Abstract-Stacking faults associated with climb-dissociated basal and prism plane dislocations in sapphire. (a-A&O& akr plastic deformation at elevated ...
OOOl-6MO/84S3.00+0.00 Press Ltd
ACID meroll. Vol. 32. No. I, pp. 97-105. 1984 Printed in Great Britain. All rights rexrvcd
STACKING
Copyright0 1984Pergamon
FAULT
ENERGY
IN SAPPHIRE
(a -A120,) K. D. P. LACERL()F, T. E. MITCHELL and A. H. HEUER Department of Metallurgy and Materials Science. Case Institute of Technology, Case Western Reserve University. Cleveland, OH 44106, U.S.A. J. P. RIVIl?RE, J. CAD02
and J. CASTAING
Laboratoire de Physique des Mattiaux, CNRS-92195, Meudon Ckdex, France D. S. PHILLIPS Department of Metallurgical and Mining Engineering, University of Illinois, Urbana, IL 61801, U.S.A. (Received I3 June 1983) Abstract-Stacking faults associated with climb-dissociated basal and prism plane dislocations in sapphire (a-A&O& akr plastic deformation at elevated temperatures have been studied. In both cases, the fault vector is l/3 (IOTO) and it is only the cation sublattice which is faulted. The fault energy on {IOTO}and { 1120) planes are similar, between 0.1 and 0.25 J/m*. Analysis of the geometry of the l/3 (lOTO) fault show that one vacancy and two distinct interstitial faults are possible in this structure;one of the interstitial faults is thought to have the lowest energy. R&um&Nous avons CtudiC les fautes d’empilement associkes a la dissociation par montke des dislocations introduites par glisaements basal et prismatique dans le saphir a-A1,OP Dans les deux CBS, le vccteur de faute est l/3 (lOTO) et seulement le sous-r&au cationique est fauti. Lcs tnergiea de fautes sur la plans { 1010) et { 11%) sent analogues et comprises entre 0.1 et 0,25 J/m*. L’analyse de la g&m&rie des fautes montre que une faute lacunaire et deux fautes interstitielles peuvent exister; il est probable que c’est l’une des fautes interstitielles qui a la plus basse Cnergie. Z--Die
Stapclfehler. die durch Kletter-Dissoziation von Versetzungen auf Basis- und
Prismenebenen in Saphir (a-A&O,) nach plastischer Verformung bei hiiheren Temperaturen vorliegen, wurden untersucht. In beiden Fallen ist der Verschiebungsvektor l/3 (IOTO); der Stapelfehler liegt ausschliil3lich im Kation-Untergitter. Die Energien der Stapelfehler auf den { lOTO}-und {l lzO}-Ebenen sind ghnlich; sic liegen zwischen 0.1 und 0,25 J/m2. Aus einer geometrischen Analyse des l/3( loTo)Fehlers folgt, da6 ein Leerstellen- und zwei Zwischengitteratom-Stapelfehler in dicser Struktur m6glich sind. Einer der Stapelfehkr vom Zwischengitteratomtyp hat wahrscheinlich die niedrigste Energie.
1. INTRODUCMON
It has been more than twenty-five years since Kronberg [1] predicted the dominance of basal slip (0001) l/3(1120) in the high temperature plastic deformation of sapphire (a-Al,O,). One of the principal assumptions underlying Kronberg’s prediction was his belief that basal dislocations would dissociate by glide into quarter partials according to the dislocation reactions 1/3(1120)-+1/3(10To)+
1/3(01To)
(1)
1/3(10To)-+l/9(2TTo)+
l/9(1120).
(2)
and
Numerous deformation experiments [2-S] involving samples deformed by basal slip and analysis of dislocation dissociation [6,7] have been published in the intervening years but the Kronberg glide dissociation is not generally observed, implying that the stacking faults produced by equations (1) and (2) in the basal plane have a very high energy. A.M
WI-2
97
On the other hand, samples deformed by basal slip do contain dissociated dislocations but the dissociation involves dislocation climb rather than glide; the faults can occur on either {1lZO} or { lOTO} prism planes [7j and appear to involve only the production of half partials via equation (1). This fault involves only the cation sublattice, as 1/3(lOTO) is a perfect vector in the approximate hcp anion sublattice. The Kronberg quarter partial [reaction (2)] has been observed in only two instances., Hockey [8] studied interfacial mismatch dislocations in cracks in Al24 that had undergone partial but spontaneous crack healing. These interfacial dislocation networks contained dislocations which had reacted according to reaction (2); however, the fault energy was so high that the faults spontaneously transformed during electron microscopy observation by the nucleation, growth and coalesccna of 1/3(lOTO) partial loops. Some non-basal crack networks were also found which contained two sets of l/3( lOTO) partials crosslinked by a set of 1/3[0001] partial dislocations. These latter partials also appear in irradiated samples [9].
98
LAGERLOF t-1al.:
STACKING FAULT ENERGY IN SAPPHIRE
The second instance of the Kronberg quarter partial has been found in sapphire deformed by prism plane slip {1120) (1 TOO) and will be shown below. This slip system occurs in crystals of suitable orientation, e.g. with zero resolved shear stress on the basal plane [IO]. The very long (0.822 nm) ( IOTO) dislocations can dissociate into three colinear partials (loTo)-+1/3(10To)
+ 1/3(10To)+
1/3(10T0)(3)
to give faults similar to that arising from reaction (l), and both glide dissociation [l I] and climb dissociation [12] have been reported. Stacking fault energies y have been deduced in these various studies by noting the distance r between the bounding 1/3(10T0) partial dislocations giving values of y between 0.2 and 0.6 J/m*. In this paper, we provide improved electron microscopy observations of r and discuss the geometry of the 1/3(10TO) fault on various planes. Specifically, we will use (i) a comparison between computed and experimental bright field images [13] of extended dislocations in samples deformed by basal slip and (ii) refined contrast analysis of weak beam images [14] of extended dislocations in samples deformed by prism plane slip to obtain better estimates -of r. In the Appendix, we further show that the observed ready &composition during prism plane slip of (lOTO) dislocations via the reaction [lo]. (lOTO) +1/3(2TTO) + l/3( 1120)
(4)
(which produces no stacking fault) yields still another estimate of y which agrees well with those derived from TEM observations. 2. EXPERIMENTAL PROCEDURE AND RESULTS 2.1. Basal slip During plastic deformation by basal slip, 1/3(11?O) dislocations form and multiply. Analysis of the dislocation microstructure by TEM in thin foils prepared from deformed samples show that a major portion of the dislocation debris consists of predominantly edge-type dislocations, primarily in the form of dislocation dipoles and elongated dislocation loops. Pure screw and mixed dislocations are rarely observed, which indicates that the mobility of such dislocations is quite high. The elastic interaction between two edge dislocations gliding on parallel slip planes increases the shear stress required for the dislocations to move past each other. The edge dislocations trap each other, and the mobility of two dislocations forming an edge-trapped dipole is very low. Further, by cross-slip of the screw segments of an edge-trapped dipole, a prismatic dislocation loop can be formed with no glide mobility whatsoever. During glide, the l/3(1120) dislocations are probably undksociuted (or dissociated only at the core), while when their motion ceases, they can
coooll
t I1201stacking faults
Fig. I. Schematic view of a climb-dissociated dipole formed after basal slip in AI,O,.
dissociate according to equation (1) by self-climb, and create the l/3( lOTo) fault on a (1120) plane [6,7]. Self-climb involves diffusion of matter from one of the partial dislocations to the other and is very fast due to the short diffusion distance and rapid diffusion path. It is likely that the self-climb process occurs for edge dislocations trapped in a dipole or a loop even before the deformation has stopped, as part of the dynamic work-hardening/recovery process [15]. This would lower the mobility further to virtually zero. Self-climb can possibly occur in “free” edge dislocations, but probably only after the deformation has stopped, and it is not certain that the self-climb will lead to the equilibrium separation of the partial dislocations. By considering the interaction energy of the two straight partial dislocations with non-colinear Burgers vectors, the stacking fault energy can readily be related to the equilibrium separation distance, r,. Following Hirth and Lothe [16] @I~*(2 ’
=
+
VI
8nr,(l -v)
(9
9*(2+v) =24nr,(l -v) where p is the shear modulus (150 GPa), v is Poisson’s ratio (0.24), and b,, b2 and b the Burgers vector of the two partials and the unidissociated dislocation respectively [see equation (l)]. By using foils cut parallel to {1lzO), i.e. normal to the stacking fault plane, the two climb-dissociated partial dislocations can be imaged using g = k3300, since g-b = f 1 and i 1 for the respective partials. For the case of no climb-dissociation the contrast would disappear since g-b = 0 for the perfect dislocation. The dislocation geometry in such foils is illustrated in Fig. 1. Due to image shift with respect to the actual position of a dislocation [17] along Cith the fact that g-b has the opposite sign for therespective partials. inside/outside contrast is obtained using g = +3JOO. The images overlap when inside contrast from the partial dislocations occur and the
LAGERLC)F
et al.:
STACKING
Fig. 2. (a) Bright field image of dislocations A and B formed after basal slip, g = 3300. (b) Weak beam dark field image of dislocations A and B, g = 3300. (c) Computer simulated image of dislocation A, g = 3300. (d) Computer simulated image of dislocation B, g = 3300.
partials appear as a strong line. For outside contrast, the contrast from the partials is well separated and two faint distinct lines can be observed. The actual positions of the partials and their separation distance can best be determined by comparison of the micrographs with computer simulated images [18]. Figure 2 shows two dislocations in a dipole with the computer simulations of the respective dislocations. Figure 2(a) is a bright field image, (b) is a weak beam dark field image, (c) is the computer simulation ?f dislocation A in bright field and (d) the simulation of dislocation B. The actual position of the partials in the computer simulated images are marked with arrows. Comparison between the TEM micrographs and the simulated images yields a separation distance between the two partials of 8 nm, which gives a value for y of a 1/3[10TO]stacking fault on a 11 120) plane of 0.16 J/m*, where the equilibrium separation distance is taken to be the maximum separation observed. Phillips et al. [7j had previously reported a separation of 7 nm and a fault energy of 0.18 J/m* for a “free” dislocation but had not performed any computer simulations. 2.2. Prism plane slip The same { IzlO} l/3( lOTO) fault can form during plastic deformation by {12 10) ( 1010) prism plane slip which has heen extensively studied at temperatures above 1400°C [lo]. This dissociation was first studied for a few [IOTO]dislocations of mixed character and
FAULT
ENERGY
IN SAPPHIRE
99
was assumed to result from glide dissociation; the stacking fault energy was found to be 0.3 J/m* [l I]. The same fault can occur on {ZllO} and {llZO} planes at 60” to the Burgers vector. This has been observed in [I OTO]dislocation loops formed by dipole breakup after prism plane slip. The estimated energy of this climb fault is 0.4 J/m* [12]. Other configurations have now been studied after prism plane slip and several additional fault planes have been identified. In these experiments, specimens were deformed in compression at 1450°C; at the end of the tests, they were quickly pulled out of the furnace and air-quenched to prevent rearrangement of the faults. Figure 3 shows an example of a symmetrical elongated loop dissociated into three 1/3[10T0] partials perpendicular to the stacking fault plane [19]. The orientations of the different segments have been determined and are along [2201], [220’13, [OTl2], [OTlZ] and [OOOI]. For an edge dislocation, when the three partials have the same contrast, the dissociation occms by pure climb [14]. The fault plane of the long [OOOl] segments of the loop is (TOlO) (Fig. 3). In the mixed segments, a { 1120) plane common to the fault and the loop is consistent with the observation (Fig. 3). This single elongated loop, then, shows the two types of stacking faults which have been observed to date. The (lOTO) 1/3[10TO] climb fault is bounded by pure edge dislocations; therefore the offset between image and dislocation is the same for the three partials and the fault energy can be directly deduced from the observed width of dissociation, assuming the dislocations are straight. We 6nd y, = 0.23 rt 0.03 J/m* and y2 = 0.16 f 0.015 J/m*. The two values come from the two different widths of the ribbons and correspond to a 1/3[lOTO] and a 2/3[10TO] fault respectively; these faults are crystalographically different, as will be shown below. The energy of the {TT~o}f l/3( lOTO) fault cannot easily be determined from the geometry of the loop (Fig. 3). The dislocation segments are short and the line tension on the inner partials gives rise to a larger dissociation. Thus, the y values we determine are lower bounds for the fault energy; we find values between 0.08 J/m* and 0.13 J/m*. For the (TT2O) planes there is no differences between 1/3[TOlO] and - 1/3[TOlO] faults [l2]. A dissociated, almost straight, dislocation has also been observed (Fig. 4a); segments parallel to (ZOl) appear to show evidence for dissociation into four partials [19], suggesting that the central partial is possibly dissociated according to equation (2). This dissociation probably occurs here in spite of a high stacking fault energy since only the difference between y for equations (2) and (3) is involved for the central partial. The fault plane is about 20” to the Burgers vector, as if a gliding split dislocation had been quenched while rotating its dissociation plane to a climb position. The thin foil was annealed, which
LAGERLOF
100
et al.:
STACKING
FAULT ENERGY
I
IN SAPPHIRE
100nm
I-- -
g = 0530
9’3300
-30.
b
-a
+30’
Fig, 3. EIongated loop observed after prism plane slip in A&O, showing climb dissociation. (a)
Mierographsunder two tiltingangles f30”. (b) Schematicrepnsentation of the loop. caused rearrangement of the dislocation (Fig. 4b) [19];the dislocation plane is 20” to the Burgers vector but the dissociation of the inner partial is no longer visible. The contrast of the partials and the dislocation configuration are very close to what BildeSorensen et al. fl 1] observed; it is likely that their dissociation also involved a climb component. As the dislocation segments are parallel to [2201], the fault plane can be neither (1210) nor (TOlO);it was determined from tilting experiments to be {lTO2). This plane is not the rhombohedral twin plane [20]. We have not yet found enough examples to contirm that this plane is a common fault plane. A detailed analysis of the contrast of the partials rationalized the uneven intensities of the contrast and permitted dete~nation of the exact position of the dislocation cores [14]; y equal to 0.25 J/m’ has been deduced, which is in the same range as those found for other stacking faults.
to experiment, in that the basal fault (0001) 1/3[OTlO] was lowest in energy (0.5 J/m2), while faults on the prism system (2110) 1/3(OlTO>and (lOTO)1/3[0tT0] had much larger energies (4 and 5 J/m* respectively). Other connations that y is fairly isotropic in A1203are given by the examples of elongated loops found in samples deformed by basal slip. At the tip of the climbdissociated loops, where the fault plane must change no constrictions were ever observed [7J (Fig. 5). Similar results occur in sampfw deformed by prism plane slip,’ where a dissociated
