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MECHANISMS FOR GRAIN BOUNDARY MIGRATION INVOLVING INTERACTIONS
BETWEEN COMPONENT DISLOCATIONS
R. Scholz, C. Bauer
To cite this version:
R. Scholz, C. Bauer. MECHANISMS FOR GRAIN BOUNDARY MIGRATION INVOLVING IN-
TERACTIONS BETWEEN COMPONENT DISLOCATIONS. Journal de Physique Colloques, 1990,
51 (C1), pp.C1-623-C1-628. �10.1051/jphyscol:1990198�. �jpa-00230367�
COLLOQUE DE PHYSIQUE
Colloque Cl, suppl6ment au nol, Tome 51, janvier 1990
MECHANISMS FOR GRAIN BOUNDARY MIGRATION INVOLVING INTERACTIONS BETWEEN COMPONENT DISLOCATIONS
R. SCHOLZ and C.L. BAUER*
Institut fiir Festktirperphysik und Elektronenmikroskopie, DDR-4020 Falle, D.R.G.
Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Resume: Les 'oints de flexion [OOL] clans les films minces bicristallis d'or, caracteris& par les deviations -elles des inclinations
<loo>
et < l l O > symnt?triques, o1r et6 fabri uts par l a depos~tion en vapeur, l a croisstuice en epitaxie, et la coalescence r6gEe sur les substrats bicristdlins&
clorure de soclium. Par la suite, l a structure et les cinttiques de nligration cles joints cle grains ont et6 eruegistrkes par ~nicroscopie electronique ell t~aistnission. L a structure des joints de gr'ains est caract6ris6e par cles rangs des dislocations cle flexjon (an)<[ 10>et/ou a<100>, dont es acernents et repartitions sor~t en fotlction de l a cl6sorientation cles grains et I'inclination cles pints. L a migration L s joints cle grams est effectuke par une 6cl1mge des dislocations de f l e x h n avoisinrntes sor es yltuls de glissanent co11jugu6s A f o m ~ e r les dislocatio~~s de flexion a<100>, renverselner~t de ce processus, et atuuhilatio~l occasionelle cles clislocations cle flexion (a/2)<110> du sigrie c o ~ i t r a i i ~ . Cettes reactions rc?duisent une force rnotrice our 1a migration des joints de grains resseniblant la force riotrice de capillaritk orcKarre pour
1.
1 joint conth~u. %S dsultats sont e11 bon accord avec 1es idees actuelles concernant l a structure cles joints de grams et les reactions entre les dislocations, et aident h 1'6lucidation des m6canismnes atorniques pour l a migration des joints de grains.
Abstract: [001] tilt boundaries i n bicrystalline thin films o f gold, characterized by occasional deviations from
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syn~inetnc <100> and <l 10> inclinations, have been roduced b y a combination o f valor deposition, epitaxial growth, and controued codescence on [OOl] bicryst&ine substrates of sodium c111oride. Subsequently, grain boundary structure and migration kinetics are recorded in situ by transmission electron microscopy. Grain botindary structure is characterized b y arrays of (a/2)<110> andlor a<100> edge dislocations, whose spacing and distribution depend on grain misorientation and grain boundary inclination. Grain boundary migration is effected by interchange o f adjacent (a/2)<110> edge dislocations tllrough plide on conjugate slip planes to fomi?<loo>
edge dislocat~ons, reversal of this process, and occasio~ial annihdat~on o f (a/2)<110> dislocations o f o poslte sign.
These reactions produce a driving force for grain boundary migra!ion, similar to the usual c?pillary 6)iving force for a continuum grain boundary. Results are in good agreement w ~ t h current concepts o f gram boundary structure and dislocation reactions, and help to elucidate atomic mechiulisms for grain boundary migration.
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INTRODUCTIONIn the past decade, great progress has been made in characterizing grain boundary structure in terms of microscopic components (repetitive atomic units, dislocation arrays, etc.) and verifying existence of these components by high-resolution transmission electron microscopy (TEM).'-~ Corresponding information on atomic movements during grain boundary migration, however, is not yet commonly available. In fact, observed grain boundary structure is seldom related explicitly to grain boundary mob~lity.~,~ The purpose of this investigation, therefore, is to examine movement of grain boundaries composed of individual (edge) dislocations directly and in situ by TEM, and to interpret results in terms of glide (and climb) of component dislocations, thereby helping to elucidate atomic mechanisms for grain boundary migration.
The remainder of this article is divided into several sections: First, relations between grain boundary structure and migration kinetics are reviewed in Sec. 2, then experimental details are outlined, experimental results presented, and analyzed in Secs. 3, 4, and 5, respectively, and, lastly, important conclusion stemming from this investigation are summarized in Sec. 6.
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BACKGROUNDRecently, special grain boundary configurations have been produced in bicrystalline thin films of gold by controlled deposition, island nucleation, epitaxial growth, and coalescence on (001) bicrystalline substrates of sodium ch~oride,~ as illustrated schematically in Fig. 1. During deposition, small islands (hatched areas) are nucleated and grow epitaxially on either side of the grain boundary in the sodium chloride substrate (solid horizontal line), as depicted in (a). Subsequently, these islands merge to form larger islands, if similarly oriented, or inclined grain boundary segments, if dissimilarly oriented, as depicted in (b).
Continuation of this process results in a distribution of holes, some of which pin grain boundaries in inclined position, as depicted in (c). Finally, the (bicrystalline) film is removed from the substrate and annealed, thus promoting closure of the smallest holes and subsequent relaxation of the unpinned grain boundary to an equilibrium position, as depicted in (d).
Therefore, grain boundary migration can be investigated as a function of grain misorientation and grain boundary inclination and, thereafter, related to concomitant grain boundary structure under controlled expelimental conditions.
An example of the initial (pinned) grain boundary configuration and subsequent relaxation is presented in Fig. 2, wherein a 20°
I0011 tilt boundary in gold is pictured (a) in the as-deposited condition, and (b), (c) following subsequent sequential anneals.
Initially, the grain boundary is oriented along symmetric <110> directions with the tip slightly inclined with respect to the film surface, as pictured in (a). From corresponding lattice fringe images, the (edge) dislocation spacing is determined to be 0.827 nm, in good agreement with calculated spacing for (a/2)<110> dislocations in a 20° [001] grain boundary (0.823 nm). After
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990198
Figure 1. Schematic illustration of sequential nucleation, epitaxial growth, and coalescence of gold on (001) bicrystalline substrates of sodium chloride: (a) formation of three (epitaxial) islands on each side of the substrate grain boundary (solid horizontal line), (b) growth of the islands (sometimes across the substrate grain boundary) to form larger epitaxial islands and inclined grain boundaries at regions of island impingement, (c) coalescence of the islands to form (six) separate holes, some of which pin the grain boundary in inclined positions, and (d) removal of the film from the bicrystalline substrate and closure of the smallest hole during subsequent annealing, thus allowing the grain boundary to relax to an equilibrium configuration.
Figure 2. Annealing sequence revealing motion of a 20° [OOl] tilt boundary in a bicrystalline thin film of gold: (a) as-deposited film with straight segments of the boundary inclined in symmetric < l 102 directions and characterized by an average dislocation spacing of 0.827 nm, (b) annealed for 60 min at 220°C, (c) reannealed for 150 min at 220%.
annealing, however, significant grain boundary'movement is discernible, as pictured in (b) and (c). Namely, curvature of the grain boundary tip decreases and component dislocations assume less orderly positions. Moreover, grain boundary displacement
5
(as measured from the tip apex) decreases with increasing time and decreasing temperature in accordance with behavior expected for a capillary driving force y/c, where y denotes effective grain boundary surface tension.Results summarized in Figs. 1 and 2 demonstrate that local grain boundary deviatlons from planarity can be produced and subsequently investigated by TEM in sltu during relaxation of the grain boundary to an equilibrium configuration. Since individual (edge) dislocations can be resolved in these (tilt) grain boundaries, the process of grain boundary migration can be investigated and analyzed in terms of interactions between component dislocations. More recent experimental results are presented in this article, wherein relationships between grain boundary structure, expressed by arrays of edge dislocations, and migration kinetics are analyzed.
3
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EXPERIMENTAL DETAILSThin films of gold were produced on bicrystalline substrates of sodium chloride, gmwn from the melt by the Czochralski technique with two seed crystals rotated with respect to one another about the common [OOl] axis by angle 8, and subsequently cleaved along common (001) faces. Gold was then deposited, on substrates heated to about 300°C, to a nominal thickness of 0.5 nrrl in a vacuum of 200 NPa by a pulsed arc techniqueg in order to produce a distribution of epitaxial islands. The substrate temperature was then reduced to 220°C, without breaking vacuum, and additional gold was deposited to a nominal total thickness of 12 nm by vapor deposition at a rate of about 0.07 nmts. Films were then removed from their underlying substrates by dissolution of sodium chloride in distilled water and mounted on copper or gold grids for subsequent examination in a JEOL JEM 100C transmission electron microscope. Further details concerning specimen preparation are presented e l ~ e w h e r e . ' ~ ~ ~ ~
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EXPERIMENTAL RESULTSA typical example of grain boundary migration is presented in Fig. 3, wherein a relaxation sequence for a 22.6O [OOlJ I l t boundary in gold subjected to local heating by the electron beam in situ is pictured. The first recorded grain boundary configuration is pictured in (a), wherein linear (horizontal) grain boundary segments, composed of (a/2)~110> dislocations, and Inclined grain boundary segments, composed of both (aM)cl lO> and ac100> dislocations in the symmetric <l 10> inclination, are visible. The inclination angle between horizontal and inclined grain boundary segments and spacing between adjacent (a/2)<110> dislocations are measured to be 27
*
l0 and 0.736 f 0.001 nm, respectively. In addition, ledges are visible at theFlgure 3. Annealing sequence revealing motion of a nominal 22.6O tilt boundary in a bicrystalline thin film of gold gold due to (localized) heating by the incident electron beam (estimated temperature: 250°C): (a) initial observation and after (b) 27, (c) 40, (d) 93, (e) 140, and (f) 193 min. A solid line, representing position of the grain boundary depicted in Fig. 3 (a), is superposed on the stationary symmetric <110> segments depicted in Figs. 3 (b) through 3 (f) in order to accentuate grain boundary movement.
Periodic spacing between adjacent (d2)<110> dislocations in the symmetric c1 10s (horizontal) inclination is 0.736 nm.
left extremity of the upper horizontal grain boundary segment. After an elapsed time of 27 min (b) local grain boondarj movement is evident by slight displacement of both extremities of the upper horizontal boundary segment, through creation and subsequent movement of grain boundary ledges. After an elapsed time of 40 min (c), however, the boundary configuration depicted in (a) is almost restored, demonstrating nearly random motion of grain boundary ledges. After an elapsed time of 93 min (d), significant grain boundary displacement, again effected by ledge movement, is evident. After an elapsed time of 140 min (e), further grain boundary displacement is evident. In this particular case, nearly random motion of grain boundary ledges over a distance of more than 15 nm in about 2 s of exposure time is recorded by the horizontal blurred dislocation images.
Finally, after an elapsed time of 193 min, the grain boundary has relaxed to a nearly equilibrium configuration and further movement is restricted to random motion of remaining (geometrical) ledges. A solid line, representing position of the grain boundary depicted in Fig. 3 (a), is superposed on the stationary symmetric c l 10s segments depicted in Figs. 3 (b) through 3 (f) in order to accentuate subsequent grain boundary displacement.
Interpretation of the grain boundary relaxation process in terms of movement (glide and climb) of component dislocations is addressed in the following section of this article.
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DISCUSSIONFrom the series of micrographs presented in Fig. 3, it is evident that grain boundary migration is effected by nearly random movement of grain boundary ledges. In general, low-angle tilt boundaries in gold may be characterized by various combinations of(a/2)~110> and ac100> edge dislocation^,'^ as illustrated schematically in Fig. 4. In the first case (a), a low-angle [OOIj symmetric tilt boundary, composed of (a/2)c110, edge dislocations, is inclined along a symmetric c100> direction, where inclination angle $ is measured with respect to the symmetric < l 102 direction. Other inclinations between symmetric <loo> and c110> directions are represented by various combinations of symmetric c110> and <loo> grain boundary segments, as Illustrated schematically in (b) through (e). Geometrically equivalent grain boundary configurations may be generated by glide of adjacent (a/2)<110> edge dislocations on conjugate slip planes to form ac100> edge dislocations. Therefore, one configuration may be transformed to the other by glide of (and reaction between) component dislocations.
Spacing between adjacent (a/2)<110> edge dislocations in a symmetric c l 10s tilt boundary h is given by the expression
where b denotes the Burgers vector. For 8 = 22.6' and b
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0.286 nm (for gold), h is computed to be 0.729 nm, in good agreement with the measured value (cf. Fig. 3) of 0.736 f 0.001 nm. In addition, structure of the inclined (non-symmetric) grain boundaries pictured in Figs. 3 (a) through 3 (f) is represented by Fig. 4 (c), since these grain boundaries subtend an angle of about 27O with the symmetric <110> inclknation. Indeed by careful examination of bright field and lattice fringe images, the characteristic (d2 [ l 101, (d2) [ l 101, (d2) [ l 1 O] ... repeat pattern, or equivalent, can be discerned.13According to the previous discussion (cf. Fig. 4), structure of [OOI] tilt boundaries may be represented by combinations of (a/2)<110> andtor ac100r edge dislocations. Typical examples are illustrated schematically in Fig. 5, wherein structure of parallel segments of symmetric (a) <loo> and (b) < l 10> tilt boundaries, represented by arrays of (dZ)cl10> edge dislocations
COLLOQUE DE PHYSIQUE
Flgure 4. Schematic illustration of (geometric) distribution of (a/2)<110> edge dislocations in a [001] tilt boundary inclined (a) 45.0 (symmetric <loo> inclination), (b) 33.7, (c) 26.6, (d) 18.4, and O0 (symmetric < l l0 > inclination) with respect to a symmetric
< l 10> inclination. Equivalent (geometric) distributions may be produced by glide of adjacent (a/2)<110> dislocations o:l conjugate slip planes to form a<100> dislocations.
and connected by non-symmetric grain boundary segments, is depicted. In principle, local grain boundary displacements (central regions) may relax to an equilibrium (planar) configuration by repetitive glide and reaction of component dislocations. In the first case (a), grain boundary movement is effected by repetitive glide of adjacent dislocations on conjugate slip planes to form a<lOO> dislocations, and subsequent decomposition of resulting a<100> dislocations to reform (a12)<110> dislocations on their original slip planes (cf. dashed square). Continuation of this process produces a planar <loo> symmetric grain boundary without reduction in the number of (a/2)<110> dislocations; i.e., dislocations react with but do not annihilate one another. In the second case (b), grain boundary movement cannot be effected merely by glide of adjacent (a/2)<110> dislocations on conjugate slip planes, because a certain subset can only glide parallel to the symmetric c1 10> grain boundary. Accordingly, the dislocation interchange process described for (a) allows pairs of dislocations of opposite sign to annihilate one another by glide on common slip planes parallel to the symmetric <l 10> (horizontal) grain boundary segment. Continuation of this process produces a planar <loo> symmetric grain boundary with fewer (a/2)<1 10> dislocations; i.e.. dislocations react with and partially annihilate one another. Configurations (a) and (b) correspond to grain boundaries pictured in Figs. 2 and 3, respectively.
Relationship between grain boundary velocity and driving force can also be deduced from the previous discussion. For the symmetric < l 10> case (cf. Fig. 5 b) and when the grain boundary tip displacement
5
is equal to a multiple of the unit ledge height h, a corresponding multiple of two (a/2)<110> dislocations of opposite sign are annihilated, thereby releasing an energy of 2 r per unit length of dislocation, wherer
denotes dislocation energy per unit length.14 A relationship between driving force (rlhk) tan cp and grain boundary (tip) velocity dvdt is given by the expressiondydt = (Mr/nh5) tan @
or
c2
= Kt,where M and n denote, respectively, grain boundary mobility (DikT) and number of atoms per unit grain boundary area, and K = (2rMInh) tan
+.
(Equivalently, the driving force may be derived from the attractive force between two (a/2)<110> dislocations of opposite sign and separated by distance 2Ejtanb.)
Therefore, grain boundary tip displacement5
varies parabolically with time and exponentially with temperature, exactly as for the capillary driving torce in a continuum grain boundary.I5 Measured values ofc2,
as obtained from the sequence partially presented in Fig. 3, are plotted as a function of time t in Fig. 6. In spite ofFlgure 5. Structure of parallel segments of symmetric (a) <loo> and (b) <l102 tilt boundaries, represented by arrays Of
(a;2)1110> edge dislocations and connected by non-symmetric grain boundary segments. In either case, local grain boundary displacement (central region) may relax to an equilibrium (planar) configuration by repetitive glide and reaction of component dislocations. The dashed square represents unit displacement of a grain boundary ledge (cf. Fig. 7).
Flgure 6. Square of grain boundary tip displacement (as measured form the tip apex)
t2
(cf. Fig. 3) as a function of time t.Temperature is estimated to be about 250°C.
considerable uncertainty of actual tip displacement, time, and temperature, results may be characterized by a linear relationship between
t2
and t, with a slope of about 10-l$ cm21s.If movement of symmetric c1 10> and <loo> tilt boundaries can be effected merely by glide andlor annihilation of (a/2)<110>
edge dislocations, why is the process of grain boundary migration thermally activated? This question can be answered by inspection of two segments defining a corner (ledge) of a faceted grain boundary, as outlined by the dashed square in Fig. 5(b) and enlarged in Fig. 7. Accordingly, creation andlor movement of a grain boundary ledge is effected by interchange of <loo>
and c1 101 grain boundary segments, denoted by ABD and AC, respectively, to <loo> and c1 10> grain boundary segments, denoted A'B'C and DA', respectively. In all cases, (local) grain boundary displacement is effected by glide of (a/2)<110>
dislocations A and B on conjugate slip planes to form a single ac100> dislocation, and subsequent dissociation of the ac100>
dislocation to formgquivalent pairs of (a/2)<110> dislocations A' and B' on their original slip planes. To a first approximation, the reaction (a12)[110]
+
(a/2) [l101+
a[100] does not result in a net change of energy. Therefore, energy changes must be associated with nearest-neighbor interactions of dislocations A and B with C and D. In fact, an estimate of these interactions yields stable positions for dislocations A and B between A-
A' and B-
B'. Therefore, grain boundary structures, illustrated schematically in Figs. 4 and 6, may not represent the lowest energy configurations. Indeed, combinations of (d2)<1102 and a<100> edge disbcations have been observed i n similar tilt boundaries.'*The associated activation energies for dislocation interchange are estimated to be of the order of those for lattice self diffusion.
Therefore, kinetics of grain boundary migration is controlled by thermal activation of dislocations from one stable position to another. Likewise, values of K, using an activation energy for volume self diffusion in gold (42 kcallmole), are computed to be about 10-j6 cm2/s, in good agreement with the measured value, thus providing confidence in the assumed mechanisms for grain boundary migration involving interactions between component dislocations. For the symmetric < l 00> inclination, however, the origin of driving force must be associated totally from short-range dislocation interactions. These differences are undoubtedly
Flgure 7. Schematic illustration of four (a/2)<110> edge dislocations (A, B, C, D) in a [OOl] tilt boundary inclined by 26.6' from a symmetric c1 102 direction (cf. Fig. 4 c). Grain boundary motion is effected by glide of dislocations A and B on conjugate slip planes to form an a<100> dislocation, and subsequent dissociation to reform (a/2)<110> dislocations A' and B' on their original slip planes.
Cl-628 COLLOQUE DE PHYSIQUE
reflected in the general shape of the grain boundaries pictured in Figs. 2 (smooth) and 3 (faceted). A more exact description of grain boundary mobility must entail careful consideration of energy change(s) associated with interactions of dislocations with several or all neighbors.
It is often observed in situ that grain boundary ledges fluctuate by as much as 12 nm in 2 S (exposure time), suggesting Only a slight bias (drift velocity) for reduction of grain boundary energy. This bias may be due to long-range attraction between (a/2)<110> dislocations of opposite sign or more subtle reduction of energy due to short-range dislocation interactions. In any event, it seems that grain boundary migration is effected by a slight bias in component dislocation energy, in much the same manner as lattice diffusion is effected by slight bias in atomic diffusion. Concomitant activation energies for these processes seems to be comparable, suggesting that "diffusion" of edge dislocations in a periodic array may be analyzed similarly to diffusion of atoms in a periodic structure.
Results stemming from this investigation suggest that deviations from symmetric grain boundary inclinations may relax to equilibrium positions merely by glide and reaction of (a/2)<110> edge dislocations on conjugate slip planes; e.g., movement of dislocations A and B in Fig, 7 to B' and A', respectively. An equivalent grain boundary displacement; e.g., from DBAC in Fig. 7 to DA'B'C, can be effected by a combination of glide and climb of edge dislocations A and B to positions B' and A', respectively, thus circumventing dislocation reactions. Previously, it was believed that movement of (low-angle) tilt boundaries was controlled by dislocation climb, because reported activation energies were comparable to those for lattice diffusion, thus implying shuffling of matter from one dislocation to another by diffusion through the intervening (perfect) lattice.14 However, it now appears that comparable activation energies for grain boundary migration are also associated with (nearest-neighbor) dislocation interactions. Indeed, rapid, nearly random movement of edge dislocations observed in the the present investigation (cf. Fig. 3 e) seems to be more characteristic of dislocation glide than dislocation climb. Definitive resolution of this issue, however, must await more detailed consideration of reactions between neighboring dislocations.
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SUMMARYGrain boundary migration in thin bicrystalline films of gold has been investigated i n situ by TEM and corresponding mechanisms have been interpreted in terms of interaction between component dislocations. Grain boundary structure is characterized by amays of (a/2)<llOz and/or aclOO> edge dislocations, whose spacing and distribution depend on grain misorientation and grain boundary inclination. Grain boundary migration is effected by interchange of adjacent (a/2)<110> edge dislocations through glide on conjugate slip planes to form a<100> edge dislocations, reversal of this process, and occasional annihilation of (&2)<1102 distocations of opposite sign. These reactions produce a driving force for grain boundary migration, similar to the usual capillary driving force for a continuum grain boundary. Results are in good agreement with current concepts Of grain boundary structure and dislocation reactions, and help to elucidate-atomic mechanisms for grain boundary migration.
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