X Ma, R.C. Pond/ Materials Science and Engineering A 481-482(2008)404-408 Misfit-relieving network parameters for b- LID and b2,_,disconnections 6(°) d l(nm) p(°) dD(nm) 0.5 1.25 35.42 3.37 1179 27.71 4.24 119.71 121.2 12264 5.96 123.89 [lll]a 4.0 12503 0.86 [01]y would require the bz components of the disconnections to be re-instated and the defect content on the habit plane determined using probe vectors in that plane. At equilibrium, the misfit along e=1225 this plane must be accommodated by the defect network, and fur- ther adjustments of defect line directions and separations may be needed. Defect content with resultant component of B per- pendicular to the final habit plane does not affect misfit relief; it 70.39 acts as a low-angle tilt boundary thereby introducing an ancil lary change in the OR. This refinement procedure for ferrous 3771 alloys will be reported fully in a separate paper [17] llll a 4. Discussion ig. 5. Schematic illustration of misfit-relieving networks ofbL LID andbD For a transformation mechanism to be feasible. the free deviates from this by a=2.5 towards the Ks Ol energy of the system containing an interface with struc- ture as described above must be favourable. In the case of the ferrous alloys studied here, the provisional solutions for and d. a schematic illustration of a misfit-relieving network of LID/disconnection networks outlined show that a range of possi- bl LID and b=1/-1 disconnections for the NW Or is shown in bilities corresponding to different ORs satisfies the geometrical Fig5(a), and a second example where the OR deviates from this constraints of the Frank-Bilby equation. Finding an optimal by a=2.5 towards the Kurdjumov-Sachs(KS)OR is depicted solution for a given material would therefore require consid in Fig. 5(b) Network parameters, 0L, d, eD and d for a rang eration of the networks energies which must be added to the of deviations o are listed in table 2 for b and b =1/-ldefects, energy of the coherent terraces [18]. Tables 2 and 3 and Fig.5 and in Table 3 for b- and b,, defects show that the LID separations, dl, increase whereas the dis- he first stage of refinement for the solutions described above connection separations, d, decrease with deviation o from the is to introduce the step character of the disconnections and hence NW towards the KS OR. Also, the line-directions of the defects define the provisional habit plane. The normal to this plane is change over this range of OR. All of these factors influence the determined by rotating the normal to the terrace plane by the free-energy through the elastic strain fields of the defects and angle y=tan-(h/dd)about an axis parallel to s and the values their core energies [19] so obtained are included in Tables 2 and 3. Further refinement Although the habit plane structures reported here are not fully refined, the provisional structures show good agreement with experimental observations in the literature. For example, Sand- Misfit-relieving network parameters for b- LID and b=1/-1 disconnections vik and Wayman [20] studied lath martensite in an Fe-Ni-Mn 60) d(nm) 8o) d (nm) wco) alloy using transmission electron microscopy(TEM).They observed an array of 1/2[11 1]a Lid dislocations with dlin 0 59.62 111.49 6.87 the range 2.6-6.3 nm, sL varying between 10 and 150from 61.04 251 113.92 screw orientation in a habit plane with y=9.45, and o ranging 8.19 between 0.16 and 3. 16.. This observation resembles closely 8.64 the array of b and b=1/-I defects predicted here(Table 2)for a=2.5, namely: d=3.77 nm, EL oriented 12.990from orientation and y=9.10. We note that in the present work 5L 10.52 was treated as a variable, whereas, in our earlier work on TiMo [7], it was taken as being the intersection of the active slip orX. Ma, R.C. Pond / Materials Science and Engineering A 481–482 (2008) 404–408 407 Fig. 5. Schematic illustration of misfit-relieving networks of bL LID and bD −1/−1 disconnections (a) for the NW OR and (b) a second example where the OR deviates from this by ω = 2.5◦ towards the KS OR. and dL. A schematic illustration of a misfit-relieving network of bL LID and bD −1/−1 disconnections for the NW OR is shown in Fig. 5(a), and a second example where the OR deviates from this by ω = 2.5◦ towards the Kurdjumov–Sachs (KS) OR is depicted in Fig. 5(b). Network parameters, θL, dL, θD and dD for a range of deviations ω are listed in Table 2 for bL and bD −1/−1 defects, and in Table 3 for bL and bD −2/−2 defects. The first stage of refinement for the solutions described above is to introduce the step character of the disconnections and hence define the provisional habit plane. The normal to this plane is determined by rotating the normal to the terrace plane by the angle ψ = tan−1(h/dD) about an axis parallel to D and the values so obtained are included in Tables 2 and 3. Further refinement Table 2 Misfit-relieving network parameters for bL LID and bD −1/−1 disconnections ω ( ◦) θL ( ◦) dL (nm) θD ( ◦) dD (nm) ψ ( ◦) 0 59.62 2.31 111.49 1.66 6.87 0.5 61.04 2.51 113.92 1.56 7.30 1.0 62.73 2.74 116.08 1.47 7.74 1.5 64.77 3.02 117.99 1.39 8.19 2.0 67.27 3.35 119.71 1.32 8.64 2.5 70.39 3.77 121.25 1.25 9.10 3.0 74.37 4.28 122.64 1.19 9.57 3.5 79.55 4.90 123.89 1.13 10.05 4.0 86.45 5.64 125.03 1.08 10.52 Table 3 Misfit-relieving network parameters for bL LID and bD −2/−2 disconnections ω ( ◦) θL ( ◦) dL (nm) θD ( ◦) dD (nm) ψ ( ◦) 0 40.46 2.77 111.49 1.33 16.77 0.5 38.18 3.05 113.92 1.25 17.77 1.0 35.42 3.37 116.08 1.18 18.77 1.5 32.01 3.76 117.99 1.11 19.80 2.0 27.71 4.24 119.71 1.05 20.82 2.5 22.23 4.80 121.25 1.00 21.84 3.0 15.14 5.48 122.64 0.95 22.88 3.5 5.96 6.23 123.89 0.90 23.89 4.0 −5.67 6.91 125.03 0.86 24.89 would require the bz components of the disconnections to be re-instated and the defect content on the habit plane determined using probe vectors in that plane. At equilibrium, the misfit along this plane must be accommodated by the defect network, and fur￾ther adjustments of defect line directions and separations may be needed. Defect content with resultant component of B per￾pendicular to the final habit plane does not affect misfit relief; it acts as a low-angle tilt boundary thereby introducing an ancil￾lary change in the OR. This refinement procedure for ferrous alloys will be reported fully in a separate paper [17]. 4. Discussion For a transformation mechanism to be feasible, the free energy of the system containing an interface with struc￾ture as described above must be favourable. In the case of the ferrous alloys studied here, the provisional solutions for LID/disconnection networks outlined show that a range of possi￾bilities corresponding to different ORs satisfies the geometrical constraints of the Frank–Bilby equation. Finding an optimal solution for a given material would therefore require consid￾eration of the networks’ energies, which must be added to the energy of the coherent terraces [18]. Tables 2 and 3 and Fig. 5 show that the LID separations, dL, increase whereas the dis￾connection separations, dD, decrease with deviation ω from the NW towards the KS OR. Also, the line-directions of the defects change over this range of OR. All of these factors influence the free-energy through the elastic strain fields of the defects and their core energies [19]. Although the habit plane structures reported here are not fully refined, the provisional structures show good agreement with experimental observations in the literature. For example, Sand￾vik and Wayman [20] studied lath martensite in an Fe–Ni–Mn alloy using transmission electron microscopy (TEM). They observed an array of 1/2[1 1 1] ¯ LID dislocations with dL in the range 2.6–6.3 nm, L varying between 10◦ and 15◦ from screw orientation in a habit plane with ψ = 9.45◦, and ω ranging between 0.16◦ and 3.16◦. This observation resembles closely the array of bL and bD −1/−1 defects predicted here (Table 2) for ω = 2.5◦, namely: dL = 3.77 nm, L oriented 12.99◦ from screw orientation and ψ = 9.10◦. We note that in the present work L was treated as a variable, whereas, in our earlier work on TiMo [7], it was taken as being the intersection of the active slip or