J. P. Hirth et al. cta Materialia 54(2006 )1917-192 11T huffle b twin 110 Fig. 7.(11 1)cubic stereographic projection showing the poles of the habit plane: PE is the experimental pole, Pp is the pole predicted by the enomenological theory (PTMC), and Pr is the pole predicted by the TM. Paths I and 2 are changes in the latter pole position produced Fig. 8.(a)Shuffle/shear of 5 produced by the hcp- a transformation twinning and LiD, respectively. (the angle is enlarged for clarity): (b) average back rotation produced by [HOLJ(hOn twins; (c)projection of a twin on the habit plane with twinning shear directions nI of the [HOK] type, were the basis of the LID in the PTMC analysis [7] that led to Since twinning cannot provide the LID, the LID must the habit plane predictions. In the present TM case, such involve slip in the plates. In addition, slip in the 8 phase twin planes are normal to the terrace plane and the twin would be expected at the plate tips, where the disconnec shear directions lie in the terrace plane(Fig. 8(c). Thus, tions pile up and produce pile-up stresses in the 8 phase. it is impossible for such LID twinning to relieve the E33 Indeed, transmission electron microscopy of the present misfit strains, accounting for the large difference in habit transformed alloy revealed dislocation tangles in both the plane predictions in the TM and PTMC cases, particularly aand 8 phases. Hecker and Stevens [20] reviewed studies when referred to the a phase. On the other hand, such of deformation in pure a-Pu phase. They find that a single prismatic twinning produces a shear E13, precisely of the crystals deform primarily by slip [22, 23]. Poles of observed type that would accommodate the coherency strain a13 slip planes are depicted in Fig 10 produced by the transformation. We postulate that this Slip directions are not known for the observed slip accommodation is the basis for the twinning shown in planes but we can speculate on possible Burgers vectors ig. 9. The transformation would produce a shear E13 giv- that lie in each of these planes, as shown in Table 2. g an angular rotation of M5(see Fig 8(a)) and the twin- There are two striking features of Table 2: one is that ning, on average, would produce an opposite shear and some of the observed slip planes require very large Bur- rotation. The rotation would tend to shift the habit plane gers vectors and the other is that many of the slip planes as predicted by the Tm closer to the experimental result as are by no means close-packed and have small d spacings indicated by path I in Fig. 7. Another approach is to consider slip planes that have rea Since the twinning disconnection Burgers vectors lie in sonably large d spacings and correspondingly large struc- the terrace plane, the twinning dislocation-transformation ture factors, as shown in Table 3. The almost complete disconnection intersections are sessile [21]. Sequentially, the lack of agreement between Tables 2 and 3 means that transformation disconnections must move first and the the Peierls approach to selecting slip systems(small b, twinning disconnections second. The intersection points large d) just does not work for a-Pu. Perhaps deformation are jogged and can only move by climb. However, because is controlled by screw dislocations that cross-slip easily of the high homologous temperature for Pu, this should (pencil glide), giving irrational or high-index slip planes not highly constrain the interface. Indeed, consideration close to the maximum resolved shear stress. (In fact Liptai of Eqs. (16)(20)in Hirth and Lothe [24] indicates that it and Friddle [23] comment that all of the observed slip is highly likely that the jogs can move athermally, creating planes were within 100 e maximum shear plane. ines of point defects at the intersection jogs Another possibility is that deformation occurs by thewith twinning shear directions g1 of the [H0K] type, were the basis of the LID in the PTMC analysis [7] that led to the habit plane predictions. In the present TM case, such twin planes are normal to the terrace plane and the twin shear directions lie in the terrace plane (Fig. 8(c)). Thus, it is impossible for such LID twinning to relieve the e33 misfit strains, accounting for the large difference in habit plane predictions in the TM and PTMC cases, particularly when referred to the a0 phase. On the other hand, such prismatic twinning produces a shear e13, precisely of the type that would accommodate the coherency strain e13 produced by the transformation. We postulate that this accommodation is the basis for the twinning shown in Fig. 9. The transformation would produce a shear e13 giv￾ing an angular rotation of 5 (see Fig. 8(a)) and the twin￾ning, on average, would produce an opposite shear and rotation. The rotation would tend to shift the habit plane as predicted by the TM closer to the experimental result as indicated by path 1 in Fig. 7. Since the twinning disconnection Burgers vectors lie in the terrace plane, the twinning dislocation–transformation disconnection intersections are sessile [21]. Sequentially, the transformation disconnections must move first and the twinning disconnections second. The intersection points are jogged and can only move by climb. However, because of the high homologous temperature for Pu, this should not highly constrain the interface. Indeed, consideration of Eqs. (16)–(20) in Hirth and Lothe [24] indicates that it is highly likely that the jogs can move athermally, creating lines of point defects at the intersection jogs. Since twinning cannot provide the LID, the LID must involve slip in the a0 plates. In addition, slip in the d phase would be expected at the plate tips, where the disconnec￾tions pile up and produce pile-up stresses in the d phase. Indeed, transmission electron microscopy of the present transformed alloy revealed dislocation tangles in both the a0 and d phases. Hecker and Stevens [20] reviewed studies of deformation in pure a-Pu phase. They find that a single crystals deform primarily by slip [22,23]. Poles of observed slip planes are depicted in Fig. 10. Slip directions are not known for the observed slip planes but we can speculate on possible Burgers vectors that lie in each of these planes, as shown in Table 2. There are two striking features of Table 2: one is that some of the observed slip planes require very large Bur￾gers vectors and the other is that many of the slip planes are by no means close-packed and have small d spacings. Another approach is to consider slip planes that have rea￾sonably large d spacings and correspondingly large struc￾ture factors, as shown in Table 3. The almost complete lack of agreement between Tables 2 and 3 means that the Peierls approach to selecting slip systems (small b, large d) just does not work for a-Pu. Perhaps deformation is controlled by screw dislocations that cross-slip easily (pencil glide), giving irrational or high-index slip planes close to the maximum resolved shear stress. (In fact Liptai and Friddle [23] comment that all of the observed slip planes were within 10 of the maximum shear plane.) Another possibility is that deformation occurs by the 5 [01 0]×[001] ' [112 ] [102] ' shuffle twin twin shear twin planes 5 a d a a b c ˚ Fig. 8. (a) Shuffle/shear of 5 produced by the hcp ! a0 transformation (the angle is enlarged for clarity); (b) average back rotation produced by [H0L] (h0l) twins; (c) projection of a twin on the habit plane. 111 101 11 1 11 0 01 1 ω 1 01 001 111 1 10 011 110 010 100 011 101 112 1 1 2 PP PE PT 1 2 Fig. 7. (1 1 1) cubic stereographic projection showing the poles of the habit plane: PE is the experimental pole, PP is the pole predicted by the phenomenological theory (PTMC), and PT is the pole predicted by the TM. Paths 1 and 2 are changes in the latter pole position produced by twinning and LID, respectively. 1922 J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925