Deformation kinking in the corundum structure

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Deformation kinking in the corundum structure C. A. MAY and K. H. G. ASHBEE H. H. Wills Physics Laboratory, University of Bristol. Bristol, England. The nature of kinking in sapphire single crystals has been studied using optical microscopy and X-ray diffraction to determine macroscopicgeometry, scanning electron microscopy to study surface features, and transmission electron microscopy to investigate dislocation arrangements. Kink bands produced by compression along .< 11]0> at temperaturesin excessof 1250°Cc0nstitutea lattice rotation about < 1[00 >. Although the surface topography suggests that kinking occurs by simple shear on basal planes, transmission electron microscopy reveals the occurrence of more complicated deformation mechanisms on basal and non-basal slip systems, and includes the creation of perfect prismatic dislocation loops which are 'vacancy' in character, low angle twist boundaries, and low angle tilt boundaries. By changing the orientation of the compression axis, it was established that kinking is eliminated when the basal plane is inclined by less than 2° to the compression axis. This is in accordance with the kinking model proposed by Frank and Stroh (1952).

INTRODUCTION Kinking is a mode of plastic deformation in crystalline materials first recognised by Mtigge (1898) who observed it in heavily buckled eyanite and other minerals. Orowan (1942) coined the word "kinking" to describe the curious inhomogeneous deformation in cadmium single crystals tested in compression. He claimed that a mechanism other than slip or twinning operates, but the flurry of investigations carried out in the early 1950's showed that this was not so, and that kink bands are produced by a special type of slip. Kink bands are characterised by lamella~ of re-oriented lattice bounded by parallel tilt walls which contain the axis of rotation. The bands are formed predominantly in hexagonal and trigonal crystals, but may be induced in crystals of higher symmetry if all but one slip system is suppressed. Gilman's (1954) work on zinc, surveys the main experimental variables, detailing the phenomenological changes with variation in angle (a) between the compression axis and the active slip plane. The main conclusions are that kinking is favoured for 2½°<~ < 2 0 °, becomes more complex at ~ > 20° and is completely suppressed for ~ <2½°. The lower limit on ~ is in accordance with Frank and Stroh's (1952) theoretical treatment, in which it is proposed that kink-bands develop by the generation of edge dislocations of opposite sign at internal stress concentrations. Under the applied stress, the edge dislocation pairs separate into tilt boundaries of the opposite sense (Figure 1). Further nucleation and extension of kink bands results in the formation of wedge-shaped regions of crystal, each misoriented with respect to its neighbours thereby producing 'stove-pipe' kinking. Hitherto, kink bands have been examined by the conventional methods of Laue X-ray back-reflection, stress birefringence, and etch-pitting. The purpose of the present work is to investigate the internal dislocation structures produced by kinking in sapphire.

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EXPERIMENTAL Sapphire and pink ruby were grown in this department by the electron-beam zone melting technique using 'Purox' alumina rods and sintered alumina-chromia rods as starting materials. The crystals exhibited a high degree of perfection, having a dislocation density of only 104 lines/sq, cm. and containing no veils (May & Shah 1969). Orientations were determined by Laue X-ray back-reflection, and compression specimens 4 mm. high × 2 mm. × 2 mm. were sliced with a diamond saw. Crystallographic details of the specimens are summarised in figure 2. The specimen height/ width ratio of 2/1 ensured elimination of elastic buckling. Before testing, the specimens were etched in boiling phosphoric acid to remove surface damage introduced by the diamond saw. In order to avoid premature failure, it was also necessary to grind and polish the specimen ends. Hard-beam compression tests were carried out at a strain rate of 5.6 x 10-5 sec-1. Temperatures of up to 1800°C in air were obtained using a watercooled radial oxy-coal gas torch. This somewhat unconventional heat source provided a steady hot zone of ½ inch, temperature fluctuations being within the limit of accuracy of a radiation pyrometer. As well as the advantage of ease of assembly, this system permitted direct observation of specimens during testing. O P T I C A L OBSERVATIONS Figure 3 shows five sapphire specimens deformed at increasing temperatures between 1350°C and 1800°C. The near (10i0) side faces suffer negligible buckling, and the symmetrical distortion typical of kinking is confined to the (0001) planes. Note that (a) and (c) in particular manifest two curved regions separated by a block of rotated, but unbent material. As the temperature of testing is raised, there is an increasing departure from the ideal kinking geometry shown in figure 1. For example, in specimen (e), bulging normal to the basal plane has considerably modified the final shape. An attempt was made to reverse the kinking process by high-temperature compression perpendicular to the long axis of specimen (c). This resulted in cleavage at the kink boundaries. Figure 4 shows a Laue back-reflection pattern taken from the kinked region of specimen (c). As expected the Laue spots are streaked in a direction perpendicular to the axis of rotation indicating a continuous variation in basal plane orientation. The large lattice curvature (~,~ 20°) has smeared the spots beyond recognition, but in cases where the angle of kinking is less than 10°, individual spots are still resolved. Annealing kinked specimens at 1950°C for 30 minutes failed to produce evidence of polygonisation. This is in contrast with the case of zinc for which Jillson (1950) reports asterism as evidence of polygonisation after annealing. Further information relating to the nature and distribution of strain within a kink band was obtained by taking Laue back-reflection patterns from faces sectioned perpendicular to the rotated planes. The patterns were identical to those obtained from the end faces, little distortion being evident. Since large distortions are accommodated in the kink boundaries, internal cleavage may be expected to relieve the strain. This is indeed the case; cracks are visible in the boundaries of specimen (d) and internal fissures parallel to basal planes were revealed by sectioning and polishing specimen (a).

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SURFACE T O P O G R A P H Y Several deformed crystals were examined with a scanning electron microscope, both in the etched and unetched conditions. For most specimens no slip lines or other surface features were observed. However, a specimen of ruby (0.02 wt% Cr203) in which the sheared band was very narrow, exhibited the surface features shown in figure 5 (a) (b). Close examination of these micrographs shows that the surface has parted into overlapping near-basal flakes between which crystallographically defined steps can be seen. Stereo-pairs of this area reveal that the 'mountain ridges' recede into the crystal, and suggest that the component lamellm are of basal orientation. It should be pointed out that the general surface markings in figure 5(a) derive from a pre-test etch, so the new surfaces exposed during kinking have not suffered chemical attack. Similar regularly spaced steps were observed on the surface of a specimen which had fractured after considerable kink deformation. However, these steps are in no way similar to river lines or hackle markings produced during fracture of brittle materials; a possible mechanism for their formation is proposed in the discussion. ELECTRON MICROSCOPY Experimental Procedure Foils were prepared by cleavage and examined in a Siemens Elmiskop 1A electron microscope which incorporates a double tilting stage. In order to convey the maximum information from extensive thin areas without loss of resolution, it has been necessary to present some of the micrographs in mosaic form. A note on the corundum structure Sapphire belongs to the rhombohedral-hexagonal crystal system, and all indices herein are referred to the hexagonal structural unit cell which has the dimensions a = 4.758A and C=12.99A. Unless otherwise stated, crystallographic directions will be referred to by plane normals. General Observations Figure 6 shows an extensive thin area. The dislocation substructure is fairly representative of crystals deformed in the lower temperature range, displaying evidence of large scale dislocation movement. This is deduced from the presence of cusped dislocations, e.g. A, the pile-up at B and the imperfectly formed hexagonal network at C. Furthermore, the average dislocation density based on the number of dislocations threading a square centimetre is 1.5 × 109, several orders of magnitude greater than that in the 'as-grown' crystal. Undeformed sapphire contains predominantly basal dislocations with Burgers vector ~(1120)arranged in symmetrical twist boundaries separated by regions of highly perfect crystal (May and Ashbee, 1968). Considering Figure 6 in detail, the pile-up at B consists of ] [11~0] dislocations gliding on the basal plane. From the projected band width, the foil thickness is estimated to be ,~2, 200A. It is deduced that the foil thickness is constant, since the transmitted intensity is even and since ~[11~0] dislocations have the same projected lengths throughout the area shown. Hence it is evident that the distorted network at c does not lie on the basal plane; the probable plane is (I2i2).

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The double images exhibited by some dislocations are attributed to anisotropic effects, and not to partial dislocation pairs. They should not be confused with the numerous tiny loops which have a line of no contrast perpendicular to g.

Non-basal Dislocations Figure 7 shows a foil in which two groups of dislocations are aligned in walls parallel to [0001 ] and a pair of dislocations labelled A which lie more or less parallel to this same direction. The foil normal was accurately determined from Kikuchi lines, and is in fact 4 ° from [1~10], i.e. the directions marked on the micrographs are only approximately correct. The dislocation walls could be tilt boundaries composed of basal edge dislocations, or pile-ups ofa~10T1)dislocations gliding on prism planes. ~[1~10] screw dislocations would be out of contrast for g 30~0. a (1010)dislocations have been reported by Klassen Neklyudova (1942) as being present during high temperature deformation, but hitherto have not been verified by electron microscopy. An a(10T0) Burgers vector interpretation is favoured since the vertical parallel lines appear to be slip traces left in the wake of prismatic dislocations which have glided out of the foil. The prismatic dislocations remaining in the foil are pinned by bubbles. The dislocations marked A in Figure 7 are probably a [ 1010] edge dislocations. This is deduced from their geometrical configuration, bearing in mind that the m a x i m u m possible thickness of the foil is 3000A.

Dislocation Loops A recurrent feature of all the foils examined is the large density of dislocation loops, most of which are between 200 and 500A diameter but some, marked A in figure 8, approach 5000A diameter. By observing the change in apparent shape of the loops as the foil is tilted in the microscope, it is possible to ascertain the planes on which the loops lie. This procedure was carried out for the area shown in figure 8(a), the tilt being 10° about [3T~8]. To simplify the analysis the tilt may be resolved into two rotation components, one of 4 ° about [1120] and one of 9 ° about [0001]. Thus the basal planes are inclined at 41 ° to the foil in 8(a) and 37 ° to the foil in 8(b). The large loops A are essentially unaffected by the C--axis rotation, but are perceptibly wider due to the tilt. Such behaviour is consistent with their lying on basal planes. Whereas round loops lying on basal planes present the same projected area after Caxis rotation, those lying on inclined planes will suffer an apparent dilation or contraction. This effect is demonstrated by loops a and b in figure 8(a) whose narrow diameters have undergone expansion and shrinkage respectively. They can therefore be assigned to planes inclined in opposite directions to the foil. The loops marked C have opposite segments resolved in figure 8(a) but are viewed end-on in figure 8(b). Hence it is concluded that these loops lie on (10T2) planes. All the loops except those labelled A lie on one or other of the three {10T2} planes. Since {10T2} are the most densely packed planes and since the loops are minute in size it is concluded that they are prismatic in nature. Consequently a systematic contrast investigation using the Groves and Kelly (1961) method was carried out to determine whether the loops are of the vacancy or interstitial type. The technique involves tilting the loop through an extinction contour and observing the change in image position in relation to the real position in the lattice.

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Figure 9 shows a sequence of micrographs with corresponding diffraction patterns, illustrating the change in loop shape with variation of (g b) $, where s is the deviation from the exact Bragg condition. In figure 9(a), the foil normal is [~315], only 15° from a possible {10i2} loop normal; hence the loop exhibits an almost symmetrical image. A large tilt corresponding to a clockwise 30° rotation about C followed by a clockwise 33° tilt about [3i~0] reduces the loop dimensions by 10% across the long axis and by 40% across the short axis (figure 9(b) ). (Tilts of this magnitude are not available with the Siemens stage; in this instance they were produced by repositioning the foil). Hence it is evident that the loop lies on (i102). In figure 9(b) the loop is imaged by the ~124 reflection with (g. b) s = 0. Rocking the foil to make (g. b) s positive (Kikuchi line between central beam and corresponding reflection) causes the image to move inside its true position (figure 9c). From the large tilt experiment, the top edge of the loop is evidently uppermost in the foil. Therefore the sense of the local bending of the reflecting planes near the loop is that characteristic of a vacancy disc. In figure 9, a string of small prismatic loops is seen lying parallel to the foil. This configuration suggests that the loops have been formed by the pinching of a helical dislocation which has subsequently left the field of view. The dot inside the large loop is also a tiny prismatic loop, presumably formed by further condensation of vacancies.

Beam heating The effect of beam heating on loops is illustrated in Figure 10. All the loops have grown considerably, presumably because further vacancies have been added. The loop viewed end-on at X is evidently a (T012) prismatic dislocation. Other dislocations are also affected; the straight dislocation above A, for example, has slipped out of the foil and the wavy dislocation below it has bowed upwards.

High temperaturekinking Foils obtained from specimen (e), Fig. 3, were much cleaner from the point of view of prismatic loops and dislocation debris. The substructure was charaeterised by meandering basal dislocations connected at infrequent nodes. INITIATION OF NON-BASAL SLIP Reducing the critical resolved shear stress on the basal plane to zero effectively suppresses the kinking mode of deformation according to Gilman's (1954) work on zinc. To confirm this observation in the case of sapphire, a specimen was prepared with ~ = 0 (refer to Fig. 2). The basal faces were polished to facilitate subsequent optical examination, and the specimen tested under conditions likely to promote kinking. The specimen sustained a load far in excess of the kinking flow stress, and at the first signs of plastic deformation, the test was halted. There were no signs of buckiing or bulging but close inspection of the surface revealed localised slip bands intersecting the polished faces at 50° to the compression axis, as measured on the scanning electron micrographs and shown in Fig. 11. Deduction of the operating slip plane is complicated by the fact that [3 in Fig. 2 is 17°, thus the angle described by the slip steps on the crystal face is not the same as the angle ofintersection

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with the basal plane, e, the observed angle between the slip planes and horizontal edge is related to 0, the angle subtended on the basal plane by the expression tan 0 =

tan

tan ~. tan 8

COS

where 8 is the angle between slip plane and C-axis. Using measured values of e (40°), ~ (17 °) and y the angle between [1120] and the compression axis (41°), trial values of 8 and ¢ for known non-basal slip systems were used. The equality is satisfied only for 8 = 0 and e = 4 1 ° corresponding to slip on the prism planes, i.e. ~(1T01).{II~0} or a (IT00).{ll~0}. These incidentally are the most favourable systems from Schmidt factor considerations.

DISCUSSION The unsuccessful attempts to reverse the kinking process or to modify it by annealing indicate that the kink boundaries in sapphire can be rather immobile. Consequently in a constant strain rate test, crack propagation and non-kinking plastic deformation can be expected. The surface feature revealed in Figure 5 together with the optically observed fissures in sectioned specimens are evidence of strain relief by fracture, and the transmission electrcn microscopy indicates the following four deformation mechanisms: (a) Slip on non-basal systems, (b) Dislocation intersections to form dislocation doublets (cusps), (c) Agglomeration into layers of aluminium and oxygen vacancies in stoichiometric proportions. (d) Recovery to form dislocation networks. T h e deviation from ideal kinking geometry is a consequence of these deformation phenomena which, as expected, occur more easily and give enhanced bulging at higher temperatures. A further contribution to non-kinking plasticity is dislocation climb which could maintain a large fraction of the imposed strain rate (Groves and Kelly 1969). There is considerable macroscopic evidence of slip. The steps revealed between the basal flakes in Figure 5(b) are no doubt caused by the release of basal dislocations following fracture within the kinked region. The slip steps in Figure 11, on the other hand, are due to slip on prismatic planes which occurs when kinking due to basal slip is inhibited. It is significant that the near (1010) faces remain perfectly flat during deformation, although 0t and y (Figure 2) are not zero. This suggests that the geometrical constraint of the square cross-section restricts shear normal to the near (lOT0) faces, inferring the operation of a second system of basal dislocations. In order to avoid elastic strains in a kinkboundary, it is necessary for the boundary to rotate as the dislocation density increases, so that it remains symmetrical with respect to the slip planes. If a boundary becomes immobile, as appears to be the case, large tangential strains will result and these may be relieved by generationof dislocations on

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prismatic planes. It requires a kink boundary asymmetry of only 1½° to create a stress of 10 Kb, which is the stress at which slip on prismatic planes was seen to occur when kinking is eliminated. Finally, it should be noted that the stress required for kinking to proceed (,~1.3 Kb.) is considerably lower than that predicted by the F r a n b S t r o h (1952) model, and lower even than the critical resolved shear stress for normal basal slip. ACKNOWLEDGEMENTS We wish to thank Dr. J. S. Shah for growing the crystals and Mr. R. B. Sinha for operating the scanning electron microscope. REFERENCES FRANK, F. C. & STROH, A. N. 1952. On the theory of kinking, Proc.Phys. Soc., 65: 811-821. GILMAN, J. J. 1954. Mechanism of ortho kink-band formation in compressed zinc monocrystals. Trans. A.LM.E., 200: 621-629. GROVES, G. W. & KELLY, A. 1961. Interstitial dislocation loops in magnesium oxide. Phil. Mag. 6: 1527-1529. GROVES, G. W. & KELLY, A. 1969. Change of shape due to dislocation climb. Phil. Mag., 19: 977-986. JILLSON, D. C. 1950. An experimental survey of deformation and annealing processes in zinc. Trans. A.LM.E., 188: 1009'1018. KLASSEN-NEKLYUDOVA, M. V. 1942. Plastic deformation of crystals of synthetic corundum..7. Tech. Phys. (U.S.S.R.)., 12: 535-551. MAY, C. A. & ASHBEE, K. H. G. 1968. Twist boundaries in alumina-chromia alloys. Phil. Mag. 18: 61-71. MAY, C. A. & SHAH, J. S. 1969. Dislocation reactions and cavitation studies in melt-grown sapphire. 3. Mater. Sci., 4: 179-187. MIIGGE, O. 1898 On slip and related phenomena in crystals. Neues3ahr.f Miner. 7: 71-158. OROWAN, E. 1942. A type of plastic deformation, new in metals. Nature, 149: 643-644.

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Vefformuugs Kincken in der Korund Stmktur Die Natur des Knicken in EinzelkristaUen von Saphir wurde mittels optischer Spektroskopie und R6ntgen Diffraktion studiert um die makroskopische Geometrie zu bestimmen, abtastende Elektron Mikroskopie um Oberfl/ichen Merkmale zu studieren und Transmission Elektron Mikroskopie um Versetzungs Anordnungen zu untersuchen. Knick B~inder durch Zusammendrtickung 1/ings (1120) bei Temperaturen iiberhalb 1250°C steUt eine Gitter Drehung um (1T00) dar. Obwohl die Oberfl/ichen Topographie hinweist, dass Knicken durch einfache Scherkraft an Grundebenen geschiht, die Transmission Elektrom Mikroskopie deutet auf das Vorkommen von komplizierteren Verformungs Mechanismi an basalen und nicht-basalen Gleit Systemen und das schliesst die Erzeugung von vollkommenen prismatischen Versetzungs Schleifen, welche 'Leerstellen' in Wesenart sind, Flachwinkel Verdrehungsgrenzen and Flachwinkel Neigungsgrenzen. Es wurde festgesetzt, dass durch eine Ver~inderung der Richtung der Znsammendriickungsachse das Knicken beseitigt wird, wenn die Grundebene sich weniger als 2° zur Zusammendrfikckungsachse neigt. Das ist in Ubereinstimmung mit dem Knick Modell, das von Frank und Stroh (1952) vorgeschlagen wurde.

La d~formation par rupture dam la structure du corim~on On a ~tudi~ la nature des ruptures dans des cristaux simples de saphir, en utilisant la microscopie optique et la diffraction de rayons-X pour d~terminer la g~om6trie macroscopique, la microscopie ~lectronique ~t balayage pour 6tudier les caract6ristiques de la surface, et la microscopie 61ectronique ~ transmission pour examiner la disposition des dislocations. Les zones de rupture produites par compression le long de <11~0> des temperatures sup~rieures ~t 1250°C constituent un r~eau mol~culaire autour de . Bien que la topographie de la surface indique que la rupture S'Ol~re en simple glissement sur des plans basiques, la microscopie 61ectronique h transmission montre l'existence de m~canismes de d6formation plus compliqu~s sur des syst~mes basiques et non-basiques de glissement, et comprend la formation de boucles parfaites de dislocation prismatiques qui ont un 'trou de r6seau', des limites de torsion h angle faible, et des limites d'inclinaison ~t angle faible. On a 6tabli qu'en changeant l'orientation de L'axe de compression on peut 61iminer la rupture quand on incline le plan basique h moins de 2° par rapport de l'axe de compression. Ceci s'accorde avec le mod61e de rupture propo3~ par Frank & Stroh (1952).

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Figure 1. Idealised kink band formation showing change in shape produced by symmetrical tilt walls. 0~is the angle between the compression axis and the basal plane, and X is the angle of kinking.

Figure 2. Compression specimen. The orientation of the basal planes with respect to the external surfaces is defined by a-----12°, 8 = 9 ° and T = 4 °. a denotes the direction [1120].

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Figure 3. Optical micrographs of sapphire single crystals compressed at (a) 1360°C (b) 1535°C (c) 1420°C (d) 1580°C (e) 1800°C. Figure 4. Laue back reflection X-ray pattern taken from the kinked region of specimen 3 (c). X-ray beam parallel to [0001].

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PLATE III

Figure 5. (a) Scanning electron micrograph of a kinked ruby crystal. (b) High magnification micrograph of the area marked by an arrow in (a).

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PLATE IV

Figure 6. Dislocation structure of sapphire deformed by kinking at 1285°C to 10% compressive strain.

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PLATE V

Figure 7.

Parallel non-basal glide bands. T h e dislocations at B are pinned at an internal cavity. T h e parallel vertical lines are attributed to {1130} slip traces.

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Plate V

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Plate V

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Plate V

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PLATE VII

Figure 8b.

Same area as 8a rotated about [3T]8] axis,

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