendicular to the terrace [15] as is the vo parallel (or anti-parallel)to sd that intersects only LID,and case for the crystal dislocation denoted b-in Fig 3 and Table 1. similarly a vector VL parallel (or anti-parallel)to 5, cutting only disconnections. Thus in the former case. the burgers vector cut 3.3. Stage 3: misfit relief per unit length, B, can be expressed as The first step is to find a network comprising one array of BL- bl sin(OD-8L) LID, and a second array of disconnections, i.e. defects b-1/-I and in the latter as or b-2/-2, that accommodates the misfit on the terrace plane Table 1 Topological parameters of interfacial defects where AD and el are the angles subtended by ED and 5lfrom br (nm) b,(nm) b(nm) h t() t(a) the positive x-axis. Eq. ( 3) can now [1I gniol, Julii v=-nE- Bl, 0135-0070-00821[2 11y [0111 and similarly for vl. Thus, both the directions and mag a The"overlap"step height, h, is defined as the smaller of the terrace plane of vD and v- can be determined, hence giving the unit vectors E spacings, i.e. (0 11)a in the present case. and E(from which od and e- are found) and the separations d406 X. Ma, R.C. Pond / Materials Science and Engineering A 481–482 (2008) 404–408 Fig. 3. Schematic illustration of the coherent dichromatic pattern; the b of can￾didate disconnections, joining sites of opposite colour, and LID, joining sites of the same colour, are also shown. 3.2. Stage 2; interfacial defects The elastic strain defined above is relieved plastically by incorporation into the interface of admissible interfacial defects. Their Burgers vectors and step heights are conveniently illustrated in the coherent dichromatic pattern, Fig. 3. Slip dislo￾cations of the martensite have b corresponding to black-to-black translation vectors, t(), for example bL = 1/2[1 1 1] ¯ ; this dis￾location do not exhibit step character when embedded in the terrace plane. Disconnections have b corresponding to black￾to-white vectors, t() − t(), in a dichromatic pattern, and two examples are depicted in Fig. 3 and their parameters are listed in Table 1. One is designated bD −1/−1 to indicate that its step goes downwards into the (lower) martensite crystal by one (1 1 1) and one (0 1 1) plane, and the other, having a step twice this height, is bD −2/−2. A schematic illustration of these discon￾nections, viewed along [1 0 1] ¯ /[1¯ 1 1] ¯ , is shown in Fig. 4. Disconnections bD −1/−1 and bD −2/−2 are glissile in the terrace plane despite their components bz. Intersections of disconnec￾tions bD −1/−1 and bD −2/−2 with slip dislocations are glissile if the b of the latter is not perpendicular to the terrace [15], as is the case for the crystal dislocation denoted bL in Fig. 3 and Table 1. 3.3. Stage 3; misfit relief The first step is to find a network comprising one array of LID, and a second array of disconnections, i.e. defects bD −1/−1 or bD −2/−2, that accommodates the misfit on the terrace plane. Table 1 Topological parameters of interfacial defects bx (nm) by (nm) bz (nm) ha t() t() bL 0.135 −0.211 0 0 – 1 2 [1 1 1] ¯ bD −1/−1 −0.135 −0.141 −0.004 −1 1 2 [1¯ 1 0] ¯ 1 2 [1 1¯ 1]¯ bD −2/−2 −0.135 −0.070 −0.008 −2 1 2 [2¯ 1¯ 1]¯ [0 1¯ 1]¯ a The “overlap” step height, h, is defined as the smaller of the terrace plane spacings, i.e. (0 1 1) in the present case. Fig. 4. Schematic illustration of a (a) bD −1/−1 and (b) bD −2/−2 disconnections in the coherent reference interface. For this stage, the small components bz of the disconnections are suppressed temporarily. Solutions can then be found using the Frank–Bilby equation either as in expression (3) for the NW OR, or alternative natural reference states with finite values of ω. The spacing of the disconnections, dD, and LID, dL, and their line directions, D and L, are treated as variable quantities in order to find solutions. A practicable procedure is as follows; since two arrays are present it is possible to choose a probe vector vD parallel (or anti-parallel) to D that intersects only LID, and similarly a vector vL parallel (or anti-parallel) to L, cutting only disconnections. Thus, in the former case, the Burgers vector cut per unit length, BL, can be expressed as BL = bL sin(θD − θL) dL (5a) and in the latter as BD = bp/q sin(θD − θL) dD , (5b) where θD and θL are the angles subtended by D and L from the positive x-axis. Eq. (3) can now be expressed as vD = −nE−1 c BL, (6) and similarly for vL. Thus, both the directions and magnitudes of vD and vL can be determined, hence giving the unit vectors D and L (from which θD and θL are found) and the separations dD