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Study of energy vs misorientation for grain boundaries in gold by crystallite rotation method—I. [001] Twist boundaries
wlI-6l6O/XS S3.W +o.oo Copyrighl 1’ lYX5 I’ergmwn Press Ltd
,kra mefull. Vol. 33. No. 6. pp. 1113-IIIY. lYX5 Printed in Grear Bribin. All rights rescr~d
STUDY OF ENERGY VS MISORIENTATION FOR GRAIN BOUNDARIES IN GOLD BY CRYSTALLITE ROTATION METHOD-I. [OOl] TWIST BOUNDARIES SIU-WA1 CHAN and R. W. BALLUFFI Department of Materials Science and Engineering. Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. (Received I6 November 1984) Abstract-Small gold crystallites (-50-80 nm dia) were welded to thin film [OOI] single crystal gold substrates at a series of predetermined [OOl]twist angles in the range O-45”. A pure [OOI]twist boundary therefore existed in each welded neck region which could be observed directly by transmission electron microscopy at normal incidence. Upon annealing, the crystallites rotated around [OOI]when the boundary energy varied with 0. .The crystallites rotated into three misorientations corresponding to the special X.1 and Z5 misorientations and a symmetry related misorientation at 0 = 45”. These results indicate the existence of grain boundary dislocation (GBD) related cusps on the boundary energy vs 0 curve at ZI and 25. The rotations occurred conservatively by the motion of screw GBDs which could be observed directly by the transmission microscopy in certain regimes of 0. The results are relevant to recent calculations of the energies of [OOI] twist boundaries and the applicability of the GBD/structural unit model for grain boundaries. R&I&--De petits cristallites d’or (_ 50 d 80 nm de diam&tre) ont Cti soudCs sure des substrats d’or monocristallins en couches minces [OOI]g une s&k d’angles de torsion [OOl]pr&dCterminis entre 0 et 45”. II existe done un joint de torsion pure [OOI]dans chaque r&ion de soudure, que nous avons pu observer directement par microscopic tlectronique en transmission sous incidence normale. Au tours d’uo revenu, les cristallites toumaient autour de [OOI]lorsque l%nergie du joint variait avec 0. Les cristallites toumaient vers trois d&orientations qui correspondaient aux cas sp&iaux Zl et Z5 et zi une d&orientation reliQ par symttrie B 0 = 45”. Ccs r&&tats montrent l’existmcc de discontinuitis IiceS aux dislocations intergranulaires (DI) sur ks courbes de l’lnergie du joint de grains en fonction de 8 pour Xl et ZS. Lcs rotations s’effectuaient de man&e conservative par le diplacement de DI vis que I’on pouvait observer directement par microscopic ilectronique en transmission pour certaines valeurs de 0. Ces r<ats concement des calculs r¢s de l’knergie de joints de torsion [OOI]et I’applicabilitt du modele DI/unitt structurale aux joints de grains. Zusammenfassmg-Kleine Goldkristallite (Durchmesser - 50-80 nm) wurden auf dhnne, einkristalline [OOl]-orientierte Goldkristalle in einer Reihe vorbestimmter [OOl]-Drillwinkel zwischen 0 und 45” aufgeschweiBt. Daher ergab sich in jedem geschweiBten Bereich einer reine [OOl]-Drillgrenze, die im Elektronenmikroskop direkt in Aufsicht beobachtet werden konnte. Wiihrend des Ausheikns rotierten die Kristallite un [OOl]. wenn sich die Komgrenzenergie mit 0 iinderte. Die Kristallite drehten sich in drei Fehlorientierungen hinein, die den besondenn Grientienmgcn Z = I und Z = 5 und einer symmetriebedingten Fehlorientierung bie 0 = 45” entsprachen. Die Brgebnisse zeigen, da13in der Kurve der Komgrenzmergie gegen den Winkel B Dellen durch das Vorhandmsein von Komgrenzversetzungen bei I: = 1 und Z = 5 auftreten. Diese Drehungen liefm konservativ iiber die Bewegung von ScbraubenKomgrenzversetzungen ab. wekhe direkt im Elektronenmikroskop Tur gewisse e-Betiche beobachtet w&m konntm. Diese E!rgebnisse haben Bedeutungfiir neuereBerechnungmder Energie von [OOl]-Drillkomgrenzm und IIir die Anwendbarkeit des Modelks von Komgrenzversetzungen und der Struktureinheitm auf Komgrenzm.
1. INTRODUCMON
According to the Coincidence Site Lattice (CSL) model for grain boundaries [l] secondary relaxations in the form of localized secondary grain boundary dislocations (GBDs) may occur in order to preserve patches of boundary of relatively high coincidence. (The degree of coincidence is customarily measured by C, the reciprocal of the fraction of atoms in coincidence.) Efforts have been underway for some time to determine the detailed core structure of [OOI] III3
twist boundaries in Au within the context of this model using both experimental and computer simulation techniques. Experimentally, the forms of the local&d (or partially localized) secondary GBDs have been studied by means of transmission electron microscopy [2], and in other work further information about the detailed atomic structure of the boundary core has been obtained by X-ray diffraction techniques [3,4]. On the simulation side, molecular statics calculations of the boundary structure and energy have been made using the pair-wise
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interatomic potential model [S-7]. A recent review of this work is given in [8]. Of considerable importance are the strengths of the secondary relaxations (i.e. GBDs) which may be present. These relaxations should produce cusps on the boundary energy, y(6), vs twist angle, 8, curve due to the elastic energy associated with them [9], and important additional information regarding the extent of the agreement (or disagreement) between observed and calculated results can therefore be obtained from a comparison of possible observed and calculated cusps. The y(0) curve for [OOI] twist boundaries has not been determined experimentally for Au, but a determination has been made [9] for the similar noble metal Cu. Unfortunately, the scatter of the Cu data is so large that any expected’secondary GBD cusps cannot be resolved f9], and only the large primary Cl cusp at 8 = 0” is evident. In. view of this situation the present work was performed to obtain experimental information about the possible presence of cusps on the y(O) curve for Au using the crystallite rotation method [lO-15J. In previous work this method has utilized specimens in which a large number of small single crystal particles ~~st~lit~) is sintered to llat single crystal substrates of the same material at random misorientations. A grain boundary exists in the neck region of each sintered crystallite and, when y(0) of the boundary varies with 6, the crystallite tends to rotate during annealing in a direction which reduces the energy of the boundary. Upon prolonged annealing the ensem-
ble of crystallites reaches a me&stable confq.uration in which each crystallite has rotated into the nearest available n-&orientation corresponding to a local minimum (cusp) on its associated grain boundary energy surface. The major minima (cusps) therefore collect the largest number of crystallites and by measuring the distribution of final miso~en~tions information about the existence of major energy cusps is obtained. A number of successful experiments of this type has been carried out with, for example, crystallites of Cu [12] and Ag [13]. In these cases clear evidence for rotations into a number of preferred misorientations was obtained from statistical measurements of the distribution of final misorientations. (In no cases were the detailed rotations of individual crystallites observed.) Very recently, N. L. Peterson and C. L. Wiley (private communication) have attempted to apply this method to the simitar f.c.c. metal Au. In this work -80 pm dia Au spheres were sintered randomly to single crystal substrates, and searches were made for crystallite rotations after anneals as long as 1700h at * 1030°C. Rather surprisingly, no detectable rotations into non-Cl cusps were found under these conditions. The explanation of this result is not obvious when viewed in the light of those obtained, for example. for Cu [ 121 and Ag [13]. In the present work we have modified and extended the above techniques in an attempt to obtain highly
BOUNDARlES
IN GOLD-i
specific information about possible cusps on the y(0) curve for [OOI]twist boundaries in Au. Considerably smaller crystallites (50-80 nm dia) were employed than previously, and a method was developed in which these crystallites could be sintered to a thin (-30 nm thick) substrate at pr~ete~in~ [OOI] twist misorientations. The specimens were then mounted on electron microscope grids and either furnace-annealed or annealed in situ on an electron microscope hot stage. Clearly observed rotations occurred at relatively low temperatures (i.e. near half the absolute melting temperature) which were monitored and measured by electron microscopy techniques. The rotations were always exclusively around [OOI], and by starting the crystallites at different angles extending over the full range from 0 to 45” and observing the directions and magnitudes of the rotations, direct information about the shape of the y(6) curve was obtained. Finally, the specimens were sufficiently thin so that the grain boundary region in each neck could be observed directly at normal incidence by transmission electron microscopy. It is well established from other work [2] that visible grids of screw GBDs are present in [OOl] twist boundaries in Au in different regimes of 8, These consist of Cl primary GBDs and C13, Cl7 and C5 secondary GBDs at 6 near 0, 22.6, 28.1 and 36.9”, respectively. Also, the diffraction contrast due to these GBDs tends to become weaker as C increases or their spacing decreases 1161. In a number of cases in the present work it was possible to observe directly the Z1 and 65 GBD structures in the neck regions and also to observe changes in these structures as the crystallites rotated. 2. EXPERIMENTAL The Au crystallites were prepared by first vapor&positing a discontinuous Au film of average thickness 30 nm on a cleaved (001) surface of NaCl held at 300°C. This film, on its substrate, was then sealed in a quartz tube in an atmosphere of Ar at 190 torr and annealed for 1.5 h at 550°C. This anneal caused the Au film to break up into a ~st~bution of discrete crystallites which were epitaxially attached to the NaCl substrate in the same orientation as the substrate. A typical view of a distribution of crystallites, in the same arrangement they had when attached to the substrate (see caption), is shown in Fig. 1. As may be seen, the crystaltites were fairly equi-axed with a tendency to be faceted. The single crystal (001) Au substrate film (w 30 nm thick) was prepared by vapor deposition at 300°C on a single crystal (001) Ag film (>200 nm thick) previously vapor deposited at 300°C on a cleaved (001) rocksalt surface. The Au crystallites (stili on their rocksalt substrates and, therefore, all in the same orientation) were welded to the Au substrate (still attached to its NaCi substrate) at a predetermined twist angle by simply pressing the two assemblies together face-to-face for
CHAN and BALLUFFI:
ENERGY OF GRAIN BOUNDARIES IN GOLD-I
Fig. 3. Oblique SEM view of crystalks substrate film.
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attached to Au
Fig. 1. Gold single crystal particles (crystallites) embedded in an evaporated amorphous carbon film. The crystallites (while epitaxially attached to the NaCI) were embedded in an amorphous carbon film which was then “lifted” off the substrate and viewed as shown.
3-5 min at 200°C as illustrated schematically in Fig. 2. After welding, the substrate was dissolved away in HI0 and HNO, and the final specimen was mounted on an electron-microscope grid. An oblique view of a typical distribution of attached crystallites is shown in Fig. 3 and a transmission electron microscopy view at normal incidence to the substrate crystal is shown in Fig. 4(a).
Specimens of the type shown in Fig. 4(a) were annealed in vacua at temperatures between 300 and 450°C for times ranging between 5 and 30min in order to provide the thermal activation required for the rotation of the crystal&s. The rotations were measured by as many as three different methods depending upon the circumstances. These included measurements of: (1) crystal rotations in [OOl] selected area diffraction patterns taken from regions including the substrate and one or two crystallites. Rotations measured by this method were accurate to - &p; (2) the spacings, d, of screw GBDs observed in the neck region [as seen, for example, in Fig. 4(c, d)]. In such cases A6 was obtained from the well known [2] relation
where A9 = angular deviation from the reference bicrystal defining the GBDs, and b = Burgers vector; and (3) rotations of the electron microscope images of the projected crystallite silhouettes as seen, for example, in Fig. 4. These rotations were usually measured relative to a twin trace in the substrate as seen, for example, in the bottom central region of Fig. 4(a). A more detailed description of the experimental techniques may be found in [17]. 3. RESULTS 3.1. Rotations fowardr the C 1 (0 = 0’) misorientation Au film ( 30nm) ‘Ag film (300 nm)
All crystal&s initially welded to the substrate at 8 f 34” rotated towards the Zl misorientation. This is shown, for example, in Fig. 4 where the crystallites seen in Fig. 4(a) were initially at 6 u 30”. After 15 min
at -4OO”C, Fig. 4(b), considerable rotation occurred,
N&l
-
3mm
sinpk
crystal
c
Fig. 2. Schematic view of the welding operation which attached the Au crystallites to the Au single crystal film at a predetermined twist angle, 0.
and for 3 of the 6 crystallites the rotation was sufficiently large that networks of Zl lattice screw GBDs with b = l/2( 110> became readily visible in the boundary region. After an additional 30min anneal, Fig. 4(c), considerably more rotation occurred, and GBD networks became visible in 4 neck regions. Also, the networks became coarser in a number of the boundaries as the misorientations
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CHAN and BALLUFFI:
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a
d
c
Fig. 4. TEM view (at normal incidence to substrate film) of crystalks attached to Au substrate filrm (a) directly after welding operation; (b) same as (a) except for I5 mia anneal at -400°C; (c) same as (b) except for additional 30min anneal at -400°C; (d) same as (c) except for additional 30min anneal at - 400°C.
approached Z 1. Finally, after an additional 30 min, Fig. 4(d), still further rotations and coarsening of the screw GBD networks occurred. It is noted that the different crystallites generally rotated at different rates (e.g. Fig. 4) and that occasionally the boundary at a neck was lost discontinuously at an intermediate stage as a result of migration. In this respect we mention that the periphery of each boundary could be seen quite distinctly in the transmission view, and that the diameter of the boundary region was almost as large as the crystallite diameter in all observations. We also point out that while the grids of the 21 lattice screw GBDs were readily observed as the crystallites
approached the Zl misorientation (0 = O”), we did not detect grids of 217 or Z 13 secondary screw GBDs in a number of specimens near the 217 and 213 misorientations. This result is undoubtedly due to the weakness of these latter GBDs and the relatively poor conditions for their observation, i.e. large specimen thicknesses, small boundary areas, and specimen bending. A diagram illustrating all of the observed rotations towards Zl is presented in Fig. 5. 3.2. Rotations ration
towards the CS (0 = 36.9”) misorien-
All crystallites
started
at
angles in the range
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Fig. 5. Diagram showing all crystallite rotations observed in present work. Direction and extent of each rotation indicated by single arrow. Circled points indicate cases whereno rotations occurred.
35” cz 6 4 40” rotated towards the Z5 (0 = 36.9”) mi~~en~tion during annealing {Fig. S). An example is shown in Fig. 6 for a crystallite started at 0 = 38.6”. Also visible in the grain boundaries in this se& of electron micrographs are the expected [2] square grids of XS secondary screw GBDs with Burgers vector b = l/10(310). As the annealing proc&ed (see caption), and the crystallite approached the exact Z5 Fig. 7. Diffraction ‘patterns from region containing the misorientation, the spacing of these screw GBDs substrate and a single crystallite.Upper8 = 35.1”(near ZS). increased according to equation (1). Lower: After rotation to 6 = 36.9”(exact ZS). Clear evidence for the rotation of a crystallite into the exact ES misorientation could also be obtained from the selected area diffraction pattern for a crys- tation as illustrated in Fig. 5. The 6 = 45” misorientallite and substrate as shown in Fig. 7. The initial tation may be regarded as a special symmetry mispattern in Fig. 7 (upper) for the near-Z5 case is highly o~entation, since the structure of a twist boundary complex and contains large numbem of closely with ~sori~n~tion 45” - A@is symmetry-related to spaced fine spots due to double diffraction. After an a boundary with misorientation 45” + AtI and has anneal of 5 min at 350°C and rotation into the exact exactly the same energy. X5 misorientation, Fig. 7 (lower), the corresponding pattern is much simpler and more regular. All singly 4. DISCUSSIONAND CONCLUSIONS diffracted and doubly diffracted spots now fall on the The present result that boundary energy-induced simple square pattern corresponding to the I;5 DSC rotations occurred provides clear evidence for the Lattice produced by the reciprocal lattices of the two existence of energy minima (cusps) on the energy diffracting crystals. versus misorientation surface for grain boundaries in 3.3. Rotations towards the 8 = 45” symmetry mti- Au. This result appears to be generally consistent orientation with the previous crystallite rotation experiments All crysMites which were started at an&s greater performed, for example, on Cu [12] and Ag [13] but than 8 = 40” rotated towards the 6 = 45” misorien- inconsistent with the recent experiments of Peterson and Wiley (private communication) on Au. The causes for the apparent inconsistency with the latter experiments are presently undetermined. All of the crystallite rotations observed in the present work were pure twist rotations around [OOI] and, therefore, the boundaries did not develop any tilt components as the crystallites rotated. Other work [IS] has shown that tilt components introduced
Fig. 6. Grid of X5 secondary screw GBDs in n&k region of crystaliite as it rota&d progressivelyfrom 8 = 38.6” in (a) towards the 25 f? = 36.9“ mi~~entatio~
in (b) and (cf.
into [OOl] twist boundaries are accommodated by families of parallel line defects corresponding to edge GBDs possessing the effective Burgers vector, ba = 5 [OOI]. Families of GBDs of this type are ex-
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I5
I 20
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8 (dog) Fig. 8. schematic curve of [OOl]twist boundary energy, y(e), vs twist angle. 0. consistent with present results (see text).
petted to introduce a trough-shaped cusp on the generalized energy vs misorientation surface of the boundary which is always centered at the pure twist misorientation. The ,observation that the iotations were always of pure twist type can therefore be understood as the result of the tendency of the system to remain at the bottom of this energy trough during the twist rotations into the Zl, CS and 6 = 45” local minima which were distributed along the trough. A y(6) curve for pure [OOl] twist boundaries which possesses a form consistent with the present results is shown in Fig. 8. The curve is constructed so that the slope of the curve at each point is the negative of the sign of the observed rate of rotation. This curve is only schematic, of course, since the present experimental results only provide information about the sign of the slope of the curve at each point. It must be emphasized that the exact depth of the cusp at IX and a number of other features of the curve shown are presently undetermined. We have drawn the curve with small “non-trapping” cusps at Z 13 and 217 which, of course, is consistent with the present rotation experiments. The presence of these non-trapping cusps can be justified on the basis of the relatively weak secondary GBDs which are known [2] to be present near 213 and 217. As pointed out in [9], the total energy of a boundary containing secondary GBDs can be approximated as the sum of the core energy plus the long range elastic energy of the GBDs. Since the latter energy is of a cusped form, we expect the y(e) curve to exhibit at least some form of cusp-like behavior at Cl3 and X17. However, these cusps can be relatively weak and non-trapping, as shown, due to possible masking effects produced by the additive core energy term (see [9]) and the relative Babcock and R. W. Balluffi (research in pm&e&) have recently detected grids of sccondarv GBDs in near-Z29 (0 = 43.6’) 10011 twist boundark in Au. This result indicates the pres&ce of an additional small nontrapping cusp at 0 = 43.6” which should be added to Fig. 8. Of course, even higher order nontrapping cusps may be present which are beyond our present capabilities of detection.
*Footnote added in proof: S. E.
BOUNDARIES
IN GOL%I
weakness of the Xl3 and 217 GBDs. It should also be noted at this point that the true depths of the cusps at, for example, Cl3 and 217, may have been underestimated in the present experiment because the long range elastic energy of the GBDs was partly relaxed when the GBD spacing became comparable to the dimensions of the grain boundary neck region at small values of A6.* The y(6) curve for [OOl] twist boundaries in the noble metals has been calculatged by means of the pairwise interatomic potential model employing a variety of potentials [5-7], and these results have been discussed very recently in [8]. As pointed out in [8], the y(0) curves calculated with a number of noble metal potentials exhibit no convincing resolvable cusp at X5. However, a small cusp appears to be present for one particular potential, i.e. the “spline 1” potential used by Wolf [6]. Additional calculations, described in (81, show that b= l/10(310) screw GBDs present in the Z5 interface tend to possess localized cores when this potential is used. This result is therefore consistent with the presence of the small cusp at Z5 on the calculated y(6) curve, the experimental observation of C5 secondary GBDs, and the Z5 cusp constructed in Fig. 8. Further work is required in order to establish and understand more thoroughly the results calculated with the pairpotential model using different potentials. The mechanism for the crystallite rotations is undoubtedly the conservative glissile loss of screw GBDs from the grid present in the boundary as first described by Pond and Smith [1 11.This process was, of course, observed directly in the regions where the screw GBDs were visible by transmission electron microscopy. Bristowe and Balluffi [19] have recently described structural unit/GBD models for [OOl] twist boundaries which possess grids of screw GBDs over all angles of misorientation. The conservative loss of these screw GBDs at all angles of misorientations (including those in which screw GBDs cannot be observed) therefore seems the most likely model for the observed rotations. In fact, the crystallite rotations observed in. the present work and previously (e.g. in [12-151) over wide ranges of misorientation may be taken as evidence that high angle grain boundaries contain ordered structures describable in terms of structural units and corresponding GBDs. The observation that thermal activation is required for crystallite rotation indicates that local barriers of some kind must be present which inhibit the otherwise glissile motion of the screw GBDs. The detailed nature of these barriers is presently unknown. Finally, we mention that crystallites of the present type can be welded to substrate crystals to form boundaries possessing tilt components. Upon subsequent annealing, the crystallites are found to rotate in order to eliminate the tilt components by the climb of edge GBDs in the grain boundaries. These results will be presented shortly in Part II of the present work [20].
CHAN and BALLUFFI:
ENERGY OF GRAIN
nck,rolc,/c’c/.~~,r~r~,~rl-This work was supported by the U.S. Department of Energy under Grant No. DE-FG02-84ER4Sl IO. REFERENCES I. R. W. Balluffi and G. B. Olson. Trans. Am. IN.
In press. 2. T. Schober and R. W. Ball&i,
Phil.
Mug.
21,
P. D. Bristowe and S. L. Sass,
109
28, 575
(1980).
J. Budai, P. D. Bristowe and S. L. Sass, Acta 699 (1983). 5. P. D. Bristowe and A. G. Cracker, Phil Mug.
4.
(1977).
13. Acra metall.
metall.
31,
A 38,487
14. 15.
16.
(1978). 6. 7. 8.
D: Wolf, Acfa mefall. 32, 735 (1984). D. Schwartz, V. Vitek and A. P. Sutton, Phil. Msg. In press. R. W. Balluffi, P. D. Bristowe, S. E. Babcock, Siu-Wai Chan, E. P. Kvam and J. S. Liu. 1. Physique. In press.
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R. W. Ballulli. P. D. Bristowe. and A. Brokman, in Aduuf~s i,r Ccvcrrrrkv: J’d. 5(cdited by M. F. Yan and A. H. Hcuer). p. 15.Am. Ceram. Sot. (1983). Grain Growth and 10. P. G. Shcwmon. in Rcc,r~:c~cr//i-_ario,l. Tesrurev. p. 165. Am. Sot. Metals. Metals Park, OH ( 1966). II. R. C. Pond and D. A. Smith. Scripta merall. 11, 77 12. G.
(1970). 3.
IN GOLD-l
9.
Min.
Engrs.
BOUNDARIES
17. 18. 19. 20.
Herrmann. H. Gleiter and G. Biro. Acfa mefall. 24, 353 (1976). H. Sautter. H. Gleiter and G. Bare. Ac~u JJWJ!~. 25.467 (1977). H. Mykura, Acta merall. 27, 243 (1979). H. Kuhn. G. Biro and H. Gleiter. Acta metal/. 27. 959 (1979). R. W. Ball&i, Y. Komem and T. Schober, Surf Sci. 31, 68 (1972). Siu-Wai Chan, Ph.D. thesis, M.I.T. (1985). T. Schober and R. W. Ball&i, Phil. Msg. 24, I65 (1971). P. D. Bristowe and R. W. Balluffi. J. Physique. In press. Siu-Wai Chan and R. W. Balluffi. To be published.
,kra mefull. Vol. 33. No. 6. pp. 1113-IIIY. lYX5 Printed in Grear Bribin. All rights rescr~d
STUDY OF ENERGY VS MISORIENTATION FOR GRAIN BOUNDARIES IN GOLD BY CRYSTALLITE ROTATION METHOD-I. [OOl] TWIST BOUNDARIES SIU-WA1 CHAN and R. W. BALLUFFI Department of Materials Science and Engineering. Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. (Received I6 November 1984) Abstract-Small gold crystallites (-50-80 nm dia) were welded to thin film [OOI] single crystal gold substrates at a series of predetermined [OOl]twist angles in the range O-45”. A pure [OOI]twist boundary therefore existed in each welded neck region which could be observed directly by transmission electron microscopy at normal incidence. Upon annealing, the crystallites rotated around [OOI]when the boundary energy varied with 0. .The crystallites rotated into three misorientations corresponding to the special X.1 and Z5 misorientations and a symmetry related misorientation at 0 = 45”. These results indicate the existence of grain boundary dislocation (GBD) related cusps on the boundary energy vs 0 curve at ZI and 25. The rotations occurred conservatively by the motion of screw GBDs which could be observed directly by the transmission microscopy in certain regimes of 0. The results are relevant to recent calculations of the energies of [OOI] twist boundaries and the applicability of the GBD/structural unit model for grain boundaries. R&I&--De petits cristallites d’or (_ 50 d 80 nm de diam&tre) ont Cti soudCs sure des substrats d’or monocristallins en couches minces [OOI]g une s&k d’angles de torsion [OOl]pr&dCterminis entre 0 et 45”. II existe done un joint de torsion pure [OOI]dans chaque r&ion de soudure, que nous avons pu observer directement par microscopic tlectronique en transmission sous incidence normale. Au tours d’uo revenu, les cristallites toumaient autour de [OOI]lorsque l%nergie du joint variait avec 0. Les cristallites toumaient vers trois d&orientations qui correspondaient aux cas sp&iaux Zl et Z5 et zi une d&orientation reliQ par symttrie B 0 = 45”. Ccs r&&tats montrent l’existmcc de discontinuitis IiceS aux dislocations intergranulaires (DI) sur ks courbes de l’lnergie du joint de grains en fonction de 8 pour Xl et ZS. Lcs rotations s’effectuaient de man&e conservative par le diplacement de DI vis que I’on pouvait observer directement par microscopic ilectronique en transmission pour certaines valeurs de 0. Ces r<ats concement des calculs r¢s de l’knergie de joints de torsion [OOI]et I’applicabilitt du modele DI/unitt structurale aux joints de grains. Zusammenfassmg-Kleine Goldkristallite (Durchmesser - 50-80 nm) wurden auf dhnne, einkristalline [OOl]-orientierte Goldkristalle in einer Reihe vorbestimmter [OOl]-Drillwinkel zwischen 0 und 45” aufgeschweiBt. Daher ergab sich in jedem geschweiBten Bereich einer reine [OOl]-Drillgrenze, die im Elektronenmikroskop direkt in Aufsicht beobachtet werden konnte. Wiihrend des Ausheikns rotierten die Kristallite un [OOl]. wenn sich die Komgrenzenergie mit 0 iinderte. Die Kristallite drehten sich in drei Fehlorientierungen hinein, die den besondenn Grientienmgcn Z = I und Z = 5 und einer symmetriebedingten Fehlorientierung bie 0 = 45” entsprachen. Die Brgebnisse zeigen, da13in der Kurve der Komgrenzmergie gegen den Winkel B Dellen durch das Vorhandmsein von Komgrenzversetzungen bei I: = 1 und Z = 5 auftreten. Diese Drehungen liefm konservativ iiber die Bewegung von ScbraubenKomgrenzversetzungen ab. wekhe direkt im Elektronenmikroskop Tur gewisse e-Betiche beobachtet w&m konntm. Diese E!rgebnisse haben Bedeutungfiir neuereBerechnungmder Energie von [OOl]-Drillkomgrenzm und IIir die Anwendbarkeit des Modelks von Komgrenzversetzungen und der Struktureinheitm auf Komgrenzm.
1. INTRODUCMON
According to the Coincidence Site Lattice (CSL) model for grain boundaries [l] secondary relaxations in the form of localized secondary grain boundary dislocations (GBDs) may occur in order to preserve patches of boundary of relatively high coincidence. (The degree of coincidence is customarily measured by C, the reciprocal of the fraction of atoms in coincidence.) Efforts have been underway for some time to determine the detailed core structure of [OOI] III3
twist boundaries in Au within the context of this model using both experimental and computer simulation techniques. Experimentally, the forms of the local&d (or partially localized) secondary GBDs have been studied by means of transmission electron microscopy [2], and in other work further information about the detailed atomic structure of the boundary core has been obtained by X-ray diffraction techniques [3,4]. On the simulation side, molecular statics calculations of the boundary structure and energy have been made using the pair-wise
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ENERGY
OF GRAIN
interatomic potential model [S-7]. A recent review of this work is given in [8]. Of considerable importance are the strengths of the secondary relaxations (i.e. GBDs) which may be present. These relaxations should produce cusps on the boundary energy, y(6), vs twist angle, 8, curve due to the elastic energy associated with them [9], and important additional information regarding the extent of the agreement (or disagreement) between observed and calculated results can therefore be obtained from a comparison of possible observed and calculated cusps. The y(0) curve for [OOI] twist boundaries has not been determined experimentally for Au, but a determination has been made [9] for the similar noble metal Cu. Unfortunately, the scatter of the Cu data is so large that any expected’secondary GBD cusps cannot be resolved f9], and only the large primary Cl cusp at 8 = 0” is evident. In. view of this situation the present work was performed to obtain experimental information about the possible presence of cusps on the y(O) curve for Au using the crystallite rotation method [lO-15J. In previous work this method has utilized specimens in which a large number of small single crystal particles ~~st~lit~) is sintered to llat single crystal substrates of the same material at random misorientations. A grain boundary exists in the neck region of each sintered crystallite and, when y(0) of the boundary varies with 6, the crystallite tends to rotate during annealing in a direction which reduces the energy of the boundary. Upon prolonged annealing the ensem-
ble of crystallites reaches a me&stable confq.uration in which each crystallite has rotated into the nearest available n-&orientation corresponding to a local minimum (cusp) on its associated grain boundary energy surface. The major minima (cusps) therefore collect the largest number of crystallites and by measuring the distribution of final miso~en~tions information about the existence of major energy cusps is obtained. A number of successful experiments of this type has been carried out with, for example, crystallites of Cu [12] and Ag [13]. In these cases clear evidence for rotations into a number of preferred misorientations was obtained from statistical measurements of the distribution of final misorientations. (In no cases were the detailed rotations of individual crystallites observed.) Very recently, N. L. Peterson and C. L. Wiley (private communication) have attempted to apply this method to the simitar f.c.c. metal Au. In this work -80 pm dia Au spheres were sintered randomly to single crystal substrates, and searches were made for crystallite rotations after anneals as long as 1700h at * 1030°C. Rather surprisingly, no detectable rotations into non-Cl cusps were found under these conditions. The explanation of this result is not obvious when viewed in the light of those obtained, for example. for Cu [ 121 and Ag [13]. In the present work we have modified and extended the above techniques in an attempt to obtain highly
BOUNDARlES
IN GOLD-i
specific information about possible cusps on the y(0) curve for [OOI]twist boundaries in Au. Considerably smaller crystallites (50-80 nm dia) were employed than previously, and a method was developed in which these crystallites could be sintered to a thin (-30 nm thick) substrate at pr~ete~in~ [OOI] twist misorientations. The specimens were then mounted on electron microscope grids and either furnace-annealed or annealed in situ on an electron microscope hot stage. Clearly observed rotations occurred at relatively low temperatures (i.e. near half the absolute melting temperature) which were monitored and measured by electron microscopy techniques. The rotations were always exclusively around [OOI], and by starting the crystallites at different angles extending over the full range from 0 to 45” and observing the directions and magnitudes of the rotations, direct information about the shape of the y(6) curve was obtained. Finally, the specimens were sufficiently thin so that the grain boundary region in each neck could be observed directly at normal incidence by transmission electron microscopy. It is well established from other work [2] that visible grids of screw GBDs are present in [OOl] twist boundaries in Au in different regimes of 8, These consist of Cl primary GBDs and C13, Cl7 and C5 secondary GBDs at 6 near 0, 22.6, 28.1 and 36.9”, respectively. Also, the diffraction contrast due to these GBDs tends to become weaker as C increases or their spacing decreases 1161. In a number of cases in the present work it was possible to observe directly the Z1 and 65 GBD structures in the neck regions and also to observe changes in these structures as the crystallites rotated. 2. EXPERIMENTAL The Au crystallites were prepared by first vapor&positing a discontinuous Au film of average thickness 30 nm on a cleaved (001) surface of NaCl held at 300°C. This film, on its substrate, was then sealed in a quartz tube in an atmosphere of Ar at 190 torr and annealed for 1.5 h at 550°C. This anneal caused the Au film to break up into a ~st~bution of discrete crystallites which were epitaxially attached to the NaCl substrate in the same orientation as the substrate. A typical view of a distribution of crystallites, in the same arrangement they had when attached to the substrate (see caption), is shown in Fig. 1. As may be seen, the crystaltites were fairly equi-axed with a tendency to be faceted. The single crystal (001) Au substrate film (w 30 nm thick) was prepared by vapor deposition at 300°C on a single crystal (001) Ag film (>200 nm thick) previously vapor deposited at 300°C on a cleaved (001) rocksalt surface. The Au crystallites (stili on their rocksalt substrates and, therefore, all in the same orientation) were welded to the Au substrate (still attached to its NaCi substrate) at a predetermined twist angle by simply pressing the two assemblies together face-to-face for
CHAN and BALLUFFI:
ENERGY OF GRAIN BOUNDARIES IN GOLD-I
Fig. 3. Oblique SEM view of crystalks substrate film.
1115
attached to Au
Fig. 1. Gold single crystal particles (crystallites) embedded in an evaporated amorphous carbon film. The crystallites (while epitaxially attached to the NaCI) were embedded in an amorphous carbon film which was then “lifted” off the substrate and viewed as shown.
3-5 min at 200°C as illustrated schematically in Fig. 2. After welding, the substrate was dissolved away in HI0 and HNO, and the final specimen was mounted on an electron-microscope grid. An oblique view of a typical distribution of attached crystallites is shown in Fig. 3 and a transmission electron microscopy view at normal incidence to the substrate crystal is shown in Fig. 4(a).
Specimens of the type shown in Fig. 4(a) were annealed in vacua at temperatures between 300 and 450°C for times ranging between 5 and 30min in order to provide the thermal activation required for the rotation of the crystal&s. The rotations were measured by as many as three different methods depending upon the circumstances. These included measurements of: (1) crystal rotations in [OOl] selected area diffraction patterns taken from regions including the substrate and one or two crystallites. Rotations measured by this method were accurate to - &p; (2) the spacings, d, of screw GBDs observed in the neck region [as seen, for example, in Fig. 4(c, d)]. In such cases A6 was obtained from the well known [2] relation
where A9 = angular deviation from the reference bicrystal defining the GBDs, and b = Burgers vector; and (3) rotations of the electron microscope images of the projected crystallite silhouettes as seen, for example, in Fig. 4. These rotations were usually measured relative to a twin trace in the substrate as seen, for example, in the bottom central region of Fig. 4(a). A more detailed description of the experimental techniques may be found in [17]. 3. RESULTS 3.1. Rotations fowardr the C 1 (0 = 0’) misorientation Au film ( 30nm) ‘Ag film (300 nm)
All crystal&s initially welded to the substrate at 8 f 34” rotated towards the Zl misorientation. This is shown, for example, in Fig. 4 where the crystallites seen in Fig. 4(a) were initially at 6 u 30”. After 15 min
at -4OO”C, Fig. 4(b), considerable rotation occurred,
N&l
-
3mm
sinpk
crystal
c
Fig. 2. Schematic view of the welding operation which attached the Au crystallites to the Au single crystal film at a predetermined twist angle, 0.
and for 3 of the 6 crystallites the rotation was sufficiently large that networks of Zl lattice screw GBDs with b = l/2( 110> became readily visible in the boundary region. After an additional 30min anneal, Fig. 4(c), considerably more rotation occurred, and GBD networks became visible in 4 neck regions. Also, the networks became coarser in a number of the boundaries as the misorientations
1116
CHAN and BALLUFFI:
ENERGY OF GRAIN BOUNDARIES
IN GOLD-I
a
d
c
Fig. 4. TEM view (at normal incidence to substrate film) of crystalks attached to Au substrate filrm (a) directly after welding operation; (b) same as (a) except for I5 mia anneal at -400°C; (c) same as (b) except for additional 30min anneal at -400°C; (d) same as (c) except for additional 30min anneal at - 400°C.
approached Z 1. Finally, after an additional 30 min, Fig. 4(d), still further rotations and coarsening of the screw GBD networks occurred. It is noted that the different crystallites generally rotated at different rates (e.g. Fig. 4) and that occasionally the boundary at a neck was lost discontinuously at an intermediate stage as a result of migration. In this respect we mention that the periphery of each boundary could be seen quite distinctly in the transmission view, and that the diameter of the boundary region was almost as large as the crystallite diameter in all observations. We also point out that while the grids of the 21 lattice screw GBDs were readily observed as the crystallites
approached the Zl misorientation (0 = O”), we did not detect grids of 217 or Z 13 secondary screw GBDs in a number of specimens near the 217 and 213 misorientations. This result is undoubtedly due to the weakness of these latter GBDs and the relatively poor conditions for their observation, i.e. large specimen thicknesses, small boundary areas, and specimen bending. A diagram illustrating all of the observed rotations towards Zl is presented in Fig. 5. 3.2. Rotations ration
towards the CS (0 = 36.9”) misorien-
All crystallites
started
at
angles in the range
CHAN
I
0
,
I
I
5
IO
15
and BALLUFFI:
-w 20 25 fffdcq)
ENERGY
. ,
1 30
35
OF GRAlN
I 40
45
Fig. 5. Diagram showing all crystallite rotations observed in present work. Direction and extent of each rotation indicated by single arrow. Circled points indicate cases whereno rotations occurred.
35” cz 6 4 40” rotated towards the Z5 (0 = 36.9”) mi~~en~tion during annealing {Fig. S). An example is shown in Fig. 6 for a crystallite started at 0 = 38.6”. Also visible in the grain boundaries in this se& of electron micrographs are the expected [2] square grids of XS secondary screw GBDs with Burgers vector b = l/10(310). As the annealing proc&ed (see caption), and the crystallite approached the exact Z5 Fig. 7. Diffraction ‘patterns from region containing the misorientation, the spacing of these screw GBDs substrate and a single crystallite.Upper8 = 35.1”(near ZS). increased according to equation (1). Lower: After rotation to 6 = 36.9”(exact ZS). Clear evidence for the rotation of a crystallite into the exact ES misorientation could also be obtained from the selected area diffraction pattern for a crys- tation as illustrated in Fig. 5. The 6 = 45” misorientallite and substrate as shown in Fig. 7. The initial tation may be regarded as a special symmetry mispattern in Fig. 7 (upper) for the near-Z5 case is highly o~entation, since the structure of a twist boundary complex and contains large numbem of closely with ~sori~n~tion 45” - A@is symmetry-related to spaced fine spots due to double diffraction. After an a boundary with misorientation 45” + AtI and has anneal of 5 min at 350°C and rotation into the exact exactly the same energy. X5 misorientation, Fig. 7 (lower), the corresponding pattern is much simpler and more regular. All singly 4. DISCUSSIONAND CONCLUSIONS diffracted and doubly diffracted spots now fall on the The present result that boundary energy-induced simple square pattern corresponding to the I;5 DSC rotations occurred provides clear evidence for the Lattice produced by the reciprocal lattices of the two existence of energy minima (cusps) on the energy diffracting crystals. versus misorientation surface for grain boundaries in 3.3. Rotations towards the 8 = 45” symmetry mti- Au. This result appears to be generally consistent orientation with the previous crystallite rotation experiments All crysMites which were started at an&s greater performed, for example, on Cu [12] and Ag [13] but than 8 = 40” rotated towards the 6 = 45” misorien- inconsistent with the recent experiments of Peterson and Wiley (private communication) on Au. The causes for the apparent inconsistency with the latter experiments are presently undetermined. All of the crystallite rotations observed in the present work were pure twist rotations around [OOI] and, therefore, the boundaries did not develop any tilt components as the crystallites rotated. Other work [IS] has shown that tilt components introduced
Fig. 6. Grid of X5 secondary screw GBDs in n&k region of crystaliite as it rota&d progressivelyfrom 8 = 38.6” in (a) towards the 25 f? = 36.9“ mi~~entatio~
in (b) and (cf.
into [OOl] twist boundaries are accommodated by families of parallel line defects corresponding to edge GBDs possessing the effective Burgers vector, ba = 5 [OOI]. Families of GBDs of this type are ex-
1118
CHAN
/ 0
and BALLUFFI:
ENERGY
OF GRAIN
II I
5
IO
I
I5
I 20
I
25
I 30
I
I
35
40
4s
8 (dog) Fig. 8. schematic curve of [OOl]twist boundary energy, y(e), vs twist angle. 0. consistent with present results (see text).
petted to introduce a trough-shaped cusp on the generalized energy vs misorientation surface of the boundary which is always centered at the pure twist misorientation. The ,observation that the iotations were always of pure twist type can therefore be understood as the result of the tendency of the system to remain at the bottom of this energy trough during the twist rotations into the Zl, CS and 6 = 45” local minima which were distributed along the trough. A y(6) curve for pure [OOl] twist boundaries which possesses a form consistent with the present results is shown in Fig. 8. The curve is constructed so that the slope of the curve at each point is the negative of the sign of the observed rate of rotation. This curve is only schematic, of course, since the present experimental results only provide information about the sign of the slope of the curve at each point. It must be emphasized that the exact depth of the cusp at IX and a number of other features of the curve shown are presently undetermined. We have drawn the curve with small “non-trapping” cusps at Z 13 and 217 which, of course, is consistent with the present rotation experiments. The presence of these non-trapping cusps can be justified on the basis of the relatively weak secondary GBDs which are known [2] to be present near 213 and 217. As pointed out in [9], the total energy of a boundary containing secondary GBDs can be approximated as the sum of the core energy plus the long range elastic energy of the GBDs. Since the latter energy is of a cusped form, we expect the y(e) curve to exhibit at least some form of cusp-like behavior at Cl3 and X17. However, these cusps can be relatively weak and non-trapping, as shown, due to possible masking effects produced by the additive core energy term (see [9]) and the relative Babcock and R. W. Balluffi (research in pm&e&) have recently detected grids of sccondarv GBDs in near-Z29 (0 = 43.6’) 10011 twist boundark in Au. This result indicates the pres&ce of an additional small nontrapping cusp at 0 = 43.6” which should be added to Fig. 8. Of course, even higher order nontrapping cusps may be present which are beyond our present capabilities of detection.
*Footnote added in proof: S. E.
BOUNDARIES
IN GOL%I
weakness of the Xl3 and 217 GBDs. It should also be noted at this point that the true depths of the cusps at, for example, Cl3 and 217, may have been underestimated in the present experiment because the long range elastic energy of the GBDs was partly relaxed when the GBD spacing became comparable to the dimensions of the grain boundary neck region at small values of A6.* The y(6) curve for [OOl] twist boundaries in the noble metals has been calculatged by means of the pairwise interatomic potential model employing a variety of potentials [5-7], and these results have been discussed very recently in [8]. As pointed out in [8], the y(0) curves calculated with a number of noble metal potentials exhibit no convincing resolvable cusp at X5. However, a small cusp appears to be present for one particular potential, i.e. the “spline 1” potential used by Wolf [6]. Additional calculations, described in (81, show that b= l/10(310) screw GBDs present in the Z5 interface tend to possess localized cores when this potential is used. This result is therefore consistent with the presence of the small cusp at Z5 on the calculated y(6) curve, the experimental observation of C5 secondary GBDs, and the Z5 cusp constructed in Fig. 8. Further work is required in order to establish and understand more thoroughly the results calculated with the pairpotential model using different potentials. The mechanism for the crystallite rotations is undoubtedly the conservative glissile loss of screw GBDs from the grid present in the boundary as first described by Pond and Smith [1 11.This process was, of course, observed directly in the regions where the screw GBDs were visible by transmission electron microscopy. Bristowe and Balluffi [19] have recently described structural unit/GBD models for [OOl] twist boundaries which possess grids of screw GBDs over all angles of misorientation. The conservative loss of these screw GBDs at all angles of misorientations (including those in which screw GBDs cannot be observed) therefore seems the most likely model for the observed rotations. In fact, the crystallite rotations observed in. the present work and previously (e.g. in [12-151) over wide ranges of misorientation may be taken as evidence that high angle grain boundaries contain ordered structures describable in terms of structural units and corresponding GBDs. The observation that thermal activation is required for crystallite rotation indicates that local barriers of some kind must be present which inhibit the otherwise glissile motion of the screw GBDs. The detailed nature of these barriers is presently unknown. Finally, we mention that crystallites of the present type can be welded to substrate crystals to form boundaries possessing tilt components. Upon subsequent annealing, the crystallites are found to rotate in order to eliminate the tilt components by the climb of edge GBDs in the grain boundaries. These results will be presented shortly in Part II of the present work [20].
CHAN and BALLUFFI:
ENERGY OF GRAIN
nck,rolc,/c’c/.~~,r~r~,~rl-This work was supported by the U.S. Department of Energy under Grant No. DE-FG02-84ER4Sl IO. REFERENCES I. R. W. Balluffi and G. B. Olson. Trans. Am. IN.
In press. 2. T. Schober and R. W. Ball&i,
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R. W. Ballulli. P. D. Bristowe. and A. Brokman, in Aduuf~s i,r Ccvcrrrrkv: J’d. 5(cdited by M. F. Yan and A. H. Hcuer). p. 15.Am. Ceram. Sot. (1983). Grain Growth and 10. P. G. Shcwmon. in Rcc,r~:c~cr//i-_ario,l. Tesrurev. p. 165. Am. Sot. Metals. Metals Park, OH ( 1966). II. R. C. Pond and D. A. Smith. Scripta merall. 11, 77 12. G.
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Herrmann. H. Gleiter and G. Biro. Acfa mefall. 24, 353 (1976). H. Sautter. H. Gleiter and G. Bare. Ac~u JJWJ!~. 25.467 (1977). H. Mykura, Acta merall. 27, 243 (1979). H. Kuhn. G. Biro and H. Gleiter. Acta metal/. 27. 959 (1979). R. W. Ball&i, Y. Komem and T. Schober, Surf Sci. 31, 68 (1972). Siu-Wai Chan, Ph.D. thesis, M.I.T. (1985). T. Schober and R. W. Ball&i, Phil. Msg. 24, I65 (1971). P. D. Bristowe and R. W. Balluffi. J. Physique. In press. Siu-Wai Chan and R. W. Balluffi. To be published.