May 5, 1996 - 73, NO. 5, 217±224. Structure of a 12 29 near-tilt grain boundary in titanium. By I. MACLAREN and M. AINDOW. School of Metallurgy and ...
PHILOSOPHICAL MAGAZINE LETTERS, 1996, VOL. 73, NO. 5, 217± 224
Structure of a 12 29 near-tilt grain boundary in titanium By I. MACLAREN and M. AINDOW School of Metallurgy and Materials, and Interdisciplinary Research Centre in Materials for High Performance Applications, The University of Birmingham, Edgbaston, Birmingham B15 2TT, England [Received in final form 12 January 1996 and accepted 23 January 1996]
ABSTRACT
The structure of a near-tilt grain boundary with 12 29 in deformed and annealed Ti has been studied using transmission electron microscopy. The observed structure has been compared with modelled structures and shown to be a good match to that expected for a stepped low-angle grain boundary.
1. INTRODUCTION It is now well established that the structure of a low-angle grain boundary (LAGB) can be described in terms of arrays of crystal dislocations in the manner proposed by Burgers (1939) and Frank (1950). In this model, the spacing d of the crystal dislocations is a function of the angle in the reduced axis± angle ( r ) pair. As one considers boundaries with successively higher values of , d decreases until the strain fields of the dislocations overlap to such an extent that such a description would cease to be physically significant. High-angle grain boundaries (HAGBs) are usually better modelled as being vicinal to a low-energy reference structure, and in crystals with cubic structures it has been demonstrated that they correspond to coincident site lattice (CSL) orientations. In this model the structure of a HAGB exhibits the reference structure with the deviation from the reference structure orientation being accommodated by arrays of crystal and/or interfacial dislocations. Perhaps the clearest demonstration of a transition from LAGB to HAGB structure is the variation in the activation energy Q for grain boundary migration with . For example, Viswanathan and Bauer (1973) studied [001] bicrystals of copper and showed that for low the value of Q was close to that for bulk diffusion whereas, for high , Q fell to much lower values. The transition between these two states occurred over a small range of , at 9 for mixed boundaries and 13 for pure tilt boundaries. This is consistent with transmission electron microscopy (TEM) observations of grain-boundary structure in cubic crystals: the highest values of at which observed structures have been matched with the LAGB model is 10 65 for a mixed character boundary in copper (Clarebrough and Forwood 1980) and 12 25 for a near-tilt boundary in NiO (Vaudin, RuÈhle and Sass 1983). For boundaries in crystals with an hexagonal crystal structure, however, there are fewer data concerning the transition from LAGBs to HAGBs. Most of the published studies have been on HAGBs for which 5 , (for example, Lay, Delavignette and Vicens (1985), Chen and King (1988a) and MacLaren and Aindow (1993a)) or on HAGBs for which 20 (for example, Grimmer, Bonnet, Lartigue and Priester (1990) and Lay, Ayed and Nouet (1992)). To the present authors’ knowledge the only published studies on boundaries with 0950± 0839/96 $12 00
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intermediate values of are the partial analyses of Chen and King (1988b) who used Bollmann’s (1970, 1982) `O’ lattice approach to model the boundary structures observed in polycrystalline Zn by TEM. They suggested that the structure observed in a boundary with 9 75 was best described as a HAGB with a 37 CSL reference structure. Moreover, it was stated that the dislocation arrangement observed in a grain boundary with 13 82 was not consistent with that which would be expected for a LAGB although no alternative reference structure was identified for this boundary. In this letter an analysis is presented of the dislocation structure observed in a near-tilt boundary with 12 29 in polycrystalline Ti. This is part of a TEM study of LAGBs and HAGBs in hcp metals (MacLaren 1995) and analyses of boundaries with higher values of will be presented elsewhere. 2. EXPERIMENTAL PROCEDURE Pieces of Ti sheet about 1 2 mm thick were cold rolled to about 0 4 mm and heattreated in vacuum at 700 C for 3 h. These were then ground to a thickness of approximately 200 m, discs 3 mm in diameter were punched out, and TEM specimens were prepared from the discs by twin-jet electropolishing. To prevent hydride formation, the acid-free solution described by Kestel (1986) was used; this contained 3 3 5 3 g LiCl and 11 2 g Mg(ClO4) 2 , in 500 cm methanol and 100 cm 2-butoxyethanol. Polishing was performed at a temperature of 40 C, a voltage of 40 V and a low flow rate. The specimens were examined using conventional diffraction contrast imaging techniques in a Philips CM20 transmission electron microscope operating at an accelerating voltage of 200 kV. Axis± angle pairs were calculated from diffraction patterns recorded in each grain at a variety of specimen orientations as described elsewhere (MacLaren and Aindow 1993b, MacLaren 1995). 3. R ESULTS The specimens exhibited a large grain size (greater than 10 m), very few dislocations within the grains, and long straight grain boundaries. Thus the samples were fully recrystallized and one would expect that the grain boundaries in such specimens would display near-equilibrium structures. Indeed regular dislocation structures were observed in all the boundaries examined, most of which fell clearly within the HAGB regime for . In this letter we present results from one boundary only which exhibits a value of which lies between the LAGB and HAGB regimes, although we note that several such boundaries were observed. A weak-beam dark-field image of the boundary is presented in fig. 1; this was recorded with g 0111 where and are used to denote the coordinate frames of the lower and upper grains respectively in the image. The facet shown in the micrograph extended for more than 6 m and a regular structure was observed over the whole length of the boundary. The calculated axis± angle pair for this boundary was ([0 014 0 396 0 409 0 452], 12 29 with an error of 0 003 on each index in r and 0 1 in . A set of higher-magnification images from the region close to the triple line are shown in figs. 2 (a), (b), (c) and (d); these are weak-beam dark-field images recorded using g 0111 0111 1101 and 0111 , respectively, with beam directions close to 1213 1123 1102 and between 1123 and 0112 , respectively. Two main sets of periodic features were observed in the boundary which were labelled sets 1 and 2. Set 1 had a spacing of 3 71 0 37 nm; these are visible in figs. 2 (a), (b) and (d). Set 2, which displayed stronger contrast, are visible in all the
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Fig. 1
Weak-beam dark-field transmission electron micrograph of a grain boundary in Ti recorded with g 0111 .
images; these features were parallel to those of set 1 with a spacing of 25 4 2 5 nm, approximately seven times that of set 1. Trace analysis was used to show that both sets had a line direction u1 equal to 0 009 0 423 0 414 0 435 with an uncertainty of about 0 02 on each index; this direction makes an angle of 1 34 with 0111 . Similarly, the line direction of the intersection of the boundary with one of the foil surfaces was found to be uBT 0 626 0 473 0 153 0 128 . The boundary plane normal n was calculated from the vector product of u1 and uBT which gave n 0 029 0 357 0 387 0 427 . Since r lies at about 88 3 to n, the boundary has predominantly tilt character. The features in set 1 displayed contrast similar to that which would be expected for moire fringes and indeed moire effects could contribute to the contrast in figs. 2 (a) and (d) since the 0111 diffracting planes of the two crystals are slightly misaligned. The moire fringe spacing of 2 45 nm which one would expect in these two images is, however, not in agreement with the measured spacing of 3 70 0 35 nm. Moreover, these features were observed with approximately the same orientation and spacing in a number of the available diffraction conditions and thus they cannot arise by this mechanism alone. It seems more plausible therefore to suggest that these features correspond to a closely spaced set of dislocations in the boundary. A third set of dislocations, lying approximately perpendicular to sets 1 and 2, is visible in fig. 2 (c). These were labelled set 3 and were only observed near the triple line where the boundary plane deviates more from the tilt orientation. The line direction of u3 of these features was found to be 0 656 0 388 0 268 0 090 ; however, only two traces could be used to determine this line direction and therefore the accuracy of this result could not be quantified.
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(b)
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(c)
(d) Weak-beam dark-field transmission electron micrographs from the grain boundary shown in Fig. 1 close to the triple line recorded with (a) g 0111 , (b) g 0111 , (c) g 1101 and (d) g 0111 .
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4. ANALYSIS AND DISCUSSI ON Since 15 for this boundary, a procedure based on the `O’-lattice approach of Bollmann (1970, 1982) was used to model the dislocation arrangement that would be expected if it adopted a LAGB-type structure. Firstly, a b net was constructed using simple lattice translation vectors in such a way as to follow the plane perpendicular to r approximately. The net was corrugated with one part of each corrugation containing vectors a2 and a3, the other part containing vectors c a2 and c a3, and with a1 vectors being common to each part. This b net was then projected onto the plane perpendicular to r to form the network shown in fig. 3 (a). The centres of the polygons were then connected to form a second network which was rotated by 90 2 83 86 about r, and the scale was reduced by 2 sin 2 to form the L net shown in fig. 3 (b). Since the angular difference between r and u1 was so small (about 3 1 ), a first approximation to the required dislocation arrangement in the boundary was calculated using the simplifying assumption that the boundary had pure tilt character with u1 r. In order to predict the dislocation structure the L net would be extended parallel to r into a honeycomb structure and the positions of the dislocations would then be given by the intersection of the boundary plane with the cell walls. The trace of the boundary plane is marked with a broad line in fig. 3 (b) and it is clear that, on this basis, one would expect a rather irregular arrangement of dislocations which is not consistent with that observed experimentally. In previous studies of LAGBs, however, it has been noted that such boundaries may facet in order to adopt a lower-energy periodic structure (Vaudin et al. 1983, Chen and King 1988a). If a similar structure were formed in the boundary considered here, one possible corrugation is that shown by the broken line in fig. 3 (b). A schematic diagram of the arrangement of dislocations that would then be found in the boundary is shown in fig. 3 (c); each dislocation in this array is labelled by its Burgers vector. In this model, the spacing of the alternate a2 and c a3 dislocations is 3 24 nm, and the spacing of the steps is 23 5 nm. It should be noted that the step spacing is an average since they will be separated alternately by six a2 dislocations (21 8 nm), and by seven a2 dislocations (25 1 nm). The uncertainty in these predicted spacings will be of the order of 5 as a result of uncertainties in the determination of r and n. This modelled structure matches the morphology of the observed dislocation network very well if the features labelled 1 correspond to pairs of a2 and c a3 dislocations, and the features labelled 2 correspond to the steps consisting of two c a3 dislocations and two a1 dislocations. The calculated spacings of these features are also consistent with those measured experimentally if the cumulative experimental errors are taken into account. If the boundary plane was rotated slightly away from the tilt orientation, then additional dislocations would be expected in the boundary. The features of set 3 may arise for precisely this reason since most of these are observed near to the triple point where the boundary plane curves slightly. Thus it would appear that the boundary structure observed here corresponds to that which would be expected on the basis of the LAGB model. This is consistent with the situation in cubic crystals where LAGB structures are exhibited by near-tilt boundaries for values of up to 13 15 . Indeed one would expect this to be the case unless there is some other low-energy reference structure formed at an orientation close to that exhibited by the boundary. Brandon (1966) proposed that the reference structure associated with a CSL of order n, would only be exhibited by a boundary within 15 n of the CSL orientation. For cubic crystals, there is
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Fig. 3
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(b)
(c)
Schematic diagrams showing the construction of the predicted dislocation network: (a) projection of the b net onto the plane perpendicular to r, where the projections of the four shortest lattice translation vectors onto this plane are shown for reference and the dot indicates the origin; (b) the corresponding L net, where the broad solid and broken lines correspond to the intersection of planar and faceted boundary planes with this L net respectively; (c) the predicted dislocation network for the faceted boundary.
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only one CSL with n 50 which has 15 ; the 41 with r 100 12 68 . Similarly, there is a paucity of CSLs and constrained CSLs for hexagonal crystals where 15 . Thus, if the boundaries observed by Chen and King (1988b) with 9 15 do exhibit HAGB-type structure, then they are probably exceptional rather than being representative of boundaries in this angular range. 5. CONCLUSIONS Transmission electron microscopy has been used to show that a near-tilt boundary with 12 29 in deformed and annealed Ti exhibited a well defined periodic dislocation structure. Geometric modelling of the structure has shown that it matched that which would be expected on the basis of a low-angle grain boundary model but only if the boundary is stepped. This is consistent with the accepted criteria for boundary structures in cubic crystals. ACKNOWLEDGMENTS The authors would like to thank Professor R. C. Pond for helpful discussions, Professor J. F. Knott for provision of laboratory facilities and Dr P. Blenkinsop for providing the materials for this study. Financial support for this work was provided by the former Science and Engineering Research Council and the Human Capital and Mobility Programme of the European Community. REFERENCES
BOLLMAN, W., 1970, Crystal Defects and Crystalline Interfaces (Berlin: Springer); 1982, Crystal L attices, Interfaces, Matrices (Geneva: Bollmann) . BRANDON, D. G., 1966, Acta metall., 14, 1479. BURGERS, J. M., 1939, Proc. K. Ned. Akad. W et., 42, 293. CHEN, F.-R., and KING, A. H., 1988a, Metall. Trans. A, 19, 2359; 1988b, Phil. Mag. A, 57, 431. CLAREBROUGH, L. M., and FORWOOD, C. T., 1980, Phil. Mag. A, 31, 783. FRANK, F. C., 1950, Proceedings of the Symposium on the Plastic Deformation of Crystalline Solids (Pittsburgh, Pennsylvania: Office of Naval Research), p. 150. GRIMMER, H., BONNET, R., LARTIGUE, S., and PRIESTER, L., 1990, Phil. Mag. A, 61, 493. KESTEL, X., 1986, Ultramicroscopy, 19, 205. LAY, S., DELAVIGNETTE, P., and VICENS, J., 1985, Phys. Stat. sol. (a), 90, 53. LAY, S., AYED, P., and NOUET, G., 1992, Acta metall. mater., 40, 2351. MACLAREN, I., 1995, PhD Thesis, The University of Birmingham. MACLAREN, I., and AINDOW, M., 1993a, Scripta metall. mater., 29, 811; 1993b, Electron Microscopy and Analysis 1993, edited by A. J. Craven, Institute of Physics Conference Series No. 138 (Bristol: Institute of Physics), p. 157. VAUDIN, M. D., RUÈHLE, M., and SASS, S. L., 1983, Acta metall., 31, 1109. VISWANATHAN, R., and BAUER, C. L., 1973, Acta metall., 21, 1099.
