- Email: [email protected]
Dislocations and twinning activated by the abrasion of Al2O3
Acta mater. 48 (2000) 1883±1895 www.elsevier.com/locate/actamat
DISLOCATIONS AND TWINNING ACTIVATED BY THE ABRASION OF Al2O3 B. J. INKSON Department of Materials, Oxford University, Parks Road, Oxford OX1 3PH, UK (Received 13 September 1999; accepted 8 December 1999) AbstractÐDefects generated at the surface of single crystal Al2O3 during abrasion on diamond have been analysed by high spatial resolution cross-sectional electron microscopy. Plastic deformation predominantly occurs by basal twinning and pyramidal slip 1/3h1120i{1101}. Basal twins have platelet morphologies, with widths d0001=2n1/6[0001] and vd0001v<<100 nm, aspect ratios d1010/d0001 or d1120/d0001 > 10, and ABCBA stacking of (0006)Al planes across twin interfaces. Basal twins and dislocations occur clustered around steps in macroscopic (0001) abraded surfaces, whereas 2{1120} and 2{1010} prismatic plane abrasion results in a more uniform 1±5% deformation twin cover with basal twin penetration>>that for basal abrasion. Extensive microcracking along {1102} rhombohedral and (0001) twin habit planes occurs, but no widespread rhombohedral twinning, prism glide or non-basal dislocation Burgers vectors were observed. Implications for surface preparation of Al2O3 are discussed. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Abrasion (mechanical properties+wear); Dislocations; Twinning; Al2O3; Surfaces & interfaces
1. INTRODUCTION
Al2O3 is an important engineering structural material, with high hardness and wear resistance making it suitable for uses such as grinding abrasives, bearings and cutting tools, as well as highly polished substrates for functional coatings. The plasticity and fracture behaviour of Al2O3 in the 0± 3008C temperature range are important controlling factors in its performance as an abrasive, as hard impact-resistant coatings and as stable substrates [1±9]. The wear and polishing of alumina builds up residual damage at the surface, which alters its surface properties. Studies of damage accumulation in Al2O3 after abrasion and impact have shown that the density of defects in the top few microns is typically so high that it is not easy to separate out the dierent deformation modes within the severe deformation zone, even by TEM [1±7]. As the size of Al2O3 components decreases, and the demand for defect-free sapphire substrates increases, it is becoming increasingly important to have a better understanding of the structure of the severe deformation zone and mechanics of Al2O3 abrasion right down to the atomic level. In this study we have characterised the severe plastic deformation zone resulting from room temperature abrasion using high spatial resolution electron microscopy. Because alumina is highly
anisotropic [1±3], the surface deformation (dislocations and twinning) have been quanti®ed as a function of the crystallography of the abraded surface by using oriented single crystals. 2. EXPERIMENTAL PROCEDURE
Commercially available bulk single crystals of Al2O3 were used (Frank & Schulte GmbH), which contained no growth twins and negligible dislocation density. Additional ruby samples containing isovalent solutes 0:320:1at:%Cr and 0:420:1at:%Fe were also examined. Abraded surfaces were prepared by grinding 2{1120}, 2{1010} and 2(0001) surfaces on 30 mm diamond using a Buehler Minimet 1000 grinder at room temperature with 5 N normal load, 10 rpm (equivalent to 0.03 m/s sliding speed) and minimal water lubrication. Throughout the text ``room temperature abrasion'' is taken to refer to the temperature of the bulk Al2O3 substrate. Localised heating of the Al2O3 wear surface during the abrasive process could not be measured in our experimental set-up. At least 200 mm of material was removed from each surface in order to ensure that there were no residual defects from initial cutting with a 30-mm grit wire saw. A single diamond grit size was used to ensure that all deformation observed was attributable to the single abrasion step, and to ensure a
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 9 9 ) 0 0 4 6 8 - 1
1884
INKSON: ABRASION OF Al2O3
relatively high deformation density for subsequent analysis. Al2O3 debris generated during the abrasion process was collected from the rim of the grinding disk for examination in the microscope. Abraded Al2O3 surfaces were glued together in pairs, dimpled perpendicular to the abraded surface using 1±5 mm diamond paste to a thickness of 30 mm, and thinned to electron transparency (<<1 mm) by ion-milling. The abraded surfaces could be accurately located in the cross-sectional samples at the glue±Al2O3 interfaces. Comparison of the structure of the thinned Al2O3 in the ``bulk'' material away from the abraded zone con®rmed that the defects examined in this paper originated from the grinding on 30 mm diamond, and not from the subsequent TEM-foil specimen preparation steps or as growth defects. High-resolution characterisation (HREM) of the abrasion deformation zones and debris was carried out in a JEOL 4000EX microscope which, operated at 400 kV, has a point resolution of 0.16 nm. Chemical analyses were carried out on an HB501 STEM at 100 kV, and surface topography imaged in a JSM 6300 SEM at 15 kV. 3. ROOM TEMPERATURE ABRASION OF Al2O3
The abrasion of Al2O3 single crystals on randomly rotating 30 mm diamond disks results in highly fractured surface topographies, as shown in Fig. 1. No marked directionality in the surface topography for any of the ground surfaces was visible in plan view, with the few visible wear tracks from individual diamond±substrate impact events being randomly oriented with respect to the under-
Fig. 1. Topography of a f1010gAl2 O3 prismatic surface abraded on 30 mm diamond grit.
lying crystallography. Any surface steps and ledges present due to twinning and dislocation initiation could not be resolved by our SEM. In cross-section the existence of a plastic deformation zone at the abraded Al2O3 surfaces becomes apparent, as ®rst shown by Hockey [1, 2]. Figure 2 shows a cross-sectional TEM image of an abraded {1120} surface, where dislocations and twinning initiated at the surface during impact with diamond grains are clearly visible. 3.1. Deformation of prismatic surfaces Al2O3 single crystals were abraded on 2{1010} and 2{1120} prismatic surfaces perpendicular to the basal plane. The dominating deformation modes were observed to be basal twinning on (0001) perpendicular to the abraded surface and dislocations gliding on non-basal slip planes (Fig. 2). Two deformation zones may be identi®ed at the prismatic surfaces, namely (i) the top surface 5 mm consisting of a very high density of dislocations, basal twins and some microcracking, and (ii) a regime of deep penetration of basal twins below the mixed zone. These basal twins, visible edge-on and perpendicular to the abraded surface in Fig. 2, are extensively characterised in Section 5. In cross-section, the density and penetration of the plastic deformation present at the abraded surface is not totally uniform, since at any instant dierent places on the surface will be in dierent stages of the abrasive cycle. The abrasive cycle consists of the build-up of surface defects by indentation and scratch events, initiation of cracking, crack growth and linking, and ®nally chipping of material leaving some remnant surface damage. In the prismatic samples, microcracking was observed to
Fig. 2. Abraded {1120} Al2O3 prismatic surface viewed in cross-section along h1100i. Note the deep penetration of very high aspect ratio deformation basal twins on (0001) perpendicular to the surface, and non-basal dislocation slip planes.
INKSON: ABRASION OF Al2O3
occur primarily on the {1102} rhombohedral planes, of which there are three families at 57.68 from the basal planes. The cracks were observed to both cut across and delineate basal twins, and are the precursor to loss of material by chipping events, leading to abrasive wear. 3.2. Deformation of (0001) basal surfaces Figures 3 and 4 show cross-sectional images of abraded (0001) surfaces. As with the prismatic surfaces, the main deformation modes observed were dislocation activity on non-basal slip planes and basal twinning on (0001). The basal twins grow as high aspect ratio platelets with a (0001) habit plane parallel to the macroscopic (0001) abrasion surface. The twins occur clustered at non-basal steps in the (0001) surface (Figs 3 and 4), and only occur to a depth of the order of the surface roughness. The depthwise penetration of basal twinning in abraded basal surfaces is thus only a fraction of that observed in prismatic abrasion using the same diamond abrasion conditions. The fact that some early investigations observed zero or negligible basal twinning after (0001) abrasion [1±3] is probably a
1885
function of the resolution of the investigative technique required in the top micron to resolve the twins. The penetration of dislocations on non-basal slip planes resulting from basal plane abrasion is comparable with that of prismatic abrasion, and is slightly greater than that of the basal twins because of the latter's crystallographic dependence of penetration (Figs 3 and 4). Microcracks were prevalent near regions of high twinning and dislocation density, both cutting across pre-existing twins in the damaged surface [Figs 3 and 4(a)], and delineating new twins formed subsequent to the cracking event [Fig. 4(b)]. Cracking occurred preferentially along (0001) twin interfaces [Fig. 4(a)], and as for prismatic surfaces along {1102} planes [Fig. 4(b)]. The {1102} rhombohedral cracks frequently exhibited atomically sharp facets many tens of nanometres in length. The intersections of the {1102} rhombohedral planes with the (1120) image plane used in Figs 3 and 4 are summarised in a stereogram (Fig. 5). Viewed down h1120i, {1102} planes are edge-on, with {0112} and {1012} planes intersecting the {1120} image plane along h2201i at 38.28 from (0001).
Fig. 3. Very heavily deformed region close to a macroscopic step in an abraded (0001) Al2O3 surface imaged down h1120i, showing basal twins, non-basal dislocation glide planes, and extensive cracking on {1102} and (0001).
1886
INKSON: ABRASION OF Al2O3
Fig. 4. Cracking at abraded (0001) Al2O3 surfaces imaged down h1120i. (a) Preferential crack paths along existing (0001) basal twin boundaries. (b) Atomically sharp f1102g crack delineating younger basal twins (upper right), with no evidence for an associated rhombohedral twin. 4. DISLOCATION ACTIVATION DURING ROOM TEMPERATURE ABRASION
After abrasion, within the severe deformation zone (top few microns) the dislocation density was generally too high for weak-beam (WB) analysis. In
Fig. 5. Stereogram summarising the intersections of rhombohedral {1102} and pyramidal {1101} planes with a (1120) projection plane in Al2O3.
regions of lower dislocation density it was clear, however, that almost all the dislocation lines did not lie in the basal plane for either the basal or pyramidal abrasion (Figs 2±4). Non-basal glide has been identi®ed in previous studies of room temperature abrasion [1, 2, 4, 6]. Dislocations viewed at an angle to their glide plane were bowed and kinked. Dislocations imaged parallel to their slip plane down h1120i zone axes had h1102i dislocation line projections at 728 from the basal planes, indicating pyramidal slip on {1101} consistent with the 1/ 3h1120i{1101} or 1/3h1011i{1101} slip systems (Fig. 6). The dislocations were out of contrast for WB imaging with g=0006 con®rming the slip system 1/3h1120i{1101}. Dislocations gliding on prism planes, (e.g. h1010i{1210}) or dislocation dipoles, both dominating features after deformation at high temperature [10, 11], were not identi®ed in these samples. More than 95% of the defects parallel to (0001) could be identi®ed at high resolution to be ultra®ne basal twins. Although it was dicult to distinguish basal twin nuclei <1 nm thick from 1=3h1120i 0001 or h1010i(0001) slip systems, a very low density of dislocations segments on (0001) appeared to exist. Imaging dislocations within the severe deformation zone at high resolution con®rmed the predominance of 1/3h1120i Burgers vectors on nonbasal slip planes. Figure 7(a) shows an HREM image of a dislocation obtained by imaging down a h1100i zone axis. The resolved Burgers vector component is bres=1/3h1120i, so the total Burgers vector is consistent with b=1/3h1120i, 2/3h1210i or 2/3h2110i. Because 2/3h1210i type dislocations are unlikely due to the very large Burgers vector, the dislocation is identi®ed as b 1=3h1120i: The contrast in the image is extended out of the (0001) plane indicating a {110n } slip plane. Although there is a possibility that the 1/3h1120i dislocation originally had a (0001) slip plane and may have extended out of (0001) by diusive self-climb (which has been observed for h1010i slip at higher temperatures [10]), (0001) slip planes are inconsistent with the analysis of dislocations in thicker parts of the TEM foils. Figures 7(b) and (c) show typical HREM images obtained from dislocations within 50 nm of the TEM foil edges imaged down h1210i zone axes. The resolved Burgers vector component are bres 1=2h1010i, so the total Burgers vector are b=1/2h1010i+nh1210i. Possible identi®cations are thus (i) b=1/3h1120i, (ii) b=1/3h2110i, (iii) b=h1100i or (iv) b=h0110i. The latter two h0110i Burgers vectors have a signi®cantly higher line energy than 1/3h1120i dislocations. In addition, no dislocations with bres=h1010i components imaged down h1210i by HREM were observed, which correspond uniquely to h1010i dislocations. It is most likely, therefore, that Figs 7(b) and (c) correspond to 1=3h1120i dislocations as in Fig. 7(a). In the
INKSON: ABRASION OF Al2O3
approx. 10 nm thick HREM foils it was not possible to determine conclusively the line directions of these dislocations, which may indeed be altered by thin foil relaxations, since even steeply inclined dislocations have short projected lengths in very thin foils. Dislocations imaged in the thicker regions of the foil by HREM had increasing projected lengths not parallel to (0001) consistent with non-basal slip planes. Of the more than 20 dislocations analysed by HREM, only one was identi®ed as having a nonbasal Burgers vector component (Fig. 8). The resolved Burgers vector component was bres 1=6h1102i consistent with a b=1/3h1011i or 1/3h0111i dislocation. Activation of 1/3h1011i {0111} type slip systems was not identi®ed by DF imaging with g=0006 in thicker parts of the foil. The dislocations observed in the abraded surfaces are thus predominantly 1/3h1120i{1101}, with minor contributions from 1/3h1120i/h1010i(0001) and 1=3h1011if0111g: Slip of the dislocations out of the (0001) basal planes means that during glide they must interact frequently with the extensive number of basal twins. 5. TWINNING DURING ABRASION
5.1. Basal twinning morphology and distribution At both abraded (0001) and prismatic single crystal surfaces extensive basal twinning occurred,
1887
enabling for the ®rst time a survey of a large number of deformation twins by HREM to be carried out. The deformation basal twins form as very high aspect ratio platelets, with major (0001) habit planes and very narrow widths d0001 along [0001] (Figs 2±4). The twins exhibit the crystallographic relationship (0001)bulk//(0001)twin and h1120ibulk ==h1120itwin [12, 13]. Under our abrasion conditions, the observed twin widths d0001 at the ground surfaces directly adjacent to the glue were less than 100 nm, with widths 2±10 nm predominating (Fig. 9). Perpendicular to the ground prismatic surfaces the twin penetration depths d1010 or d1120 were up to 10 mm, resulting in the extremely large aspect ratios d1010/d0001 or d1120/d0001 of over 100 (Fig. 2). The aspect ratios of the twins parallel to the (0001) ground surfaces were also typically >20 (Figs 3 and 4), however these twins were more frequently terminated by cracks penetrating the (0001) surface. For any given twin, the twin width d0001 decreased with distance from the Al2O3 surface, indicating that the partial dislocations forming the twin originate at the surface. Along the [0001] direction of the ground prismatic surfaces, perpendicular to the habit planes of the deformation twin platelets, the twins occurred with a density of 1±2/mm (Fig. 2). Most twins were solitary, although occasional clusters of Two to ®ve twins were observed. Assuming that the TEM cross-sections examined were representative
Fig. 6. 1/3h1120i{1101} dislocations with h1102i projected line direction imaged down h1120i.
INKSON: ABRASION OF Al2O3
1888
Fig. 7. HREM images of dislocations within the severe deformation zone. (a) b=1/3h1120i{110n } dislocation imaged down a h1100i zone axis with resolved Burgers vector component bres=1/3h1120i. (b, c) 1/3h1120i or h1100i dislocations imaged down a h1210i zone axis with bres=1/2h1010i.
sampling in the [0001] direction for ground prismatic surfaces, then the proportion of ground surface area which had twinned during deformation lay between 1 and 5% in this study. The density of twins is expected to vary locally, depending on the extent of the abrasive cycle at any particular location. Twinning at the basal surfaces was noticeably more clustered at steps in the macroscopic (0001) surface (Fig. 3). For all samples the density of twins observed decreased in sample areas not in direct contact with residual glue, since very short twins, penetrating less than 200 nm into the surface, were removed by ion-milling.
5.2. Basal twin interfaces Figure 10 shows HREM images of basal twins generated at abraded {1010} surfaces. The imaging zone axes are h1120i and the bright maxima correspond to ``hole columns'' in the Al basal planes. Distinct O and Al columns cannot currently be resolved by HREM, making it very dicult to investigate subtle changes resulting from relaxations in Al or O positions. Simulations here and elsewhere show that these twin interfaces are consistent
with an ABCBA type stacking of Al basal planes [14]. Subtle variations proposed in the Al positions at the twin interfaces due to relaxations around the hole positions, such as examples referred to by Geipel et al. as ``type II'' and ``type II±glide'' [14], could not be distinguished experimentally here. No HREM observations made from more than 200 deformation twins in the abraded samples (either for pure Al2O3 or ruby samples containing 0:320:1at:%Cr and 0.420.1at.%Fe) were consistent with ``type I'' basal twins which have a mirror plane of symmetry lying in an O basal plane, and thus a ABCCBA stacking of Al basal planes [15]. This suggests that the ABCBA type stacking has a lower energy as predicted by the static-lattice calculations of Kenway [16].
5.3. Formation mechanism of basal twins Two shear mechanisms have been proposed for the formation of basal twins in alumina, both of which produce twins with an ABCBA type stacking of Al basal planes across the twin interface and are consistent with Veit's measurements of twinning elements [12, 17, 18]. Figure 11 illus-
INKSON: ABRASION OF Al2O3
1889
Fig. 7 (continued)
trates these two models. The glide of 1/3h1010i partial dislocations on (0003) glide planes lying through the centre of the buckled Al planes enables basal twin formation to occur without charge transfer [17] [Fig. 11(a)]. This mechanism shears all Al±Al bonds in the slip plane, and half of the adjacent Al±O bonds. Because of the movement of holes, a single partial automatically generates a twin two (0006) planes thick [17]. The net result, therefore, of the passage of n partials must be a basal twin with width 2n 1=60001: The second twinning model proposes dislocation glide on Al±O glide planes instead of Al±Al glide planes [13, 18, 19]. There are two Al±O glide planes for every Al±Al glide plane. Basal twins can be formed by 1/3h1010i partial dislocations dissociated
into two 1/3h0110i type partials dislocations moving on (0006) Al±O glide planes according to equation (1) [18]: 1=3h1010i 4 1=3h0110i 1=3h1100i:
1
If the two 1/3h0110i type partial dislocations are widely separated [r.h.s. of equation (1)] this mechanism of glide can form twins with widths n 1=60001: It is dicult, however, to see how decoupled 1/3h0110i partials satisfying equation (1) could be independently generated and subsequently co-ordinate their motion [11]. Furthermore, two widely separated partials [r.h.s. equation (1)] have twice the line energy of one single partial [l.h.s. equation (1)]. Recent HREM and weak-beam observations support the fact that only net 1/3h1010i
1890
INKSON: ABRASION OF Al2O3
partial dislocations every (0003) are observed, never single uncoupled 1/3h0110i dislocations [20]. The formation of a single delocalised 1/3h1010i partial [l.h.s. of equation (1)] instead of two 1/ 3h0110i type partial dislocations [r.h.s. of (1)] is energetically favourable. Core structures of 1/ 3h1010i partial dislocations delocalised on to two closely spaced (0006) Al±O glide planes are shown in Figs 11(b) and (c), which can be compared with the compact core gliding on Al±Al glide planes [Fig. 11(a)]. We cannot currently resolve the dierences in the Fig. 11 core structures by HREM. Furthermore, all these 1/3h1010i core structures have the same long range strain ®elds, and thus cannot be distinguished by WB-TEM. All of the 1=3h1010i core structures, gliding on Al±Al or Al± O slip planes, generate basal twins with widths 2n 1=60001, consistent with deformation twins observed here where the width could be measured [for example in Fig. 10(a)]. It has thus not been possible to distinguish between these two deformation twinning models, and it remains for atomistic simulations of the dislocation cores to help con®rm which slip plane is the more likely. It should be noted that we additionally observed one twin apparently of width 211/6[0001], which is inconsistent with pure 1/3h1010i slip [Fig. 10(b)]. Statistically insigni®cant, this observation may be aected by MoireÂ-type ¯uctuations in the contrast along the (0001) interfaces of the order <2 nm, as
also observed by other authors [14] (Fig. 12). These patches of Moire fringes are frequent in occurrence and irregular in contrast, whose existence has been attributed to the cutting of partial dislocation loops spawned by spiral dislocation sources [14]. Twinning dislocations threading through the thin TEM foil at an angle may give rise to overlap of the twin variants and thus Moire fringes. In our samples, the twins had a very high aspect ratio and wedge morphology, resulting from widely separated twinning partials ``popped-in'' from the surface. The partial dislocations occurred at too low a frequency to attribute the sporadic and often localised MoireÂ-type ¯uctuations solely to threading dislocations (Fig. 12). Localised thin foil relaxation eects seem to contribute to the fringes, since the original twin boundaries macroscopically are almost parallel to (0001). The structure of twin boundaries that we observe may also be complicated by their interaction with the high density of dislocations gliding on pyramidal slip planes. Interaction must occur if twinning partials collide with bulk dislocations, if bulk dislocations gliding on non-basal slip planes try to cut across twins, and if dislocations cross-slip into and glide along the (0001) twin interfaces.
Fig. 8. HREM image of a 1/3h1011i{0111} dislocation with resolved Burgers vector component bres=1/6h1102i imaged down h1120i.
Fig. 9. Distribution of basal twin widths measured by HREM along [0001] for two {1010} ground surfaces, surface 1(56 twins) and surface 2 (47 twins).
5.4. Rhombohedral twinning In addition to basal twinning, rhombohedral twinning is a frequently observed deformation mode in Al2O3 [21, 22]. Three families of rhombohedral planes, (1102), (1012) and (0112), lie at 57.68 from the basal plane (Fig. 5), and it is known that the intersection of twins from these three families play a key role in initiating cracks inside Al2O3 bulk samples leading to failure [22]. The abraded surfaces were systematically examined for rhombohedral twins. Viewed down h1120i one rhombohedral plane is edge on, with the other
INKSON: ABRASION OF Al2O3
two intersecting the {1120} plane along h2201i (Fig. 5). No high density of clearly de®ned rhombohedral twins was observed, but occasional defects parallel to {1102} within the severe deformation zone did exist (Fig. 13). No diraction pattern consistent with a rhombohedral twin could be obtained from these defects, and at high resolution the contrast was extremely complex and non-repeating, unlike the clearly de®ned rhomobohedral twins in Al2O3 and Fe2O3 studied elsewhere [Fig. 13(b)], [21, 23]. This suggests that either such defects are dislocations on {1011} or {1102} planes with projected
1891
Fig. 11. Basal twin formation by the glide of 1/3h1010i partial dislocations. (a) Compact 1/3h1010i partial core gliding on Al±Al slip plane. (b) Delocalisation of 1/3h1010i partial core on to two adjacent Al±O slip planes. (c) 1/3h1010i partial core delocalised on non-adjacent Al±O slip planes.
line directions close to h1101i imaged along h1120i, or that the defects are surface localised precursors to well-de®ned (width >2 nm) rhombohedral twins. In order to con®rm that heating during ion-beam milling did not result in the ``annealing out'' of substantial rhombohedral twins in the TEM specimens, Al2O3 debris generated during the abrasion process was collected from the rim of the grinding disk for examination in the microscope. This debris was dispersed ultrasonically in alcohol, then dropped directly on to a lacey carbon grid without thinning. Figure 14 shows debris collected from abrasion of the 0001Al2 O3 surface. This debris was predominately crystalline, with some nanocrystalline/ amorphous conglomerates. Nanocrystalline or amorphous regions were not observed at the Al2O3 abraded surfaces, and may form as the result of repeated impacts of the debris during third body wear. The crystalline debris particles were frequently facetted on (0001) and {1102} planes, which are the
Fig. 10. HREM images of basal deformation twins, taken down h1120i zone axes at 5025 nm defocus and 925 nm thickness, where the bright maxima correspond to the ``hole columns'' in the h1120i projection. (a) Width 28 1=60001: (b) Width 211/6[0001].
Fig. 12. MoireÂ-type contrast ¯uctuations at a basal twin boundary imaged by HREM.
INKSON: ABRASION OF Al2O3
1892
Fig. 14. Structure of the Al2O3 abrasion debris. (a) Crystalline particles heavily facetted on (0001) and {1102} planes. (b) 18 nm basal twin (between the two arrows) at a (0001) fracture surface. Fig. 13. (a) Defect macroscopically on {1102}, imaged down h1120i. (b) HREM imaging shows no evidence for rhombohedral twinning, and complex non-repeating contrast across a band of approx. width 5 nm.
fracture surfaces observed on the abraded surface cross-sections. Basal twinning and dislocations were identi®ed in the debris particles [Fig. 14(b)], but to date no rhombohedral twins have been observed either within the particles or at the {1102} fracture surfaces. The structure of the abrasion debris was thus consistent with the cross-sectional TEM surface observations. 6. DISCUSSION
High stresses generated during the abrasion of Al2O3 by diamond lead to signi®cant plastic deformation and crack initiation [1±6]. The post-mortem examination of abraded surfaces randomly samples the abrasive cycle at dierent stages across the examined surface. The abrasive cycle for Al2O3 single crystals abraded on diamond consists of the build-up of dislocations and twinning in response to compressive and tensile deformation, the initiation of cracking, crack growth and linking, and ®nally
chipping of material leaving some remnant surface damage. This residual damage is then built upon by successive impact events until new cracking occurs. By using single crystals it has been possible to separate out the eects of surface initiated damage and the role of crystallography in single Al2O3 grains, from additional grain-boundary initiated failure and grain pull-out common in polycrystalline alumina [4±6]. The dominant plastic deformation modes activated for both basal and prismatic abrasion are observed to be basal twinning (1±5% of ground surface area in this study) and 1/3h1120i dislocations gliding on non-basal slip planes. Defect densities vary across and into the surface according to local degree of damage. The average dislocation penetration was found to be similar for the prismatic and basal abrasion surfaces due to the pyramidal-type slip planes. The penetration of the basal twins into the substrate, however, has a crystallographic dependency, with the degree of penetration determined by the orientation of the (0001) basal plane with respect to the abrasion surface [3]. This results in twin penetration from prismatic abrasion>>basal abrasion, so more material will have to be removed by subsequent pol-
INKSON: ABRASION OF Al2O3
ishing steps to eradicate residual basal twins. Basal twin penetration in polycrystalline samples may be con®ned by grain boundaries [5]. Our abrasive tests were nominally carried out at room temperature (see Section 2); however, localised heating of the Al2O3 wear surface will occur due to some undetermined component of frictional heating. Relating our observations of defect initiation to the other relevant studies on (nominally) room temperature deformation of Al2O3 there is some scatter in observations, which have all been made under dierent experimental conditions such as loading modes, crystallography of samples, grain size and resolution of characterisation techniques [1±9, 19, 20]. Consistent trends throughout the reported experimental data are (i) widespread activation of basal twinning [1±9, 19, 20], (ii) sporadic or negligible rhombohedral twinning activation [1± 7], (iii) activation of 1/3h1120i or 1/3h1011i slip on pyramidal planes [1, 4, 7], and (iv) non-activation of prism slip [1, 2, 4]. This reported behaviour of Al2O3 close to room temperature thus contrasts with the plasticity at temperatures of 4008C and upwards, where widespread prism h1010if1210g, basal 1/3h1120i(0001) and rhombohedral twinning deformation modes are well documented [10]. Using HREM analysis, the morphology and distribution of the basal twins have been characterised. All basal twins were observed to be platelets with a (0001) habit plane, widths d0001<<100 nm (Fig. 9) and very high aspect ratios d1010/d0001 or d1120 =d0001 > 10: The twinning partials were generated at the surface of the crystal, and the extremely high aspect ratio of the twin platelets indicates a large propagation distance of twinning partials for a given net shear. This suggests a relatively low twin boundary energy [16] and deep penetration of the threshold stress ®eld required for migration. On the atomic scale, the twin widths were predominantly 2n 1=60001 [Fig. 10(a)], consistent with the glide of 1/3h1010i partials with dierent core structures [17, 18] (Section 5.3). The twin (0001) interface structures were consistent with ABCBA type stacking of Al (0006) planes, as observed for twins formed at 3008C by indentation [17], rather than ABCCBA stacking [15]. The presence of isovalent solutes 0.3 2 0.1at.%Cr and 0.4 2 0.1at.%Fe in ruby samples appeared to have no eect on the structure or distribution of the twins and no segregation was detected by STEM analysis. The abrasive process may activate one of the three types of twinning partials, 1=30110, 1=31100 or 1/3[1010], depending on the local diamond± alumina interaction conditions which are ill-de®ned for abrasion. The total net shear resulting from the glide of p 1/3h1010i twinning partials must lie in the basal plane according to equation (2), where p=a+b+c:
1893
Shear of p 1=3h1010i partials a=30110 b=31100 c=31010
2
This net shear can theoretically vary between p=3h1010i p a, b or c, and zero ( p/3=a=b=c ), depending on the activation of dierent 1/3h1010i type twinning partials with dierent Schmid factors, although such partial mixing has not yet been experimentally observed. HREM and WB-TEM analysis of the bulk dislocations shows that the dominant slip system activated is b = 1/3h1120i, with a negligible number of non-basal 1/3h1011i Burgers vectors. The net shear from the slip of dislocations is thus also in the basal plane. Due to the crystallography and character of dislocation Burgers vectors, a marked asymmetry is generated at the single crystal abraded surfaces. Twins and dislocations penetrating prismatic surfaces will cause a net shear lying on (0001) with deep penetration into the surface. For basal abrasion, however, the net shear will be parallel to the surface and the residual stress gradient generated by this excess volume will thus be more surface localised. Initial measurements of the residual stress in our abraded samples by the optical ¯uorescence technique have proved inconclusive [24, and D. R. Clarke, personal communication]. The position of the R2 Cr ¯uorescence line for polished and abraded samples could not be distinguished (using a probe 2 mm in diameter and approx. 10 mm deep), indicating that the residual stress in the single crystals may be too small and/or too surface localised to be resolved from the bulk by this method (D. R. Clarke, personal communication). It should be emphasised that the abraded surfaces have spatially varying defect contents, across as well as into the surface, ranging from locally high defect densities particularly at surface steps (as in Fig. 3) to low defect densities shortly after a chipping event has occurred. These variations result in locally varying residual stresses, which are randomly sampled by optical ¯uorescence in a manner depending on the probe diameter (lateral averaging) and shape (depth averaging). Work is still underway to see if multiple measurements with ®ner probes can resolve stress variations across single abraded surfaces, as well as between dierent crystallographic orientations. Consistent with other studies, we observed a marked shift in the glide plane of the 1/3h1120i dislocations from basal to pyramidal planes, and no h1010i{1210} prism glide was observed [1, 2, 4, 7]. The density of dislocations with Burgers vectors out of the basal plane, such as 1/3h1011i and 1/3h2021i (Fig. 8), [4], and possible rhombohedral twin nuclei was found to be extremely low or non-existent in the TEM samples or abrasion debris (Section 5.4). The rhombohedral twinning shear, s = 0.202, is less than s = 0.635 for basal twinning [12, 22, 23].
1894
INKSON: ABRASION OF Al2O3
However, despite this and the large driving force to accommodate shear stresses out of the basal plane during impact events, the scarcity of rhombohedral twinning indicates a diculty in activation of the slip system forming the twins [1±5, 7]. The most recent model for rhombohedral twinning suggests the co-ordinated movement of a complicated zonal partial dislocation complex with a 1/21.9h0111i core [21], which may need extreme stresses or high temperature for activation. Our experimental conditions were outside the conditions required for activation and growth of clearly identi®able rhombohedral twins, although occasional rhombohedral twins have been observed to be activated at room temperature at grain boundaries in polycrystalline samples or under indents [2, 5, 6]. The lack of rhombohedral twinning and nonbasal Burgers vectors to accommodate non-basal stresses, and the absence of other stress relief mechanisms such as deformation of variably oriented grains, grain rotation or grain boundary dislocation sources, results in a very large driving force for crack initiation in these room temperature abraded samples. Widespread {1102} rhombohedral cracking without associated rhombohedral twinning was observed in the abraded TEM samples (Figs 3 and 4), and the crystalline abrasion debris had a predominance of rhombohedral and basal facets (Fig. 12). Microcracks were observed to be de¯ected along the interfaces of basal twins causing delamination (Figs 4 and 12). The basal twin morphology of high aspect ratio plates produces a very high density of parallel twin interfaces for a given twinned volume of crystal, which act as eective barriers for dislocations on pyramidal glide planes as well as de¯ecting cracks. Across twin interfaces {1101} planes rotate by 35.28, and {1102} by 64.88. Although the activation of rhombohedral twinning might be desirable to delay the onset of surface initiated cracking, it has been clearly shown by Heuer that intersections of the three rhombohedral twinning systems, (1102), (1012) and (0112) with each other and with basal twins can result in signi®cant subsurface crack initiation leading to failure [6, 22]. Activation of basal twins (which are all parallel and thus do not interact with one another) in the absence of rhombohedral twinning may therefore not actually be detrimental to the overall abrasion rate and production of high-quality crack-free Al2O3 surfaces, since subsurface intragranular crack initiation is inhibited. The activation of bene®cial non-basal Burgers vectors, which could alleviate stress during impacts and delay the onset of surface cracking and chipping, however, appears to be fatally lacking. Despite signi®cant plastic ¯ow, single crystal Al2O3 still fails in a brittle manner during abrasion.
7. CONCLUSIONS
1. Abraded 0001Al2 O3 surfaces exhibited a severe plastic deformation zone principally limited to the depth of the surface roughness, with high densities of basal twins occurring clustered at surface steps parallel to the macroscopic 0001Al2 O3 plane. 2. The damage penetration of abraded prismatic 2f1010gAl2 O3 or 2f1120gAl2 O3 surfaces was much greater than that for 0001Al2 O3 due to the crystallographic penetration of basal twins on (0001). 3. Deformation basal twins had platelet morphologies, with widths vd0001v<<100 nm, and large aspect ratios d1010/d0001 or d1120/d0001 > 10. 4. At high resolution, basal twins had widths d0001=2n1/6[0001] and ABCBA stacking of (0006)Al planes across twin interfaces, consistent with 1/3h1010i partial dislocations gliding on Al±Al or Al±O slip planes. Twins were nucleated at the abraded surfaces. 5. Isovalent solutes 0.3 2 0.1at.%Cr and 0:420:1at:%Fe in ruby samples had no eect on the structure or distribution of the basal twins, and no segregation was detected. 6. Dislocations within the severe deformation zone were predominantly pyramidal 1=3h1120if1101g, with minor contributions from 1=3h1120i= h1010i 0001 and 1/3h1011i{0111}. 7. No rhombohedral twinning, h1010i{1210} prism glide or widespread non-basal dislocation Burgers vectors were observed in either the abraded substrates or crystalline abrasion debris, in contrast to deformation >4008C. 8. Directional stress build-up, due to basal twin shears and dislocation Burgers vectors lying on (0001), is thought to help initiate the observed extensive microcracking along {1102} rhombohedral and (0001) twin habit planes leading to abrasive wear. Subsurface cracking due to rhombohedral twin intersections did not occur.
AcknowledgementsÐB.J. Inkson would particularly like to thank Professor M. RuÈhle for support whilst at the MaxPlanck-Institut fuÈr Metallforschung, Stuttgart, and The Royal Society for additional funding. Professor D.R. Clarke is gratefully acknowledged for comments and photoluminescence measurements. CWRU Professor A.H. Heuer, K.P.D. LagerloÈf and P. Pirouz, and Dr H. Wu are thanked for enlightening discussions, and a referee for comments. REFERENCES 1. 2. 3. 4.
Hockey, B. J., J. Am. Ceram. Soc., 1971, 54(5), 223. Hockey, B. J., Proc. Br. Ceram. Soc., 1972, 20, 95. Becher, P. F., J. Am. Ceram. Soc., 1976, 59(34), 143. Barceinas-SaÂnchez, J. D. O. and Rainforth, W. M., Acta mater., 1998, 46(18), 6475. 5. Zarudi, I., Zhang, L. C. and Mai, Y.-W., J. Mater. Sci., 1996, 31, 905.
INKSON: ABRASION OF Al2O3 6. Zarudi, I., Zhang, L. C. and Cockayne, D., J. Mater. Sci., 1998, 33, 1639. 7. Wang, Y. and Mikkola, D. E., J. Am. Ceram. Soc., 1992, 75(12), 3252. 8. Lankford, J., J. Mater. Sci., 1977, 12, 791. 9. Lankford, J., J. Mater. Sci., 1978, 13, 351. 10. LagerloÈf, K. P. D., Heuer, A. H., Castaing, J., RivieÁre, J. P. and Mitchell, T. E., J. Am. Ceram. Soc., 1994, 77(2), 385. 11. Heuer, A. H., LagerloÈf, K. P. D. and Castaing, J., Phil. Mag. A, 1998, 78(3), 747. 12. Veit, K., Neues Jb. Miner. Geol. BeilBd, 1921, 45, 121. 13. Kronberg, M. L., Acta metall., 1957, 5, 507. 14. Geipel, T., Bilde-Sùrensen, J. B., Lawlor, B. F., Pirouz, P., LagerloÈf, K. P. D. and Heuer, A. H., Acta mater., 1996, 44(5), 2165. 15. Kaplan, W. D., Kenway, P. R. and Brandon, D. G., Acta metall. mater., 1995, 43(2), 835.
1895
16. Kenway, P. R., J. Am. Ceram. Soc., 1994, 77(2), 349. 17. Bilde-Sùrensen, J. B., Lawlor, B. F., Geipel, T., Pirouz, P., Heuer, A. H. and LagerloÈf, K. P. D., Acta mater., 1996, 44(5), 2145. 18. Chen, S.-J. and Howitt, D. G., Acta metall. mater., 1992, 40(12), 3249. 19. Hockey, B. J., in Deformation of Ceramic Materials, ed. R. C. Bradt and R. E. Tressler. Plenum Press, New York, 1975, p. 167. 20. Chen, S.-J. and Howitt, D. G., Phil. Mag. A, 1998, 78(3), 765. 21. Geipel, T., LagerloÈf, K. P. D., Pirouz, P. and Heuer, A. H., Acta mater., 1994, 42(4), 1367. 22. Heuer, A. H., Phil. Mag., 1966, 13, 379. 23. Bursill, L. A. and Lin, P. J., Phil. Mag. Lett., 1989, 60(1), 1. 24. Ma, Q. and Clarke, D. R., Acta metall. mater., 1993, 41(6), 1817.
DISLOCATIONS AND TWINNING ACTIVATED BY THE ABRASION OF Al2O3 B. J. INKSON Department of Materials, Oxford University, Parks Road, Oxford OX1 3PH, UK (Received 13 September 1999; accepted 8 December 1999) AbstractÐDefects generated at the surface of single crystal Al2O3 during abrasion on diamond have been analysed by high spatial resolution cross-sectional electron microscopy. Plastic deformation predominantly occurs by basal twinning and pyramidal slip 1/3h1120i{1101}. Basal twins have platelet morphologies, with widths d0001=2n1/6[0001] and vd0001v<<100 nm, aspect ratios d1010/d0001 or d1120/d0001 > 10, and ABCBA stacking of (0006)Al planes across twin interfaces. Basal twins and dislocations occur clustered around steps in macroscopic (0001) abraded surfaces, whereas 2{1120} and 2{1010} prismatic plane abrasion results in a more uniform 1±5% deformation twin cover with basal twin penetration>>that for basal abrasion. Extensive microcracking along {1102} rhombohedral and (0001) twin habit planes occurs, but no widespread rhombohedral twinning, prism glide or non-basal dislocation Burgers vectors were observed. Implications for surface preparation of Al2O3 are discussed. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Abrasion (mechanical properties+wear); Dislocations; Twinning; Al2O3; Surfaces & interfaces
1. INTRODUCTION
Al2O3 is an important engineering structural material, with high hardness and wear resistance making it suitable for uses such as grinding abrasives, bearings and cutting tools, as well as highly polished substrates for functional coatings. The plasticity and fracture behaviour of Al2O3 in the 0± 3008C temperature range are important controlling factors in its performance as an abrasive, as hard impact-resistant coatings and as stable substrates [1±9]. The wear and polishing of alumina builds up residual damage at the surface, which alters its surface properties. Studies of damage accumulation in Al2O3 after abrasion and impact have shown that the density of defects in the top few microns is typically so high that it is not easy to separate out the dierent deformation modes within the severe deformation zone, even by TEM [1±7]. As the size of Al2O3 components decreases, and the demand for defect-free sapphire substrates increases, it is becoming increasingly important to have a better understanding of the structure of the severe deformation zone and mechanics of Al2O3 abrasion right down to the atomic level. In this study we have characterised the severe plastic deformation zone resulting from room temperature abrasion using high spatial resolution electron microscopy. Because alumina is highly
anisotropic [1±3], the surface deformation (dislocations and twinning) have been quanti®ed as a function of the crystallography of the abraded surface by using oriented single crystals. 2. EXPERIMENTAL PROCEDURE
Commercially available bulk single crystals of Al2O3 were used (Frank & Schulte GmbH), which contained no growth twins and negligible dislocation density. Additional ruby samples containing isovalent solutes 0:320:1at:%Cr and 0:420:1at:%Fe were also examined. Abraded surfaces were prepared by grinding 2{1120}, 2{1010} and 2(0001) surfaces on 30 mm diamond using a Buehler Minimet 1000 grinder at room temperature with 5 N normal load, 10 rpm (equivalent to 0.03 m/s sliding speed) and minimal water lubrication. Throughout the text ``room temperature abrasion'' is taken to refer to the temperature of the bulk Al2O3 substrate. Localised heating of the Al2O3 wear surface during the abrasive process could not be measured in our experimental set-up. At least 200 mm of material was removed from each surface in order to ensure that there were no residual defects from initial cutting with a 30-mm grit wire saw. A single diamond grit size was used to ensure that all deformation observed was attributable to the single abrasion step, and to ensure a
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 9 9 ) 0 0 4 6 8 - 1
1884
INKSON: ABRASION OF Al2O3
relatively high deformation density for subsequent analysis. Al2O3 debris generated during the abrasion process was collected from the rim of the grinding disk for examination in the microscope. Abraded Al2O3 surfaces were glued together in pairs, dimpled perpendicular to the abraded surface using 1±5 mm diamond paste to a thickness of 30 mm, and thinned to electron transparency (<<1 mm) by ion-milling. The abraded surfaces could be accurately located in the cross-sectional samples at the glue±Al2O3 interfaces. Comparison of the structure of the thinned Al2O3 in the ``bulk'' material away from the abraded zone con®rmed that the defects examined in this paper originated from the grinding on 30 mm diamond, and not from the subsequent TEM-foil specimen preparation steps or as growth defects. High-resolution characterisation (HREM) of the abrasion deformation zones and debris was carried out in a JEOL 4000EX microscope which, operated at 400 kV, has a point resolution of 0.16 nm. Chemical analyses were carried out on an HB501 STEM at 100 kV, and surface topography imaged in a JSM 6300 SEM at 15 kV. 3. ROOM TEMPERATURE ABRASION OF Al2O3
The abrasion of Al2O3 single crystals on randomly rotating 30 mm diamond disks results in highly fractured surface topographies, as shown in Fig. 1. No marked directionality in the surface topography for any of the ground surfaces was visible in plan view, with the few visible wear tracks from individual diamond±substrate impact events being randomly oriented with respect to the under-
Fig. 1. Topography of a f1010gAl2 O3 prismatic surface abraded on 30 mm diamond grit.
lying crystallography. Any surface steps and ledges present due to twinning and dislocation initiation could not be resolved by our SEM. In cross-section the existence of a plastic deformation zone at the abraded Al2O3 surfaces becomes apparent, as ®rst shown by Hockey [1, 2]. Figure 2 shows a cross-sectional TEM image of an abraded {1120} surface, where dislocations and twinning initiated at the surface during impact with diamond grains are clearly visible. 3.1. Deformation of prismatic surfaces Al2O3 single crystals were abraded on 2{1010} and 2{1120} prismatic surfaces perpendicular to the basal plane. The dominating deformation modes were observed to be basal twinning on (0001) perpendicular to the abraded surface and dislocations gliding on non-basal slip planes (Fig. 2). Two deformation zones may be identi®ed at the prismatic surfaces, namely (i) the top surface 5 mm consisting of a very high density of dislocations, basal twins and some microcracking, and (ii) a regime of deep penetration of basal twins below the mixed zone. These basal twins, visible edge-on and perpendicular to the abraded surface in Fig. 2, are extensively characterised in Section 5. In cross-section, the density and penetration of the plastic deformation present at the abraded surface is not totally uniform, since at any instant dierent places on the surface will be in dierent stages of the abrasive cycle. The abrasive cycle consists of the build-up of surface defects by indentation and scratch events, initiation of cracking, crack growth and linking, and ®nally chipping of material leaving some remnant surface damage. In the prismatic samples, microcracking was observed to
Fig. 2. Abraded {1120} Al2O3 prismatic surface viewed in cross-section along h1100i. Note the deep penetration of very high aspect ratio deformation basal twins on (0001) perpendicular to the surface, and non-basal dislocation slip planes.
INKSON: ABRASION OF Al2O3
occur primarily on the {1102} rhombohedral planes, of which there are three families at 57.68 from the basal planes. The cracks were observed to both cut across and delineate basal twins, and are the precursor to loss of material by chipping events, leading to abrasive wear. 3.2. Deformation of (0001) basal surfaces Figures 3 and 4 show cross-sectional images of abraded (0001) surfaces. As with the prismatic surfaces, the main deformation modes observed were dislocation activity on non-basal slip planes and basal twinning on (0001). The basal twins grow as high aspect ratio platelets with a (0001) habit plane parallel to the macroscopic (0001) abrasion surface. The twins occur clustered at non-basal steps in the (0001) surface (Figs 3 and 4), and only occur to a depth of the order of the surface roughness. The depthwise penetration of basal twinning in abraded basal surfaces is thus only a fraction of that observed in prismatic abrasion using the same diamond abrasion conditions. The fact that some early investigations observed zero or negligible basal twinning after (0001) abrasion [1±3] is probably a
1885
function of the resolution of the investigative technique required in the top micron to resolve the twins. The penetration of dislocations on non-basal slip planes resulting from basal plane abrasion is comparable with that of prismatic abrasion, and is slightly greater than that of the basal twins because of the latter's crystallographic dependence of penetration (Figs 3 and 4). Microcracks were prevalent near regions of high twinning and dislocation density, both cutting across pre-existing twins in the damaged surface [Figs 3 and 4(a)], and delineating new twins formed subsequent to the cracking event [Fig. 4(b)]. Cracking occurred preferentially along (0001) twin interfaces [Fig. 4(a)], and as for prismatic surfaces along {1102} planes [Fig. 4(b)]. The {1102} rhombohedral cracks frequently exhibited atomically sharp facets many tens of nanometres in length. The intersections of the {1102} rhombohedral planes with the (1120) image plane used in Figs 3 and 4 are summarised in a stereogram (Fig. 5). Viewed down h1120i, {1102} planes are edge-on, with {0112} and {1012} planes intersecting the {1120} image plane along h2201i at 38.28 from (0001).
Fig. 3. Very heavily deformed region close to a macroscopic step in an abraded (0001) Al2O3 surface imaged down h1120i, showing basal twins, non-basal dislocation glide planes, and extensive cracking on {1102} and (0001).
1886
INKSON: ABRASION OF Al2O3
Fig. 4. Cracking at abraded (0001) Al2O3 surfaces imaged down h1120i. (a) Preferential crack paths along existing (0001) basal twin boundaries. (b) Atomically sharp f1102g crack delineating younger basal twins (upper right), with no evidence for an associated rhombohedral twin. 4. DISLOCATION ACTIVATION DURING ROOM TEMPERATURE ABRASION
After abrasion, within the severe deformation zone (top few microns) the dislocation density was generally too high for weak-beam (WB) analysis. In
Fig. 5. Stereogram summarising the intersections of rhombohedral {1102} and pyramidal {1101} planes with a (1120) projection plane in Al2O3.
regions of lower dislocation density it was clear, however, that almost all the dislocation lines did not lie in the basal plane for either the basal or pyramidal abrasion (Figs 2±4). Non-basal glide has been identi®ed in previous studies of room temperature abrasion [1, 2, 4, 6]. Dislocations viewed at an angle to their glide plane were bowed and kinked. Dislocations imaged parallel to their slip plane down h1120i zone axes had h1102i dislocation line projections at 728 from the basal planes, indicating pyramidal slip on {1101} consistent with the 1/ 3h1120i{1101} or 1/3h1011i{1101} slip systems (Fig. 6). The dislocations were out of contrast for WB imaging with g=0006 con®rming the slip system 1/3h1120i{1101}. Dislocations gliding on prism planes, (e.g. h1010i{1210}) or dislocation dipoles, both dominating features after deformation at high temperature [10, 11], were not identi®ed in these samples. More than 95% of the defects parallel to (0001) could be identi®ed at high resolution to be ultra®ne basal twins. Although it was dicult to distinguish basal twin nuclei <1 nm thick from 1=3h1120i 0001 or h1010i(0001) slip systems, a very low density of dislocations segments on (0001) appeared to exist. Imaging dislocations within the severe deformation zone at high resolution con®rmed the predominance of 1/3h1120i Burgers vectors on nonbasal slip planes. Figure 7(a) shows an HREM image of a dislocation obtained by imaging down a h1100i zone axis. The resolved Burgers vector component is bres=1/3h1120i, so the total Burgers vector is consistent with b=1/3h1120i, 2/3h1210i or 2/3h2110i. Because 2/3h1210i type dislocations are unlikely due to the very large Burgers vector, the dislocation is identi®ed as b 1=3h1120i: The contrast in the image is extended out of the (0001) plane indicating a {110n } slip plane. Although there is a possibility that the 1/3h1120i dislocation originally had a (0001) slip plane and may have extended out of (0001) by diusive self-climb (which has been observed for h1010i slip at higher temperatures [10]), (0001) slip planes are inconsistent with the analysis of dislocations in thicker parts of the TEM foils. Figures 7(b) and (c) show typical HREM images obtained from dislocations within 50 nm of the TEM foil edges imaged down h1210i zone axes. The resolved Burgers vector component are bres 1=2h1010i, so the total Burgers vector are b=1/2h1010i+nh1210i. Possible identi®cations are thus (i) b=1/3h1120i, (ii) b=1/3h2110i, (iii) b=h1100i or (iv) b=h0110i. The latter two h0110i Burgers vectors have a signi®cantly higher line energy than 1/3h1120i dislocations. In addition, no dislocations with bres=h1010i components imaged down h1210i by HREM were observed, which correspond uniquely to h1010i dislocations. It is most likely, therefore, that Figs 7(b) and (c) correspond to 1=3h1120i dislocations as in Fig. 7(a). In the
INKSON: ABRASION OF Al2O3
approx. 10 nm thick HREM foils it was not possible to determine conclusively the line directions of these dislocations, which may indeed be altered by thin foil relaxations, since even steeply inclined dislocations have short projected lengths in very thin foils. Dislocations imaged in the thicker regions of the foil by HREM had increasing projected lengths not parallel to (0001) consistent with non-basal slip planes. Of the more than 20 dislocations analysed by HREM, only one was identi®ed as having a nonbasal Burgers vector component (Fig. 8). The resolved Burgers vector component was bres 1=6h1102i consistent with a b=1/3h1011i or 1/3h0111i dislocation. Activation of 1/3h1011i {0111} type slip systems was not identi®ed by DF imaging with g=0006 in thicker parts of the foil. The dislocations observed in the abraded surfaces are thus predominantly 1/3h1120i{1101}, with minor contributions from 1/3h1120i/h1010i(0001) and 1=3h1011if0111g: Slip of the dislocations out of the (0001) basal planes means that during glide they must interact frequently with the extensive number of basal twins. 5. TWINNING DURING ABRASION
5.1. Basal twinning morphology and distribution At both abraded (0001) and prismatic single crystal surfaces extensive basal twinning occurred,
1887
enabling for the ®rst time a survey of a large number of deformation twins by HREM to be carried out. The deformation basal twins form as very high aspect ratio platelets, with major (0001) habit planes and very narrow widths d0001 along [0001] (Figs 2±4). The twins exhibit the crystallographic relationship (0001)bulk//(0001)twin and h1120ibulk ==h1120itwin [12, 13]. Under our abrasion conditions, the observed twin widths d0001 at the ground surfaces directly adjacent to the glue were less than 100 nm, with widths 2±10 nm predominating (Fig. 9). Perpendicular to the ground prismatic surfaces the twin penetration depths d1010 or d1120 were up to 10 mm, resulting in the extremely large aspect ratios d1010/d0001 or d1120/d0001 of over 100 (Fig. 2). The aspect ratios of the twins parallel to the (0001) ground surfaces were also typically >20 (Figs 3 and 4), however these twins were more frequently terminated by cracks penetrating the (0001) surface. For any given twin, the twin width d0001 decreased with distance from the Al2O3 surface, indicating that the partial dislocations forming the twin originate at the surface. Along the [0001] direction of the ground prismatic surfaces, perpendicular to the habit planes of the deformation twin platelets, the twins occurred with a density of 1±2/mm (Fig. 2). Most twins were solitary, although occasional clusters of Two to ®ve twins were observed. Assuming that the TEM cross-sections examined were representative
Fig. 6. 1/3h1120i{1101} dislocations with h1102i projected line direction imaged down h1120i.
INKSON: ABRASION OF Al2O3
1888
Fig. 7. HREM images of dislocations within the severe deformation zone. (a) b=1/3h1120i{110n } dislocation imaged down a h1100i zone axis with resolved Burgers vector component bres=1/3h1120i. (b, c) 1/3h1120i or h1100i dislocations imaged down a h1210i zone axis with bres=1/2h1010i.
sampling in the [0001] direction for ground prismatic surfaces, then the proportion of ground surface area which had twinned during deformation lay between 1 and 5% in this study. The density of twins is expected to vary locally, depending on the extent of the abrasive cycle at any particular location. Twinning at the basal surfaces was noticeably more clustered at steps in the macroscopic (0001) surface (Fig. 3). For all samples the density of twins observed decreased in sample areas not in direct contact with residual glue, since very short twins, penetrating less than 200 nm into the surface, were removed by ion-milling.
5.2. Basal twin interfaces Figure 10 shows HREM images of basal twins generated at abraded {1010} surfaces. The imaging zone axes are h1120i and the bright maxima correspond to ``hole columns'' in the Al basal planes. Distinct O and Al columns cannot currently be resolved by HREM, making it very dicult to investigate subtle changes resulting from relaxations in Al or O positions. Simulations here and elsewhere show that these twin interfaces are consistent
with an ABCBA type stacking of Al basal planes [14]. Subtle variations proposed in the Al positions at the twin interfaces due to relaxations around the hole positions, such as examples referred to by Geipel et al. as ``type II'' and ``type II±glide'' [14], could not be distinguished experimentally here. No HREM observations made from more than 200 deformation twins in the abraded samples (either for pure Al2O3 or ruby samples containing 0:320:1at:%Cr and 0.420.1at.%Fe) were consistent with ``type I'' basal twins which have a mirror plane of symmetry lying in an O basal plane, and thus a ABCCBA stacking of Al basal planes [15]. This suggests that the ABCBA type stacking has a lower energy as predicted by the static-lattice calculations of Kenway [16].
5.3. Formation mechanism of basal twins Two shear mechanisms have been proposed for the formation of basal twins in alumina, both of which produce twins with an ABCBA type stacking of Al basal planes across the twin interface and are consistent with Veit's measurements of twinning elements [12, 17, 18]. Figure 11 illus-
INKSON: ABRASION OF Al2O3
1889
Fig. 7 (continued)
trates these two models. The glide of 1/3h1010i partial dislocations on (0003) glide planes lying through the centre of the buckled Al planes enables basal twin formation to occur without charge transfer [17] [Fig. 11(a)]. This mechanism shears all Al±Al bonds in the slip plane, and half of the adjacent Al±O bonds. Because of the movement of holes, a single partial automatically generates a twin two (0006) planes thick [17]. The net result, therefore, of the passage of n partials must be a basal twin with width 2n 1=60001: The second twinning model proposes dislocation glide on Al±O glide planes instead of Al±Al glide planes [13, 18, 19]. There are two Al±O glide planes for every Al±Al glide plane. Basal twins can be formed by 1/3h1010i partial dislocations dissociated
into two 1/3h0110i type partials dislocations moving on (0006) Al±O glide planes according to equation (1) [18]: 1=3h1010i 4 1=3h0110i 1=3h1100i:
1
If the two 1/3h0110i type partial dislocations are widely separated [r.h.s. of equation (1)] this mechanism of glide can form twins with widths n 1=60001: It is dicult, however, to see how decoupled 1/3h0110i partials satisfying equation (1) could be independently generated and subsequently co-ordinate their motion [11]. Furthermore, two widely separated partials [r.h.s. equation (1)] have twice the line energy of one single partial [l.h.s. equation (1)]. Recent HREM and weak-beam observations support the fact that only net 1/3h1010i
1890
INKSON: ABRASION OF Al2O3
partial dislocations every (0003) are observed, never single uncoupled 1/3h0110i dislocations [20]. The formation of a single delocalised 1/3h1010i partial [l.h.s. of equation (1)] instead of two 1/ 3h0110i type partial dislocations [r.h.s. of (1)] is energetically favourable. Core structures of 1/ 3h1010i partial dislocations delocalised on to two closely spaced (0006) Al±O glide planes are shown in Figs 11(b) and (c), which can be compared with the compact core gliding on Al±Al glide planes [Fig. 11(a)]. We cannot currently resolve the dierences in the Fig. 11 core structures by HREM. Furthermore, all these 1/3h1010i core structures have the same long range strain ®elds, and thus cannot be distinguished by WB-TEM. All of the 1=3h1010i core structures, gliding on Al±Al or Al± O slip planes, generate basal twins with widths 2n 1=60001, consistent with deformation twins observed here where the width could be measured [for example in Fig. 10(a)]. It has thus not been possible to distinguish between these two deformation twinning models, and it remains for atomistic simulations of the dislocation cores to help con®rm which slip plane is the more likely. It should be noted that we additionally observed one twin apparently of width 211/6[0001], which is inconsistent with pure 1/3h1010i slip [Fig. 10(b)]. Statistically insigni®cant, this observation may be aected by MoireÂ-type ¯uctuations in the contrast along the (0001) interfaces of the order <2 nm, as
also observed by other authors [14] (Fig. 12). These patches of Moire fringes are frequent in occurrence and irregular in contrast, whose existence has been attributed to the cutting of partial dislocation loops spawned by spiral dislocation sources [14]. Twinning dislocations threading through the thin TEM foil at an angle may give rise to overlap of the twin variants and thus Moire fringes. In our samples, the twins had a very high aspect ratio and wedge morphology, resulting from widely separated twinning partials ``popped-in'' from the surface. The partial dislocations occurred at too low a frequency to attribute the sporadic and often localised MoireÂ-type ¯uctuations solely to threading dislocations (Fig. 12). Localised thin foil relaxation eects seem to contribute to the fringes, since the original twin boundaries macroscopically are almost parallel to (0001). The structure of twin boundaries that we observe may also be complicated by their interaction with the high density of dislocations gliding on pyramidal slip planes. Interaction must occur if twinning partials collide with bulk dislocations, if bulk dislocations gliding on non-basal slip planes try to cut across twins, and if dislocations cross-slip into and glide along the (0001) twin interfaces.
Fig. 8. HREM image of a 1/3h1011i{0111} dislocation with resolved Burgers vector component bres=1/6h1102i imaged down h1120i.
Fig. 9. Distribution of basal twin widths measured by HREM along [0001] for two {1010} ground surfaces, surface 1(56 twins) and surface 2 (47 twins).
5.4. Rhombohedral twinning In addition to basal twinning, rhombohedral twinning is a frequently observed deformation mode in Al2O3 [21, 22]. Three families of rhombohedral planes, (1102), (1012) and (0112), lie at 57.68 from the basal plane (Fig. 5), and it is known that the intersection of twins from these three families play a key role in initiating cracks inside Al2O3 bulk samples leading to failure [22]. The abraded surfaces were systematically examined for rhombohedral twins. Viewed down h1120i one rhombohedral plane is edge on, with the other
INKSON: ABRASION OF Al2O3
two intersecting the {1120} plane along h2201i (Fig. 5). No high density of clearly de®ned rhombohedral twins was observed, but occasional defects parallel to {1102} within the severe deformation zone did exist (Fig. 13). No diraction pattern consistent with a rhombohedral twin could be obtained from these defects, and at high resolution the contrast was extremely complex and non-repeating, unlike the clearly de®ned rhomobohedral twins in Al2O3 and Fe2O3 studied elsewhere [Fig. 13(b)], [21, 23]. This suggests that either such defects are dislocations on {1011} or {1102} planes with projected
1891
Fig. 11. Basal twin formation by the glide of 1/3h1010i partial dislocations. (a) Compact 1/3h1010i partial core gliding on Al±Al slip plane. (b) Delocalisation of 1/3h1010i partial core on to two adjacent Al±O slip planes. (c) 1/3h1010i partial core delocalised on non-adjacent Al±O slip planes.
line directions close to h1101i imaged along h1120i, or that the defects are surface localised precursors to well-de®ned (width >2 nm) rhombohedral twins. In order to con®rm that heating during ion-beam milling did not result in the ``annealing out'' of substantial rhombohedral twins in the TEM specimens, Al2O3 debris generated during the abrasion process was collected from the rim of the grinding disk for examination in the microscope. This debris was dispersed ultrasonically in alcohol, then dropped directly on to a lacey carbon grid without thinning. Figure 14 shows debris collected from abrasion of the 0001Al2 O3 surface. This debris was predominately crystalline, with some nanocrystalline/ amorphous conglomerates. Nanocrystalline or amorphous regions were not observed at the Al2O3 abraded surfaces, and may form as the result of repeated impacts of the debris during third body wear. The crystalline debris particles were frequently facetted on (0001) and {1102} planes, which are the
Fig. 10. HREM images of basal deformation twins, taken down h1120i zone axes at 5025 nm defocus and 925 nm thickness, where the bright maxima correspond to the ``hole columns'' in the h1120i projection. (a) Width 28 1=60001: (b) Width 211/6[0001].
Fig. 12. MoireÂ-type contrast ¯uctuations at a basal twin boundary imaged by HREM.
INKSON: ABRASION OF Al2O3
1892
Fig. 14. Structure of the Al2O3 abrasion debris. (a) Crystalline particles heavily facetted on (0001) and {1102} planes. (b) 18 nm basal twin (between the two arrows) at a (0001) fracture surface. Fig. 13. (a) Defect macroscopically on {1102}, imaged down h1120i. (b) HREM imaging shows no evidence for rhombohedral twinning, and complex non-repeating contrast across a band of approx. width 5 nm.
fracture surfaces observed on the abraded surface cross-sections. Basal twinning and dislocations were identi®ed in the debris particles [Fig. 14(b)], but to date no rhombohedral twins have been observed either within the particles or at the {1102} fracture surfaces. The structure of the abrasion debris was thus consistent with the cross-sectional TEM surface observations. 6. DISCUSSION
High stresses generated during the abrasion of Al2O3 by diamond lead to signi®cant plastic deformation and crack initiation [1±6]. The post-mortem examination of abraded surfaces randomly samples the abrasive cycle at dierent stages across the examined surface. The abrasive cycle for Al2O3 single crystals abraded on diamond consists of the build-up of dislocations and twinning in response to compressive and tensile deformation, the initiation of cracking, crack growth and linking, and ®nally
chipping of material leaving some remnant surface damage. This residual damage is then built upon by successive impact events until new cracking occurs. By using single crystals it has been possible to separate out the eects of surface initiated damage and the role of crystallography in single Al2O3 grains, from additional grain-boundary initiated failure and grain pull-out common in polycrystalline alumina [4±6]. The dominant plastic deformation modes activated for both basal and prismatic abrasion are observed to be basal twinning (1±5% of ground surface area in this study) and 1/3h1120i dislocations gliding on non-basal slip planes. Defect densities vary across and into the surface according to local degree of damage. The average dislocation penetration was found to be similar for the prismatic and basal abrasion surfaces due to the pyramidal-type slip planes. The penetration of the basal twins into the substrate, however, has a crystallographic dependency, with the degree of penetration determined by the orientation of the (0001) basal plane with respect to the abrasion surface [3]. This results in twin penetration from prismatic abrasion>>basal abrasion, so more material will have to be removed by subsequent pol-
INKSON: ABRASION OF Al2O3
ishing steps to eradicate residual basal twins. Basal twin penetration in polycrystalline samples may be con®ned by grain boundaries [5]. Our abrasive tests were nominally carried out at room temperature (see Section 2); however, localised heating of the Al2O3 wear surface will occur due to some undetermined component of frictional heating. Relating our observations of defect initiation to the other relevant studies on (nominally) room temperature deformation of Al2O3 there is some scatter in observations, which have all been made under dierent experimental conditions such as loading modes, crystallography of samples, grain size and resolution of characterisation techniques [1±9, 19, 20]. Consistent trends throughout the reported experimental data are (i) widespread activation of basal twinning [1±9, 19, 20], (ii) sporadic or negligible rhombohedral twinning activation [1± 7], (iii) activation of 1/3h1120i or 1/3h1011i slip on pyramidal planes [1, 4, 7], and (iv) non-activation of prism slip [1, 2, 4]. This reported behaviour of Al2O3 close to room temperature thus contrasts with the plasticity at temperatures of 4008C and upwards, where widespread prism h1010if1210g, basal 1/3h1120i(0001) and rhombohedral twinning deformation modes are well documented [10]. Using HREM analysis, the morphology and distribution of the basal twins have been characterised. All basal twins were observed to be platelets with a (0001) habit plane, widths d0001<<100 nm (Fig. 9) and very high aspect ratios d1010/d0001 or d1120 =d0001 > 10: The twinning partials were generated at the surface of the crystal, and the extremely high aspect ratio of the twin platelets indicates a large propagation distance of twinning partials for a given net shear. This suggests a relatively low twin boundary energy [16] and deep penetration of the threshold stress ®eld required for migration. On the atomic scale, the twin widths were predominantly 2n 1=60001 [Fig. 10(a)], consistent with the glide of 1/3h1010i partials with dierent core structures [17, 18] (Section 5.3). The twin (0001) interface structures were consistent with ABCBA type stacking of Al (0006) planes, as observed for twins formed at 3008C by indentation [17], rather than ABCCBA stacking [15]. The presence of isovalent solutes 0.3 2 0.1at.%Cr and 0.4 2 0.1at.%Fe in ruby samples appeared to have no eect on the structure or distribution of the twins and no segregation was detected by STEM analysis. The abrasive process may activate one of the three types of twinning partials, 1=30110, 1=31100 or 1/3[1010], depending on the local diamond± alumina interaction conditions which are ill-de®ned for abrasion. The total net shear resulting from the glide of p 1/3h1010i twinning partials must lie in the basal plane according to equation (2), where p=a+b+c:
1893
Shear of p 1=3h1010i partials a=30110 b=31100 c=31010
2
This net shear can theoretically vary between p=3h1010i p a, b or c, and zero ( p/3=a=b=c ), depending on the activation of dierent 1/3h1010i type twinning partials with dierent Schmid factors, although such partial mixing has not yet been experimentally observed. HREM and WB-TEM analysis of the bulk dislocations shows that the dominant slip system activated is b = 1/3h1120i, with a negligible number of non-basal 1/3h1011i Burgers vectors. The net shear from the slip of dislocations is thus also in the basal plane. Due to the crystallography and character of dislocation Burgers vectors, a marked asymmetry is generated at the single crystal abraded surfaces. Twins and dislocations penetrating prismatic surfaces will cause a net shear lying on (0001) with deep penetration into the surface. For basal abrasion, however, the net shear will be parallel to the surface and the residual stress gradient generated by this excess volume will thus be more surface localised. Initial measurements of the residual stress in our abraded samples by the optical ¯uorescence technique have proved inconclusive [24, and D. R. Clarke, personal communication]. The position of the R2 Cr ¯uorescence line for polished and abraded samples could not be distinguished (using a probe 2 mm in diameter and approx. 10 mm deep), indicating that the residual stress in the single crystals may be too small and/or too surface localised to be resolved from the bulk by this method (D. R. Clarke, personal communication). It should be emphasised that the abraded surfaces have spatially varying defect contents, across as well as into the surface, ranging from locally high defect densities particularly at surface steps (as in Fig. 3) to low defect densities shortly after a chipping event has occurred. These variations result in locally varying residual stresses, which are randomly sampled by optical ¯uorescence in a manner depending on the probe diameter (lateral averaging) and shape (depth averaging). Work is still underway to see if multiple measurements with ®ner probes can resolve stress variations across single abraded surfaces, as well as between dierent crystallographic orientations. Consistent with other studies, we observed a marked shift in the glide plane of the 1/3h1120i dislocations from basal to pyramidal planes, and no h1010i{1210} prism glide was observed [1, 2, 4, 7]. The density of dislocations with Burgers vectors out of the basal plane, such as 1/3h1011i and 1/3h2021i (Fig. 8), [4], and possible rhombohedral twin nuclei was found to be extremely low or non-existent in the TEM samples or abrasion debris (Section 5.4). The rhombohedral twinning shear, s = 0.202, is less than s = 0.635 for basal twinning [12, 22, 23].
1894
INKSON: ABRASION OF Al2O3
However, despite this and the large driving force to accommodate shear stresses out of the basal plane during impact events, the scarcity of rhombohedral twinning indicates a diculty in activation of the slip system forming the twins [1±5, 7]. The most recent model for rhombohedral twinning suggests the co-ordinated movement of a complicated zonal partial dislocation complex with a 1/21.9h0111i core [21], which may need extreme stresses or high temperature for activation. Our experimental conditions were outside the conditions required for activation and growth of clearly identi®able rhombohedral twins, although occasional rhombohedral twins have been observed to be activated at room temperature at grain boundaries in polycrystalline samples or under indents [2, 5, 6]. The lack of rhombohedral twinning and nonbasal Burgers vectors to accommodate non-basal stresses, and the absence of other stress relief mechanisms such as deformation of variably oriented grains, grain rotation or grain boundary dislocation sources, results in a very large driving force for crack initiation in these room temperature abraded samples. Widespread {1102} rhombohedral cracking without associated rhombohedral twinning was observed in the abraded TEM samples (Figs 3 and 4), and the crystalline abrasion debris had a predominance of rhombohedral and basal facets (Fig. 12). Microcracks were observed to be de¯ected along the interfaces of basal twins causing delamination (Figs 4 and 12). The basal twin morphology of high aspect ratio plates produces a very high density of parallel twin interfaces for a given twinned volume of crystal, which act as eective barriers for dislocations on pyramidal glide planes as well as de¯ecting cracks. Across twin interfaces {1101} planes rotate by 35.28, and {1102} by 64.88. Although the activation of rhombohedral twinning might be desirable to delay the onset of surface initiated cracking, it has been clearly shown by Heuer that intersections of the three rhombohedral twinning systems, (1102), (1012) and (0112) with each other and with basal twins can result in signi®cant subsurface crack initiation leading to failure [6, 22]. Activation of basal twins (which are all parallel and thus do not interact with one another) in the absence of rhombohedral twinning may therefore not actually be detrimental to the overall abrasion rate and production of high-quality crack-free Al2O3 surfaces, since subsurface intragranular crack initiation is inhibited. The activation of bene®cial non-basal Burgers vectors, which could alleviate stress during impacts and delay the onset of surface cracking and chipping, however, appears to be fatally lacking. Despite signi®cant plastic ¯ow, single crystal Al2O3 still fails in a brittle manner during abrasion.
7. CONCLUSIONS
1. Abraded 0001Al2 O3 surfaces exhibited a severe plastic deformation zone principally limited to the depth of the surface roughness, with high densities of basal twins occurring clustered at surface steps parallel to the macroscopic 0001Al2 O3 plane. 2. The damage penetration of abraded prismatic 2f1010gAl2 O3 or 2f1120gAl2 O3 surfaces was much greater than that for 0001Al2 O3 due to the crystallographic penetration of basal twins on (0001). 3. Deformation basal twins had platelet morphologies, with widths vd0001v<<100 nm, and large aspect ratios d1010/d0001 or d1120/d0001 > 10. 4. At high resolution, basal twins had widths d0001=2n1/6[0001] and ABCBA stacking of (0006)Al planes across twin interfaces, consistent with 1/3h1010i partial dislocations gliding on Al±Al or Al±O slip planes. Twins were nucleated at the abraded surfaces. 5. Isovalent solutes 0.3 2 0.1at.%Cr and 0:420:1at:%Fe in ruby samples had no eect on the structure or distribution of the basal twins, and no segregation was detected. 6. Dislocations within the severe deformation zone were predominantly pyramidal 1=3h1120if1101g, with minor contributions from 1=3h1120i= h1010i 0001 and 1/3h1011i{0111}. 7. No rhombohedral twinning, h1010i{1210} prism glide or widespread non-basal dislocation Burgers vectors were observed in either the abraded substrates or crystalline abrasion debris, in contrast to deformation >4008C. 8. Directional stress build-up, due to basal twin shears and dislocation Burgers vectors lying on (0001), is thought to help initiate the observed extensive microcracking along {1102} rhombohedral and (0001) twin habit planes leading to abrasive wear. Subsurface cracking due to rhombohedral twin intersections did not occur.
AcknowledgementsÐB.J. Inkson would particularly like to thank Professor M. RuÈhle for support whilst at the MaxPlanck-Institut fuÈr Metallforschung, Stuttgart, and The Royal Society for additional funding. Professor D.R. Clarke is gratefully acknowledged for comments and photoluminescence measurements. CWRU Professor A.H. Heuer, K.P.D. LagerloÈf and P. Pirouz, and Dr H. Wu are thanked for enlightening discussions, and a referee for comments. REFERENCES 1. 2. 3. 4.
Hockey, B. J., J. Am. Ceram. Soc., 1971, 54(5), 223. Hockey, B. J., Proc. Br. Ceram. Soc., 1972, 20, 95. Becher, P. F., J. Am. Ceram. Soc., 1976, 59(34), 143. Barceinas-SaÂnchez, J. D. O. and Rainforth, W. M., Acta mater., 1998, 46(18), 6475. 5. Zarudi, I., Zhang, L. C. and Mai, Y.-W., J. Mater. Sci., 1996, 31, 905.
INKSON: ABRASION OF Al2O3 6. Zarudi, I., Zhang, L. C. and Cockayne, D., J. Mater. Sci., 1998, 33, 1639. 7. Wang, Y. and Mikkola, D. E., J. Am. Ceram. Soc., 1992, 75(12), 3252. 8. Lankford, J., J. Mater. Sci., 1977, 12, 791. 9. Lankford, J., J. Mater. Sci., 1978, 13, 351. 10. LagerloÈf, K. P. D., Heuer, A. H., Castaing, J., RivieÁre, J. P. and Mitchell, T. E., J. Am. Ceram. Soc., 1994, 77(2), 385. 11. Heuer, A. H., LagerloÈf, K. P. D. and Castaing, J., Phil. Mag. A, 1998, 78(3), 747. 12. Veit, K., Neues Jb. Miner. Geol. BeilBd, 1921, 45, 121. 13. Kronberg, M. L., Acta metall., 1957, 5, 507. 14. Geipel, T., Bilde-Sùrensen, J. B., Lawlor, B. F., Pirouz, P., LagerloÈf, K. P. D. and Heuer, A. H., Acta mater., 1996, 44(5), 2165. 15. Kaplan, W. D., Kenway, P. R. and Brandon, D. G., Acta metall. mater., 1995, 43(2), 835.
1895
16. Kenway, P. R., J. Am. Ceram. Soc., 1994, 77(2), 349. 17. Bilde-Sùrensen, J. B., Lawlor, B. F., Geipel, T., Pirouz, P., Heuer, A. H. and LagerloÈf, K. P. D., Acta mater., 1996, 44(5), 2145. 18. Chen, S.-J. and Howitt, D. G., Acta metall. mater., 1992, 40(12), 3249. 19. Hockey, B. J., in Deformation of Ceramic Materials, ed. R. C. Bradt and R. E. Tressler. Plenum Press, New York, 1975, p. 167. 20. Chen, S.-J. and Howitt, D. G., Phil. Mag. A, 1998, 78(3), 765. 21. Geipel, T., LagerloÈf, K. P. D., Pirouz, P. and Heuer, A. H., Acta mater., 1994, 42(4), 1367. 22. Heuer, A. H., Phil. Mag., 1966, 13, 379. 23. Bursill, L. A. and Lin, P. J., Phil. Mag. Lett., 1989, 60(1), 1. 24. Ma, Q. and Clarke, D. R., Acta metall. mater., 1993, 41(6), 1817.