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Deformation twinning at low temperatures in a Hf–V–Nb cubic laves phase
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Acta mater. Vol. 46, No. 8, pp. 2913±2927, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00418-7
DEFORMATION TWINNING AT LOW TEMPERATURES IN A Hf±V±Nb CUBIC LAVES PHASE D. E. LUZZI, G. RAO{, T. A. DOBBINS and D. P. POPE Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272, U.S.A. (Received 20 December 1996; accepted 24 October 1997) AbstractÐDeformation twinning in the C15 cubic laves phase of the Hf±V±Nb alloy system is analyzed at temperatures between 77 K and room temperature by conventional and high-resolution TEM. In order to reduce the stacking fault energy (SFE), alloy compositions are chosen such that the cubic laves phase composition is close to a region of C14 phase stability. A high density of stacking defects of intrinsic character in the as-homogenized alloy con®rms that the SFE has been reduced. Twinning is observed at all temperatures placing a low upper limit on any thermally activated deformation process. Twin clusters are observed which are narrow and have a similar distribution to the stacking defects in the undeformed alloy. The structure of twins and stacking defects is solved via HREM combined with image calculations. Finally, the mechanism of twinning is discussed and the use of alloying to control the SFE or to re®ne the microstructure in order to increase the low temperature ductility in these intermetallic compounds with complex cubic crystal structures is proposed. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
Extensive ductility has been produced at ambient temperature in ternary Hf±V±Nb alloys containing a cubic laves phase [1]. This result is of interest from a technological point-of-view as many laves phases have high melting temperatures and good high temperature mechanical properties, but also have a high ductile±brittle transition temperature. From a scienti®c point-of-view, the laves phases are a large structural class of intermetallic compounds with a complex, ordered crystal structure; developing an understanding of the origins and modes of low temperature ductility has intrinsic merit. It is now well-established that the low temperature deformation mode in the Hf±V±Nb cubic laves phase is mechanical twinning [2, 3]. The mechanism by which the twinning occurs has not been de®nitively established [4] as simple shear which produces twinning in elemental f.c.c. crystal structures leads to atomic site con¯icts in the more complex f.c.c. laves phases. Low temperature ductility in the Hf±V±Nb cubic laves phase has only been produced in two phase alloys in which the laves phase HfV2+Nb coexists with a V±Nb b.c.c. solid solution [1±3]. Single phase alloys of the laves phase are brittle in compression in polycrystalline form; no single crystal studies have been done. These results indicate that the fracture stress for the polycrystalline laves phase {Present address: Applied Materials Corporation, Santa Clara, California, U.S.A.
is lower than the twinning stress. The presence of a hydrostatic stress component due to the coexistent b.c.c. phase in the two phase alloys is evidently suf®cient to raise the fracture stress above the twinning stress. Reduction of the twinning stress of the laves phase such that twinning occurs in the single phase alloy would be an important step forward in the development of laves phase structural alloys. It has been suggested that twinning may be enhanced in cubic laves phases by reducing the SFE [2]. This statement was based on the observation that lowering the SFE in f.c.c. copper alloys enhances twinning [5]. Recent analysis of the Hf±V±Nb ternary phase diagram has shown that, in addition to a broad phase ®eld of the cubic C15 laves phase, a small composition region exists within which the hexagonal C14 laves phase is stable [6]. If the assumption is made that the stacking fault energy (SFE) of the cubic C15 laves phase will be reduced at compositions close to the composition range of hexagonal C14 stability, then the eect of SFE on deformation twinning in complex cubic materials can be explored. In this paper, the occurrence of stacking defects and deformation twins in Hf±V±Nb ternary alloys is analyzed. In order to reduce the SFE, alloy compositions were chosen such that the cubic laves phase composition is closer to the region of C14 phase stability than that of previous investigations. The distribution and structure of stacking defects and twins is characterized using conventional and
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high-resolution transmission electron microscopy (HREM). Finally, the possibility of using alloying to control the SFE or to re®ne the microstructure in order to increase the ambient temperature ductility in these intermetallic compounds with complex cubic crystal structures is discussed. 2. EXPERIMENTAL DETAILS
Ternary alloys of composition Hf13V62Nb25 (Alloy A) and Hf10V64Nb26 (Alloy B) were prepared by arc melting elemental Hf (99.99% purity), V (99.6% purity) and Nb (99.7%) under Ar atmosphere in a water-cooled copper hearth using a nonconsumable W electrode. Buttons were annealed at 1273 K for 100 h under vacuum and water quenched. Compression specimens of dimensions 4 4 8 mm and 3 3 4.5 mm were cut from the as-homogenized buttons by electron-discharge machining. Specimens were compressed to approximately 1% plastic strain at temperatures between the liquid nitrogen boiling point and room temperature. The room temperature tests were performed on an Instron Model 1125 mechanical testing machine at a strain rate of 2.6 10ÿ5/s. Low temperature compression tests were conducted on an Instron Model 4206 mechanical testing machine equipped with a dewar for immersion within a constant temperature bath. These tests were run at a strain rate of 1 10ÿ3/s at temperatures of 271, 269, 201 and 77 K. Electron microscopy specimens were prepared from the as-homogenized material and from material after compressive deformation. Thin slices of 250 mm were cut using an electron-discharge machine and then mechanically polished to 100 mm
thickness. Mechanical dimpling on a South Bay Technologies dimpling machine was done until the center of the dimple was approximately 20 mm thick. Electron transparent regions were produced by ion milling at liquid nitrogen temperature in a Gatan Duomill until perforation. Five kV Ar ions were used for thinning with a sputtering angle of 158. Conventional electron microscopy was done on a JEOL 2010 at Kyoto University operated at a voltage of 200 kV. HREM imaging was done using JEOL 4000 s at the University of Pennsylvania and Kyoto University. All HREM images were recorded at a voltage of 400 kV. Analysis of the HREM results was accomplished through comparison with calculated images of model structures. The calculations used the well-established multislice and electron-optical method [7] as contained in the MacTempas suite of programs version 1.6.2 installed on an Apple Macintosh Quadra 800 at Kyoto University.
3. RESULTS
3.1. Ternary alloy microstructure and phase compositions A section of the Hf±V±Nb ternary phase diagram [6] is depicted in Fig. 1 with the alloy compositions of Livingston and Hall [2], Chu and Pope [3], and that of the present study indicated. As can be seen, the alloy composition of the present study should contain a C15 laves phase with a composition closer to the composition region of C14 stability. Based on the phase diagram analysis of Chu and Pope [6], it is predicted that the composition of the laves phase of Alloy A should be
Fig. 1. Partial Hf±V±Nb ternary phase diagram at 1273 K reproduced from the work of Chu and Pope [6]. The small C14 phase ®eld (l1) can be seen towards the Nb-rich side of the larger C15 phase ®eld (l2). The V±Nb b.c.c. solid solution (g) is seen at the right. The alloy compositions of Livingston and Hall [2] (L), Chu and Pope [3] (C) and of the present work (A, B) are shown. In the ®gure, the thick lines are phase boundaries and boundaries of multiphase regions. The thin lines are tie lines with the open circles marking the compositions tested in the original analysis of Chu and Pope.
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Fig. 2. As-homogenized microstructure of Alloy A of the present study. Phases of higher average atomic number appear lighter in this image taken with backscattered electrons in a SEM. Large precipitates of the cubic laves phase are contained within a two phase matrix composed of the V±Nb b.c.c. solid solution and the laves phase. Physical connections between the large precipitates and the smaller precipitates of the two phase region indicate that compositional homogenization has occurred; three such connections are indicated by arrows.
Fig. 3. High magni®cation TEM micrograph of a large cubic laves precipitate in an undeformed specimen taken with the electron beam nearly parallel to the [110] crystallographic direction. A large number of crystallographically straight defects can be seen with two orientations in this image.
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Fig. 4. [110] zone axis electron diraction pattern from a large cubic laves precipitate in an undeformed specimen. Rods of diuse scattering due to planar defects can be seen lying along the [111] direction.
Hf23V58Nb19. Compositional analysis by wavelength dispersive spectroscopy in a scanning electron microscope (SEM) referenced to standards was consistent with this prediction indicating a composition of the laves phase of Hf23.0V57.8Nb19.2 [8]. The as-annealed microstructure of Alloy A is shown in Fig. 2; the microstructure of Alloy B is essentially the same. This is a back-scattered electron image taken in an SEM of a polished and etched cross-section. The alloy contains large precipitates of the Hf containing laves phase (light grey). The precipitates are surrounded by a coarsened eutectic two phase matrix containing the laves phase and a V-rich b.c.c. solid solution (dark grey). The SEM results show that Alloy A is a hypereutectic alloy which passed through a two phase liquid/laves phase region before reaching the eutectic temperature at which the remaining liquid solidi®ed into a two-phase b.c.c. solid solution/laves eutectic phase. With no mechanical treatment to break-up the as-grown dendritic structure, the annealing treatment resulted in a coarsened eutectic matrix surrounding the large laves phase precipitates. Many physical connections between the large laves precipitates and the smaller laves grains of the eutectic phase (three are marked with arrows) indicate that the annealing treatment did induce com-
positional homogenization of the b.c.c. and laves phases. 3.2. Defect microstructure in undeformed samples A high magni®cation TEM micrograph of an area of a large cubic laves phase precipitate is shown in Fig. 3 with the orientation of the electron beam near the [110] zone axis. Within the precipitate a large number of defects are seen in two orientations corresponding to the two {111} type planes contained in the [110] zone. The faults are all thin which is expected if they are stacking faults. The spacing of the faults varies from less than 1 nm to over 130 nm in this area of the precipitate which is typical of the alloy. The detailed structure of the faults will be explored in the next section. An electron diraction pattern of the [110] zone of the cubic laves phase is shown in Fig. 4. In addition to the diraction spots, extensive streaking is seen with the orientation of the streaks being a h111i crystallographic direction. It was con®rmed by recording diraction patterns at specimen orientations away from the h110i zone axes that these intensity features are rods of diuse scattering rather than sheets. The shape of the diuse scattering con®rms that planar defects are present in the material lying parallel to the {111} planes of the laves phase. The length of the rods of diuse scat-
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tering is consistent with fault thicknesses of crystal lattice dimensions. The large diuse scattering evident in Fig. 4 is not seen in the diraction patterns from the undeformed laves phase in the alloy of Chu and Pope [9]. The higher intensity of diuse scattering indicates a higher density of defects in the undeformed laves phase at the present composition. This conclusion is supported by comparing h110i zone TEM images of laves grains from the present alloy and that of the previous work [9]. In the work of Livingston and Hall, the authors state that TEM examination showed no twins or faults in the undeformed laves phase [2]. The results of Figs 3 and 4 and the comparisons with prior work are all consistent with an increased density of stacking defects at cubic laves phase compositions closer to the region of stability of the hexagonal laves phase. 3.3. Stacking fault structure in undeformed alloy In the Hf±V±Nb alloy, it has been shown that Hf and V do not form antisite defects, but rather the Nb atoms substitute on both the Hf and V sites in the correct proportion to avoid antisite defects or constitutional vacancies [10]. At the composition of Alloy A of the present study, the expected composition of the Hf sites will therefore be Hf23+Nb10 whereas the V sites will have a composition of V58+Nb9. In the image calculations which follow, the composition of each site was correctly taken into account by adjusting the occupancy of the sites within the model structures. The C15 laves phase has a complex f.c.c. crystal structure containing 24 atoms in the unit cell. Defect analysis using HREM is straightforward, however, if experimental imaging conditions are con®rmed by comparison with calculated images of model structures. As in elemental f.c.c. crystals, the stacking sequence of (111) atomic planes can be written . . . abcabcabc. . . In the laves phase however, each letter of the sequence is comprised of four distinct atomic planes giving . . . aAacbBbagCgb . . . The capital letters, ABC, are planes of V atoms arranged in a net as shown in Fig. 5(a), and the greek letters represent Hf atoms positioned above and below the vacancies in the V layers. The small roman letters, abc, represent planes of V atoms with one-third the atomic density of the other V {The V close-packed columns are the most common feature in HREM images of the cubic laves phase when imaged down a h110i zone axis. In fact, the conditions in which other atomic columns are uniquely imaged, Hf atoms for example, are con®ned to speci®c specimen thicknesses and objective lens defocus values and therefore will typically not be imaged in the HREM. A more in-depth discussion of HREM imaging of the cubic laves phase will be published elsewhere [11].
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layers. Due to the packing arrangement, interplanar spacings of the aA-type are three times that of the ac-type. In Fig. 5(a), the [110] direction is shown by an arrow. The [110] projection of the laves phase structure is depicted schematically in Fig. 5(b) with the Hf atoms as large circles and the V atoms as small ®lled circles, either grey or black. Viewed in this direction, the atomic planes containing the net of V atoms contain alternating close-packed columns of V atoms (black) and columns with 50% vacancies (grey). The close-packed V columns are the intersections of the two nets of V atoms, on the (111) and (111) lattice planes, which lie parallel to the [110] direction. The calculated HREM image of this structure is shown in Fig. 5(c) for the imaging conditions of the present study. The white dot contrast in the calculated image is of the close-packed V columns only.{ Since only one of the four planes which comprise the (111) plane sequence of the laves phase is imaged, the same method of analysis of the defect structure as applied in the HREM analysis of f.c.c. materials can be used. Considering the orientation and thickness of the planar defects, it was initially assumed that they are stacking faults, either intrinsic or extrinsic, in the Hf23V58Nb19 cubic laves phase. The removal of a single 111 layer which comprises an f.c.c. intrinsic stacking fault can also be considered as a single layer of twinned crystal. An extrinsic fault, in which an extra 111 layer is inserted is equivalent to two layers of twinned crystal. In an edge-on HREM image, an extrinsic stacking fault will be twice the thickness of an intrinsic fault. Also, considering the normal advance of f.c.c. 111 layers (abcabc) as successive 1208 phase shifts, then the removal of one layer in an intrinsic fault produces a 1208 phase advance in the position of the f.c.c. crystal across the fault. The addition of an extra 111 layer produces a net 1208 phase retardation in the position of the f.c.c. crystal across the fault. This analysis has been developed for the Hf±V±Nb alloy in another paper [12]. Figure 6 is an HREM image of a defect lying on a (111) plane imaged down the [110] zone axis in which the fault lies parallel to the electron beam direction and is viewed edge on. Applying the above analysis [12], it can be seen that the thickness of the fault is a single laves 111 layer consistent with the fault having intrinsic character. The line traces in the ®gure along (111) planes intersecting the fault show an advance in the position of the planes also consistent with intrinsic character. In order to better see the shift of the lattice planes as they cross the fault, the ®gure should be viewed at a glancing angle along the traced lines.
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Fig. 5. (a) Schematic diagram of the net of V atoms lying parallel to the (111) crystallographic planes of the cubic laves phase (or the basal plane of the hexagonal laves phases). In the drawing, the V atoms are in the ``A'' locations. Projections of the ``B'' and ``C'' lattice sites are indicated. The ``X'' characters are the projected locations of adjacent Hf atoms after twinning by homogeneous shear (cf. Section 4.3). The direction of the incident electron beam, taken to be [110] in the cubic phase is indicated by an arrow; (b) [110] projection of the HfV2 C15 crystal structure. The primary crystallographic directions are marked with arrows. The Hf atoms are large/white; the V atoms are small/shaded. The close-packed columns of V atoms are shaded black; (c) HREM image calculation for the [110] zone axis at a thickness of 4.18 nm and an objective lens underfocus of ÿ60 nm. The strong white contrast is from the close-packed columns of V atoms.
3.4. Defect microstructure in deformed samples Plastic deformation was seen in specimens deformed in compression at all temperatures down to 77 K. A TEM image of the coarsened eutectic matrix microstructure in a sample which has undergone com-
pressive deformation is shown in Fig. 7. A high density of laves phase precipitates are seen which are clustered in this image. The b.c.c. solid solution at the upper left and lower and upper right in the ®gure shows evidence of extensive dislocation slip indicating
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Fig. 6. HREM micrograph of a stacking fault lying on a (111) crystallographic plane in a large precipitate of the Hf23V58Nb19 cubic laves phase of alloy A. The thickness of the fault and the shift of the (111) lattice planes across the fault are consistent with intrinsic character.
that plastic deformation has occurred by dislocation glide. In contrast, within the cubic laves phase, straight defects are seen. These defects were found to be both twins and stacking faults by HREM as will be shown below. In the ®gure, the large extent of twinning within these small laves grains can be clearly seen. Often, a twin cluster composed of many ®ne twin bands was found to extend across the entire grain, as seen in the ®gure. Twinning also occurs within the large laves precipitates and was investigated in detail. Images showed that multiple twinning systems can operate within the same grain during compressive deformation of this alloy. Figure 8 is a TEM image of a large laves precipitate taken with the crystal oriented with the electron beam along the [110] zone axis. The grain in this image is over ®ve microns in size and the thickness increases rapidly away from the specimen edge. In the image, taken from a thin region along the specimen edge, clear evidence of clusters of deformation twin bands can be seen. In the remainder of the paper, the grouping of many ®ne twin bands as seen in Fig. 8 will be termed a twin cluster, the term twin band will refer to the standard crystallographic twin, namely matrix/twin/matrix and a single twin interface, as
seen in the HREM study below, will be termed a twin. A diraction pattern from the twin cluster of Fig. 8 is shown in Fig. 9. One set of twin re¯ections are seen and the twin plane is clearly the (111) crystallographic plane. Diuse streaks can also be seen running through the diraction pattern aligned with the diraction spots of the twin plane. These streaks have a similar appearance to those in Fig. 4 and are due to rods of diuse scattering aligned along the [111] crystallographic direction. The presence of these rods of diuse intensity indicate that the twin bands formed within this alloy at the current levels of induced plastic strain tend to be quite narrow. The twin cluster of Figs 8 and 9 is shown at higher magni®cation in Fig. 10 with the specimen tilted o of the [110] zone in order to increase the diraction contrast between the matrix and twin. As can be seen in the image, the twin cluster is composed entirely of thin twin bands with no twin bands present of the large widths seen in previous studies [2, 3]. The total width of the twin cluster is 110 nm. Within this width, 18 twin bands are present with an average width of 6.1 nm. The twin bands vary in width from less than 1 nm to a maximum of 8.6 nm. The thinnest twin bands have a
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Fig. 7. TEM micrograph of the microstructure of the two phase matrix region of Alloy A after compressive deformation. The cluster of laves phase precipitates show evidence of extensive twinning. The b.c.c. matrix at the upper left and lower right exhibits the result of dislocation activity.
Fig. 8. TEM micrograph of twin clusters in a large precipitate of the laves phase. The magni®cation of this micrograph is similar to that of Fig. 7. The spacing between twin clusters is similar to the spacing of stacking defects seen in large precipitates prior to deformation, cf. Figure 3.
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Fig. 9. [110] zone axis electron diraction pattern of a twin band from a large precipitate. Extensive diffuse streaking, indicative of many ®ne twins is seen running parallel to the twin plane diraction spots.
width equal to one or two (111) layer spacings of the cubic laves phase. The even number of twins indicates that the twin cluster is bounded by matrix crystal on either side. This is the case with all twin clusters found in the large precipitates. In addition to the extensive evidence of deformation twinning seen in both large and small grains of the laves phase, one thin region of the hexagonal C14 laves crystal structure was found. The layer had a width equal to three repeats of the hexagonal lattice (6 d111 cubic) and was in a large laves grain of a deformed specimen. However, the hexagonal layer was isolated within the cubic laves matrix and was not associated with a deformation twin cluster. Whether this hexagonal layer was formed during deformation or was a hexagonal intergrowth which was present in the undeformed alloy cannot be known. Although no hexagonal intergrowths were seen in the undeformed alloy, it is possible that a low density of such intergrowths could be missed due to the unavoidably low sampling in HREMbased investigations. 3.5. Structure of deformation twins HREM imaging was conducted to study the microstructure of the twin clusters and the structure of individual twins including the identity of the twin plane. In the images which follow, the white dot contrast corresponds to the close-packed columns of V(Nb) atoms which lie along the h110i crystallographic directions. As in the images of the
undeformed alloy contained in Section 3.3, one of every four laves planes is imaged. An HREM image of a twin cluster taken down the [110]matrixv[110]twin tilt axis is shown in Fig. 11. The twins lie horizontally in the image. The total height of the image is 72 nm; within this length, many twin bands of varying widths exist. With the twin planes de®ned as the (111) atomic planes, the large arrows drawn on the ®gure indicate the (111) atomic planes of the matrix and twin. By viewing the image along the arrows, the many thin twin bands can be seen. The gradual variation in the appearance of the crystal structure with position is due to the changes in specimen thickness and tilt, as well as the small changes in electron beam orientation due to the convergence of the electron probe. The single arrow indicates the location of a twin band with a thickness equal to a single 111 layer. Nearby, the double arrow indicates the location of a twin band of thickness equal to two 111 layers. The thickest twin band seen in this specimen was 21 111 layers thick or 8.95 nm. Within this image, no sequences of 111 layers are seen which could be identi®ed with either hexagonal laves structure, C14 or C36. A magni®ed view of the boxed area of Fig. 11 is shown in Fig. 12. Using the arguments developed in Section 3.3, the character of the two faults can be unambiguously determined. In the ®gure, line traces are drawn on the (111) planes of the matrix in order to accentuate the phase shift of these planes
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Fig. 10. Higher magni®cation view of the central twin cluster of Fig. 8. The twin cluster is bounded by matrix on either side. Twin bands range in thickness from lattice dimensions to approximately 8 nm.
as they cross the fault. As can be seen, these planes advance one-third of the plane spacing as they cross the lower fault; this is the correct plane shift for an intrinsic stacking fault [12]. This result is also consistent with the thickness of the fault being one 111 layer. In contrast, the (111) planes are retarded by one-third the plane spacing as they cross the upper fault. This is the expected phase shift for an extrinsic stacking fault and is consistent with the thickness of the fault being two 111 layers [12]. A [110]matrix zone axis image calculation for the imaging conditions of Fig. 12 is shown in Fig. 13 for the extrinsic stacking fault. By comparing the simulation with the image of the lower fault in Fig. 12, it can be seen that the internal structure of the fault is also correct, namely the white dots associated with the close-packed V columns of the extra 111 layer of the extrinsic fault are in the correct position with respect to the V columns in the 111 layers bounding the fault. Measurements taken from the image show that the position of the line of
white dots within the fault lie exactly on the center line as expected; this is easily seen by examining at a glancing angle the constant interlayer spacing of the 111 planes of Fig. 12. Figure 14 is a magni®ed view of a twin between two relatively thick laths (8.95 and 3.41 nm, respectively). The twin plane is indicated by the arrows in the ®gure. Figure 15 contains three image calculations for the same imaging conditions of Fig. 14 of three possible twin structures. The ®rst is for the twin lying on the V net, the A, B, or C atomic plane of the laves (111) plane sequence described in Section 3.3 resulting in a plane sequence of . . . aAacbBbagCgabBbcaAa . . . . The second image calculation is for a twin lying on a Hf layer, the a, b, or g atomic plane of the sequence resulting in a plane sequence of . . . aAacbBbagCgCgabBbcaAa . . . . The ®nal calculation is for a twin lying on the V layer of lower atomic density, the a, b, or c atomic plane of the sequence resulting in a plane sequence of . . .aAacbBbabBbcaAa . . . . By comparing Fig. 14
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This conclusion is based on the observation that the volume fraction of the laves phase as seen in Fig. 2 exceeds that predicted from the lever rule when applied to Fig. 1 even when factoring in the lower atomic density of the laves phase. In the present work, an identical alloy preparation regimen was followed to that in the original work on the phase diagram [6]. In the original work on the phase diagram [6], optical microscopy was used to characterize the alloy microstructure and X-ray ¯uorescence spectroscopy by energy dispersive spectroscopy (EDS) in an SEM was used to determine the composition of dierent phases. At the resolution of the optical microscope, the ®ne eutectic structure as seen in the matrix of Fig. 2 would not be resolved. The EDS analysis would have been conducted at an electron voltage of at least 20 kV in order to ensure adequate excitation of the electrons in the Hf L-shell. At this voltage, the activated volume within the alloy would greatly exceed the grain size of the eutectic phases and thus the measurement would be of the average composition of the two phase region rather than that of the b.c.c. solid solution. With one of the phases being the laves phase which contains a higher concentration of Hf, the b.c.c. solid solution would thus contain a reduced Hf concentration. Based on volume fraction estimates from SEM micrographs of the two phase eutectic region, a Hf solubility limit of 4% is estimated for the b.c.c. solid solution phase at these alloy compositions. This value is consistent with the measurement of the composition of the b.c.c. solid solution in a single phase sample of the original work [6] as well as the volume fraction of laves phase and b.c.c. solid solution seen in the work of Livingston and Hall [2]. 4.1. Eect of Nb composition on defect structure
Fig. 11. HREM overview of the structure of a twin cluster viewed down the [110] tilt axis between the matrix and the twin. The thickest twin band can be seen just below the middle of the ®gure and is 21 d111, or 8.95 nm thick. Twin bands with thicknesses of d111 and 2 d111 can be seen at the single and double arrow, respectively. By sighting at a glancing angle along the arrows at the bottom of the ®gure, the many ®ne twin bands contained within this twin cluster can be seen.
with Figs 15(a)±(c), it can be seen that the HREM image matches only the image calculation of Fig. 15(a). The twin plane is the V net. 4. DISCUSSION
The results in Figs 1 and 2 indicate that the position of the phase boundary of the g b.c.c. solid solution actually exists at lower Hf concentrations.
The observation of a large number of stacking defects in the undeformed alloy is a positive indication that the SFE of the laves phase can be lowered by alloying. The intrinsic character of these stacking faults is in contrast to previous results in cubic laves phases including those of the Hf±V±Nb alloy system. The ®rst reports of fault character in the laves phases was in the compounds TiCr2 and TiCo2 [13]. In that study, the authors found that all faults were extrinsic using conventional TEM analysis. In the alloy studied by Livingston and Hall, no stacking defects were seen in the alloy prior to mechanical deformation [2]. In that of Chu and Pope, some stacking faults were seen although the density of these stacking faults was insucient to produce visible streaking in electron diraction patterns [9]. These faults have recently been con®rmed to be of extrinsic character [14]. This alloy behavior may be related to the relative free energy of the dierent laves structures at dierent Nb concentration. Referring to Fig. 1, it can be
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Fig. 12. Higher magni®cation view of the boxed area of Fig. 11. The single and double layer twin bands can be seen to be an intrinsic and an extrinsic stacking fault, respectively, based on thickness and the shift of planes as they cross the faults.
seen that the composition of the laves phases in the studies of Livingston and Hall [2] and Chu and Pope [3] and the present study are progressively shifted towards more Nb-rich concentrations with the Nb replacing both V and Hf in the compound. At the same time, the composition is moved closer to the phase ®eld in which the hexagonal C14 structure is stable. The observations of Livingston and Hall suggest that the cubic laves phase, C15, is quite stable at lower Nb concentration. The presence of extrinsic stacking faults in the alloy of Chu and Pope is consistent with a tendency towards the formation of the C36 hexagonal structure since extrinsic stacking faults have a 111 layer stacking sequence equivalent to a layer of this structure. The intrinsic stacking faults of the present study indicate a tendency towards the formation of the C14 hexagonal structure since intrinsic stacking faults have a 111 layer stacking sequence equivalent to a layer of this structure. This trend towards C14 stability with increasing Nb content concludes with the C14 struc-
Fig. 13. HREM image calculation of the internal contrast of the double layer twin band of Fig. 12. It can be seen that the position of the white contrast in the center of the fault is correct for an extrinsic stacking fault.
ture becoming the equilibrium crystal structure, at least at 1273 K. This shift in stability from C15 to C36 to C14 is similar to that seen in the Mg±Cu±Zn alloy system in which the substitution of Zn for Cu produces this sequence of equilibrium crystal structures [15]. This behavior has been related to the valence elec-
Fig. 14. High magni®cation view of a twin in the cubic laves phase.
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4.2. Deformation in the two-phase alloy
Fig. 15. HREM image calculations for twins in which the twin plane lies on the V net (a), a Hf atomic plane (b) and the lower density V atomic plane (c). Comparison of the calculations with the image of Fig. 14 con®rms that the twin plane is the V net as sketched in Fig. 5(a). The arrows indicate the twin plane.
tron concentration (VEC) with the C15 structure the most stable at a VEC of 1.5, C36 the most stable at a VEC of 1.8 and C14 the most stable at a VEC of 2.0 [16]. In the present alloy system however, the VEC of the binary HfV2 is 2.0 and the addition of Nb lowers the VEC in direct contradiction to the above reported trend. A straightforward comparison based on VEC may not be possible since, in the present alloy, the Nb substitutes on both the Hf and V sublattices [10], whereas in the Mg±Cu±Zn alloy system, the Zn substitutes solely on the Cu sublattice. However, the compound HfFe2, which also has a VEC of 2.0, has the hexagonal C14 structure at room temperature. Although, a simpli®ed quantity such as the VEC cannot be the explanation of the varying phase stability in the current alloy system, electronic eects must play the determining role. Although the atomic size ratio of the constituents will determine that the structure will be one of the laves phase structures, there is no atomic size related dierence among the three laves phase structures.
In the present alloy, TEM observations show that plastic yielding occurs throughout the microstructure. It seems apparent that the two phase region carries a large amount of the plastic deformation as extensive dislocation activity and twinning were seen in the b.c.c. phase and laves phase, respectively. It might be expected, based on these results, that the production of an alloy with a small grain size may be a route to increase the room temperature ductility of a two phase alloy containing this laves phase. This would involve choosing both an appropriate alloy composition and thermomechanical processing conditions to produce a uniform microstructure containing small grains. Some deformation twinning was also seen in the large laves precipitates. This deformation occurs in clusters surrounded by crystal showing no indication of deformation. Each twin cluster contains an even number of twins such that the crystal on either side of the cluster has the matrix orientation. Measurement of the spacing between the twin clusters shows that they are similar to the spacing of stacking defects in the undeformed alloy as seen in Fig. 3. This raises the interesting question of whether the stacking defects play a role in the formation of twins. A lower SFE indicates that the energy dierence between a correct (ab) sequence and an incorrect (ba) sequence of 111 layers is reduced. If the occurrence of twinning is controlled by this energy dierence, then this should increase the occurrence of twinning. As the SFE is lowered, the occurrence of stacking faults within the material should increase. A potential positive implication is that a stacking fault begins with an incorrect stacking sequence and this is the correct phase shift for the twin. Thus a stacking defect is in some ways a nascent twin. The presence of a stacking fault may also produce a local softening of the crystal lattice thereby reducing the energy barrier to twinning dislocation propagation. The observation of a thin layer of hexagonal C14 in a deformed specimen raises the possibility that deformation induced phase transformations can occur in the cubic laves phase. The formation of a lath of C14 involves the passage of twinning dislocations on every other cubic 111 layer as opposed to every layer as required for twin formation. If the observed hexagonal layer was formed during deformation, it may indicate that a change in deformation mechanism from cubic twinning to transformation toughening is just being detected at the composition of the laves phase of this study. As the composition is moved to more Nb rich compositions closer to the region of C14 stability, the transformation toughening mechanism may become an important deformation mechanism at low temperatures.
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4.3. Twinning mechanism in Hf±V±Nb ternary alloys The results clearly show that twinning occurs at room temperature within the laves phase of the current two phase Hf±V±Nb alloy. This extends the results of previous studies to more Nb-rich compositions. More importantly, plastic deformation of the alloy was seen at temperatures down to the liquid nitrogen boiling point. This observation indicates that the deformation mechanism either does not require thermal activation, or at most, has a small activation barrier. Direct imaging of the twinned lattice structure by HREM provides clear evidence, when combined with image calculations, that the V net is the twin plane. Twinning on the Hf plane will never produce mirror symmetry across the plane without large diffusive movements of V atoms. Twinning on the lower density V planes can produce mirror symmetry, but with atom position con¯icts between the Hf atoms on the lattice planes directly adjacent to the twin plane. Twins on this plane would require large lattice expansions at the twin, or local atom relaxations away from twin symmetric positions. Twinning on the V net is thus the only twin structure which allows true mirror symmetry across the twin plane without large local lattice expansion. The HREM results also show that the twinning does not induce a permanent change in the structure of the aAa-type Hf±V±Hf layers of each 111 layer away from the twin plane. Movement of the Hf atoms out of position with respect to the vacancies in the V net would result in necessary lattice expansion which would be easily detected by HREM. Thus these triplet atomic planes are rigid blocks before and after twinning has occurred. Three possible mechanisms have been proposed by which twinning can occur in the cubic laves phase as summarized by Hazzledine [4]. These are shear via synchro-Shockley partial dislocations, homogeneous shear proportional to the distance from the twin plane followed by atom shues into the correct twin positions, or shear of rigid lattice units followed by limited atomic shues, Bilby± Crocker twinning. In fact, there is no dierence between the ®nal two mechanisms in the cubic laves phase. In Fig. 5(a), the projected positions of the B and C layers on the A net are labeled. During twinning, a B layer will be sheared into the A positions. With the spacing between the A V atomic plane and the adjacent a Hf atomic planes being 3 d888, the Hf atomic plane closer to the twin plane will have sheared ®ve-eights of the distance towards the correct twinned position and the Hf atomic plane farther from the twin plane will have sheared eleven-eighths of the distance towards the correct twinned position. Thus each will be displaced from their correct a positions by three-eighths of the distance to the projected g or b positions, respectively. The projections of these positions around the center
site on the A atomic plane are marked with ``X'' in Fig. 5(a). Both of these positions are mechanically unstable with respect to relaxation into the a lattice position as they do not reach the saddle point between the adjacent V atoms. Therefore, it can be expected that they will relax into the a positions on the time scale of the atomic vibrational period. This relaxation will be athermal and is certainly too fast to be considered as a separate process (i.e. atomic shue) from the passage of the twinning dislocation. It is therefore physically reasonable to consider the aAa-type 111 layers as rigid layers. With the triplet atomic layers remaining rigid, the twinning deformation must occur in the acb-type layers with each atomic plane separated by d888. The result of the passage of a Shockley twinning dislocation through this layer will be to move the bBb triplet layer to gCg positions. If a complete Shockley dislocation, 1/6[121], were to pass between the c and b planes, the acb layer would be changed into a acg layer resulting in atom position con¯ict between the c V atoms and the g Hf atoms. Similarly, passage of the dislocation between the a and c planes leads to an aag layer with atom position con¯ict between the a Hf atoms and the ``a'' V atoms. In order to avoid this con¯ict, the V atoms must move from the c or ``a'' positions to the b positions, respectively. This can be accomplished by diusive atomic shues after the passage of the Shockley dislocation, or by having the Shockley dislocation dissociated into two partial dislocations, 1/6[211] + 1/6[112], on the two adjacent atomic planes of the acb layer, the so-called synchroSchockley partial dislocations. The present results provide indirect evidence against a mechanism based on shear with subsequent atomic shues. This mechanism requires diusional atomic displacements which would be a thermally-activated process. The present observation of plastic deformation at 77 K limits the amount of thermal activation available for any diffusional process. Assuming that the diusive jumps would be via a vacancy mechanism, the activation energy for vacancy transport on this lattice plane should be quite low. Although it is not yet proved, as no evidence for dissociation of Shockley dislocations into synchro-Shockley partial dislocations has been produced, this mechanism seems to be the most robust in terms of the experimental results. Clearly, experimental studies of the core structure of twinning dislocations in the cubic laves phase are needed. 4.4. Implications for ambient temperature ductility in laves phases The deformation of the alloy of the present study is primarily being carried by the two-phase matrix consisting of small grains of the laves phase surrounded by a b.c.c. solid solution. The small laves precipitates within the matrix show extensive twin-
LUZZI et al.: DEFORMATION TWINNING
ning indicating that large deformations are possible if the laves phase is constrained from undergoing crack nucleation. This observation suggests one possible route to enhance the room temperature ductility of alloys containing this ternary cubic laves phase. If the appropriate alloy composition and thermomechanical processing conditions are selected, it should be possible to produce a two phase alloy with a re®ned grain size similar to that seen in the matrix of the alloy of the present study. This approach could produce an increase in room temperature and low temperature ductility. A second possibility for increasing the ductility of alloys containing the laves phase is to lower the yield stress for twinning to a level at which it occurs prior to the onset of fracture in the absence of a hydrostatic stress component from a coexistent ductile phase. This is the motivation underlying explorations based on lowering the SFE of the laves phase. As the cubic SFE is lowered, the possibility that thicker hexagonal intergrowths will occur increases. It is possible that such an intergrowth has been seen in the present alloy; however, as mentioned above, it is impossible to determine if this intergrowth was produced during annealing or during compressive deformation. It is unlikely that a single stacking fault will impede the progress of a twin in the cubic laves phase. However, as the thickness of the hexagonal phase increases, this hexagonal region will present a barrier to the propagation of a twin. While the eect of this for twinning on the 111 (0001) layers parallel to the hexagonal intergrowth may be small, twinning on 111 layers which intersect the fault may become increasingly dicult. These hexagonal intergrowths may therefore have an impact on the polycrystalline ductility of the material. At some thickness of hexagonal intergrowth, the von Mises criterion for polycrystalline ductility of ®ve independent deformation systems will be violated. This will result in a compromised ability of the laves phase to accommodate the surrounding material and therefore increased brittle behavior. 5. SUMMARY
Twinning at low temperatures in the C15 cubic laves phase of the Hf±V±Nb alloy system has been investigated by conventional and high-resolution TEM. An alloy was chosen such that the composition of the laves phase was closer to the phase ®eld of the C14 hexagonal laves phase in order to reduce the SFE. A large concentration of stacking faults in the as-homogenized alloy con®rmed that the SFE had been reduced in the present alloy. These stacking defects were determined to be of intrinsic character in contrast to that seen at other compositions. The distribution of stacking defects in the undeformed alloy and of twin deformation
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clusters in the alloy after compressive deformation are similar. Twinning was observed at all temperatures between 77 K and room temperature indicating that the twinning mechanism is either athermal or has a very low activation barrier. The twin plane was determined to be the net of V atoms which comprises the highest density atomic plane in the laves phase. All of the data is consistent with a twinning mechanism based on the passage of synchro-Shockley partial dislocations although the dissociation of a Shockley dislocation into two synchro-Shockley partial dislocations cannot be observed at the resolutions available. Based on the results of this work, two possible routes to improve the room temperature ductility of alloys containing a cubic laves phase are suggested. The ®rst relies upon re®ning the grain size since extensive deformation was observed in the ®ne-grained two phase matrix of the present alloy. The second involves the selection of alloy composition such that the SFE of the cubic phase is reduced. AcknowledgementsÐThis research was supported by the Oce of Naval Research (Grant No. N0001491-J-1165; grant ocer G. Yoder) and the Department of Energy (Grant No. DE-FG02-97ER45641; project ocer T. Fitzsimmons). Experiments by the author in Japan were supported by the National Science Foundation (Grant No. INT-94-14511). Research facilities at Penn were supported by the National Science Foundation MRL program (Grant No. DMR91-20668). DEL would like to thank M. Yamaguchi for providing experimental and computational facilities at Kyoto University.
REFERENCES 1. Inoue, K. and Tachikawa, K., IEEE Transactions Magnetism, 1977, MAG-13, 840. 2. Livingston, J. D. and Hall, E. L., J. Mater. Res., 1990, 5, 5. 3. Chu, F. and Pope, D. P., Mater. Sci. Engng., 1993, A170, 39. 4. Hazzledine, P. M., in Twinning in Advanced Materials, 403, ed. M. H. Yoo and M. Wuttig. TMS, Warrendale, PA, 1994. 5. Venables, J. A., in Deformation Twinning, 77, ed. R. E. Reed-Hill, J. P. Hirth and H. C. Rogers. Gordon & Breach, New York, 1964. 6. Chu, F. and Pope, D. P., Scripta metall. mater., 1992, 26, 399. 7. Buseck, P. R., Cowley, J. M. and Eyring, L., High Resolution Electron Microscopy and Associated Techniques. Oxford University Press, New York, 1988. 8. Dobbins, T. A. Masters thesis, University of Pennsylvania, 1995. 9. Pope, D. P. and Chu, F., Phil. Mag., 1994, 69, 409. 10. Chu, F. and Pope, D. P., Scripta metall. mater., 1993, 28, 331. 11. Luzzi, D. E. (in preparation). 12. Luzzi, D. E., Scripta mater., 1997, 37, 713. 13. Allen, C. W., Delavignette, P. and Amelinckx, S., Physica status solidi (a), 1972, 9, 237. 14. Chu, F. 1996 (Private communication). 15. Klee, H. and Witte, H., Z. phys. Chem., 1953/54, 202, 352. 16. Laves, F. and Witte, H., Metallwirtsch, 1936, 15, 840.
Acta mater. Vol. 46, No. 8, pp. 2913±2927, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00418-7
DEFORMATION TWINNING AT LOW TEMPERATURES IN A Hf±V±Nb CUBIC LAVES PHASE D. E. LUZZI, G. RAO{, T. A. DOBBINS and D. P. POPE Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272, U.S.A. (Received 20 December 1996; accepted 24 October 1997) AbstractÐDeformation twinning in the C15 cubic laves phase of the Hf±V±Nb alloy system is analyzed at temperatures between 77 K and room temperature by conventional and high-resolution TEM. In order to reduce the stacking fault energy (SFE), alloy compositions are chosen such that the cubic laves phase composition is close to a region of C14 phase stability. A high density of stacking defects of intrinsic character in the as-homogenized alloy con®rms that the SFE has been reduced. Twinning is observed at all temperatures placing a low upper limit on any thermally activated deformation process. Twin clusters are observed which are narrow and have a similar distribution to the stacking defects in the undeformed alloy. The structure of twins and stacking defects is solved via HREM combined with image calculations. Finally, the mechanism of twinning is discussed and the use of alloying to control the SFE or to re®ne the microstructure in order to increase the low temperature ductility in these intermetallic compounds with complex cubic crystal structures is proposed. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
Extensive ductility has been produced at ambient temperature in ternary Hf±V±Nb alloys containing a cubic laves phase [1]. This result is of interest from a technological point-of-view as many laves phases have high melting temperatures and good high temperature mechanical properties, but also have a high ductile±brittle transition temperature. From a scienti®c point-of-view, the laves phases are a large structural class of intermetallic compounds with a complex, ordered crystal structure; developing an understanding of the origins and modes of low temperature ductility has intrinsic merit. It is now well-established that the low temperature deformation mode in the Hf±V±Nb cubic laves phase is mechanical twinning [2, 3]. The mechanism by which the twinning occurs has not been de®nitively established [4] as simple shear which produces twinning in elemental f.c.c. crystal structures leads to atomic site con¯icts in the more complex f.c.c. laves phases. Low temperature ductility in the Hf±V±Nb cubic laves phase has only been produced in two phase alloys in which the laves phase HfV2+Nb coexists with a V±Nb b.c.c. solid solution [1±3]. Single phase alloys of the laves phase are brittle in compression in polycrystalline form; no single crystal studies have been done. These results indicate that the fracture stress for the polycrystalline laves phase {Present address: Applied Materials Corporation, Santa Clara, California, U.S.A.
is lower than the twinning stress. The presence of a hydrostatic stress component due to the coexistent b.c.c. phase in the two phase alloys is evidently suf®cient to raise the fracture stress above the twinning stress. Reduction of the twinning stress of the laves phase such that twinning occurs in the single phase alloy would be an important step forward in the development of laves phase structural alloys. It has been suggested that twinning may be enhanced in cubic laves phases by reducing the SFE [2]. This statement was based on the observation that lowering the SFE in f.c.c. copper alloys enhances twinning [5]. Recent analysis of the Hf±V±Nb ternary phase diagram has shown that, in addition to a broad phase ®eld of the cubic C15 laves phase, a small composition region exists within which the hexagonal C14 laves phase is stable [6]. If the assumption is made that the stacking fault energy (SFE) of the cubic C15 laves phase will be reduced at compositions close to the composition range of hexagonal C14 stability, then the eect of SFE on deformation twinning in complex cubic materials can be explored. In this paper, the occurrence of stacking defects and deformation twins in Hf±V±Nb ternary alloys is analyzed. In order to reduce the SFE, alloy compositions were chosen such that the cubic laves phase composition is closer to the region of C14 phase stability than that of previous investigations. The distribution and structure of stacking defects and twins is characterized using conventional and
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high-resolution transmission electron microscopy (HREM). Finally, the possibility of using alloying to control the SFE or to re®ne the microstructure in order to increase the ambient temperature ductility in these intermetallic compounds with complex cubic crystal structures is discussed. 2. EXPERIMENTAL DETAILS
Ternary alloys of composition Hf13V62Nb25 (Alloy A) and Hf10V64Nb26 (Alloy B) were prepared by arc melting elemental Hf (99.99% purity), V (99.6% purity) and Nb (99.7%) under Ar atmosphere in a water-cooled copper hearth using a nonconsumable W electrode. Buttons were annealed at 1273 K for 100 h under vacuum and water quenched. Compression specimens of dimensions 4 4 8 mm and 3 3 4.5 mm were cut from the as-homogenized buttons by electron-discharge machining. Specimens were compressed to approximately 1% plastic strain at temperatures between the liquid nitrogen boiling point and room temperature. The room temperature tests were performed on an Instron Model 1125 mechanical testing machine at a strain rate of 2.6 10ÿ5/s. Low temperature compression tests were conducted on an Instron Model 4206 mechanical testing machine equipped with a dewar for immersion within a constant temperature bath. These tests were run at a strain rate of 1 10ÿ3/s at temperatures of 271, 269, 201 and 77 K. Electron microscopy specimens were prepared from the as-homogenized material and from material after compressive deformation. Thin slices of 250 mm were cut using an electron-discharge machine and then mechanically polished to 100 mm
thickness. Mechanical dimpling on a South Bay Technologies dimpling machine was done until the center of the dimple was approximately 20 mm thick. Electron transparent regions were produced by ion milling at liquid nitrogen temperature in a Gatan Duomill until perforation. Five kV Ar ions were used for thinning with a sputtering angle of 158. Conventional electron microscopy was done on a JEOL 2010 at Kyoto University operated at a voltage of 200 kV. HREM imaging was done using JEOL 4000 s at the University of Pennsylvania and Kyoto University. All HREM images were recorded at a voltage of 400 kV. Analysis of the HREM results was accomplished through comparison with calculated images of model structures. The calculations used the well-established multislice and electron-optical method [7] as contained in the MacTempas suite of programs version 1.6.2 installed on an Apple Macintosh Quadra 800 at Kyoto University.
3. RESULTS
3.1. Ternary alloy microstructure and phase compositions A section of the Hf±V±Nb ternary phase diagram [6] is depicted in Fig. 1 with the alloy compositions of Livingston and Hall [2], Chu and Pope [3], and that of the present study indicated. As can be seen, the alloy composition of the present study should contain a C15 laves phase with a composition closer to the composition region of C14 stability. Based on the phase diagram analysis of Chu and Pope [6], it is predicted that the composition of the laves phase of Alloy A should be
Fig. 1. Partial Hf±V±Nb ternary phase diagram at 1273 K reproduced from the work of Chu and Pope [6]. The small C14 phase ®eld (l1) can be seen towards the Nb-rich side of the larger C15 phase ®eld (l2). The V±Nb b.c.c. solid solution (g) is seen at the right. The alloy compositions of Livingston and Hall [2] (L), Chu and Pope [3] (C) and of the present work (A, B) are shown. In the ®gure, the thick lines are phase boundaries and boundaries of multiphase regions. The thin lines are tie lines with the open circles marking the compositions tested in the original analysis of Chu and Pope.
LUZZI et al.: DEFORMATION TWINNING
Fig. 2. As-homogenized microstructure of Alloy A of the present study. Phases of higher average atomic number appear lighter in this image taken with backscattered electrons in a SEM. Large precipitates of the cubic laves phase are contained within a two phase matrix composed of the V±Nb b.c.c. solid solution and the laves phase. Physical connections between the large precipitates and the smaller precipitates of the two phase region indicate that compositional homogenization has occurred; three such connections are indicated by arrows.
Fig. 3. High magni®cation TEM micrograph of a large cubic laves precipitate in an undeformed specimen taken with the electron beam nearly parallel to the [110] crystallographic direction. A large number of crystallographically straight defects can be seen with two orientations in this image.
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Fig. 4. [110] zone axis electron diraction pattern from a large cubic laves precipitate in an undeformed specimen. Rods of diuse scattering due to planar defects can be seen lying along the [111] direction.
Hf23V58Nb19. Compositional analysis by wavelength dispersive spectroscopy in a scanning electron microscope (SEM) referenced to standards was consistent with this prediction indicating a composition of the laves phase of Hf23.0V57.8Nb19.2 [8]. The as-annealed microstructure of Alloy A is shown in Fig. 2; the microstructure of Alloy B is essentially the same. This is a back-scattered electron image taken in an SEM of a polished and etched cross-section. The alloy contains large precipitates of the Hf containing laves phase (light grey). The precipitates are surrounded by a coarsened eutectic two phase matrix containing the laves phase and a V-rich b.c.c. solid solution (dark grey). The SEM results show that Alloy A is a hypereutectic alloy which passed through a two phase liquid/laves phase region before reaching the eutectic temperature at which the remaining liquid solidi®ed into a two-phase b.c.c. solid solution/laves eutectic phase. With no mechanical treatment to break-up the as-grown dendritic structure, the annealing treatment resulted in a coarsened eutectic matrix surrounding the large laves phase precipitates. Many physical connections between the large laves precipitates and the smaller laves grains of the eutectic phase (three are marked with arrows) indicate that the annealing treatment did induce com-
positional homogenization of the b.c.c. and laves phases. 3.2. Defect microstructure in undeformed samples A high magni®cation TEM micrograph of an area of a large cubic laves phase precipitate is shown in Fig. 3 with the orientation of the electron beam near the [110] zone axis. Within the precipitate a large number of defects are seen in two orientations corresponding to the two {111} type planes contained in the [110] zone. The faults are all thin which is expected if they are stacking faults. The spacing of the faults varies from less than 1 nm to over 130 nm in this area of the precipitate which is typical of the alloy. The detailed structure of the faults will be explored in the next section. An electron diraction pattern of the [110] zone of the cubic laves phase is shown in Fig. 4. In addition to the diraction spots, extensive streaking is seen with the orientation of the streaks being a h111i crystallographic direction. It was con®rmed by recording diraction patterns at specimen orientations away from the h110i zone axes that these intensity features are rods of diuse scattering rather than sheets. The shape of the diuse scattering con®rms that planar defects are present in the material lying parallel to the {111} planes of the laves phase. The length of the rods of diuse scat-
LUZZI et al.: DEFORMATION TWINNING
tering is consistent with fault thicknesses of crystal lattice dimensions. The large diuse scattering evident in Fig. 4 is not seen in the diraction patterns from the undeformed laves phase in the alloy of Chu and Pope [9]. The higher intensity of diuse scattering indicates a higher density of defects in the undeformed laves phase at the present composition. This conclusion is supported by comparing h110i zone TEM images of laves grains from the present alloy and that of the previous work [9]. In the work of Livingston and Hall, the authors state that TEM examination showed no twins or faults in the undeformed laves phase [2]. The results of Figs 3 and 4 and the comparisons with prior work are all consistent with an increased density of stacking defects at cubic laves phase compositions closer to the region of stability of the hexagonal laves phase. 3.3. Stacking fault structure in undeformed alloy In the Hf±V±Nb alloy, it has been shown that Hf and V do not form antisite defects, but rather the Nb atoms substitute on both the Hf and V sites in the correct proportion to avoid antisite defects or constitutional vacancies [10]. At the composition of Alloy A of the present study, the expected composition of the Hf sites will therefore be Hf23+Nb10 whereas the V sites will have a composition of V58+Nb9. In the image calculations which follow, the composition of each site was correctly taken into account by adjusting the occupancy of the sites within the model structures. The C15 laves phase has a complex f.c.c. crystal structure containing 24 atoms in the unit cell. Defect analysis using HREM is straightforward, however, if experimental imaging conditions are con®rmed by comparison with calculated images of model structures. As in elemental f.c.c. crystals, the stacking sequence of (111) atomic planes can be written . . . abcabcabc. . . In the laves phase however, each letter of the sequence is comprised of four distinct atomic planes giving . . . aAacbBbagCgb . . . The capital letters, ABC, are planes of V atoms arranged in a net as shown in Fig. 5(a), and the greek letters represent Hf atoms positioned above and below the vacancies in the V layers. The small roman letters, abc, represent planes of V atoms with one-third the atomic density of the other V {The V close-packed columns are the most common feature in HREM images of the cubic laves phase when imaged down a h110i zone axis. In fact, the conditions in which other atomic columns are uniquely imaged, Hf atoms for example, are con®ned to speci®c specimen thicknesses and objective lens defocus values and therefore will typically not be imaged in the HREM. A more in-depth discussion of HREM imaging of the cubic laves phase will be published elsewhere [11].
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layers. Due to the packing arrangement, interplanar spacings of the aA-type are three times that of the ac-type. In Fig. 5(a), the [110] direction is shown by an arrow. The [110] projection of the laves phase structure is depicted schematically in Fig. 5(b) with the Hf atoms as large circles and the V atoms as small ®lled circles, either grey or black. Viewed in this direction, the atomic planes containing the net of V atoms contain alternating close-packed columns of V atoms (black) and columns with 50% vacancies (grey). The close-packed V columns are the intersections of the two nets of V atoms, on the (111) and (111) lattice planes, which lie parallel to the [110] direction. The calculated HREM image of this structure is shown in Fig. 5(c) for the imaging conditions of the present study. The white dot contrast in the calculated image is of the close-packed V columns only.{ Since only one of the four planes which comprise the (111) plane sequence of the laves phase is imaged, the same method of analysis of the defect structure as applied in the HREM analysis of f.c.c. materials can be used. Considering the orientation and thickness of the planar defects, it was initially assumed that they are stacking faults, either intrinsic or extrinsic, in the Hf23V58Nb19 cubic laves phase. The removal of a single 111 layer which comprises an f.c.c. intrinsic stacking fault can also be considered as a single layer of twinned crystal. An extrinsic fault, in which an extra 111 layer is inserted is equivalent to two layers of twinned crystal. In an edge-on HREM image, an extrinsic stacking fault will be twice the thickness of an intrinsic fault. Also, considering the normal advance of f.c.c. 111 layers (abcabc) as successive 1208 phase shifts, then the removal of one layer in an intrinsic fault produces a 1208 phase advance in the position of the f.c.c. crystal across the fault. The addition of an extra 111 layer produces a net 1208 phase retardation in the position of the f.c.c. crystal across the fault. This analysis has been developed for the Hf±V±Nb alloy in another paper [12]. Figure 6 is an HREM image of a defect lying on a (111) plane imaged down the [110] zone axis in which the fault lies parallel to the electron beam direction and is viewed edge on. Applying the above analysis [12], it can be seen that the thickness of the fault is a single laves 111 layer consistent with the fault having intrinsic character. The line traces in the ®gure along (111) planes intersecting the fault show an advance in the position of the planes also consistent with intrinsic character. In order to better see the shift of the lattice planes as they cross the fault, the ®gure should be viewed at a glancing angle along the traced lines.
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Fig. 5. (a) Schematic diagram of the net of V atoms lying parallel to the (111) crystallographic planes of the cubic laves phase (or the basal plane of the hexagonal laves phases). In the drawing, the V atoms are in the ``A'' locations. Projections of the ``B'' and ``C'' lattice sites are indicated. The ``X'' characters are the projected locations of adjacent Hf atoms after twinning by homogeneous shear (cf. Section 4.3). The direction of the incident electron beam, taken to be [110] in the cubic phase is indicated by an arrow; (b) [110] projection of the HfV2 C15 crystal structure. The primary crystallographic directions are marked with arrows. The Hf atoms are large/white; the V atoms are small/shaded. The close-packed columns of V atoms are shaded black; (c) HREM image calculation for the [110] zone axis at a thickness of 4.18 nm and an objective lens underfocus of ÿ60 nm. The strong white contrast is from the close-packed columns of V atoms.
3.4. Defect microstructure in deformed samples Plastic deformation was seen in specimens deformed in compression at all temperatures down to 77 K. A TEM image of the coarsened eutectic matrix microstructure in a sample which has undergone com-
pressive deformation is shown in Fig. 7. A high density of laves phase precipitates are seen which are clustered in this image. The b.c.c. solid solution at the upper left and lower and upper right in the ®gure shows evidence of extensive dislocation slip indicating
LUZZI et al.: DEFORMATION TWINNING
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Fig. 6. HREM micrograph of a stacking fault lying on a (111) crystallographic plane in a large precipitate of the Hf23V58Nb19 cubic laves phase of alloy A. The thickness of the fault and the shift of the (111) lattice planes across the fault are consistent with intrinsic character.
that plastic deformation has occurred by dislocation glide. In contrast, within the cubic laves phase, straight defects are seen. These defects were found to be both twins and stacking faults by HREM as will be shown below. In the ®gure, the large extent of twinning within these small laves grains can be clearly seen. Often, a twin cluster composed of many ®ne twin bands was found to extend across the entire grain, as seen in the ®gure. Twinning also occurs within the large laves precipitates and was investigated in detail. Images showed that multiple twinning systems can operate within the same grain during compressive deformation of this alloy. Figure 8 is a TEM image of a large laves precipitate taken with the crystal oriented with the electron beam along the [110] zone axis. The grain in this image is over ®ve microns in size and the thickness increases rapidly away from the specimen edge. In the image, taken from a thin region along the specimen edge, clear evidence of clusters of deformation twin bands can be seen. In the remainder of the paper, the grouping of many ®ne twin bands as seen in Fig. 8 will be termed a twin cluster, the term twin band will refer to the standard crystallographic twin, namely matrix/twin/matrix and a single twin interface, as
seen in the HREM study below, will be termed a twin. A diraction pattern from the twin cluster of Fig. 8 is shown in Fig. 9. One set of twin re¯ections are seen and the twin plane is clearly the (111) crystallographic plane. Diuse streaks can also be seen running through the diraction pattern aligned with the diraction spots of the twin plane. These streaks have a similar appearance to those in Fig. 4 and are due to rods of diuse scattering aligned along the [111] crystallographic direction. The presence of these rods of diuse intensity indicate that the twin bands formed within this alloy at the current levels of induced plastic strain tend to be quite narrow. The twin cluster of Figs 8 and 9 is shown at higher magni®cation in Fig. 10 with the specimen tilted o of the [110] zone in order to increase the diraction contrast between the matrix and twin. As can be seen in the image, the twin cluster is composed entirely of thin twin bands with no twin bands present of the large widths seen in previous studies [2, 3]. The total width of the twin cluster is 110 nm. Within this width, 18 twin bands are present with an average width of 6.1 nm. The twin bands vary in width from less than 1 nm to a maximum of 8.6 nm. The thinnest twin bands have a
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Fig. 7. TEM micrograph of the microstructure of the two phase matrix region of Alloy A after compressive deformation. The cluster of laves phase precipitates show evidence of extensive twinning. The b.c.c. matrix at the upper left and lower right exhibits the result of dislocation activity.
Fig. 8. TEM micrograph of twin clusters in a large precipitate of the laves phase. The magni®cation of this micrograph is similar to that of Fig. 7. The spacing between twin clusters is similar to the spacing of stacking defects seen in large precipitates prior to deformation, cf. Figure 3.
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Fig. 9. [110] zone axis electron diraction pattern of a twin band from a large precipitate. Extensive diffuse streaking, indicative of many ®ne twins is seen running parallel to the twin plane diraction spots.
width equal to one or two (111) layer spacings of the cubic laves phase. The even number of twins indicates that the twin cluster is bounded by matrix crystal on either side. This is the case with all twin clusters found in the large precipitates. In addition to the extensive evidence of deformation twinning seen in both large and small grains of the laves phase, one thin region of the hexagonal C14 laves crystal structure was found. The layer had a width equal to three repeats of the hexagonal lattice (6 d111 cubic) and was in a large laves grain of a deformed specimen. However, the hexagonal layer was isolated within the cubic laves matrix and was not associated with a deformation twin cluster. Whether this hexagonal layer was formed during deformation or was a hexagonal intergrowth which was present in the undeformed alloy cannot be known. Although no hexagonal intergrowths were seen in the undeformed alloy, it is possible that a low density of such intergrowths could be missed due to the unavoidably low sampling in HREMbased investigations. 3.5. Structure of deformation twins HREM imaging was conducted to study the microstructure of the twin clusters and the structure of individual twins including the identity of the twin plane. In the images which follow, the white dot contrast corresponds to the close-packed columns of V(Nb) atoms which lie along the h110i crystallographic directions. As in the images of the
undeformed alloy contained in Section 3.3, one of every four laves planes is imaged. An HREM image of a twin cluster taken down the [110]matrixv[110]twin tilt axis is shown in Fig. 11. The twins lie horizontally in the image. The total height of the image is 72 nm; within this length, many twin bands of varying widths exist. With the twin planes de®ned as the (111) atomic planes, the large arrows drawn on the ®gure indicate the (111) atomic planes of the matrix and twin. By viewing the image along the arrows, the many thin twin bands can be seen. The gradual variation in the appearance of the crystal structure with position is due to the changes in specimen thickness and tilt, as well as the small changes in electron beam orientation due to the convergence of the electron probe. The single arrow indicates the location of a twin band with a thickness equal to a single 111 layer. Nearby, the double arrow indicates the location of a twin band of thickness equal to two 111 layers. The thickest twin band seen in this specimen was 21 111 layers thick or 8.95 nm. Within this image, no sequences of 111 layers are seen which could be identi®ed with either hexagonal laves structure, C14 or C36. A magni®ed view of the boxed area of Fig. 11 is shown in Fig. 12. Using the arguments developed in Section 3.3, the character of the two faults can be unambiguously determined. In the ®gure, line traces are drawn on the (111) planes of the matrix in order to accentuate the phase shift of these planes
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Fig. 10. Higher magni®cation view of the central twin cluster of Fig. 8. The twin cluster is bounded by matrix on either side. Twin bands range in thickness from lattice dimensions to approximately 8 nm.
as they cross the fault. As can be seen, these planes advance one-third of the plane spacing as they cross the lower fault; this is the correct plane shift for an intrinsic stacking fault [12]. This result is also consistent with the thickness of the fault being one 111 layer. In contrast, the (111) planes are retarded by one-third the plane spacing as they cross the upper fault. This is the expected phase shift for an extrinsic stacking fault and is consistent with the thickness of the fault being two 111 layers [12]. A [110]matrix zone axis image calculation for the imaging conditions of Fig. 12 is shown in Fig. 13 for the extrinsic stacking fault. By comparing the simulation with the image of the lower fault in Fig. 12, it can be seen that the internal structure of the fault is also correct, namely the white dots associated with the close-packed V columns of the extra 111 layer of the extrinsic fault are in the correct position with respect to the V columns in the 111 layers bounding the fault. Measurements taken from the image show that the position of the line of
white dots within the fault lie exactly on the center line as expected; this is easily seen by examining at a glancing angle the constant interlayer spacing of the 111 planes of Fig. 12. Figure 14 is a magni®ed view of a twin between two relatively thick laths (8.95 and 3.41 nm, respectively). The twin plane is indicated by the arrows in the ®gure. Figure 15 contains three image calculations for the same imaging conditions of Fig. 14 of three possible twin structures. The ®rst is for the twin lying on the V net, the A, B, or C atomic plane of the laves (111) plane sequence described in Section 3.3 resulting in a plane sequence of . . . aAacbBbagCgabBbcaAa . . . . The second image calculation is for a twin lying on a Hf layer, the a, b, or g atomic plane of the sequence resulting in a plane sequence of . . . aAacbBbagCgCgabBbcaAa . . . . The ®nal calculation is for a twin lying on the V layer of lower atomic density, the a, b, or c atomic plane of the sequence resulting in a plane sequence of . . .aAacbBbabBbcaAa . . . . By comparing Fig. 14
LUZZI et al.: DEFORMATION TWINNING
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This conclusion is based on the observation that the volume fraction of the laves phase as seen in Fig. 2 exceeds that predicted from the lever rule when applied to Fig. 1 even when factoring in the lower atomic density of the laves phase. In the present work, an identical alloy preparation regimen was followed to that in the original work on the phase diagram [6]. In the original work on the phase diagram [6], optical microscopy was used to characterize the alloy microstructure and X-ray ¯uorescence spectroscopy by energy dispersive spectroscopy (EDS) in an SEM was used to determine the composition of dierent phases. At the resolution of the optical microscope, the ®ne eutectic structure as seen in the matrix of Fig. 2 would not be resolved. The EDS analysis would have been conducted at an electron voltage of at least 20 kV in order to ensure adequate excitation of the electrons in the Hf L-shell. At this voltage, the activated volume within the alloy would greatly exceed the grain size of the eutectic phases and thus the measurement would be of the average composition of the two phase region rather than that of the b.c.c. solid solution. With one of the phases being the laves phase which contains a higher concentration of Hf, the b.c.c. solid solution would thus contain a reduced Hf concentration. Based on volume fraction estimates from SEM micrographs of the two phase eutectic region, a Hf solubility limit of 4% is estimated for the b.c.c. solid solution phase at these alloy compositions. This value is consistent with the measurement of the composition of the b.c.c. solid solution in a single phase sample of the original work [6] as well as the volume fraction of laves phase and b.c.c. solid solution seen in the work of Livingston and Hall [2]. 4.1. Eect of Nb composition on defect structure
Fig. 11. HREM overview of the structure of a twin cluster viewed down the [110] tilt axis between the matrix and the twin. The thickest twin band can be seen just below the middle of the ®gure and is 21 d111, or 8.95 nm thick. Twin bands with thicknesses of d111 and 2 d111 can be seen at the single and double arrow, respectively. By sighting at a glancing angle along the arrows at the bottom of the ®gure, the many ®ne twin bands contained within this twin cluster can be seen.
with Figs 15(a)±(c), it can be seen that the HREM image matches only the image calculation of Fig. 15(a). The twin plane is the V net. 4. DISCUSSION
The results in Figs 1 and 2 indicate that the position of the phase boundary of the g b.c.c. solid solution actually exists at lower Hf concentrations.
The observation of a large number of stacking defects in the undeformed alloy is a positive indication that the SFE of the laves phase can be lowered by alloying. The intrinsic character of these stacking faults is in contrast to previous results in cubic laves phases including those of the Hf±V±Nb alloy system. The ®rst reports of fault character in the laves phases was in the compounds TiCr2 and TiCo2 [13]. In that study, the authors found that all faults were extrinsic using conventional TEM analysis. In the alloy studied by Livingston and Hall, no stacking defects were seen in the alloy prior to mechanical deformation [2]. In that of Chu and Pope, some stacking faults were seen although the density of these stacking faults was insucient to produce visible streaking in electron diraction patterns [9]. These faults have recently been con®rmed to be of extrinsic character [14]. This alloy behavior may be related to the relative free energy of the dierent laves structures at dierent Nb concentration. Referring to Fig. 1, it can be
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Fig. 12. Higher magni®cation view of the boxed area of Fig. 11. The single and double layer twin bands can be seen to be an intrinsic and an extrinsic stacking fault, respectively, based on thickness and the shift of planes as they cross the faults.
seen that the composition of the laves phases in the studies of Livingston and Hall [2] and Chu and Pope [3] and the present study are progressively shifted towards more Nb-rich concentrations with the Nb replacing both V and Hf in the compound. At the same time, the composition is moved closer to the phase ®eld in which the hexagonal C14 structure is stable. The observations of Livingston and Hall suggest that the cubic laves phase, C15, is quite stable at lower Nb concentration. The presence of extrinsic stacking faults in the alloy of Chu and Pope is consistent with a tendency towards the formation of the C36 hexagonal structure since extrinsic stacking faults have a 111 layer stacking sequence equivalent to a layer of this structure. The intrinsic stacking faults of the present study indicate a tendency towards the formation of the C14 hexagonal structure since intrinsic stacking faults have a 111 layer stacking sequence equivalent to a layer of this structure. This trend towards C14 stability with increasing Nb content concludes with the C14 struc-
Fig. 13. HREM image calculation of the internal contrast of the double layer twin band of Fig. 12. It can be seen that the position of the white contrast in the center of the fault is correct for an extrinsic stacking fault.
ture becoming the equilibrium crystal structure, at least at 1273 K. This shift in stability from C15 to C36 to C14 is similar to that seen in the Mg±Cu±Zn alloy system in which the substitution of Zn for Cu produces this sequence of equilibrium crystal structures [15]. This behavior has been related to the valence elec-
Fig. 14. High magni®cation view of a twin in the cubic laves phase.
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4.2. Deformation in the two-phase alloy
Fig. 15. HREM image calculations for twins in which the twin plane lies on the V net (a), a Hf atomic plane (b) and the lower density V atomic plane (c). Comparison of the calculations with the image of Fig. 14 con®rms that the twin plane is the V net as sketched in Fig. 5(a). The arrows indicate the twin plane.
tron concentration (VEC) with the C15 structure the most stable at a VEC of 1.5, C36 the most stable at a VEC of 1.8 and C14 the most stable at a VEC of 2.0 [16]. In the present alloy system however, the VEC of the binary HfV2 is 2.0 and the addition of Nb lowers the VEC in direct contradiction to the above reported trend. A straightforward comparison based on VEC may not be possible since, in the present alloy, the Nb substitutes on both the Hf and V sublattices [10], whereas in the Mg±Cu±Zn alloy system, the Zn substitutes solely on the Cu sublattice. However, the compound HfFe2, which also has a VEC of 2.0, has the hexagonal C14 structure at room temperature. Although, a simpli®ed quantity such as the VEC cannot be the explanation of the varying phase stability in the current alloy system, electronic eects must play the determining role. Although the atomic size ratio of the constituents will determine that the structure will be one of the laves phase structures, there is no atomic size related dierence among the three laves phase structures.
In the present alloy, TEM observations show that plastic yielding occurs throughout the microstructure. It seems apparent that the two phase region carries a large amount of the plastic deformation as extensive dislocation activity and twinning were seen in the b.c.c. phase and laves phase, respectively. It might be expected, based on these results, that the production of an alloy with a small grain size may be a route to increase the room temperature ductility of a two phase alloy containing this laves phase. This would involve choosing both an appropriate alloy composition and thermomechanical processing conditions to produce a uniform microstructure containing small grains. Some deformation twinning was also seen in the large laves precipitates. This deformation occurs in clusters surrounded by crystal showing no indication of deformation. Each twin cluster contains an even number of twins such that the crystal on either side of the cluster has the matrix orientation. Measurement of the spacing between the twin clusters shows that they are similar to the spacing of stacking defects in the undeformed alloy as seen in Fig. 3. This raises the interesting question of whether the stacking defects play a role in the formation of twins. A lower SFE indicates that the energy dierence between a correct (ab) sequence and an incorrect (ba) sequence of 111 layers is reduced. If the occurrence of twinning is controlled by this energy dierence, then this should increase the occurrence of twinning. As the SFE is lowered, the occurrence of stacking faults within the material should increase. A potential positive implication is that a stacking fault begins with an incorrect stacking sequence and this is the correct phase shift for the twin. Thus a stacking defect is in some ways a nascent twin. The presence of a stacking fault may also produce a local softening of the crystal lattice thereby reducing the energy barrier to twinning dislocation propagation. The observation of a thin layer of hexagonal C14 in a deformed specimen raises the possibility that deformation induced phase transformations can occur in the cubic laves phase. The formation of a lath of C14 involves the passage of twinning dislocations on every other cubic 111 layer as opposed to every layer as required for twin formation. If the observed hexagonal layer was formed during deformation, it may indicate that a change in deformation mechanism from cubic twinning to transformation toughening is just being detected at the composition of the laves phase of this study. As the composition is moved to more Nb rich compositions closer to the region of C14 stability, the transformation toughening mechanism may become an important deformation mechanism at low temperatures.
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4.3. Twinning mechanism in Hf±V±Nb ternary alloys The results clearly show that twinning occurs at room temperature within the laves phase of the current two phase Hf±V±Nb alloy. This extends the results of previous studies to more Nb-rich compositions. More importantly, plastic deformation of the alloy was seen at temperatures down to the liquid nitrogen boiling point. This observation indicates that the deformation mechanism either does not require thermal activation, or at most, has a small activation barrier. Direct imaging of the twinned lattice structure by HREM provides clear evidence, when combined with image calculations, that the V net is the twin plane. Twinning on the Hf plane will never produce mirror symmetry across the plane without large diffusive movements of V atoms. Twinning on the lower density V planes can produce mirror symmetry, but with atom position con¯icts between the Hf atoms on the lattice planes directly adjacent to the twin plane. Twins on this plane would require large lattice expansions at the twin, or local atom relaxations away from twin symmetric positions. Twinning on the V net is thus the only twin structure which allows true mirror symmetry across the twin plane without large local lattice expansion. The HREM results also show that the twinning does not induce a permanent change in the structure of the aAa-type Hf±V±Hf layers of each 111 layer away from the twin plane. Movement of the Hf atoms out of position with respect to the vacancies in the V net would result in necessary lattice expansion which would be easily detected by HREM. Thus these triplet atomic planes are rigid blocks before and after twinning has occurred. Three possible mechanisms have been proposed by which twinning can occur in the cubic laves phase as summarized by Hazzledine [4]. These are shear via synchro-Shockley partial dislocations, homogeneous shear proportional to the distance from the twin plane followed by atom shues into the correct twin positions, or shear of rigid lattice units followed by limited atomic shues, Bilby± Crocker twinning. In fact, there is no dierence between the ®nal two mechanisms in the cubic laves phase. In Fig. 5(a), the projected positions of the B and C layers on the A net are labeled. During twinning, a B layer will be sheared into the A positions. With the spacing between the A V atomic plane and the adjacent a Hf atomic planes being 3 d888, the Hf atomic plane closer to the twin plane will have sheared ®ve-eights of the distance towards the correct twinned position and the Hf atomic plane farther from the twin plane will have sheared eleven-eighths of the distance towards the correct twinned position. Thus each will be displaced from their correct a positions by three-eighths of the distance to the projected g or b positions, respectively. The projections of these positions around the center
site on the A atomic plane are marked with ``X'' in Fig. 5(a). Both of these positions are mechanically unstable with respect to relaxation into the a lattice position as they do not reach the saddle point between the adjacent V atoms. Therefore, it can be expected that they will relax into the a positions on the time scale of the atomic vibrational period. This relaxation will be athermal and is certainly too fast to be considered as a separate process (i.e. atomic shue) from the passage of the twinning dislocation. It is therefore physically reasonable to consider the aAa-type 111 layers as rigid layers. With the triplet atomic layers remaining rigid, the twinning deformation must occur in the acb-type layers with each atomic plane separated by d888. The result of the passage of a Shockley twinning dislocation through this layer will be to move the bBb triplet layer to gCg positions. If a complete Shockley dislocation, 1/6[121], were to pass between the c and b planes, the acb layer would be changed into a acg layer resulting in atom position con¯ict between the c V atoms and the g Hf atoms. Similarly, passage of the dislocation between the a and c planes leads to an aag layer with atom position con¯ict between the a Hf atoms and the ``a'' V atoms. In order to avoid this con¯ict, the V atoms must move from the c or ``a'' positions to the b positions, respectively. This can be accomplished by diusive atomic shues after the passage of the Shockley dislocation, or by having the Shockley dislocation dissociated into two partial dislocations, 1/6[211] + 1/6[112], on the two adjacent atomic planes of the acb layer, the so-called synchroSchockley partial dislocations. The present results provide indirect evidence against a mechanism based on shear with subsequent atomic shues. This mechanism requires diusional atomic displacements which would be a thermally-activated process. The present observation of plastic deformation at 77 K limits the amount of thermal activation available for any diffusional process. Assuming that the diusive jumps would be via a vacancy mechanism, the activation energy for vacancy transport on this lattice plane should be quite low. Although it is not yet proved, as no evidence for dissociation of Shockley dislocations into synchro-Shockley partial dislocations has been produced, this mechanism seems to be the most robust in terms of the experimental results. Clearly, experimental studies of the core structure of twinning dislocations in the cubic laves phase are needed. 4.4. Implications for ambient temperature ductility in laves phases The deformation of the alloy of the present study is primarily being carried by the two-phase matrix consisting of small grains of the laves phase surrounded by a b.c.c. solid solution. The small laves precipitates within the matrix show extensive twin-
LUZZI et al.: DEFORMATION TWINNING
ning indicating that large deformations are possible if the laves phase is constrained from undergoing crack nucleation. This observation suggests one possible route to enhance the room temperature ductility of alloys containing this ternary cubic laves phase. If the appropriate alloy composition and thermomechanical processing conditions are selected, it should be possible to produce a two phase alloy with a re®ned grain size similar to that seen in the matrix of the alloy of the present study. This approach could produce an increase in room temperature and low temperature ductility. A second possibility for increasing the ductility of alloys containing the laves phase is to lower the yield stress for twinning to a level at which it occurs prior to the onset of fracture in the absence of a hydrostatic stress component from a coexistent ductile phase. This is the motivation underlying explorations based on lowering the SFE of the laves phase. As the cubic SFE is lowered, the possibility that thicker hexagonal intergrowths will occur increases. It is possible that such an intergrowth has been seen in the present alloy; however, as mentioned above, it is impossible to determine if this intergrowth was produced during annealing or during compressive deformation. It is unlikely that a single stacking fault will impede the progress of a twin in the cubic laves phase. However, as the thickness of the hexagonal phase increases, this hexagonal region will present a barrier to the propagation of a twin. While the eect of this for twinning on the 111 (0001) layers parallel to the hexagonal intergrowth may be small, twinning on 111 layers which intersect the fault may become increasingly dicult. These hexagonal intergrowths may therefore have an impact on the polycrystalline ductility of the material. At some thickness of hexagonal intergrowth, the von Mises criterion for polycrystalline ductility of ®ve independent deformation systems will be violated. This will result in a compromised ability of the laves phase to accommodate the surrounding material and therefore increased brittle behavior. 5. SUMMARY
Twinning at low temperatures in the C15 cubic laves phase of the Hf±V±Nb alloy system has been investigated by conventional and high-resolution TEM. An alloy was chosen such that the composition of the laves phase was closer to the phase ®eld of the C14 hexagonal laves phase in order to reduce the SFE. A large concentration of stacking faults in the as-homogenized alloy con®rmed that the SFE had been reduced in the present alloy. These stacking defects were determined to be of intrinsic character in contrast to that seen at other compositions. The distribution of stacking defects in the undeformed alloy and of twin deformation
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clusters in the alloy after compressive deformation are similar. Twinning was observed at all temperatures between 77 K and room temperature indicating that the twinning mechanism is either athermal or has a very low activation barrier. The twin plane was determined to be the net of V atoms which comprises the highest density atomic plane in the laves phase. All of the data is consistent with a twinning mechanism based on the passage of synchro-Shockley partial dislocations although the dissociation of a Shockley dislocation into two synchro-Shockley partial dislocations cannot be observed at the resolutions available. Based on the results of this work, two possible routes to improve the room temperature ductility of alloys containing a cubic laves phase are suggested. The ®rst relies upon re®ning the grain size since extensive deformation was observed in the ®ne-grained two phase matrix of the present alloy. The second involves the selection of alloy composition such that the SFE of the cubic phase is reduced. AcknowledgementsÐThis research was supported by the Oce of Naval Research (Grant No. N0001491-J-1165; grant ocer G. Yoder) and the Department of Energy (Grant No. DE-FG02-97ER45641; project ocer T. Fitzsimmons). Experiments by the author in Japan were supported by the National Science Foundation (Grant No. INT-94-14511). Research facilities at Penn were supported by the National Science Foundation MRL program (Grant No. DMR91-20668). DEL would like to thank M. Yamaguchi for providing experimental and computational facilities at Kyoto University.
REFERENCES 1. Inoue, K. and Tachikawa, K., IEEE Transactions Magnetism, 1977, MAG-13, 840. 2. Livingston, J. D. and Hall, E. L., J. Mater. Res., 1990, 5, 5. 3. Chu, F. and Pope, D. P., Mater. Sci. Engng., 1993, A170, 39. 4. Hazzledine, P. M., in Twinning in Advanced Materials, 403, ed. M. H. Yoo and M. Wuttig. TMS, Warrendale, PA, 1994. 5. Venables, J. A., in Deformation Twinning, 77, ed. R. E. Reed-Hill, J. P. Hirth and H. C. Rogers. Gordon & Breach, New York, 1964. 6. Chu, F. and Pope, D. P., Scripta metall. mater., 1992, 26, 399. 7. Buseck, P. R., Cowley, J. M. and Eyring, L., High Resolution Electron Microscopy and Associated Techniques. Oxford University Press, New York, 1988. 8. Dobbins, T. A. Masters thesis, University of Pennsylvania, 1995. 9. Pope, D. P. and Chu, F., Phil. Mag., 1994, 69, 409. 10. Chu, F. and Pope, D. P., Scripta metall. mater., 1993, 28, 331. 11. Luzzi, D. E. (in preparation). 12. Luzzi, D. E., Scripta mater., 1997, 37, 713. 13. Allen, C. W., Delavignette, P. and Amelinckx, S., Physica status solidi (a), 1972, 9, 237. 14. Chu, F. 1996 (Private communication). 15. Klee, H. and Witte, H., Z. phys. Chem., 1953/54, 202, 352. 16. Laves, F. and Witte, H., Metallwirtsch, 1936, 15, 840.