《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_monoclinic martensite transformation

Availableonlineatwww.sciencedirect.com SCIENCE Acta materialia ELSEVIER Acta Materialia 54(2006)1917-1925 www.actamat-journals.com on the fcc- monoclinic martensite transformation in a pu-1.7 at. Ga alloy J.P. Hirth J. N. Mitchell.Ds. schwartz T.E. mitchell Structure-Property Relations Group, MST-8, Mail Stop G755, Los Alamos ory, Los Alamos, NM 87545, US.A b Nuclear Materials Science Group, Los Alamos National Laboratory, Los Alamos, NM87545, USA Received 23 September 2005: received in revised form 12 December 2005: accepted 14 December 2005 Available online 28 February 2006 Abstract The face-centered cubic 8- monoclinic martensite transformation in a Pu-1.7 at Ga alloy is analyzed in terms of the defect- based topological model. Disconnections and terrace planes for the transformation are deduced. The predicted habit plane is in good agreement with experimental results Observed twinning is associated directly with the transformation strain. The lattice invariant defor- mation is connected with slip in the a plates. Implications for hysteresis in the transformation as observed by dilatometry and calorim etry are discussed o 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved Keywords: Plutonium; Crystal structure; Martensitic phase transformations; Interface defects: Dislocation boundaries 1. Introduction (010) planes are perfectly coplanar with no puckering. The stacking of these planes is ABAB; the arrangement of Face-centered cubic(fcc)8-phase plutonium is stabilized atoms in the A and B planes is the same but they are at room temperature by the addition of less than about I rotated by 180 with respect to each other. The near neigh at Ga. Stabilized plutonium alloys, such as the Pu-1.7 bors and their bond lengths for the eight types of atoms are at Ga alloy considered here, undergo a martensitic trans- given in Table 1. These were calculated using the atomic formation on cooling from the fcc 8 phase to the mono- positions determined by Zachariasen and Ellinger [3] for clinic o' phase at about -100C. The latter is called a' pure a-Pu, and the unit cell dimensions appropriate for rather than a because ois supersaturated with Ga and a Pu-1.7 at Ga published by Hecker [4]. There are short refers to pure plutonium. The presence of Ga in the a' bonds from about 2.6 to 2.8 A in length, and longer bonds phase has the effect of expanding the unit cell volume by of 3. 2-3. 7 A in length. Atoms I and 3 have 12 near neigh about 1.8% relative to the pure a phase, but does not bors while all the rest have 14; the number of short bonds change the crystal structure. Notable characteristics of this varies from 5 for atom I to 3 for atom 8. Atom 8 has a sig- transformation include a significant reversion hysteresis of nificantly longer average bond length than the others: 150-200C, a >20% volume contraction, and incom- 3. 28 A compared to approximately 3. 16 A pleteness of the transformation during cooling [1, 2]. The crystallography of the 8-a'transformation, and As shown in Fig. 1, the monoclinic unit cell (space group of twinning, is greatly facilitated by the replacement of P21/m)of Pu contains 16 atoms in 8 different positions with the monoclinic phase by a hexagonal close packed (hcp) pairs of atoms related by the screw diad. The atoms in the pseudostructure, an innovation introduced by Crocker [5]. As indicated in Fig. I and Table 1, most atoms in the a' phase in fact have 14 nearest neighbors, rather than 12 ing author.Tel:+15056670938;fax:+150566780 in the hep structure. The pairs of atoms in the(0 10) planes E-jmail address: temitchellalanl gov (T E. Mitchell). above and below that need to be ignored for the hep 1359-6454/$30.00 O 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:l0.1016 actant2005.12030

On the fcc ! monoclinic martensite transformation in a Pu–1.7 at.% Ga alloy J.P. Hirth a , J.N. Mitchell b , D.S. Schwartz b , T.E. Mitchell a,* a Structure–Property Relations Group, MST-8, Mail Stop G755, Los Alamos National Laboratory, Los Alamos, NM 87545, USA b Nuclear Materials Science Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 23 September 2005; received in revised form 12 December 2005; accepted 14 December 2005 Available online 28 February 2006 Abstract The face-centered cubic d ! monoclinic a0 martensite transformation in a Pu–1.7 at.% Ga alloy is analyzed in terms of the defect￾based topological model. Disconnections and terrace planes for the transformation are deduced. The predicted habit plane is in good agreement with experimental results. Observed twinning is associated directly with the transformation strain. The lattice invariant defor￾mation is connected with slip in the a0 plates. Implications for hysteresis in the transformation as observed by dilatometry and calorim￾etry are discussed. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Plutonium; Crystal structure; Martensitic phase transformations; Interface defects; Dislocation boundaries 1. Introduction Face-centered cubic (fcc) d-phase plutonium is stabilized at room temperature by the addition of less than about 1 at.% Ga. Stabilized plutonium alloys, such as the Pu–1.7 at.% Ga alloy considered here, undergo a martensitic trans￾formation on cooling from the fcc d phase to the mono￾clinic a0 phase at about 100 C. The latter is called a0 rather than a because a0 is supersaturated with Ga and a refers to pure plutonium. The presence of Ga in the a0 phase has the effect of expanding the unit cell volume by about 1.8% relative to the pure a phase, but does not change the crystal structure. Notable characteristics of this transformation include a significant reversion hysteresis of 150–200 C, a >20% volume contraction, and incom￾pleteness of the transformation during cooling [1,2]. As shown in Fig. 1, the monoclinic unit cell (space group P21/m) of Pu contains 16 atoms in 8 different positions with pairs of atoms related by the screw diad. The atoms in the (0 1 0) planes are perfectly coplanar with no puckering. The stacking of these planes is ABAB; the arrangement of atoms in the A and B planes is the same but they are rotated by 180 with respect to each other. The near neigh￾bors and their bond lengths for the eight types of atoms are given in Table 1. These were calculated using the atomic positions determined by Zachariasen and Ellinger [3] for pure a-Pu, and the unit cell dimensions appropriate for Pu–1.7 at.% Ga published by Hecker [4]. There are short bonds from about 2.6 to 2.8 A˚ in length, and longer bonds of 3.2–3.7 A˚ in length. Atoms 1 and 3 have 12 near neigh￾bors while all the rest have 14; the number of short bonds varies from 5 for atom 1 to 3 for atom 8. Atom 8 has a sig￾nificantly longer average bond length than the others: 3.28 A˚ compared to approximately 3.16 A˚ . The crystallography of the d ! a0 transformation, and of twinning, is greatly facilitated by the replacement of the monoclinic phase by a hexagonal close packed (hcp) pseudostructure, an innovation introduced by Crocker [5]. As indicated in Fig. 1 and Table 1, most atoms in the a0 phase in fact have 14 nearest neighbors, rather than 12 in the hcp structure. The pairs of atoms in the (0 1 0) planes above and below that need to be ignored for the hcp 1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.12.030 * Corresponding author. Tel.: +1 505 667 0938; fax: +1 505 667 8021. E-mail address: temitchell@lanl.gov (T.E. Mitchell). www.actamat-journals.com Acta Materialia 54 (2006) 1917–1925

1918 J. P. Hirth et al. cta Materialia 54(2006 )1917-192 (IPS) solutions by Choudry and Crocker [8 and Adler et al. [9]. These solutions were applied to the Pu-1.7 at Ga alloy and correlated with transmission electron micros- copy observations by Zocco et al. [7]. The lattice corre- spondence in the latter analysis were consistent with the plane and direction parallelism mentioned in the paragraph These IPS solutions followed the procedures of the phe nomenological theory [10, 1l] of martensite transforma- tions (PTMc) for cases where the lattice invariant deformation(LID)was associated with twinning in the a phase. The PTMC, given a lattice correspondence and a LID, determines an IPS solution that gives a strain-free habit plane and a transformation shear displacement on that plane. However, while the transformation is implicitly related to possible transformation defects, the defects are usually not explicitly determined An alternative topological model(TM) has been devel- oped by Pond and Hirth [12, 13]. This approach first con- siders the transformation defects and then predicts a consistent habit plane and lattice orientation relationship directly from the geometry of the defects. The defects are identified as transformation disconnections. also called transformation dislocations. As shown in Fig. 2, the dis- connections have both step and dislocation character [14]. Fig. 1. Four monoclinic unit cells(dotted lines)of a-Pu viewed along In the propagation of the martensite transformation, the 010 The eight different equivalent sites are labeled. The blue aton disconnections move a diffusionless m (layer A)are all at y=0.75 while the orange atoms (layer B) are at coherent terrace planes that separate the two phases. The =0.25. The A and B layers are identical except for a rotation of 180. Lid is treated in the final step of the analysis as the defor- The larger unit cell shown with dashed lines has a monoclinic p angle of mation required to relieve misfit strain in the terrace plane 116. 80 (close to 120. for the hcp cll) instead of 101. 82 for the smaller with displacement perpendicular to that of the transforma tion shear In the TM, one can define a stress-free habit plane that pseudostructure are indicated in Table I by parentheses. In involves only transformation disconnections and LID all cases there are six near neighbors in the(010)plane, as defects(slip or twinning dislocations )in the habit plane there are in the(000 1) plane of the hcp structure. Hence, The PTmc solutions only yield such a solution if there is this structure can be mapped into a hcp structure without no misfit between the matrix and product phases normal changing atom neighbors. The neighbors in parentheses to the terrace plane. Otherwise the TM and PTMC solu in Table I become shuffled into 12-fold coordination with tions would coincide only if the PTMC structure acquired other atoms. After analyzing transformations from 8 to additional dislocations with a Burgers vector normal to the the hcp pseudostructure, and the formation of twins terrace plane [14]. Pond et al. [15] have compared the TM herein, the pseudostructure can be transformed to a' by and the PTmC predictions for the p-transformation means of shuffles and one shear. The shear does not corre- in a Ti-Mo alloy and for the orthorhombic to monoclinic spond to a difference between the 120 angle of the hcp unit transformation in ZrO2[16]. In both cases, the lattice misfit cell and the 101.82 B angle of the monoclinic unit cell; is small and the difference between the two models is small rather, the shear corresponds to the difference in the but significant. High-resolution transmission electron 116.80 angle of the monoclinic angle of the double size microscopy has been applied to both systems [16, 17]. unit cell outlined by dashed lines in Fig. I. The a and c axes revealing coherent terrace/disconnection structures at the of the latter unit cell are parallel to pseudo-close-packed interface, as predicted by the TM directions in the(010)plane. Additional details are given The lattice misfit is large in the case of the Pu-Ga alloy Fig. 4 and in Section 2. Another important feature, where there is a 20% volume contraction associated with found by Olsen [6], is the near parallelism of the (11 1)s the 8a transformation. Thus, a comparison of the TM and (010)a planes as well as of the [1 10] and [100] and PTMC models for this case may yield significant directions There have been several studies of the transformation The a' martensite plates have a large aspect ratio in the crystallography, as reviewed by Zocco et al. [7], but perti- Pu-1.7 at Ga alloy as revealed in Fig 3. Here, we ana- nent to the present work are the invariant plane strain lyze the ideal stress-free habit plane and orientation rela-

pseudostructure are indicated in Table 1 by parentheses. In all cases there are six near neighbors in the (0 1 0) plane, as there are in the (0 0 0 1) plane of the hcp structure. Hence, this structure can be mapped into a hcp structure without changing atom neighbors. The neighbors in parentheses in Table 1 become shuffled into 12-fold coordination with other atoms. After analyzing transformations from d to the hcp pseudostructure, and the formation of twins therein, the pseudostructure can be transformed to a0 by means of shuffles and one shear. The shear does not corre￾spond to a difference between the 120 angle of the hcp unit cell and the 101.82 b angle of the monoclinic unit cell; rather, the shear corresponds to the difference in the 116.80 angle of the monoclinic angle of the double size unit cell outlined by dashed lines in Fig. 1. The a and c axes of the latter unit cell are parallel to pseudo-close-packed directions in the (0 1 0) plane. Additional details are given in Fig. 4 and in Section 2. Another important feature, found by Olsen [6], is the near parallelism of the (1 1 1)d and (0 1 0)a planes as well as of the ½110 d and [1 0 0]a directions. There have been several studies of the transformation crystallography, as reviewed by Zocco et al. [7], but perti￾nent to the present work are the invariant plane strain (IPS) solutions by Choudry and Crocker [8] and Adler et al. [9]. These solutions were applied to the Pu–1.7 at.% Ga alloy and correlated with transmission electron micros￾copy observations by Zocco et al. [7]. The lattice corre￾spondences in the latter analysis were consistent with the plane and direction parallelism mentioned in the paragraph above. These IPS solutions followed the procedures of the phe￾nomenological theory [10,11] of martensite transforma￾tions (PTMC) for cases where the lattice invariant deformation (LID) was associated with twinning in the a0 phase. The PTMC, given a lattice correspondence and a LID, determines an IPS solution that gives a strain-free habit plane and a transformation shear displacement on that plane. However, while the transformation is implicitly related to possible transformation defects, the defects are usually not explicitly determined. An alternative topological model (TM) has been devel￾oped by Pond and Hirth [12,13]. This approach first con￾siders the transformation defects and then predicts a consistent habit plane and lattice orientation relationship directly from the geometry of the defects. The defects are identified as transformation disconnections, also called transformation dislocations. As shown in Fig. 2, the dis￾connections have both step and dislocation character [14]. In the propagation of the martensite transformation, the disconnections move in a diffusionless manner across coherent terrace planes that separate the two phases. The LID is treated in the final step of the analysis as the defor￾mation required to relieve misfit strain in the terrace plane with displacement perpendicular to that of the transforma￾tion shear. In the TM, one can define a stress-free habit plane that involves only transformation disconnections and LID defects (slip or twinning dislocations) in the habit plane. The PTMC solutions only yield such a solution if there is no misfit between the matrix and product phases normal to the terrace plane. Otherwise the TM and PTMC solu￾tions would coincide only if the PTMC structure acquired additional dislocations with a Burgers vector normal to the terrace plane [14]. Pond et al. [15] have compared the TM and the PTMC predictions for the b ! a0 transformation in a Ti–Mo alloy and for the orthorhombic to monoclinic transformation in ZrO2 [16]. In both cases, the lattice misfit is small and the difference between the two models is small but significant. High-resolution transmission electron microscopy has been applied to both systems [16,17], revealing coherent terrace/disconnection structures at the interface, as predicted by the TM. The lattice misfit is large in the case of the Pu–Ga alloy, where there is a 20% volume contraction associated with the d ! a0 transformation. Thus, a comparison of the TM and PTMC models for this case may yield significant differences. The a0 martensite plates have a large aspect ratio in the Pu–1.7 at.% Ga alloy as revealed in Fig. 3. Here, we ana￾lyze the ideal stress-free habit plane and orientation rela- 8 8 8 8 8 8 8 8 8 1 1 1 1 1 1 7 7 7 7 7 7 8 8 8 8 8 8 8 7 7 7 7 7 7 2 2 2 2 1 1 1 1 1 1 3 3 3 3 3 3 5 5 5 5 5 5 6 6 6 6 4 4 4 4 4 4 4 4 5 5 5 5 5 5 3 3 3 3 3 3 2 2 2 2 6 6 6 6 8 8 c a Fig. 1. Four monoclinic unit cells (dotted lines) of a-Pu viewed along [0 1 0]. The eight different equivalent sites are labeled. The blue atoms (layer A) are all at y = 0.75 while the orange atoms (layer B) are at y = 0.25. The A and B layers are identical except for a rotation of 180. The larger unit cell shown with dashed lines has a monoclinic b angle of 116.80 (close to 120 for the hcp cell) instead of 101.82 for the smaller unit cell. 1918 J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925

J. P. Hirth et al. 1 Acta Materialia 54(2006)1917-1925 Table l t. Ga Pu ator Average bond length No short bonds No long bonds 3. 3.223.432. 3.223.432.78 3.403.213.17 345364)2.663.4 3.45364)2.663.4 2.602.62 8399 3.46 3.393.37 3.393.37 3 3.533.383.16 31 3.22 3.22 3.533.31 3.43 3.383.232.80 2.783.48 Short bonds(<2.80 A)are in italic type. Bonds extending into an adjacent layer are in bold type and occur in pairs(because of the mirror plane). Bond lengths up to 3.73 A are given; those not normally considered to be part of the 12-fold coordination are in parentheses. The 12 nearest neighbors are used to determine the average bond length nship at the near planar center of the broad faces of the structure, are the in-plane displacement vectors that would plate. produce the transformation shear in the a phase. The vec- tors are [1021,,24[502]a, and 24[7021 and correspond to 2. Transformation model the three 1(1010) Shockley partial Burgers vectors in the hcp pseudostructure. Electron microscopy [7]indicates that The first step in the TM is to select a terrace plane. On [100] is the actual line direction of the disconnections. The the basis of the pseudostructure proposed by Crocker [5] misfit of the average along these lines with the and the observations of Olsen [6], we select(010)o// close-packed directions in 8 is least for the [302 , direction (1 11) as the coherent reference terrace plane. The However, if one studies the spacings of atoms along the (010)a plane is shown in Fig. 4. While only the terrace transformation shear directions, one notes that there is lit- plane is needed in the TM, this choice is near to that in tle variation for the [102] direction whereas the variation the lattice correspondence in the IPS approaches [7-9]. is large for both the [502 and 702 directions. This indi The(0 10)a plane is then related to the (0001) hep plane cates that the shuffles entailed in completing the transfo in the pseudostructure. The [100],[102], and [302 mation from the hep pseudostructure to the a' phase are directions in Fig. 4 correspond to the close-packed minimized for the [1 02] case and this is postulated to be 120)directions in the hcp(0001) plane. One of these the reason for the system to select the [100] disconnection directions must be related to the disconnection line direc- line on. The vectors shown in Fig 4, each normal to one of Hence, the configuration of the transformation discon the directions that would be close-packed in the pseudo- nections is that illustrated in Fig. 5. The terrace plane is

tionship at the near planar center of the broad faces of the plate. 2. Transformation model The first step in the TM is to select a terrace plane. On the basis of the pseudostructure proposed by Crocker [5] and the observations of Olsen [6], we select (0 1 0)a// (1 1 1)d as the coherent reference terrace plane. The (0 1 0)a plane is shown in Fig. 4. While only the terrace plane is needed in the TM, this choice is near to that in the lattice correspondence in the IPS approaches [7–9]. The (0 1 0)a plane is then related to the (0 0 0 1) hcp plane in the pseudostructure. The [1 0 0]a, ½102 a, and ½ 3 02 a directions in Fig. 4 correspond to the close-packed h1 12 0i directions in the hcp (0 0 0 1) plane. One of these directions must be related to the disconnection line direc￾tion. The vectors shown in Fig. 4, each normal to one of the directions that would be close-packed in the pseudo￾structure, are the in-plane displacement vectors that would produce the transformation shear in the a0 phase. The vec￾tors are 1 12 ½102 a, 1 24 ½5 02 a, and 1 24 ½7 02 a and correspond to the three 1 3 h1 01 0i Shockley partial Burgers vectors in the hcp pseudostructure. Electron microscopy [7] indicates that [1 0 0]a is the actual line direction of the disconnections. The misfit of the average spacing along these lines with the close-packed directions in d is least for the ½3 02 a direction. However, if one studies the spacings of atoms along the transformation shear directions, one notes that there is lit￾tle variation for the [1 0 2]a direction whereas the variation is large for both the ½5 02 a and ½7 02 a directions. This indi￾cates that the shuffles entailed in completing the transfor￾mation from the hcp pseudostructure to the a0 phase are minimized for the [1 0 2]a case and this is postulated to be the reason for the system to select the [1 0 0]a disconnection line. Hence, the configuration of the transformation discon￾nections is that illustrated in Fig. 5. The terrace plane is Table 1 Bond lengths (A˚ ) in Pu–1.7 at.% Ga Pu atom number 1 2 3 4 5 6 7 8 Average bond length No. short bonds No. long bonds 1 2.61 2.60 3.43 2.58 3.73 3.12 5 7 3.61 3.22 3.43 2.78 3.22 3.43 2.78 2 2.61 2.62 3.39 3.40 3.21 3.17 4 10 3.61 3.45 (3.64) 2.66 3.48 3.45 (3.64) 2.66 3.48 3 2.60 2.62 3.28 3.26 3.67 3.16 4 8 3.43 3.39 2.68 3.46 3.39 2.68 3.46 4 3.43 3.39 3.28 2.59 2.64 3.14 4 10 3.43 3.39 3.37 (3.34) 2.76 3.39 3.37 (3.34) 2.76 5 3.26 2.59 2.73 3.53 3.38 3.16 4 10 3.53 3.45 2.68 3.34 (3.53) 3.45 2.68 3.34 (3.53) 6 3.67 2.64 2.73 3.31 3.23 3.17 4 10 3.53 3.22 (3.64) 3.46 2.76 3.22 (3.64) 3.46 2.76 7 2.58 3.40 3.53 3.31 2.80 3.17 4 10 3.45 3.43 2.66 3.42 (3.51) 3.43 2.66 3.42 (3.51) 8 3.73 3.21 3.38 3.23 2.80 3.28 3 11 3.45 2.78 3.48 (3.51) 3.53 2.78 3.48 (3.51) 3.53 Short bonds (62.80 A˚ ) are in italic type. Bonds extending into an adjacent layer are in bold type and occur in pairs (because of the mirror plane). Bond lengths up to 3.73 A˚ are given; those not normally considered to be part of the 12-fold coordination are in parentheses. The 12 nearest neighbors are used to determine the average bond length. J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925 1919

J. P. Hirth et al. cta Materialia 54(2006 )1917-192 normal to[1001 h 702] a δ 02 b Fig. 2. Free surface ledges on the a and a phases(a) brought Fig 4. Single (010)layer of the a monoclinic phase, showing six unit form a disconnection(b). Ledge overlap produces a step h. cells, the three[100][302 and [102] pseudo-close-packed directions, and Difference in height and inclination produces a dislocation 02], and [102] shear transformation directions. The nents bi and bx. 5 is the line direction. vectors in the diagram correspond to Shockley partials in the hcp pseudolattice. The larger unit cell shown in Fig. I is also shown here in dashed lines. Note that the dashed lines are parallel to [100] and[102 (010)a(normal to x2), the line direction 5 is [100](parallel x3),and xI- direction is parallel to one of the(1010 structure. The 5 angular difference between the latter directions in the hcp pseudostructure which in turn is two directions is allowed for in the next section. The inter- approximately parallel to the [102] direction in the o face-plane component of the Burgers vector of the disco 10 um Fig 3. Optical photomicrograph of a Pu-2 at. %Ga alloy following cooling to-155C, holding for 60 min, and warming to room temperature. Note the light-colored paths of a-Pu within the 8-Pu matrix. Gray-scale variations within grains show that the lighter cores of the grains are relatively rich in Ga Note that the paths have four orientations in each grain, corresponding to the four lll planes in the 8 matrix

(0 1 0)a (normal to x2), the line direction n is [1 0 0]a (parallel to x3), and x1-direction is parallel to one of the h1 01 0i directions in the hcp pseudostructure which in turn is approximately parallel to the [1 0 2]a direction in the a0 structure. The 5 angular difference between the latter two directions is allowed for in the next section. The inter￾face-plane component of the Burgers vector of the discon￾Fig. 3. Optical photomicrograph of a Pu–2 at.% Ga alloy following cooling to 155 C, holding for 60 min, and warming to room temperature. Note the light-colored paths of a0 -Pu within the d-Pu matrix. Gray-scale variations within grains show that the lighter cores of the grains are relatively rich in Ga. Note that the paths have four orientations in each grain, corresponding to the four {1 1 1} planes in the d matrix. [1 02] [100] [3 02 ] [102 ] normal to [100 ] [7 02 ] [502 ] 1 24 [7 02 ] 1 24 [50 2 ] 1 12 [102 ] 5˚ Fig. 4. Single (0 1 0) layer of the a0 monoclinic phase, showing six unit cells, the three [1 0 0], ½3 02, and ½102 pseudo-close-packed directions, and the three ½5 02, ½7 02, and [1 0 2] shear transformation directions. The vectors in the diagram correspond to Shockley partials in the hcp pseudolattice. The larger unit cell shown in Fig. 1 is also shown here in dashed lines. Note that the dashed lines are parallel to [1 0 0] and ½102 pseudo-close packed directions. Fig. 2. Free surface ledges on the a0 and d phases (a) brought together to form a disconnection (b). Ledge overlap produces a step of height h. Difference in height and inclination produces a dislocation with compo￾nents b1 and b2. n is the line direction. 1920 J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925

J. P. Hirth et al. I Acta Materialia 54(2006)1917-1925 habit plane Fig. 5. Disconnections, terrace planes, and misfit strains at 8/a interface. 6. (a) Habit plane when disconnections remove misfit in the tion(b)Tilt wall produced by the b'2 component nections shown in Fig. 5 is b1 =D102. In order to calcu- late strains and the magnitude of the Burgers vectors, we =6.0 as given by Eq.(B 8)of Pond et al. [15].One half ise the lattice parameters cited by Zocco et al. [71, as of o partitions to each phase and so the habit plane in the 8 slightly modified by Lawson et al. [18]: as=0.4626 nm, phase is inclined to the terrace plane by o=0+o/2= aa=0.6199 nm, ba=0.4630 nm, ca=1070 nm, and 23.10. As shown in Fig. 6(a), the rotation 0 as produced B=101.820. For the fcc/hep disconnection, the step height by the step crystallographic orientation is changed by /2 is twice the spacing of the close-packed planes. Hence, the in each phase by the tilt wall corresponding quantities depicted in Fig. 5 are the ledge The lid defects remove the misfit E33=E33 and give added rotation of the a' lattice that changes the habit plane h=da1o=0.4630nm referred to o' but leaves the habit plane referred to 8 the Burgers vector normal to the terrace plane unchanged. Hence we compare the 8 habit plane angle of 23. 1 with the other results, since it is unchanged by the b2=2(a-di1)=-0.0712mm LID, which differs in the different approaches. The experi the normal strain component along the xz-direction ments of Zocco et al. [7]give 0= 22.2 and the IPS/PTMC analysis of Zocco et al. [7] gives 0= 12.8. As depicted in E2=b2/2am1=-0.1332 the stereographic projection in Fig. 7, the angular traces of the rotations of the habit planes from(111)s also differ and the normal strain component along the x3-direction The habit plane prediction of the TM is in much better B3=(100x-[10/1106=-0.053 agreement with experiment than that of the PTMC. The For the xr-direction, we define the Burgers vector and En in following analysis suggests that the agreement of the TM the median coherent reference lattice [13]. Thus the misfit may be even better. The normal to[10O],which would strain along xl, given by(bla-b18)/(b1a+b18),is coincide with the [1010 direction of the transformation partial in the hep pseudostructure, is inclined to the 1-)/2(02+n1) [102] direction by 5(see Fig. 4). Hence, in the comple tion of the transformation from hcp to a, in addition to =-0.1365nm/0.1820nm=-0.7499and 0.1820mm The choice of the angle is arbitrary in the following sense We have fixed the coincidence of the two structures along [100J(see Fig. 4), and have selected the normal to this 3. Results direction to define the angle. The shear then fixes an orthogonal box and the remainder of the atoms transform The procedure for predicting the habit plane is illus- by shuffles. One could pick another direction resulting in trated in Fig. 6(a). The strains and Burgers vectors are different shears and shuffles. Clearly, however, the mean transformed to the x, coordinates fixed on the habit plane. monoclinic structure is rotated with respect to the hcp exactly pacing is then selected so that the misfit pseudostructure, so any choice would lead to some shear strain G is exactly compensated by the average strain b1/L with consequences similar to those of the present selection of the disconnections, an analog of misfit removal in thin- Studies [19] of twinning in Pu-1.7 at Ga revealed new Im overlayers. This gives 0= 19.8 as determined from twinning systems in addition to those predicted by Crocker Eq(B 2)of Pond et al. [15]. The b, components of the dis- [5]. An example of the observed twinning is shown in connections produce a tilt wall and a corresponding misori- Fig 9: we note that the configuration is consistent with entation(rotation) from the original(1 11)//(0 1O)a of Fig. 8(c). These twins [7, 19], all of the(hOk) prismatic type

nections shown in Fig. 5 is b1 ¼ 1 12 ½102 a. In order to calcu￾late strains and the magnitude of the Burgers vectors, we use the lattice parameters cited by Zocco et al. [7], as slightly modified by Lawson et al. [18]: ad = 0.4626 nm, aa = 0.6199 nm, ba = 0.4630 nm, ca = 1.070 nm, and b = 101.82. For the fcc/hcp disconnection, the step height is twice the spacing of the close-packed planes. Hence, the corresponding quantities depicted in Fig. 5 are the ledge height h ¼ da 010 ¼ 0:4630 nm the Burgers vector normal to the terrace plane b2 ¼ 2ðda 020 dd 111Þ¼0:0712 nm the normal strain component along the x2-direction e22 ¼ b2=2dd 111 ¼ 0:1332 and the normal strain component along the x3-direction e33 ¼ ð½100 a ½110 dÞ=½110 d ¼ 0:0537 For the x1-direction, we define the Burgers vector and e11 in the median coherent reference lattice [13]. Thus the misfit strain along x1, given by ðb1a b1dÞ= 1 2 ðb1a þ b1dÞ, is e11 ¼ 1 12 ½102 a 1 6 ½1 12 d 1 2 1 12 ½102 a þ 1 6 ½1 12 d ¼ 0:1365 nm=0:1820 nm ¼ 0:7499 and b1 ¼ 0:1820 nm. 3. Results The procedure for predicting the habit plane is illus￾trated in Fig. 6(a). The strains and Burgers vectors are transformed to the x0 i coordinates fixed on the habit plane. The disconnection spacing is then selected so that the misfit strain e0 11 is exactly compensated by the average strain b0 1=L of the disconnections, an analog of misfit removal in thin- film overlayers. This gives h = 19.8 as determined from Eq. (B.2) of Pond et al. [15]. The b0 2 components of the dis￾connections produce a tilt wall and a corresponding misori￾entation (rotation) from the original (1 1 1)d//(0 1 0)a of u = 6.6 as given by Eq. (B.8) of Pond et al. [15]. One half of u partitions to each phase and so the habit plane in the d phase is inclined to the terrace plane by x = h + u/2 = 23.1. As shown in Fig. 6(a), the rotation h as produced by the step crystallographic orientation is changed by u/2 in each phase by the tilt wall. The LID defects remove the misfit e0 33 ¼ e33 and give added rotation of the a0 lattice that changes the habit plane referred to a0 but leaves the habit plane referred to d unchanged. Hence we compare the d habit plane angle of 23.1 with the other results, since it is unchanged by the LID, which differs in the different approaches. The experi￾ments of Zocco et al. [7] give h = 22.2 and the IPS/PTMC analysis of Zocco et al. [7] gives h = 12.8. As depicted in the stereographic projection in Fig. 7, the angular traces of the rotations of the habit planes from (1 1 1)d also differ. The habit plane prediction of the TM is in much better agreement with experiment than that of the PTMC. The following analysis suggests that the agreement of the TM may be even better. The normal to [1 0 0]a, which would coincide with the ½1 01 0 direction of the transformation partial in the hcp pseudostructure, is inclined to the [1 0 2]a direction by 5 (see Fig. 4). Hence, in the comple￾tion of the transformation from hcp to a0 , in addition to shuffles there is a shear e13 that produces this rotation. The choice of the angle is arbitrary in the following sense. We have fixed the coincidence of the two structures along [1 0 0]a (see Fig. 4), and have selected the normal to this direction to define the angle. The shear then fixes an orthogonal box and the remainder of the atoms transform by shuffles. One could pick another direction resulting in different shears and shuffles. Clearly, however, the mean monoclinic structure is rotated with respect to the hcp pseudostructure, so any choice would lead to some shear with consequences similar to those of the present selection. Studies [19] of twinning in Pu–1.7 at.% Ga revealed new twinning systems in addition to those predicted by Crocker [5]. An example of the observed twinning is shown in Fig. 9: we note that the configuration is consistent with Fig. 8(c). These twins [7,19], all of the (h0k) prismatic type T T x1 x x ′ 2 2 x ′1 h λ L terrace plane habit plane T T T T T T T T x ′ φ 1 α′ δ θ b a Fig. 6. (a) Habit plane when disconnections remove misfit in the x0 1- direction. (b) Tilt wall produced by the b0 2 component. Fig. 5. Disconnections, terrace planes, and misfit strains at d/a interface. J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925 1921

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 the

with 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

J. P. Hirth et al. 1 Acta Materialia 54(2006)1917-1925 10 um Fig 9. Optical photomicrograph(1000x) of twinned a' platelets in a Pu-1.7 at. %Ga alloy Table 2 ossible burgers vectors in order of increasing magnitude and sponding observed slip planes from Fig. 11 [10] (A Observed slip planes 010] (100,(001),(102),(101) (213) (323 7.7 (001),(111),(112),(114),(118) 1114 (213 (010) 120 1114 (213) [ l121 (010) [011 (100).(411) (100),(111) 13 (415) [120 14.20 (101),(213),(323) 14. (101),(213) (001) Table 3 Fig. 10. [010]stereographic projection of slip plane poles in a. Observe ossible slip planes in order of decreasing d-spacing and corresponding slip planes are shown as poles with indices in parentheses and corre- sponding possible slip directions are shown as zones (large circles)with Slip plane d-spacing(A) Possible Burgers vectors indices in brackets. Intersection of a pole with a zone gives a slip system. (113).(113) [l0[10 (201) (004) [100010][103[10 otion of zonal dislocations, much like pyramidal slip in (203) [1003D001[ol[0 hcp metals [24]. For the present purposes, it is not neces (211),(2l1) 1l1lll1.[11 sary to know what the exact slip mechanism is. A likely (014),(014) 2.35 [100] slip plane for LID would be(323), and, statistically, a (114),(114) 10.[10] Burgers vector such as [101] inclined to the terrace plane ( 302) 2.0 [010]

motion of zonal dislocations, much like pyramidal slip in hcp metals [24]. For the present purposes, it is not neces￾sary to know what the exact slip mechanism is. A likely slip plane for LID would be ð3 23Þ, and, statistically, a Burgers vector such as [1 0 1] inclined to the terrace plane Fig. 9. Optical photomicrograph (1000·) of twinned a0 platelets in a Pu–1.7 at.% Ga alloy. (001) (100) (010) [120] (2 13 ) (3 23 ) (4 11 ) (4 15) (213) (112) (1 02) (118) [1 10] (114 ) [1 10] [1 11 ] [1 20] [011] (101) (111) Fig. 10. [0 1 0] stereographic projection of slip plane poles in a0 . Observed slip planes are shown as poles with indices in parentheses and corre￾sponding possible slip directions are shown as zones (large circles) with indices in brackets. Intersection of a pole with a zone gives a slip system. Table 2 Possible Burgers vectors in order of increasing magnitude and corre￾sponding observed slip planes from Fig. 11 Possible b jbj (A˚ ) Observed slip planes [0 1 0] 4.63 (1 0 0), (0 0 1), ð102Þ, (1 0 1) [1 0 0] 6.20 (0 0 1), (0 1 0) [1 1 0] 7.74 (0 0 1) ½11 0 7.74 (0 0 1), (1 1 1), (1 1 2), ð1 14Þ, (1 1 8) [0 0 1] 10.70 (1 0 0), (0 1 0) [1 2 0] 11.14 ð2 13Þ ½120 11.14 (2 1 3) [1 0 1] 11.21 (0 1 0) [0 1 1] 11.66 (1 0 0), ð4 11Þ ½0 11 11.66 (1 0 0), (1 1 1) [1 1 1] 12.13 ½1 11 12.13 ð415Þ [2 1 0] 13.23 ½210 13.23 ½111 14.20 (1 0 1), ð2 13Þ, ð3 23Þ ½1 11 14.20 (1 0 1), (2 1 3) Table 3 Possible slip planes in order of decreasing d-spacing and corresponding Burgers vectors Slip plane d-spacing (A˚ ) Possible Burgers vectors ð113Þ, ð1 13Þ 2.78 [1 1 0], ½110 (2 0 1) 2.77 [0 1 0] (0 0 4) 2.69 [1 0 0], [0 1 0], [1 1 0], ½110 ð2 03Þ 2.59 [0 1 0] (0 2 0) 2.41 [1 0 0], [0 0 1], [1 0 1], ½101 ð2 11Þ, (2 1 1) 2.40 [0 1 1], ½1 11, ½01 1, ½111 (0 1 4), ð01 4Þ 2.35 [1 0 0] ð1 14Þ, ð114Þ 2.33 ½110, [1 1 0] ð3 02Þ 2.03 [0 1 0] J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925 1923

J. P. Hirth et al. Acta Materialia 54(2006)1917-192 4. Discussion The defect-based TM gives predictions for the martens- ite habit planes in closer agreement with experiment than do the IPS/PTMC theories. Because of the large magnitude of b2 in the present case, differences between the two types of theory are expected [15]. The strains involved in the transformation are large, though, so it may be questioned whether a terrace/disconnection model of the interface applies. An alternative would be a nominally planar inter- Trace of (323) face with large local disregistry, resembling that in a high angle grain boundary or disclination. Electron microscopy Fig.I1.Trace of (323)slip plane intersecting a habit plane. Burgers could only resolve this question by lattice imaging, which vector bL, arbitrarily inclined to the terrace plane, has in-terrace-plane has not yet been achieved in Pu, largely due to its strong omponents bi and b propensity to oxidize Molecular dynamics simulations of the interface would help to resolve this issue. Nevertheless would be expected. Fig 1l shows the trace of the(323) the near parallelism of (111)8//010) and of plane. The Burgers vector would have both b1 and b3 [11018 //[1001 are consistent with a disconnection/terrace components in general. The b3 component would relieve plane structure and encourage us to accept its feasibility the E33 coherency strain. The b1 component would in part A final discussion point concerns the large hysteresis elieve the Eu strain hence fewer disconnections would observed for the reverse ato 8 transformation. This needed to achieve a strain-free habit plane and the and other noteworthy features of the 8 to o' transforma angle o would decrease from 23. 1. Thus, this effect tion are best illustrated with dilatometry observations. would also bring the TM and experiment into closer Fig. 12 shows the results from low-temperature dilatome- agreement as shown by path 2 in Fig. 7. The LID would try of a Pu-1.7 Ga at alloy and its significant contrac- also provide added rotation of the habit plane referred to tion, large transformation hysteresis (227C), and the the aphase. We cannot be more quantitative about the incomplete nature of the transformation(18%). Other LID effects without more details on the slip systems features of this particular experiment include the re-initia namely slip directions for the various slip systems and tion of transformation upon heating and the small steps their critical resolved shear stresses for slip. However, that occur during reversion. The former is attributed to the qualitative trends are consistent with the experimental partial relief of stresses built up during the accommoda results tion of the 20% volume change [1]. The reversion steps onset:-1117C start(RT) reversion end 2: 114.9 reversion end 1: 111.4C 1.isothermal second onset:-949°c reversion onset 93. 1'C end-66.3"C temperature(C) ig. 12. Dilatometry of a Pu-1.7 at Ga alloy through the transformation and reversion. The transformation starts at-l12C, proceeds during cooling 155C, and re-initiates during warming at -95C. The reversion starts at 93C and finishes at 115C, producing a transformation The transformation produced 24 vol%a

would be expected. Fig. 11 shows the trace of the ð3 23Þ plane. The Burgers vector would have both b1 and b3 components in general. The b3 component would relieve the e33 coherency strain. The b1 component would in part relieve the e11 strain. Hence, fewer disconnections would be needed to achieve a strain-free habit plane and the angle x would decrease from 23.1. Thus, this effect would also bring the TM and experiment into closer agreement as shown by path 2 in Fig. 7. The LID would also provide added rotation of the habit plane referred to the a0 phase. We cannot be more quantitative about the LID effects without more details on the slip systems, namely slip directions for the various slip systems and their critical resolved shear stresses for slip. However, the qualitative trends are consistent with the experimental results. 4. Discussion The defect-based TM gives predictions for the martens￾ite habit planes in closer agreement with experiment than do the IPS/PTMC theories. Because of the large magnitude of b2 in the present case, differences between the two types of theory are expected [15]. The strains involved in the transformation are large, though, so it may be questioned whether a terrace/disconnection model of the interface applies. An alternative would be a nominally planar inter￾face with large local disregistry, resembling that in a high￾angle grain boundary or disclination. Electron microscopy could only resolve this question by lattice imaging, which has not yet been achieved in Pu, largely due to its strong propensity to oxidize. Molecular dynamics simulations of the interface would help to resolve this issue. Nevertheless, the near parallelism of (1 1 1)d//(0 1 0)a and of ½ 110 d==½100 a are consistent with a disconnection/terrace plane structure and encourage us to accept its feasibility. A final discussion point concerns the large hysteresis observed for the reverse a0 to d transformation. This and other noteworthy features of the d to a0 transforma￾tion are best illustrated with dilatometry observations. Fig. 12 shows the results from low-temperature dilatome￾try of a Pu–1.7 Ga at.% alloy and its significant contrac￾tion, large transformation hysteresis (227 C), and the incomplete nature of the transformation (18%). Other features of this particular experiment include the re-initia￾tion of transformation upon heating and the small steps that occur during reversion. The former is attributed to partial relief of stresses built up during the accommoda￾tion of the 20% volume change [1]. The reversion steps Fig. 11. Trace of ð32 3Þ slip plane intersecting a habit plane. Burgers vector bL, arbitrarily inclined to the terrace plane, has in-terrace-plane components b1 and b2. Fig. 12. Dilatometry of a Pu–1.7 at.% Ga alloy through the transformation and reversion. The transformation starts at 112 C, proceeds during cooling and an isothermal at 155 C, and re-initiates during warming at 95 C. The reversion starts at 93 C and finishes at 115 C, producing a transformation hysteresis of 204 C. The transformation produced 24 vol.% a0 . 1924 J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925

J.P. Hirth et al. Acta Materialia 54(2006)1917-1925 have been described by Schwartz et al. [25]. Mitchell et al. discussions. This project was funded by the US Depart [2]. and Blobaum et al. [26], and are believed to corre- ment of Energy under Contract No. W-7405-ENG-36 spond to the cooperative reversion of many platelets to the 8 phase; they appear to be the result of an interplay References between the autocatalytically driven reversion of a cas cade of individual martensite units, and self-quenching [1] Hecker SS. Harbur DR, Zocco TG. Prog Mater Sci2004:49:429 caused by small changes of temperature and/or stress [2] Mitchell JN, Stan M, Schwartz DS, Boehlert C]. Metall Mater Trans accompanying each individual transformation burst. The 2004:35A:2267. large hysteresis is likely to be due to the high density of [3] Zachariasen WH, Ellinger F. Acta Cryst 1963: 16: 777 defects- interface dislocations. twins and lattice disloca 1] Hecker SS. Martensitic transformations in plutonium. Los Alamos tions-introduced during the 8 to transformation, as National Laboratory Report LA-UR-831715: 1983 J Crocker AG. J Nucl Mater 1965: 16: 306 well as residual stresses. These defects and locally high [6] Olsen CE. J Nucl Mater 1989: 168:326 stresses are likely to constrain the reverse motion of the [7] Zocco TG, Stevens MF, Adler PH, Sheldon rl, Olson GB. Acta a' platelets, causing their transformation back to the fcc Metall Mater 1991: 38: 2275 8 phase to be shifted to higher temperature [8] Choudry MA, Crocker AG. J Nucl Mater 1985: 127: 119 [9] Adler PH, Olson GB, Margolies DS. Acta Metall 1986: 34: 2053 l0] Wechsler MS, Lieberman DS, Read TA. Trans AIME 5. Conclusions 1953;197:1503 [ll] Bowles JS, Mackenzie JK. Acta Metall 1954; 2: 129 1. A defect-based topological model for the Pu-1.7 at [12] Pond RC, Hirth JP. Solid State Phys 1994: 47: 287 Ga martensite transformation of 8 to a gives a predic- [1]Hirth JP, Pond RC. Acta Mater 1996: 44: 4749 tion of the habit plane in good agreement with experi- [15] Pond RC, Celotto S, Hirth JP. Acta Mater 2003: 5 1:5385 mental results [16] Pond RC, Ma x, Hirth JP. In: Proceedings of ICOMAT conference 2. Experimentally observed twinning in a'is associated directly with the transformation strain and not with [17] Chen I-W, Chiao Y-H. Acta Metall 1985:33: 1827 the liD [18] Lawson AC, Roberts JA, Martinez B, Richardson Jr Jw. Philos Mag 3. LiD by slip is qualitatively consistent with the model [19] Zocco TG, Sheldon RI, Rizzo HEJ Nucl Mater1991:: 183:80 and with electron microscopy observations. 20] Hecker SS, Stevens MF. Los Alamos Sci 2000: 26: 336 4. Quantitative treatment of the LID cannot be performed [21] Pond RC, Sarrazat F Interf Sci 1996; 4: 99 without information on slip planes and directions as well [22] Bronisz SE, Tate RE. In: Kay Al, Waldron MB,editors.Proceedings as critical resolved shear stresses for slip on these Hal;1965.p.558 23]Liptai RG, Friddle RJ. In: Miner WN, editor. Proceedings of 4th international conference on plutonium and other actinides. Net York(NY): Metallurgical Society; 1970. p 406. Acknowledgements []Hirth JP, Lothe J. Theory of dislocations. Malabar (FL): Krieger; 225] Schwartz DS, Mitchell JN, Pete D, Ramos MR J Metal 2003: 55: 28 The authors thank Ramiro Pereyra and Darryl Lovato [26]Blobaum KJM, Krenn CR, Mitchell JN, Haslam JJ, Wall MA, for their superb metallography and T.G. Zocco for useful Massalski TB, et al. Metall Mater Trans A [in press]

have been described by Schwartz et al. [25], Mitchell et al. [2], and Blobaum et al. [26], and are believed to corre￾spond to the cooperative reversion of many a0 platelets to the d phase; they appear to be the result of an interplay between the autocatalytically driven reversion of a cas￾cade of individual martensite units, and self-quenching caused by small changes of temperature and/or stress accompanying each individual transformation burst. The large hysteresis is likely to be due to the high density of defects – interface dislocations, twins, and lattice disloca￾tions – introduced during the d to a0 transformation, as well as residual stresses. These defects and locally high stresses are likely to constrain the reverse motion of the a0 platelets, causing their transformation back to the fcc d phase to be shifted to higher temperature. 5. Conclusions 1. A defect-based topological model for the Pu–1.7 at.% Ga martensite transformation of d to a0 gives a predic￾tion of the habit plane in good agreement with experi￾mental results. 2. Experimentally observed twinning in a0 is associated directly with the transformation strain and not with the LID. 3. LID by slip is qualitatively consistent with the model and with electron microscopy observations. 4. Quantitative treatment of the LID cannot be performed without information on slip planes and directions as well as critical resolved shear stresses for slip on these systems. Acknowledgements The authors thank Ramiro Pereyra and Darryl Lovato for their superb metallography and T.G. Zocco for useful discussions. This project was funded by the US Depart￾ment of Energy under Contract No. W-7405-ENG-36. References [1] Hecker SS, Harbur DR, Zocco TG. Prog Mater Sci 2004;49:429. [2] Mitchell JN, Stan M, Schwartz DS, Boehlert CJ. Metall Mater Trans 2004;35A:2267. [3] Zachariasen WH, Ellinger F. Acta Cryst 1963;16:777. [4] Hecker SS. Martensitic transformations in plutonium. Los Alamos National Laboratory Report LA-UR-83-1715; 1983. [5] Crocker AG. J Nucl Mater 1965;16:306. [6] Olsen CE. J Nucl Mater 1989;168:326. [7] Zocco TG, Stevens MF, Adler PH, Sheldon RI, Olson GB. Acta Metall Mater 1991;38:2275. [8] Choudry MA, Crocker AG. J Nucl Mater 1985;127:119. [9] Adler PH, Olson GB, Margolies DS. Acta Metall 1986;34:2053. [10] Wechsler MS, Lieberman DS, Read TA. Trans AIME 1953;197:1503. [11] Bowles JS, Mackenzie JK. Acta Metall 1954;2:129. [12] Pond RC, Hirth JP. Solid State Phys 1994;47:287. [13] Hirth JP, Pond RC. Acta Mater 1996;44:4749. [14] Hirth JP. J Phys Chem Solids 1994;55:985. [15] Pond RC, Celotto S, Hirth JP. Acta Mater 2003;51:5385. [16] Pond RC, Ma X, Hirth JP. In: Proceedings of ICOMAT conference [in press]. [17] Chen I-W, Chiao Y-H. Acta Metall 1985;33:1827. [18] Lawson AC, Roberts JA, Martinez B, Richardson Jr JW. Philos Mag 2002;B82:1837. [19] Zocco TG, Sheldon RI, Rizzo HF. J Nucl Mater 1991;183:80. [20] Hecker SS, Stevens MF. Los Alamos Sci 2000;26:336. [21] Pond RC, Sarrazat F. Interf Sci 1996;4:99. [22] Bronisz SE, Tate RE. In: Kay AI, Waldron MB, editors. Proceedings of 3rd international conference on plutonium. London: Chapman & Hall; 1965. p. 558. [23] Liptai RG, Friddle RJ. In: Miner WN, editor. Proceedings of 4th international conference on plutonium and other actinides. New York (NY): Metallurgical Society; 1970. p. 406. [24] Hirth JP, Lothe J. Theory of dislocations. Malabar (FL): Krieger; 1992. [25] Schwartz DS, Mitchell JN, Pete DV, Ramos MR. J Metal 2003;55:28. [26] Blobaum KJM, Krenn CR, Mitchell JN, Haslam JJ, Wall MA, Massalski TB, et al. Metall Mater Trans A [in press]. J.P. Hirth et al. / Acta Materialia 54 (2006) 1917–1925 1925