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The structure of kinks at dislocation interphase boundaries and their role in boundary migration—I. Experimental observation of kink motion
Acta metall, mater. Vol. 38, No. 6, pp. 881-887, 1990 Printed in Great Britain. All rights reserved
0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc
THE STRUCTURE OF KINKS AT DISLOCATION INTERPHASE BOUNDARIES A N D THEIR ROLE IN B O U N D A R Y MIGRATION--I. EXPERIMENTAL OBSERVATION OF KINK MOTION J. M. HOWE and N. PRABHU Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received 15 December 1989)
Abstract--The role of kinks in dislocation ledge motion during precipitation of~' plates in an A1-Ag alloy was studied by conventional, high-resolution and in situ hot-stage TEM techniques. It is shown that kinks are necessary for motion of the dislocation interphase boundary and that kinks may be produced by orientation, thermal and intersection events. Analysis of the behavior of kinks at the interphase boundary utilizing isotropic dislocation theory is in reasonable agreement with experimental observations. R6saun6--Le r61e des d6crochements dans le mouvement des marches dues aux dislocations au cours de la pr6cipitation des plaquettes y' dans un alliage A1-Ag est 6tudi6 par les techniques de MET in situ chaud. On montre que les d6crochements sont n6cessaires pour le mouvement du joint de dislocation d'interphase et que des decrochements peuvent provenir d'6v6nements li6s ~il'orientation, ~ila temp6rature et ~i l'intersection. L'analyse du comportement des d6crochements au joint d'interphase en utilisant la th6orie de l'61asticit6 isotrope est en accord raisonnable avec les observations experimentales. Zus~mmenfassunw-Die Rolle der Kinken in der Bewegung yon Versetzungsstufen w/ihrend der Ausscheidung von 7'-Platten wurde an einer AI-Mg-Legierung mittels konventioneller, hochaufl6sender und in-situ Elektronenmikroskopie im Heiztisch untersucht. Es wird gezeigt, dab Kinken fiir die Bewegung der versetzungshaltigen Phasengrenzfl/iche n6tig sind und dab sie durch Orientierungsthermische und Schneidprozesse erzeugt werden k6nnen. Die Analyse des Kinkverhaltens an der Phasengrenzfl/iche mittels isotroper Versetzungstheorie stimmt hinreichend gut mit den Beobachtungen fiberein.
1. INTRODUCTION The necessity of kinks for the motion of homophase and interphase boundaries has been recognized for some time [1, 2]. However, it is just recently that the resolution of transmission electron microscopes (TEMs) has been improved to the point that kinks in interphase boundaries can be observed at or near the atomic level [3, 4]. This study, which consists of experimental and analytical Parts I and II, respectively, examines the role of kinks on interphase boundary motion during a diffusional phase transformation. In the particular transformation under consideration, namely, the precipitation of 7' Ag2AI plates in dilute A1-Ag alloys, the moving interphase boundary is a Shockley partial dislocation ledge [5]. Diffusional growth of precipitates by similar dislocation ledges has been reported for many different systems [6, 7]. Kinks in a dislocation are of three types [8]: (i) geometric kinks are present by necessity when a dislocation segment spans a Peierls valley, i.e. has an irrational line direction, (ii) at thermal equilibrium, a dislocation line contains a concentration of thermal kinks, and (iii) intersection kinks can be produced AM 38/6~A
if two nonparallel dislocations intersect. Each of these mechanisms may therefore be important for the motion of a dislocation ledge at an interphase boundary. However, it is only recently that kinks have been observed in dislocation ledges at interphase boundaries [3]. In Part I of this study, all three types of kinks are shown to be present in dislocation ledges, The effects of these kinks on interphase boundary kinetics are analyzed in Part II.
2. EXPERIMENTAL The material, heat treatments, sample preparation methods and electron microscopy techniques employed in this study are described in detail in previous papers [3, 4, 9]. Briefly, an AI-4.2 at.% Ag alloy was solution annealed for 30 min at 350°C. Specimens were electropolished and dislocation ledges on the faces near or at the edges of 7' precipitate plates were examined by conventional, in situ hot-stage and high-resolution T E M using Philips EM301, Kratos EM1500 and JEOL 200CX microscopes, respectively. 881
882
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES---I
Fig. 1. (a) Bright-field image showing microscopic kinks at the edge of a ~' precipitate oriented perpendicular to the electron beam in a (111)~ ]1(0001):., zone axis, (b) high-resolution image showing the atomic structure of a kink such as the one indicated by an arrow in (a) and also several single-atom kinks (arrows) present due to slight deviation of the interface from a (110)~IL(1 l~0)r, orientation, and (c) high-resolution image showing a nearly random interphase boundary structure (indicated by black dots) at an edge along the (TT2)~tl(lI00).,, direction. 3. RESULTS AND DISCUSSION 3.1. Orientation kinks Figure l(a) shows a bright-field T E M image at the edge of a ~' precipitate plate oriented perpendicular to the electron beam in a (111)5 II(0001)r, zone axis with g = ~02. The precipitate edge, which is cornposed of an array of Shockley partial dislocations stacked vertically, parallels the close-packed (0]'l )~ ll( 2 I i 0 ) , / direction on the left side of Fig. l(a). As the interphase boundary bends away from this close-packed direction to assume an orientation near the;, direction so that 0, the angle
between the line direction and the close-packed direction approaches 23 °, microscopic kinks about 3 n m high form in the dislocation array. However, the edges of the kinks remain parallel to the close-packed (0il>~ll(2ii0L,, and (i01)511(1~10)r, directions in the structures, as evident in Fig. 1(a). These kinks are geometrically necessary since the interphase dislocations must cross the ( 0 i l ) 5 L[(2Ti0)r, Peierls valleys common to both structures to align near the (ii2)~H(II00)~,, directions. Such behavior is expected for curved dislocations which are trying to minimize their elastic energy in close-packed structures [10], as illustrated in Fig. 2. In this case where
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES--I _e~ 2,~0-". . . . . . . . . . ......... +--
...........
and 2], the concentration of positive and negative kinks in the dislocation should obey the relationship [101 ck+ - ck = tan O/hk
. . . . . . . . . Id (hk) . . . . . . . . . . . . . . . . . . . . . . . . . Fig. 2. Illustration of positive and negative geometric kinks (Ck+ and ck ) of width w spaced a distance l apart in a dislocation segment which crosses at an angle 0 to the Peierls hills (dashed lines) and valleys (solid lines) with separation
d:hk" the dislocations are at the interphase boundary, the chemical change across the interface will also constrain the dislocations to parallel the close-packed directions [11]. It is important to note that the spacing between the kinks in Fig. l(a) decreases while their height remains largely unchanged as the deviation from an exact (0T1),II(2Ti0)~., orientation increases from left to right in the image. This is predicted from a simple kink model, as discussed below, Figure l(b) is a complementary high-resolution TEM image which shows the atomic structure of a large kink, such as the one indicated by an arrow in Fig. l(a). From this image it is apparent that the entire interphase boundary parallels close-packed (110)~11(11-50)~, directions on an atomic scale, and that slight deviations from this exact orientation of about 8 ° on either side of the large kink are accommodated by kinks only one atom plane high, as indicated by the arrows in Fig. l(b). Again, these kinks are geometrically necessary in order for the Shockley partial dislocations at the precipitate edge to span the low-energy Peierls valleys common to both structures. The interphase boundary appears atomically fiat and sharp in between the kinks, and the width of each kink (w in Fig. 2~ appears to be no more than a few atoms, probably due to the significant elastic and chemical components associated with the dislocation interphase boundary. It has been shown by in situ hot-stage TEM [4, 12] that growth of the precipitate edges occurs by the motion of kinks, such as those in Fig. l(a) and (b), parallel to the close-packed ( l l 0 ) , l l ( l l ~ 0 ) ~ , interphase boundary, Figure l(c) shows an additional image at the corner of a kink larger than the ones in Fig. l(a) and (b). The edge of the kink on the left side of the corner parallels a ( 0 i l ) , [ [ ( 2 T i 0 ) . / d i r e c t i o n as before, but the actual corner is relatively flat and almost exactly parallels a (TT2),II(1T00)~, direction. At this large angle of about 30 ° from the close-packed (ll0)~II(2iT0);., direction the kinks are as closely spaced as the interatomic separation along the (ii2)~[[(1T00)~, direction (~0.494nm), and the dislocation interface can be envisioned as disordered. That is, atomic attachment could take place randomly along the dislocation line and it would probably display growth kinetics similar to that of a disordered ledge [6, 13]. If the average dislocation line is at an angle 0 with respect to the direction of the Peierls valleys [Figs l(a)
883
(1)
where Ck. is the concentration of kinks that accommodate the angle, ek is the concentration of kinks that oppose the angle (Fig. 2) and h k is the kink height (in Fig. 2, hk is equal to d, the separation between adjacent Peierls valleys). It has been shown [10] that e v e n for small 0, Ck+>>ck and therefore, that it is reasonable to let Ck = 0 in equation (1) when examining orientation kinks in dislocations which are at an angle to the Peierls valleys. The densities of kinks in Fig. l(a-c)demonstrate that this relationship is followed at both the atomic and microscopic levels. The angles 0 from the (110)~H(II'~0)~, directions were measured as 8 and 30 ° for Fig. I(b) and (c), and the corresponding kink densities were determined as 0.569 and 2.338 nm-~, respectively, using equation (1) with hk = d = 0.247 nm. These values differ by 5 and 10%, respectively, from the kink densities of 0.538 and 2.591 nm -1, which were measured directly from the micrographs in Fig. 1. The difference is less for the single-atom kinks in Fig. l(b) because their spacing can be measured accurately as opposed to Fig. l(c), where the high kink density makes experimental measurement both difficult and subjective. Similarly, the angle 0 in Fig. l(a) was measured experimentally as 23 ° and the average height of the kinks was measured as 2.38 nm. Using equation (1), the predicted kink density is 0.178 n m - 1 which is within 6% of the value of 0.167 nm-l, measured directly from the micrograph. Therefore, it is apparent that the kink density increases proportionally with the deviation of a dislocation interface from a low-energy orientation, and this will influence the growth kinetics of the interface accordingly. No orientation kinks are available for growth when the dislocation ledges lie along (110),11 (11~0)~., directions and 0 = 0, and an abundance of kinks is available for growth when 0 is greater than about 20 ° since the kinks become as closely spaced as their width. This orientation effect must be taken into account when analyzing the growth rates of individual dislocation ledges as discussed further in Part II. 3.2. Thermal kinks
Figure 3 shows an example of precipitate growth by double-kink nucleation in a Shockley partial dislocation ledge, taken during an in situ hot-stage experiment at 375°C, The edge of the plate in this image parallels a ( l l 0 ) ~ l l ( l l ~ 0 ) . / direction and is enclosed within the thin foil, which is in a (110)~ II(11~0)~,, zone axis with g220,3g diffraction conditions. In this image, two dislocation ledges which are staggered at the plate edge contain similar kinks labelled A - B and A ' - B ' about 10-15 nm wide and about 130 nm apart. These kinks were immobile and appeared to be associated with dislocations that
884
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES---I along (110)~IL(11~0)~., directions, which provide a configuration that is conducive to thermal nucleation of double kinks. The concentration of thermal kinks ck that are present in a dislocation ledge along (I10)~[[(11~0);., is given by [10] ck = ck+ + ck = (2/a) e~-6F*/kr~
Fig. 3, Weak-beam dark-field image showing an approximately 4,0 nm high double-kink (arrow) nucleating in a dislocation ledge segment A-A' along a (II0)~LI(II'~0),/ direction at the edge of a 7' plate during growth. The segment A-A' can be compared to segment B-B', which does not have a double kink. were on the plate faces and out of contrast in this image. The linear (110)~11(11~0);., precipitate edges in between the kinks were also stationary, presumably because there were no kinks present for propagation of the interphase boundary. Suddenly, nucleation of a double kink occurred near the center of dislocation segment A-A', at the position indicated by an arrow in Fig. 3, Once nucleated, opposite ends of the 4.0 nm kink propagated along the length of the dislocation A - A ' as illustrated schematically in Fig. 4, thereby advancing the plate edge about 4.0 nm. This reaction was completed in about 5 s, and provides direct experimental evidence that interphase boundary dislocations can propagate by double-kink nucleation, The formation of kinks in dislocation ledges by double-kink nucleation demonstrates that thermal nucleation of kinks is also a mechanism for motion of interphase boundaries. Observation of doublekink nucleation on dislocations in metals is difficult since the Peierls stress is generally low and it has been observed mainly in materials with a high Peierls stress, such as covalently bonded semiconductors [10, 14]. The reason for double-kink nucleation in dislocation ledges at the ~/y' interface is probably because the chemical component of the ~/7' interphase boundary energy [11] produces an effect similar to a high Peierls stress. This yields low-energy valleys
(2)
where ck+ and c~- are the concentrations of kinks on either side of the double-kink and for this case ck+ = cw, a is the width of a single kink (which is equal to the spacing between atoms in the closepacked direction), AF* is the free energy for doublekink formation, k is Boltzmann's constant and T is temperature. Equation (2) predicts that the kink density of the interphase boundary will increase with temperature, and that an otherwise immobile interface lying in a Peierls valley can advance by the thermal nucleation of double kinks when no geometric kinks are present. This equation can be used to estimate the free energy for double-kink nucleation from the data in Fig. 3 if it is assumed that ck = 2/130 nm, or that only one thermal double-kink nucleates along the 130nm segment A-A' in Fig. 3. Based on this assumption and using the values of a = 0.286 nm, k = 1.3806 x 10 -23 J/K and T = 648 K yields an energy for double-kink formation of 6.10 x 10-2°J or 0.34 eV. This value may be cornpared with the experimentally determined energy [15] of 0.19 eV for double-kink formation in the cornpound Ag2A1, and it is sufficiently reasonable to suggest that further experiments of this type may be able to provide quite accurate values for AF*. The velocity of the resulting kinks is proportional to the driving force for growth. If it is assumed that the double kink in Fig. 3 can be approximated as a large semihexagonal bow-out in the dislocation as sketched in Fig. 4, the line tension of the dislocation d E / d L can be calculated using the following formula [10] d E / d L = ;~s = ~b2/4rt( 1 - v)
x [(1 - 3 v / 2 ) l n ( L / p ) + 2.00v - 1.05] (3)
where/~ is the elastic modulus, b is the Burgers vector, v is Poisson's ratio, L is the length of a segment of the hexagon, p is the core radius and E is the elastic energy. Calculation of the line tension is of interest because it allows determination of the structural component of the dislocation ledge interphase boundary energy 7s that results as the kink is formed. A ~_ A~ This energy must be overcome for the boundary to r z L.---------~ I move forward. If it is assumed that L = 4.62nm .... ~_~. ~ - - - ' 1 ~ (4.0nm/cos 30°), b = a / 6 ( l l 2 ) = p = 0 . 1 6 5 n m and v the elastic constants [10] # =2.65 × 10~° Pa and ~---k--~ v = 0,347 for AI are used in equation (3), the value for the dislocation interfacial energy is 7~= Fig. 4. Illustration of a semihexagondouble-kink configura- 1.16 x 10- l0 J/m. This value is reasonable when comtion in an edge dislocation with b in the plane of the figure, pared to the line tension of a straight dislocation as for the kink in segment A-A' in Fig. 3. The height of the kink is L/cos 30° and the edges move with velocityv parallel segment with b = a / 6 ( 1 1 2 ) [10], and particularly to the dislocation line direction ~ as indicated by arrows, considering the limitations of measurement of the
HOWE and PRABHU:
KINKS AT INTERPHASE BOUNDARIES--I
885
kink height from the T E M image and the assumption
3.3. Intersection kinks
of a semihexagonal kink. It is very difficult to obtain any kind of similar estimate by other methods, More careful examination and measurement of double-kink configurations at interphase boundaries using atomic-resolution images such as the one in Fig. l(b) may yield quite accurate values for the interracial energy, and this topic deserves further investigation,
One additional series of in situ images obtained for a plate edge during dissolution at about 425°C is shown in Fig. 5(a-c). In these figures a dislocation ledge, which is largely out of contrast in the g0:2,3g diffraction conditions used, nucleated at the intersecting precipitate labelled A in Fig. 5(a). The dislocation propagated upward, across the three dislocation ledges stacked at the edge of the precipitate plate along (ll0)~ll(1120)?,, labelled 1-3 in Fig. 5(a) and (c). The position of the moving dislocation is indicated by arrows in Fig. 5(a-c), and the interaction between this dislocation produced kinks in dislocations 1-3, clearly visible in Fig. 5(c) after 5 s. These kinks are about 35 nm wide, and the movement of the kinks with the passage of the horizontal dislocation caused each of the vertical dislocations at the precipitate edge to recede about 35-50 nm to the left, as seen by comparing their positions in Fig. 5(a) and (c). These results demonstrate that dislocation intersections can provide kinks which expedite the motion of dislocation ledges, as suggested previously [12, 16]. It is interesting to examine the dislocation reactions involved in the formation and propagation of the kinks in Fig. 5(a-c). The three parallel dislocations at the precipitate edge lie mainly along a low-energy ( 110)~ II( 11~0),/ direction. The crossing dislocation which lies two {111} planes above has a curved configuration just after nucleation [Fig. 5(a)], but after 5 s it also nearly parallels a close-packed ( l l0>~ p[( l l~0>~., direction, as is apparent from the average direction of the three kinks in Fig. 5(c). A complete contrast analysis was not performed on these dislocations, but it is reasonable to assume that they are a/6[l'2T] and a/6[2Tf] edge Shockley partials as determined in several previous analyses [5, 9, 17], with the Burgers vectors b and line directions illustrated in Fig. 6(a). As the crossing a/6[2Ti] dislocation moves upward, reaction occurs with the parallel a / 6 [ i 2 i ] dislocations to produce the node illustrated in Fig. 6(b). This reaction appears energetically favorable since Frank's criterion [10] shows that
~
. . . . .
~+
~
;~ ~.
.
.
.
.
.
Fig. 5. (a) Weak-beam dark-field image showing nucleation of a dislocation ledge (arrow) on the face of a ?' plate by an intersecting edge-on plate (labelled A) during precipitate disolution. Three dislocations in a parallel array on the precipitate are also indicated. (b) The same area after 3 s showing movement of the new ledge (out of contrast and indicated by an arrow) vertically, and (c) the same area after 5 s showing 35 nm kinks (arrows) which formed in dislocations I-3 as the new dislocation ledge continued to move upward. The three dislocations in (c) have migrated about 35-50 nm to the left as a result of the crossing dislocation,
a/6[i2i] + a/6[2ii] ~ a/6[ii2]
(4a)
a2/6 + a2/6 > a2/6.
(4b)
However, it should be noted that this inequality only approximates the actual situation, since the crossing dislocation probably lies two {111} planes above the three parallel dislocations. The resulting a/6[]'T2] dislocation in the node now acts as a kink which is at an angle of at least 30 + to any of the close-packed ( ! 10)~ JJ(11~0);., directions. It is also in a pure screw orientation with respect to the a/6['f2T] Burgers vector and only 30 ° from pure screw a/612]']'] and a/6[i]'2] Burgers vectors. This kink should be able to migrate like a disordered interface because its atomic structure is similar to that shown in Fig. l(c). Therefore, as the a/6121T] dislocation moves upward, the
886
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES--I
(a)
~= T01 , L
~
OTI --~ b j= o/6[TZT] ~-/.. 60* -, f b2= Q/6[eTT] " " "x~Out of Contrast "-.. x.. Tn Contrast
sufficiently small, the dislocation network may be capable of continually providing kinks to influence the overall migration kinetics of the interface [12]. Otherwise, dislocation intersections are expected to provide only local temporary means for interphase boundary migration which do not have a major effect on the overall migration rate. This effect is considered further in Part II. 3.4. Summary
The results from these TEM analyses demonstrate that geometric, thermal and intersection kinks can all be present in dislocation ledges at interphase (bI boundaries. These kinks can be of atomic dimensions ~1-- Tol as in Fig. l(b), or they may be tens of nanometers i~ ~ _ _ wide as in Fig. 5(c). When this information is com~¢2= aT I b i= a/6[ 12i] bined with experimental results from in situ studies of ledge growth which show that Shockley partial disiob = a/S[2TT] -i----k---J.... cation ledges are largely immobile when they lie along 2 I ~ ~"-. low-energy (110)~11(11~0)¢ directions [4, 12], it be[ b3-- Q/6[TT2] " - - , . comes apparent that at least two and possibly three factors need to be taken into account in kinetic analyses of interphase boundary motion involving dislocation ledges; namely, (i) the dependence of kink Fig. 6. (a) Illustration of the initial dislocation configuration in Fig. 5 considering only one dislocation in the parallel density on ledge orientation, (ii) the dependence of array with bl = a/6[l'2T] and the Crossing dislocation with kink density on temperature, and (iii) the dependence b2 = a/6[2IT], and (b) formation of a kink or node with of kink density on interledge or misfit dislocation b~ = a/6[IT2] by interaction of the two dislocations. The spacing in the case of crossing dislocation networks. corresponding line directions ~ and ~2 are also shown, and Factors (i) and (ii) have been discussed with reference dislocation segments for which g.b ~ 0 are indicated by heavy lines while those with g.b = 0 are shown by dashed to grain-boundary migration [2] and solid-vapor lines, interface migration [19], and analogous concepts apply to the nucleation of kinks in dislocation ledges reaction in equation (4) produces a favorable disloca- at interphase boundaries. These are, that the kink tion configuration in terms of both the elastic energy density increases proportionally with the deviation of and the mechanism needed for migration of the a ledge from a low-energy orientation due to geometinterfaces. It is also interesting to note that the ric considerations, and that the kink density increases contrast of the kinks in Fig. 5(a-c) increases with time with temperature due to thermal nucleation of in the sequence as the a/6[T2T] and a/6[2TT] disloca- double-kinks. In addition, the kink density due to tions react and develop into well-defined nodes. This intersecting dislocations can also be important for behavior is expected for a diffraction vector g = 0~2, interphase boundaries which contain regular netwhere a/6[T2i] and a/6[TT2] dislocations have works in solid-solid transformations and, as meng-h = + 1 while an a/6[21"T] dislocation has g.b = 0. tioned above, this should also be included when Similar dislocation reactions and contrast behavior appropriate. A few simple modifications which allow have been observed to occur in partial dislocations on incorporation of these effects into current kinetic twin interfaces [18]. analyses of ledge growth at interphase boundaries are Figure 5(a-c) show that dislocation interfaces can discussed in Part II. advance by kinks produced at dislocation intersections, although this is expected to have a large effect on the overall growth kinetics of an interphase 4. CONCLUSIONS boundary only when a regular network of crossed The results from the TEM observations of dislocaledge or misfit dislocations is present. The concentration interphase boundaries in this investigation tion of intersection kinks ck that is present in a demonstrate that: dislocation ledge along a ( 110>~II< 11~0>~, Peierls valley is given simply as (i) the atomic structure and migration behavior of dislocation interphase boundaries can be observed by ck = 2 - ' (5) high-resolution and in situ TEM techniques; (ii) orientation, thermal and intersection kinks where 2 is the interledge or misfit dislocation spacing can all be present at dislocation interphase boundand the kinks are all assumed to be positive. If 2 is aries;
HOWE and PRABHU:
(iii) m a n y characteristics o f interphase boundaries can
KINKS AT INTERPHASE BOUNDARIES--I
kinks in dislocation be approximately
described using isotropic elasticity a n d dislocation theory; a n d (iv) kinks are necessary for the m o t i o n o f dislocation interphase boundaries. Acknowledgements--The authors are grateful to Professor S. Mahajan for a helpful discussion regarding Fig. 6 and to Professor H. I. Aaronson for a critical review of the manuscript This research was supported by grants from the National Science Foundation (Grant No. DMR-8610439) and Alcoa. Use of the JEOL 200CX and Kratos EM-1500 electron microscopes at the LBL NCEM is gratefully acknowledged. REFERENCES 1. H. 1. Aaronson, C. Laird and K. R. Kinsman, Phase Transformations, pp. 313 398. Am. Soc. Metals, Metals Park, Ohio (1970) 2. H. Gleiter, Acta metall. 17, 853 (1969). 3. J. M. Howe, U Dahmen and R. Gronsky, Phil. Mag. A 56, 31 (1987). 4. J. M. Howe, Phase Transformations '87, pp. 637q~39. Inst. Metals, London (1988). 5. J. A. Hren and G. Thomas, Metall Soc. A.I.M.E. 227, 308 (1963).
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6. H. I. Aaronson, J. K. Lee and K. C, Russell, Precipitation Processes in Solids, pp. 31 85. Metall. Soc. A.I.M.E., Warrendale, Pa (1977). 7, H. I. Aaronson, J. Microscopy 102, 275 (1974). 8, J. P. Hirth, Physical Metallurgy--Part II, pp. 1234-1235. North Holland, Amsterdam (1983). 9. J. M. Howe, H. I. Aaronson and R. Gronsky, Acta metall. 33, 639 (1985). 10. J. P. Hirth and J. Lothe, Theory o f Dislocations, 2nd edn, pp. 173, 243, 490-492, 532 546. Wiley, New York (1982). 11. K. B. Alexander, F. K. LeGoues, D. E. Laughlin and H.I. Aaronson, Acta metall. 32, 2241 (1984). 12. C. Laird and H. I. Aaronson, Acta metall. 17, 505 (1969). 13. R. Trivedi, Proc. Int. Conf. on Solid-.Solid Phase Transformations, pp. 477-502. Metall. Soc. A.I.M.E., Warrendale, Pa (1982). 14. P. B. Hirsch, Dislocations and Properties of Real Materials', pp. 333-348. Inst. Metals, London (1985). 15. P. Guyot and J. E. Dorn, Can. J. Phys. 45, 983 (1967). 16. S. A. Hackney and G. J. Shiflet, Acta metall. 35, 1007 (1987). 17. C. Laird and H. I. Aaronson, Acta metall. 15, 73 (1967). 18. S. Mahajan and G. Y. Chin, Acta metall. 22, 1113 (1974), 19. W. K. Burton, N. Cabrera and F. C. Frank, Phil. Trans. R. Soc. A243, 299 (195C~51).
0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc
THE STRUCTURE OF KINKS AT DISLOCATION INTERPHASE BOUNDARIES A N D THEIR ROLE IN B O U N D A R Y MIGRATION--I. EXPERIMENTAL OBSERVATION OF KINK MOTION J. M. HOWE and N. PRABHU Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received 15 December 1989)
Abstract--The role of kinks in dislocation ledge motion during precipitation of~' plates in an A1-Ag alloy was studied by conventional, high-resolution and in situ hot-stage TEM techniques. It is shown that kinks are necessary for motion of the dislocation interphase boundary and that kinks may be produced by orientation, thermal and intersection events. Analysis of the behavior of kinks at the interphase boundary utilizing isotropic dislocation theory is in reasonable agreement with experimental observations. R6saun6--Le r61e des d6crochements dans le mouvement des marches dues aux dislocations au cours de la pr6cipitation des plaquettes y' dans un alliage A1-Ag est 6tudi6 par les techniques de MET in situ chaud. On montre que les d6crochements sont n6cessaires pour le mouvement du joint de dislocation d'interphase et que des decrochements peuvent provenir d'6v6nements li6s ~il'orientation, ~ila temp6rature et ~i l'intersection. L'analyse du comportement des d6crochements au joint d'interphase en utilisant la th6orie de l'61asticit6 isotrope est en accord raisonnable avec les observations experimentales. Zus~mmenfassunw-Die Rolle der Kinken in der Bewegung yon Versetzungsstufen w/ihrend der Ausscheidung von 7'-Platten wurde an einer AI-Mg-Legierung mittels konventioneller, hochaufl6sender und in-situ Elektronenmikroskopie im Heiztisch untersucht. Es wird gezeigt, dab Kinken fiir die Bewegung der versetzungshaltigen Phasengrenzfl/iche n6tig sind und dab sie durch Orientierungsthermische und Schneidprozesse erzeugt werden k6nnen. Die Analyse des Kinkverhaltens an der Phasengrenzfl/iche mittels isotroper Versetzungstheorie stimmt hinreichend gut mit den Beobachtungen fiberein.
1. INTRODUCTION The necessity of kinks for the motion of homophase and interphase boundaries has been recognized for some time [1, 2]. However, it is just recently that the resolution of transmission electron microscopes (TEMs) has been improved to the point that kinks in interphase boundaries can be observed at or near the atomic level [3, 4]. This study, which consists of experimental and analytical Parts I and II, respectively, examines the role of kinks on interphase boundary motion during a diffusional phase transformation. In the particular transformation under consideration, namely, the precipitation of 7' Ag2AI plates in dilute A1-Ag alloys, the moving interphase boundary is a Shockley partial dislocation ledge [5]. Diffusional growth of precipitates by similar dislocation ledges has been reported for many different systems [6, 7]. Kinks in a dislocation are of three types [8]: (i) geometric kinks are present by necessity when a dislocation segment spans a Peierls valley, i.e. has an irrational line direction, (ii) at thermal equilibrium, a dislocation line contains a concentration of thermal kinks, and (iii) intersection kinks can be produced AM 38/6~A
if two nonparallel dislocations intersect. Each of these mechanisms may therefore be important for the motion of a dislocation ledge at an interphase boundary. However, it is only recently that kinks have been observed in dislocation ledges at interphase boundaries [3]. In Part I of this study, all three types of kinks are shown to be present in dislocation ledges, The effects of these kinks on interphase boundary kinetics are analyzed in Part II.
2. EXPERIMENTAL The material, heat treatments, sample preparation methods and electron microscopy techniques employed in this study are described in detail in previous papers [3, 4, 9]. Briefly, an AI-4.2 at.% Ag alloy was solution annealed for 30 min at 350°C. Specimens were electropolished and dislocation ledges on the faces near or at the edges of 7' precipitate plates were examined by conventional, in situ hot-stage and high-resolution T E M using Philips EM301, Kratos EM1500 and JEOL 200CX microscopes, respectively. 881
882
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES---I
Fig. 1. (a) Bright-field image showing microscopic kinks at the edge of a ~' precipitate oriented perpendicular to the electron beam in a (111)~ ]1(0001):., zone axis, (b) high-resolution image showing the atomic structure of a kink such as the one indicated by an arrow in (a) and also several single-atom kinks (arrows) present due to slight deviation of the interface from a (110)~IL(1 l~0)r, orientation, and (c) high-resolution image showing a nearly random interphase boundary structure (indicated by black dots) at an edge along the (TT2)~tl(lI00).,, direction. 3. RESULTS AND DISCUSSION 3.1. Orientation kinks Figure l(a) shows a bright-field T E M image at the edge of a ~' precipitate plate oriented perpendicular to the electron beam in a (111)5 II(0001)r, zone axis with g = ~02. The precipitate edge, which is cornposed of an array of Shockley partial dislocations stacked vertically, parallels the close-packed (0]'l )~ ll( 2 I i 0 ) , / direction on the left side of Fig. l(a). As the interphase boundary bends away from this close-packed direction to assume an orientation near the
between the line direction and the close-packed direction approaches 23 °, microscopic kinks about 3 n m high form in the dislocation array. However, the edges of the kinks remain parallel to the close-packed (0il>~ll(2ii0L,, and (i01)511(1~10)r, directions in the structures, as evident in Fig. 1(a). These kinks are geometrically necessary since the interphase dislocations must cross the ( 0 i l ) 5 L[(2Ti0)r, Peierls valleys common to both structures to align near the (ii2)~H(II00)~,, directions. Such behavior is expected for curved dislocations which are trying to minimize their elastic energy in close-packed structures [10], as illustrated in Fig. 2. In this case where
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES--I _e~ 2,~0-". . . . . . . . . . ......... +--
...........
and 2], the concentration of positive and negative kinks in the dislocation should obey the relationship [101 ck+ - ck = tan O/hk
. . . . . . . . . Id (hk) . . . . . . . . . . . . . . . . . . . . . . . . . Fig. 2. Illustration of positive and negative geometric kinks (Ck+ and ck ) of width w spaced a distance l apart in a dislocation segment which crosses at an angle 0 to the Peierls hills (dashed lines) and valleys (solid lines) with separation
d:hk" the dislocations are at the interphase boundary, the chemical change across the interface will also constrain the dislocations to parallel the close-packed directions [11]. It is important to note that the spacing between the kinks in Fig. l(a) decreases while their height remains largely unchanged as the deviation from an exact (0T1),II(2Ti0)~., orientation increases from left to right in the image. This is predicted from a simple kink model, as discussed below, Figure l(b) is a complementary high-resolution TEM image which shows the atomic structure of a large kink, such as the one indicated by an arrow in Fig. l(a). From this image it is apparent that the entire interphase boundary parallels close-packed (110)~11(11-50)~, directions on an atomic scale, and that slight deviations from this exact orientation of about 8 ° on either side of the large kink are accommodated by kinks only one atom plane high, as indicated by the arrows in Fig. l(b). Again, these kinks are geometrically necessary in order for the Shockley partial dislocations at the precipitate edge to span the low-energy Peierls valleys common to both structures. The interphase boundary appears atomically fiat and sharp in between the kinks, and the width of each kink (w in Fig. 2~ appears to be no more than a few atoms, probably due to the significant elastic and chemical components associated with the dislocation interphase boundary. It has been shown by in situ hot-stage TEM [4, 12] that growth of the precipitate edges occurs by the motion of kinks, such as those in Fig. l(a) and (b), parallel to the close-packed ( l l 0 ) , l l ( l l ~ 0 ) ~ , interphase boundary, Figure l(c) shows an additional image at the corner of a kink larger than the ones in Fig. l(a) and (b). The edge of the kink on the left side of the corner parallels a ( 0 i l ) , [ [ ( 2 T i 0 ) . / d i r e c t i o n as before, but the actual corner is relatively flat and almost exactly parallels a (TT2),II(1T00)~, direction. At this large angle of about 30 ° from the close-packed (ll0)~II(2iT0);., direction the kinks are as closely spaced as the interatomic separation along the (ii2)~[[(1T00)~, direction (~0.494nm), and the dislocation interface can be envisioned as disordered. That is, atomic attachment could take place randomly along the dislocation line and it would probably display growth kinetics similar to that of a disordered ledge [6, 13]. If the average dislocation line is at an angle 0 with respect to the direction of the Peierls valleys [Figs l(a)
883
(1)
where Ck. is the concentration of kinks that accommodate the angle, ek is the concentration of kinks that oppose the angle (Fig. 2) and h k is the kink height (in Fig. 2, hk is equal to d, the separation between adjacent Peierls valleys). It has been shown [10] that e v e n for small 0, Ck+>>ck and therefore, that it is reasonable to let Ck = 0 in equation (1) when examining orientation kinks in dislocations which are at an angle to the Peierls valleys. The densities of kinks in Fig. l(a-c)demonstrate that this relationship is followed at both the atomic and microscopic levels. The angles 0 from the (110)~H(II'~0)~, directions were measured as 8 and 30 ° for Fig. I(b) and (c), and the corresponding kink densities were determined as 0.569 and 2.338 nm-~, respectively, using equation (1) with hk = d = 0.247 nm. These values differ by 5 and 10%, respectively, from the kink densities of 0.538 and 2.591 nm -1, which were measured directly from the micrographs in Fig. 1. The difference is less for the single-atom kinks in Fig. l(b) because their spacing can be measured accurately as opposed to Fig. l(c), where the high kink density makes experimental measurement both difficult and subjective. Similarly, the angle 0 in Fig. l(a) was measured experimentally as 23 ° and the average height of the kinks was measured as 2.38 nm. Using equation (1), the predicted kink density is 0.178 n m - 1 which is within 6% of the value of 0.167 nm-l, measured directly from the micrograph. Therefore, it is apparent that the kink density increases proportionally with the deviation of a dislocation interface from a low-energy orientation, and this will influence the growth kinetics of the interface accordingly. No orientation kinks are available for growth when the dislocation ledges lie along (110),11 (11~0)~., directions and 0 = 0, and an abundance of kinks is available for growth when 0 is greater than about 20 ° since the kinks become as closely spaced as their width. This orientation effect must be taken into account when analyzing the growth rates of individual dislocation ledges as discussed further in Part II. 3.2. Thermal kinks
Figure 3 shows an example of precipitate growth by double-kink nucleation in a Shockley partial dislocation ledge, taken during an in situ hot-stage experiment at 375°C, The edge of the plate in this image parallels a ( l l 0 ) ~ l l ( l l ~ 0 ) . / direction and is enclosed within the thin foil, which is in a (110)~ II(11~0)~,, zone axis with g220,3g diffraction conditions. In this image, two dislocation ledges which are staggered at the plate edge contain similar kinks labelled A - B and A ' - B ' about 10-15 nm wide and about 130 nm apart. These kinks were immobile and appeared to be associated with dislocations that
884
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES---I along (110)~IL(11~0)~., directions, which provide a configuration that is conducive to thermal nucleation of double kinks. The concentration of thermal kinks ck that are present in a dislocation ledge along (I10)~[[(11~0);., is given by [10] ck = ck+ + ck = (2/a) e~-6F*/kr~
Fig. 3, Weak-beam dark-field image showing an approximately 4,0 nm high double-kink (arrow) nucleating in a dislocation ledge segment A-A' along a (II0)~LI(II'~0),/ direction at the edge of a 7' plate during growth. The segment A-A' can be compared to segment B-B', which does not have a double kink. were on the plate faces and out of contrast in this image. The linear (110)~11(11~0);., precipitate edges in between the kinks were also stationary, presumably because there were no kinks present for propagation of the interphase boundary. Suddenly, nucleation of a double kink occurred near the center of dislocation segment A-A', at the position indicated by an arrow in Fig. 3, Once nucleated, opposite ends of the 4.0 nm kink propagated along the length of the dislocation A - A ' as illustrated schematically in Fig. 4, thereby advancing the plate edge about 4.0 nm. This reaction was completed in about 5 s, and provides direct experimental evidence that interphase boundary dislocations can propagate by double-kink nucleation, The formation of kinks in dislocation ledges by double-kink nucleation demonstrates that thermal nucleation of kinks is also a mechanism for motion of interphase boundaries. Observation of doublekink nucleation on dislocations in metals is difficult since the Peierls stress is generally low and it has been observed mainly in materials with a high Peierls stress, such as covalently bonded semiconductors [10, 14]. The reason for double-kink nucleation in dislocation ledges at the ~/y' interface is probably because the chemical component of the ~/7' interphase boundary energy [11] produces an effect similar to a high Peierls stress. This yields low-energy valleys
(2)
where ck+ and c~- are the concentrations of kinks on either side of the double-kink and for this case ck+ = cw, a is the width of a single kink (which is equal to the spacing between atoms in the closepacked direction), AF* is the free energy for doublekink formation, k is Boltzmann's constant and T is temperature. Equation (2) predicts that the kink density of the interphase boundary will increase with temperature, and that an otherwise immobile interface lying in a Peierls valley can advance by the thermal nucleation of double kinks when no geometric kinks are present. This equation can be used to estimate the free energy for double-kink nucleation from the data in Fig. 3 if it is assumed that ck = 2/130 nm, or that only one thermal double-kink nucleates along the 130nm segment A-A' in Fig. 3. Based on this assumption and using the values of a = 0.286 nm, k = 1.3806 x 10 -23 J/K and T = 648 K yields an energy for double-kink formation of 6.10 x 10-2°J or 0.34 eV. This value may be cornpared with the experimentally determined energy [15] of 0.19 eV for double-kink formation in the cornpound Ag2A1, and it is sufficiently reasonable to suggest that further experiments of this type may be able to provide quite accurate values for AF*. The velocity of the resulting kinks is proportional to the driving force for growth. If it is assumed that the double kink in Fig. 3 can be approximated as a large semihexagonal bow-out in the dislocation as sketched in Fig. 4, the line tension of the dislocation d E / d L can be calculated using the following formula [10] d E / d L = ;~s = ~b2/4rt( 1 - v)
x [(1 - 3 v / 2 ) l n ( L / p ) + 2.00v - 1.05] (3)
where/~ is the elastic modulus, b is the Burgers vector, v is Poisson's ratio, L is the length of a segment of the hexagon, p is the core radius and E is the elastic energy. Calculation of the line tension is of interest because it allows determination of the structural component of the dislocation ledge interphase boundary energy 7s that results as the kink is formed. A ~_ A~ This energy must be overcome for the boundary to r z L.---------~ I move forward. If it is assumed that L = 4.62nm .... ~_~. ~ - - - ' 1 ~ (4.0nm/cos 30°), b = a / 6 ( l l 2 ) = p = 0 . 1 6 5 n m and v the elastic constants [10] # =2.65 × 10~° Pa and ~---k--~ v = 0,347 for AI are used in equation (3), the value for the dislocation interfacial energy is 7~= Fig. 4. Illustration of a semihexagondouble-kink configura- 1.16 x 10- l0 J/m. This value is reasonable when comtion in an edge dislocation with b in the plane of the figure, pared to the line tension of a straight dislocation as for the kink in segment A-A' in Fig. 3. The height of the kink is L/cos 30° and the edges move with velocityv parallel segment with b = a / 6 ( 1 1 2 ) [10], and particularly to the dislocation line direction ~ as indicated by arrows, considering the limitations of measurement of the
HOWE and PRABHU:
KINKS AT INTERPHASE BOUNDARIES--I
885
kink height from the T E M image and the assumption
3.3. Intersection kinks
of a semihexagonal kink. It is very difficult to obtain any kind of similar estimate by other methods, More careful examination and measurement of double-kink configurations at interphase boundaries using atomic-resolution images such as the one in Fig. l(b) may yield quite accurate values for the interracial energy, and this topic deserves further investigation,
One additional series of in situ images obtained for a plate edge during dissolution at about 425°C is shown in Fig. 5(a-c). In these figures a dislocation ledge, which is largely out of contrast in the g0:2,3g diffraction conditions used, nucleated at the intersecting precipitate labelled A in Fig. 5(a). The dislocation propagated upward, across the three dislocation ledges stacked at the edge of the precipitate plate along (ll0)~ll(1120)?,, labelled 1-3 in Fig. 5(a) and (c). The position of the moving dislocation is indicated by arrows in Fig. 5(a-c), and the interaction between this dislocation produced kinks in dislocations 1-3, clearly visible in Fig. 5(c) after 5 s. These kinks are about 35 nm wide, and the movement of the kinks with the passage of the horizontal dislocation caused each of the vertical dislocations at the precipitate edge to recede about 35-50 nm to the left, as seen by comparing their positions in Fig. 5(a) and (c). These results demonstrate that dislocation intersections can provide kinks which expedite the motion of dislocation ledges, as suggested previously [12, 16]. It is interesting to examine the dislocation reactions involved in the formation and propagation of the kinks in Fig. 5(a-c). The three parallel dislocations at the precipitate edge lie mainly along a low-energy ( 110)~ II( 11~0),/ direction. The crossing dislocation which lies two {111} planes above has a curved configuration just after nucleation [Fig. 5(a)], but after 5 s it also nearly parallels a close-packed ( l l0>~ p[( l l~0>~., direction, as is apparent from the average direction of the three kinks in Fig. 5(c). A complete contrast analysis was not performed on these dislocations, but it is reasonable to assume that they are a/6[l'2T] and a/6[2Tf] edge Shockley partials as determined in several previous analyses [5, 9, 17], with the Burgers vectors b and line directions illustrated in Fig. 6(a). As the crossing a/6[2Ti] dislocation moves upward, reaction occurs with the parallel a / 6 [ i 2 i ] dislocations to produce the node illustrated in Fig. 6(b). This reaction appears energetically favorable since Frank's criterion [10] shows that
~
. . . . .
~+
~
;~ ~.
.
.
.
.
.
Fig. 5. (a) Weak-beam dark-field image showing nucleation of a dislocation ledge (arrow) on the face of a ?' plate by an intersecting edge-on plate (labelled A) during precipitate disolution. Three dislocations in a parallel array on the precipitate are also indicated. (b) The same area after 3 s showing movement of the new ledge (out of contrast and indicated by an arrow) vertically, and (c) the same area after 5 s showing 35 nm kinks (arrows) which formed in dislocations I-3 as the new dislocation ledge continued to move upward. The three dislocations in (c) have migrated about 35-50 nm to the left as a result of the crossing dislocation,
a/6[i2i] + a/6[2ii] ~ a/6[ii2]
(4a)
a2/6 + a2/6 > a2/6.
(4b)
However, it should be noted that this inequality only approximates the actual situation, since the crossing dislocation probably lies two {111} planes above the three parallel dislocations. The resulting a/6[]'T2] dislocation in the node now acts as a kink which is at an angle of at least 30 + to any of the close-packed ( ! 10)~ JJ(11~0);., directions. It is also in a pure screw orientation with respect to the a/6['f2T] Burgers vector and only 30 ° from pure screw a/612]']'] and a/6[i]'2] Burgers vectors. This kink should be able to migrate like a disordered interface because its atomic structure is similar to that shown in Fig. l(c). Therefore, as the a/6121T] dislocation moves upward, the
886
HOWE and PRABHU: KINKS AT INTERPHASE BOUNDARIES--I
(a)
~= T01 , L
~
OTI --~ b j= o/6[TZT] ~-/.. 60* -, f b2= Q/6[eTT] " " "x~Out of Contrast "-.. x.. Tn Contrast
sufficiently small, the dislocation network may be capable of continually providing kinks to influence the overall migration kinetics of the interface [12]. Otherwise, dislocation intersections are expected to provide only local temporary means for interphase boundary migration which do not have a major effect on the overall migration rate. This effect is considered further in Part II. 3.4. Summary
The results from these TEM analyses demonstrate that geometric, thermal and intersection kinks can all be present in dislocation ledges at interphase (bI boundaries. These kinks can be of atomic dimensions ~1-- Tol as in Fig. l(b), or they may be tens of nanometers i~ ~ _ _ wide as in Fig. 5(c). When this information is com~¢2= aT I b i= a/6[ 12i] bined with experimental results from in situ studies of ledge growth which show that Shockley partial disiob = a/S[2TT] -i----k---J.... cation ledges are largely immobile when they lie along 2 I ~ ~"-. low-energy (110)~11(11~0)¢ directions [4, 12], it be[ b3-- Q/6[TT2] " - - , . comes apparent that at least two and possibly three factors need to be taken into account in kinetic analyses of interphase boundary motion involving dislocation ledges; namely, (i) the dependence of kink Fig. 6. (a) Illustration of the initial dislocation configuration in Fig. 5 considering only one dislocation in the parallel density on ledge orientation, (ii) the dependence of array with bl = a/6[l'2T] and the Crossing dislocation with kink density on temperature, and (iii) the dependence b2 = a/6[2IT], and (b) formation of a kink or node with of kink density on interledge or misfit dislocation b~ = a/6[IT2] by interaction of the two dislocations. The spacing in the case of crossing dislocation networks. corresponding line directions ~ and ~2 are also shown, and Factors (i) and (ii) have been discussed with reference dislocation segments for which g.b ~ 0 are indicated by heavy lines while those with g.b = 0 are shown by dashed to grain-boundary migration [2] and solid-vapor lines, interface migration [19], and analogous concepts apply to the nucleation of kinks in dislocation ledges reaction in equation (4) produces a favorable disloca- at interphase boundaries. These are, that the kink tion configuration in terms of both the elastic energy density increases proportionally with the deviation of and the mechanism needed for migration of the a ledge from a low-energy orientation due to geometinterfaces. It is also interesting to note that the ric considerations, and that the kink density increases contrast of the kinks in Fig. 5(a-c) increases with time with temperature due to thermal nucleation of in the sequence as the a/6[T2T] and a/6[2TT] disloca- double-kinks. In addition, the kink density due to tions react and develop into well-defined nodes. This intersecting dislocations can also be important for behavior is expected for a diffraction vector g = 0~2, interphase boundaries which contain regular netwhere a/6[T2i] and a/6[TT2] dislocations have works in solid-solid transformations and, as meng-h = + 1 while an a/6[21"T] dislocation has g.b = 0. tioned above, this should also be included when Similar dislocation reactions and contrast behavior appropriate. A few simple modifications which allow have been observed to occur in partial dislocations on incorporation of these effects into current kinetic twin interfaces [18]. analyses of ledge growth at interphase boundaries are Figure 5(a-c) show that dislocation interfaces can discussed in Part II. advance by kinks produced at dislocation intersections, although this is expected to have a large effect on the overall growth kinetics of an interphase 4. CONCLUSIONS boundary only when a regular network of crossed The results from the TEM observations of dislocaledge or misfit dislocations is present. The concentration interphase boundaries in this investigation tion of intersection kinks ck that is present in a demonstrate that: dislocation ledge along a ( 110>~II< 11~0>~, Peierls valley is given simply as (i) the atomic structure and migration behavior of dislocation interphase boundaries can be observed by ck = 2 - ' (5) high-resolution and in situ TEM techniques; (ii) orientation, thermal and intersection kinks where 2 is the interledge or misfit dislocation spacing can all be present at dislocation interphase boundand the kinks are all assumed to be positive. If 2 is aries;
HOWE and PRABHU:
(iii) m a n y characteristics o f interphase boundaries can
KINKS AT INTERPHASE BOUNDARIES--I
kinks in dislocation be approximately
described using isotropic elasticity a n d dislocation theory; a n d (iv) kinks are necessary for the m o t i o n o f dislocation interphase boundaries. Acknowledgements--The authors are grateful to Professor S. Mahajan for a helpful discussion regarding Fig. 6 and to Professor H. I. Aaronson for a critical review of the manuscript This research was supported by grants from the National Science Foundation (Grant No. DMR-8610439) and Alcoa. Use of the JEOL 200CX and Kratos EM-1500 electron microscopes at the LBL NCEM is gratefully acknowledged. REFERENCES 1. H. 1. Aaronson, C. Laird and K. R. Kinsman, Phase Transformations, pp. 313 398. Am. Soc. Metals, Metals Park, Ohio (1970) 2. H. Gleiter, Acta metall. 17, 853 (1969). 3. J. M. Howe, U Dahmen and R. Gronsky, Phil. Mag. A 56, 31 (1987). 4. J. M. Howe, Phase Transformations '87, pp. 637q~39. Inst. Metals, London (1988). 5. J. A. Hren and G. Thomas, Metall Soc. A.I.M.E. 227, 308 (1963).
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6. H. I. Aaronson, J. K. Lee and K. C, Russell, Precipitation Processes in Solids, pp. 31 85. Metall. Soc. A.I.M.E., Warrendale, Pa (1977). 7, H. I. Aaronson, J. Microscopy 102, 275 (1974). 8, J. P. Hirth, Physical Metallurgy--Part II, pp. 1234-1235. North Holland, Amsterdam (1983). 9. J. M. Howe, H. I. Aaronson and R. Gronsky, Acta metall. 33, 639 (1985). 10. J. P. Hirth and J. Lothe, Theory o f Dislocations, 2nd edn, pp. 173, 243, 490-492, 532 546. Wiley, New York (1982). 11. K. B. Alexander, F. K. LeGoues, D. E. Laughlin and H.I. Aaronson, Acta metall. 32, 2241 (1984). 12. C. Laird and H. I. Aaronson, Acta metall. 17, 505 (1969). 13. R. Trivedi, Proc. Int. Conf. on Solid-.Solid Phase Transformations, pp. 477-502. Metall. Soc. A.I.M.E., Warrendale, Pa (1982). 14. P. B. Hirsch, Dislocations and Properties of Real Materials', pp. 333-348. Inst. Metals, London (1985). 15. P. Guyot and J. E. Dorn, Can. J. Phys. 45, 983 (1967). 16. S. A. Hackney and G. J. Shiflet, Acta metall. 35, 1007 (1987). 17. C. Laird and H. I. Aaronson, Acta metall. 15, 73 (1967). 18. S. Mahajan and G. Y. Chin, Acta metall. 22, 1113 (1974), 19. W. K. Burton, N. Cabrera and F. C. Frank, Phil. Trans. R. Soc. A243, 299 (195C~51).