Vacancy loss at grain boundaries in quenched polycrystalline gold

VACANCY LOSS AT GRAIN BOUNDARIES IN QUENCHED POLYCRYSTALLINE GOLD-t R. W. SIEGEL$ Materials Science Division. Argonne National Laboratory. Argonne, Illinois 60439 S. M. CHANG Department of Materials Science. State University of New York at Stony Brook Stony Brook. New York 11794

R. W. BALLUFFI Department of Materials Science and Engineering, Massachusetts Institute of Technology. Cambridge. Massachusetts 02139 U.S.A. (Receiwd

11 September 1979)

Abstract-Vacancy loss at a variety of grain boundaries in 99.999 wt.“, pure polycrystalline gold quenched from 930 C and aged at 60 C was studied by transmission electron microscopy. The vacancy precipitate (stacking-fault tetrahedra) free zones. which formed in the regions adjacent to grain boundaries due to vacancy loss at these sinks during quenching, were analyzed. The vacancy sink efficiency of both small-angle and non-special large-angle grain boundaries was found to be high in the presence of the large chemical potential of the quenched-in vacancies. While there is some evidence that the sink efftciency at small angles is somewhat smaller than at large angles. the results are not inconsistent with a constant vacancy sink efficiency for all of the small-angle and non-special large-angle boundaries observed. On the other hand, the sink efficiency of the special Z = 3 coherent twin boundary is significantly lower than for the non-special boundaries. The results are discussed relative to other work in the field, and it is concluded that: (I) both small-angle and non-special large-angle boundaries operate as highly effective sinks at high vacancy chemical potentials; (2) the sink efficiency tends to fall off as the chemical potential decreases or the boundary becomes more special, i.e.. more ordered. R&rum&-Nous avons ttudie par microscopic tlectronique en transmission la perte de lacunes sur divers joints de grains dans I’or polycristallin de purett 99.999$, (en poids) trempi depuis 930°C et vieilli a 6OC. Nous avons analyse les zones sans precipitb lacunaires (thraMres de defauts d’empilement) qui se forment de part et d’autre des joints de grains par suite de la perte de lacunes sur ces pieges au tours de la trempe. Nous avons trouve une efficaciti de piegeage des lacunes importante, tant pour les sous-joints que pour les joints ordinaires de forte d&orientation en presence d’un grand potentiel chimique de lacunes de trempe. Bien qu’il semble que l’efficacitt de piigeage soit Itgerement plus faible dans le cas des petites d&orientations que dans le cas des grands angles, ces rbultats sont compatibles avec une efficacite de piegeage des lacunes constante pour tous les sous-joints et joints ordinaires de forte desorientation observes. Par contre, l’efficacite de pitgeage du joint de macle coherent special Z = 3 est nettement plus faible que celle des joints ordinaires. Nous discutons ces resultats que nous comparons a ceux d’autres travaux et nous concluons: (I) que les sous-joints et les joints ordinaires de forte desorientation apparaissent comme des pieges tres eflicaces pour des potentiels chimiques lacunaires ilevts; (2) que l’efficacite de pitgeage tend a ditcroitre lorsque le potentiel chimique diminue ou que le joint de grains devient plus special c’est a dire plus ordonne. Zusammenfassung-In reinem (99,999 Gew.-y,) polykristallinem Gold, das von 930°C abgeschreckt und bei 60-C ausgelagert worden war. wurde das Ausheilen der Leerstellen an einer Vielfalt verschiedener Korngrenzen mittles Durchstrahlungselektronenmikroskopie studiert. Die Bereiche ohne Leerstellenausscheidungen (Stapelfehlertetraeder), die sich wtihrend des Abschreckens wegen Leerstellenausheilung nahe den Korngrenzen ausbildeten. wurden analysiert. Die Wirksamkeit sowohl von Klein- als such von nichtspeziellen GroBwinkelkorngrenzen als Leerstellensenken war wegen des hohen chemisthen Potentiales der eingeschreckten Leerstellen hoch. Wenn es such gewisse Hinweise dafiir gibt, daf3 die Wirksamkeit der Kleinwinkelkorngrenzen etwas geringer ist als die der GroBwinkelkorngrenzen. so sind die Ergebnisse doch vertraglich mit einer konstanten Senkenwirksamkeit slmtlicher beobachteter Korngrenzen. Andererseits ist die Senkenwirksamkeit der speziellen kohlrenten Zwillingsgrenze E = 3 deutlich geringer als die nicht-speziellen GroBwinkelkorngrenzen. Die Ergebnisse werden im Hinblick auf andere Arbeiten zu dieser Fragestellung diskutiert. Es ergibt sich, daB (1) sowohl Kleinwinkelkorngrenzen als such nicht spezielle GroBwinkelkomgrenzen hochwirksame Senken unter der Bedingung hoher chemischer Potentiale durch Leerstellen darstellen, und (2) die Senkenwirksamkeit abfiillt, wenn das chemische Potential kleiner wird oder die Korngrenze spezieller, d.h. besser geordnet wird. t Work supported by the National Science Foundation and the U.S. Department of Energy. 1 Formerly at: Department of Materials Science, State University of New York at Stony Brook. Stony Brook, New York 11794. U.S.A. 249

250

SIEGEL

et al.: VACANCY

LOSS AT GRAIN

1. INTRODUCTlON It has frequently been observed [l-5] that the precipitation of supersaturated vacancies is significantly reduced in the vicinity of grain boundaries. There is general agreement that this phenomenon is caused by a decrease in the vacancy concentration near the boundary brought on by the annihilation of excess vacancies at the grain boundary (see [6] for example). Under these conditions the nucleation rate for vacancy precipitation is reduced, and a denuded zone completely free of precipitates often results. Despite the frequent observation of such vacancyprecipitate denudation at grain boundaries, relatively little systematic work has been done with this phenomenon to obtain quantitative information about the efficiency of grain boundaries as vacancy sinks. An early observation of vacancy-precipitate-free regions near grain boundaries was concerned with the formation of cavities at the oxidized surface of boundaries. aluminum near intersecting grain Doherty and Davis [2] first showed that small surface pits were formed at an electropolished surface of aluminum single crystals during cooling from an elevated temperature. The formation of these pits was attributed to the condensation of supersaturated vacancies at the surface upon which an oxide layer had formed. Pits. however, did not form in the vicinity of grain boundaries. Basu and Elbaum [33 subsequentlv measured the width of the denuded retion adjacent to a number of ‘general’ grain boundariest in aluminum specimens cooled under a variety of conditions. For all observed boundaries, with the exception of the easily identified coherent twin boundary, they reported that the width of the denuded zone was insensitive to the crystal misorientation angle. They therefore concluded that these boundaries, which possessed misorientation angles ranging from 2 to SO”, were equally effective sinks for vacancies in a1uminum.S In contrast to this, they found n.6 denudation at the coherent twin and therefore concluded that it must be a poor sink. On the other hand, Segall [S] observed stacking-fault tetrahedron denudation at a coherent twin boundary in quenched gold

t A ‘general’ grain boundary is defined as a boundary randomly selected in a polycrystalline specimen. Such a boundary may. or may not. be a ‘special’ boundary; i.e., possess an ordered structure with relatively short wavelength periodicity. The probability of finding special boundaries in a collection of general boundaries depends upon the specimen texture. history. etc. This problem is extensively discussed in [7], $ We note that these boundaries included both smallangle and large-angle boundaries. Small-angle boundaries consist of planar arrays of discrete lattice dislocations at spacings which decrease as the misorientation angle increases. At about 15’ the dislocation cores begin to overlap. and the grain-boundary structure makes a transition to a structure consisting of a continuous slab of bad material. We classify boundaries of the latter type as largeangle boundaries.

BOUNDARIES

and concluded that it had acted as an effective vacancy sink. However, the denudation in this case was not compared with that at other, non-special boundaries. In more recent work, Burke and Stuckey [4] have measured zones denuded of vacancy precipitates at general grain boundaries in quenched and annealed pure aluminum and various aluminum alloys. Of particular interest was their observation that very little variation in the grain boundary sink efficiency existed for boundaries in an Al-1.5%Zn alloy with misorientations > c 3”, but that a significant decrease occurred for smaller misorientations. This result suggests that the efficiency of small-angle boundaries, consisting of well-spaced lattice dislocations, decreases noticeably near 3” in at least Al-Zn alloys. Unfortunately, no specific data regarding the question of sink efficiency versus boundary misorientation was presented for either pure aluminum or the other alloys studied in [4]. In the present work a quantitative study has been carried out of the extent of vacancy-precipitate denudation at grain boundaries in quenched and annealed polycrystalline gold in order to obtain information about the efficiency of a variety of grain boundaries as vacancy sinks under conditions of high vacancy supersaturation. The quenching and annealing conditions were selected so that the vacancy precipitation took place in the form of stacking-fault tetrahedra. Precipitation of tliis type was advantageous, since the formation of stacking-fault tetrahedra has been studied extensively [9] and since the geometry of these precipitates is particularly well defined enabling direct measurements .of the precipitated vacancy concentration to be made [IO]. The stacking-fault tetrahedron denudation in the specimen interior was studied using transmission electron microscopy of thin-film specimens extracted from the bulk. A range of grain boundaries, including both small- and large-angle boundaries, was studied, and the crystallographic parameters defining each boundary were measured in an effort to find possible variations in the sink efficiency with boundary geometry, i.e., structure. The present results are compared with those from previous work on grain boundaries as sinks (and sources) of vacancies, and an attempt is made to summarize the current state of the field.

2. EXPERIMENTAL

PROCEDURE

A polycrystalline gold specimen was quenched from 930°C to room temperature and subsequently annealed at 60°C for the excess vacancies to precipitate fully in the form of stacking-fault tetrahedra. Electron microscope samples were then electropolished from the bulk specimen and used for the direct observation of the tetrahedron-free regions adjacent to the observed grain boundaries, which were chosen at random.

SIEGEL er al.: VACANCY LOSS AT GRAIN BOUNDARIES 2.1

Spechen

preparatiorl

The specimen was a ribbon-shaped polycrystalline foil of 99.999 wt.“, nominal purity (Grade 59) supplied by Cominco American, Inc.. with a gauge length approximately 8.0 cm long. 0.46 cm wide and 0.015 cm thick. The specimen shape and quenching technique were similar to those used in previous investigations [lo] in quenched gold. The specimen, mounted on a copper frame in a draft-free box, was cleaned and then resistance heated to 930°C for three hours in order to anneal it and f&y stabilize the grain structure. An optical pyrometer was used to measure the specimen temperature, which was maintained uniform to It 2°C along the entire gauge length. After annealing, the specimen was held at 930°C for about 5 min with the specimen gauge length approximately 1 cm above the surface of the water quenching medium. Subsequently, the specimen was quenched by rapidly lowering it into the water at (25 k l)‘C, where it remained for _ 3 min. The specimen gauge length entered the water simultaneously along ail points in the edge-on direction to minimize straining due to quenching and to insure a uniform quenching rate along the entire gauge length. The specimen was then removed from the frame and aged for 24 h at 60 + 3’C. After this aging. which allowed all of the quenched-in vacancies to precipitate, the gauge length was cut from the specimen and then carefully cut horizontdly along a center line into two parts, the lower part. which was the first to enter the water during the quench, and the upper part. The lower and upper parts of the specimen were examined separately. Electron microscope samples were electropolished from the bulk specimen using the standard cyanide electrolyte [I 13. During thinning the sample always preferentially perforated in one or two areas. The thin regions around these holes were then examined in transmission at 100 kV in a Philips EM 300 electron microscope.

2.2 Analtssis of vacancy precipitate free iones Areas denuded of stacking-fault tetrahedra near grain boundaries were observed by electron microscopy. An average of five overlapping electron micrographs taken of regions adjacent to each of the grain boundaries observed were used, with their accompanying diffraction patterns, for the analysis of each vacancy-precipitate-free zone. A total of fourteen grain boundaries were investigated from the lower part of the specimen, and seven grain boundaries from the upper part of the same quenched and aged specimen. On contact prints of the electron micrographs, lines parallel to the grain-boundary trace were drawn with a spacing corresponding to AX = 1500 A measured perpendicular to the grain-boundary trace (see Fig. l(a)). The tetrahedron sizes and densities within each volume interval (corresponding to AX =

251

I500 AI were measured separately. The tetrahedron number and sizes were measured using a Zeiss Particfe-Size Anafyzer. In order to obtain the precipitate densities. the sample thickness was determined in the normal manner. using dislocation slip traces and ‘or the width of annealing twins. The fractional concentration of vacancies which precipitate in the form of stacking-fault tetrahedra is given by c: = (a/4) i&N,. where a is the lattice parameter. N, is the number of tetrahedra per cm3. and I.., is the root-mean-square tet~dhedron edge length. The precipitated vacancy concentration. CT. within each interWI, thus calculated. varied with distance. s. measured perpendicular to and awa! from the grain boundary. An example of the observed vlariation of c: with s in the vicinity of the boundary shown in Fig. I(a) is presented in Fig. I(b). in which a histogram of c: as a function of s is shown for the region on one side of the boundary. It can be seen from this esample that cz increased from zero in the volume adjacent to the grain boundary to a constant value. which was observed to be equal to the value of c: in the bulk of the grains (i.e.. at s = x 1. where a uniform precipi-

tated vacancy concentration existed unperturbed by the grain boundaries. Values of c:(x = x ) were found to be (2.0 5 0.4) x IO-“ for the lower part of the specimen. and (1.5 i 0.5) x 10m4 for the upper part of the same specimen. It is seen in Fig. l(a) that the tetrahedron size reached a maximum in a region near the edge of the denuded zone. This result is entirely consistent with the nucleation and growth mechanisms responsible for the denuded zone. Immediately after quenching, the nucleation rate of tetrahedra, which is an increasing function of vacancy concentration, increased with distance measured away from the grain boundaries due to the vacancy .concentration gradient created during the quench (see Fig. 4 of Ref. [6]). During subsequent annealing in the regions near grain boundaries a competition developed between the vacancy precipitates (stacking-fault tetrahedra) and the grain boundary for the annihilation of supersaturated vacancies. This resulted in a region of maximum tetrahedron size in which a relatively small number of tetrahedra were nucleated and were able to compete effectively for a relatively large number of excess vacancies owing to the rather high vacancy sink efficiency of stacking-fault tetrahedra [IO, 12. 133. An apparent effective width, H.‘,of the vacancy-precipitate-free region in the vicinity of a grain boundary was arbitrarily chosen to be the value of x at which the vacancy con~ntration was 407{ of that in the volume unaffected by vacancy losses at the grain boundary. i.e., ct(x = w’) = (O.S)ca(x = x ), as shown in Fig. l(b). In order to obtain the actual width, H‘.of the denuded region from the apparent width, )L.‘.the orientation of the grain-boundary plane relative to the sample surface must be taken into account. If @ is the angle between the respective normals to the electron-microscope sample surface and the grain-bound-

SIEGEL er al.: VACANCY LOSS AT GRAIN BOUNDARIES

252

-7%AX

n

Ql5pm

(a)

0.5pm

I.6

(b)

0

0

12

use. It was occasionally observed that there was far greater denudation on one side of the boundary than on the other. These observations apparently resulted from the presence of additional vacancy sinks, and could be understood in the following ways. Some regions near grain boundaries were observed to contain a relatively high dislocation density. Since these dislocations are also sinks for vacancies during the quench, the width of the denuded region in such regions is not simply related to the sink efficiency of the gram boundary. Such data were therefore eliminated. Another, less obvious, difficulty can arise from the presence of a junction of three grain boundaries (OA, OB, and 6C) in the specimen shown schematically in Fig. 3. If one of the boundaries. OB, lies nearly parallel to the sample surface it is possible to obtain an electron-microscope sample that contains a grain boundary, OA, on one side of which the width, w, is considerably greater than that on the other. For such an occurrence it is clear that the larger of the two observed values of w (e.g., that measured on the right side of OA in Fig. 3) is not that of the denuded region associated with the observed grain boundary, OA, and should be eliminated from further consideration.

1.6

a(pm)

2.3 Determination Fig. 1. (a) Stacking-fault tetrahedra in the vicinity of a boundary with nt = q2 = [MO]. Lines parallel to the grain

boundary were drawn with a spacing corresponding to AX= 15OOAmeasured perpendicular to the grain-boundary trace. (b) The precipitated concentration, c:, for the grain boundary shown in Fig. 1 (a), as a function of the distance, x, measured perpendicular to, and away from, the grain-boundary trace. The apparent effective vacancy-precipitate-free width, w’. was chosen to be the value of x at which the vacancy concentration was 40% of the vacancy concentration far from the boundary.

is shown graphically in Fig. 2. Each grain boundary usually yielded two measurements of w (wi and w2 in Table 1) corresponding to the regions on each side of the grain boundary. However, in a few cases these data were not suitable for

ary plane, then w = w’ sin +. This correction

Fig. 2. A schematic side view of an electron microscope sample, in which $ is the angle between the respective normals to the foil surface and the grain-boundary plane. The apparent effective vacancy-precipitate-free width obtained directly from the electron micrographs, w’, is related to the actual vacancy-precipitate-free width. W, by w = w’sin *.

of grain-boundary

misorientation

The crystallographic parameters defining each grain boundary, i.e., the crystal misorientation across the boundary and the orientation of the grainboundary plane, were obtained from measurements on selected-area diffraction patterns from each of the crystal grains and images of each boundary. The crystal misorientation of the two crystals (Crystals 1 and 2) adjoining each boundary was determined in terms of the rotation, R, required to rotate Crystal 1 into. the orientation of Crystal 2. The rotation R was expressed in terms of an angle/axis pair, fJ/[u u w], where 0 is the angle of rotation about the axis [u tl w] which produces the observed misorientation. Here, [u u w] is referred to the unit cell

Fig. 3. A schematic figure showing a junction of three grain boundaries OA, OB, and OC. The measured denuded width from the right side of OA, w>, is larger than that from the other side. w,, and does not represent the actual vacancy-precipitate-free width associated with grainboundary OA.

SIEGEL

et al.: VACANCY Table

LOSS

I. Grain

boundary

8 9 10 II 12 13 14

35.3/[01T] 45.qi[OOT] 45.0’[007] 18.4/[OOT]

BOUNDARIES

data

R2 R, R2 R, R2 Same as R2 Same as R,

71.2 69.4 78.1 9.0 69.4 59.0 66.0

15.4 11.8 41.9 36.5 20.8 5.1 37.5

1.6 1.2 0.9 0.8 1.3 1.4 1.6

1.0 1.3 0.9 0.9 1.3 1.9

25.0:[21 I] 30.0 ‘[2 I I] 29.0’[21 l]

Same as Rz Same as R2 Same as R,

68.0 79.6 65.5

14.5 27.0 40.0

1.7 1.9 1.4

1.3 1.9 1.4

ZO.Oi[ loo] 13.8’[100] 34.8’[100] 2.0/[ 1001

40.4”[0.48 0.72 0.50] 47.0![0.28 0.12 O.%] 56.4,‘[0.59 0.24 01773 1X.6 [O. 1 I 0.020.991

62.5 85.0 80.5 53.0

2.0 29.0 40.0 24.0

1.4 2.1 1.7 1.4

1.9 1.4 1.1

4.2,‘[ 1001 8.4![100] 4.2/[100] 2.0![ loo] 2.5”[100] 1.8’[100] 3.0,‘[ loo]

6

AT GRAIN

coordinate system of Crystal 1, and 0 is measyred clockwise while sighting along [u L’w]. For all boundaries studied it was found that relatively low-index crystal directions in Crystals 1 and 2, i.e., n, and n2. were closely normal to the specimen surface, and hence, to each other (see Table I). It was therefore convenient to consider the final rotation as the product of two successive rotations. The first rotation, RA, produced n2 parallel lo n,. The second rotation. R,. corresponding to a rotation around the axis n,, produced the final observed misorientation. The various orientations and rotations were measured on selected-area diffraction patterns from Crystals 1 and 2 using standard techniques. The sizes of the diflraction spots were minimized by defocusing the illumination in order to allow more accurate measurements. The results, expressed as angle/axis pairs, are given in Table 1. The orientation of the grain-boundary plane was defined in terms of the angles $ and 4. The angle 1(1 (already defined above-see Fig. 2) was obtained from the projected width of the grain boundary, p, and the thickness of the electron microscope specimen, t, according to the equation JI = tan-’ (tip). The angle 4 was taken as the angle between the trace of the intersection of the grain-boundary plane and the specimen surface and the [OlT] direction in Crystal 1 (which was present in the specimen surface for every boundary observed). The results are given in Table 1. 3. RESULTS As described in section 2.1. the specimen gauge length, after quenching and aging, was cut into two parts along a center line parallel to the specimen edge. These two parts of the specimen were examined separately by transmission electron microscopy. The lower part of the specimen, which was the first to enter the quenching medium, contained an average bulk tetrahedron density (far away from grain boundaries, etc.) equal to (2.3 * 0.5) x 1014cm-3, corresponding to a fractional concentration of precipitated

Same Same Same Same Same

as as as as as

vacancies of (2.0 k 0.4) x 10e4. The quenching rate of the specimen was not measured. but can be roughly estimated from the work of Flynn et al. [14]. The quenched-in resistivity increment in gold from a quenching temperature of 930°C was plotted as a function of quenching rate using their data. Using a value for the vacancy contribution to the resistivity of pI: = 1.5 @2 cm/at.?; vacancies, the quenching rate was estimated from the quenched-in resistivity corresponding to the measured quenched-in vacancy concentration. In this manner a quenching rate of approx. 5 x 1O’“C s- ’ was estimated for this part of the specimen. On the other hand. in the upper part of the same quenched and aged specimen a somewhat lower precipitated vacancy concentration, C~(X= XC) = (1.5 -r_0.5) x 10-Q. was found. From this value a lower quenching rate of 3.5 k 104°C s-’ was estimated in the same manner. In all, 14 grain boundaries (numbered 1-14) were analyzed from the lower part of the specimen (see Table 1). Of these fourteen boundaries seven, i.e., Boundaries l-7. possessed misorientations corresponding to simple rotations around [lOO], while the misorientations of three (Boundaries 8-10) corresponded to simple rotations around [Zll]. The remainder possessed more complex misorientations. (We note that the high incidence of crystals with nl = n2 = [lOO] may be attributed to the strong preferred orientation, i.e., cube texture, present in the rolled and annealed sheet specimen.) Boundaries l-7 were small-angle boundaries with misorientations <9’, whereas the remainder were all large-angle boundaries. The boundary planes adopted a range of orientations, and none of the boundaries were of either simple twist or tilt type. Finally. inspection of the data in Table 1 for the high-angle boundaries shows that none were special boundaries possessing relatively high density coincidence lattices and short wavelength periodicities. None of the observed boundaries possessed coincidence-site lattices with X .I 25, where 1 is the reciprocal of the fraction of atoms in coincidence. It is noted

254

SIEGEL et al.: VACANCY LOSS AT GRAIN BOUNDARIES

that Boundaries 8-10 might conceivably be classified as plane-matching boundaries [7], since the (422) planes of Crystals 1 and 2 were closely matched across these boundaries. However, boundaries with matched planes with indices as high as (422) are not expected to be able to support physically distinguishable grain-boundary dislocations and to possess other attributes of special boundaries [ 151. The measured widths of the denuded zones in Crystals 1 and 2 on either side of each boundary, wI and wt, are listed in the last two columns of Table 1 and are displayed in Fig. 4. The data for the small-angle boundaries (Boundaries l-7) were plotted versus the rotation angle, 0, since we were particularly interested in a possible decrease of the sink efficiency at small angles (as observed by Burke and Stuckey [4]). Also, since the m&orientations of all of these boundaries were simple rotations around [lOO], it seemed possible that a fairly systematic variation of w (w, and w2) with 13could occur even though the orientations of the boundary planes varied considerably. The data for the large-angle boundaries (Boundaries 8-14) were simply displayed in Fig. 4 according to the boundary number, and no attempt was made to correlate w (wI or wl) with tiie parameters defining these boundaries. This procedure was used, since it is well established that the structure of general high-angle boundaries may vary markedly and is not a simple monotonic function of any single boundary parameter. Seven grain boundaries from the upper part of the specimen were also investigated in a similar manner. However, these data exhibited considerably greater scatter than those presented in Table 1 (Chang [16]). This result is in agreement with that of Burke and Stuckey [4] who found that the denuded zone became more variable as the quenching rate was decreased. We therefore disregard these data in the following.

3.0yI

SMALL-ANGLE

I OO

1

2

1

4 e (drgmrl

BOUNDARIES

I

I

6

S

The results in Fig. 4 for the small-angle boundaries indicate no significant tendency of the vacancy sink efficiency to decrease with decreasing misorientation in the range 1.8 < 13I 8.4”. The efficiency of the large-angle boundaries appears also to be independent of boundary type within the accuracy of the present measurements. The efficiencies of the small- and large-angle boundaries appear to be quite similar. The average denuded zone width for the large-angle boundaries (1.6 + 0.3 pm) is about 33% larger than that for the small-angle boundaries (1.2 f 0.3 pm), as indicated in Fig. 4. However, it is not clear that this difference exceeds the uncertainty in the results. We, therefore, conclude for the present that, while there is some evidence that the efficiencies of small-angle boundaries may be somewhat smaller than those of the large-angle boundaries, the results are not inconsistent with a constant vacancy sink efficiency for all of these observed ‘boundaries. In the course of the present work a single qualitative observation (Fig. Sa) was recorded of the denuded zone in the vicinity of a coherent (Ill) annealing twin, which, of course, is a special large-angle boundary (with 2 = 3) that can be described in terms of the 70.5”/( 110) angle/axis pair. It can be seen that a denuded zone was present at this boundary, but that the width of the zone was unambiguously smaller than those at the non-special large-angle boundaries listed in Table 1 (Fig. 4). This result therefore indicates that the sink efficiency of the highly ordered special coherent twin boundary is significantly lower than that of the non-special boundaries. In further support of this conclusion, a previously unpublished result from earlier work on quenched gold [9] is presented in Fig. Sb. which shows denuded zones in the vicinities of coherent and semicoherent twin-boundary segments. Again, considerably greater denudation

LARGE-ANGLE

I

8

I

I

BOUNDARIES

I1

I

9 10 II 12 13 Groin Boundary Numbu

II

14

Fig. 4. The effective denuded zone width, w = w, or w2, plotted as a function of grain-boundary misorientation angle b, for the small-angle boundaries. Denuded zone widths for large-angle boundaries are displayed according to grain-bound&y number (see Table 1). Overlapping valuelare denoted by the number 2. The average values of w for the small- and large-angle boundaries are indicated as are the regions within their respective standard deviations.

255

SIEGEL et at.: VACANCY LOSS AT GRAIN BOUNDARIES

I

J

1

I 0.5pm

km (a)

(b)

I

J 0.5pm (cl

Fig. 5. (a) Stacking-fault tetrahedron denudation at a coherent annealing twin, from the same quenched gold specimen from which the results of Fig. 4 (Table I) were obtained. (b) Stacking-fault tetrahedron denudation at semicoherent and coherent twin-boundary segments in quenched gold: an unpublished result from earlier work [9]. The semicoherent boundary is shown in the center. bounded on either side by coherent twin boundaries. (c) Stacking-fault tetrahedron denudation at isolated lattice dislocations in the same specimen shown in (b).

occurred at the short semicoherent boundary segment shown than at the coherent twin boundaries lying to either side of it. 4. DISCUSSION The present result that the vacancy-precipitate denuded zones caused by all of the small-angle and non-speciaI targe-angle grain boundaries were quite similar is readily explained on the basis that all of these boundaries acted as efficient sinks for the highly supersaturated vacancies produced by the rapid quenching. It is easily shown (see the Appendix) that small-angle grain boundaries should act as highly effective planar sinks down to misorientation angles as small as 0 = O.W, if the individual dislocations comprising the boundaries act as perfect line sinks.t Previous work by Seidman and Balluffi Cl73 indicates that individual dislocations indeed act as highly efficient sinks in quenched gold when the vacancy chemical potentiai is large. In the present work the chemicai potential was large, i.e., pK 5 0.7 eV, and it therefore follows that the small-angle boundaries in the present work should have acted as highly efficient sinks. Further evidence for this is presented in Fig. 5(c). in which stacking-fault tetrahedron denudation at isolated lattice dislocations is clearly shown. This electron micrograph was obtained from the ident We define a perfect vacancy sink as a sink which is able to annihilate vacancies at a sufficiently high rate so that the local vacancy concentration in its vicinjty is maintained essentiaBy at equilibrium.

tical specimen as that shown in Fig. S(b). A comparison of these two micrographs shows that the effective width (radius) of the denuded region about a dislocation is of the same magnitude is that at the semicoherent twin boundary, while both are significantly larger than that at the coherent boundary. It is difficult to conclude whether the present result that the average denudation for the large-angie boundaries was 5 339~ wider than for the small-angle boundaries is a significant effect or not. If so, it would indicate that the dislocations did not act individually as completely perfect line sinks in the small-angle boundaries. The present results for the non-special boundaries are not inconsistent with those of Basu and Elbaum [3] who found a vacancy sink efficiency for grain boundaries in aluminum which remained essentially constant for boundaries with misorientations ranging from 2-50”. However, the vacancy chemical potential in the Basu and Elbaum experiments was smaller than in the present work, i.e., it was probably less than 0.1 eV. Nevertheless, there is reason to believe that dislocations in aluminum act as good vacancy sinks at Iower p,. than in gold because of aluminum’s higher stacking-fault energy and the non-dissociated nature of its dislocations 118, 191. It is interesting that Basu and Elbaum found coherent twins to be inoperative as vacancy sinks in their work, in contrast to the clear evidence presented by Segall [S] and in the present work for the vacancy-sink action of coherent twin boundaries in rapidly quenched gold. Their result was most probably due to the smaller vacancy chemical potential in their experiments.

SIEGEL et al.: VACANCY LOSS AT GRAIN BOUNDARIES

256

Table 2. Observations of grain boundaries as vacancy sinks (sources) Metal

pc,(eV)

Observation

Reference

Au

0.7

Present work

Al

SO.1

cu

z lo-’

Non-special boundaries good sinks; Z = 3 special twin boundary poorer sink Non-special boundaries good sinks; I: = 3 special twin boundary inoperative Special boundaries with 3 6 I: < 15 inoperative; non-special boundaries operative

In view of the above results, the reason for the apparently lower sink efficiency of small-angle boundaries with 0 < -3” in the Al-Zn alloy observed by Burke and Stuckey [4] is not clear. It seems possible, however, that this result may have been due to the vacancy-current-induced transport of zinc atoms to the dislocations during the annealing after quenching. Anthony [20] has shown that zinc solute atoms in aluminum tend to be enriched at vacancy sinks during post-quench vacancy annealing. Furthermore, the vacancy current to each dislocation should have been proportional to the dislocation spacing (or K’) in the range of misorientations under consideration. Therefore, the degree of segregation should have increased with decreasing misorientation and may have reached a sufficient level near 19= 3” to have caused the observed decrease in sink efficiency. The observed decrease in the width of the denuded zone at the coherent twin boundary indicates a relatively low vacancy sink efficiency for this special coherent boundary. As discussed elsewhere [21], a special boundary of this type undoubtedly acts as a vacancy sink by having grain-boundary dislocations (GBDs) climb across its face. The low efficiency of this boundary must then have been due to: (1) a relatively low rate of vacancy migration across the twinboundary face, which tended to reduce the collection efficiency of the climbing GBDs, and (2) a relatively small density of climbing GBDs due, at least in part, to the relatively large Burgers vector and line tension of the GBDs in the highly ordered (low Z) boundary. It is interesting to note that Jaeger and Gleiter [22] have recently reported that special boundaries possessing X values between 3 and I5 did not operate as vacancy sources in copper during Herring-Nabarro creep with pv 2: lo- ’ eV. On the other hand, nonspecial boundaries were apparently good sources. In conclusion, all of these results, which are summarized in Table 2, suggest that: (1) All grain boundaries act as vacancy sinks (and sources) when (~1 is sufficiently large. However, the

efficiency of at least the special Z = 3 twin boundary is generally lower than that of non-special boundaries ; (2) When 1pv( decreases the vacancy sink efficiencies of the boundaries apparently tend to decrease, and at

131

WI

sufficiently low values of 1~1 many special boundaries no longer operate as sinks. Further discussion of grain boundaries as pointdefect sinks may be found in [21].

Acknowledgemenrs-This work was supported in part by the National Slice Foundation under Grant No. GK-3435 (R.W.S. and S.M.C.), and in part by the U.S. Department of Energy under Contracts No. ER-78S-02-5002.A000 (R.W.B.) and No. W-31-10!9-ENG-38 (R.W.S.).

REFERENCES 1. P. B. Hirsch, J. Silcox, R. E. Smallman and K. H. Westmacott. Phil. Moo. 3. 897 (1958). 2. P. E. Dohe& and RI S.. Davis, A&a Metall. 7, 118 (1959). 3. B. K. Basu and C. Elbaum, Acta Metall. 13, 1117 (1965). 4. J. Burke and D. Stuckey, Phil. Msg. 31, 1069 (1975). 5. K.-D. Rasch, R. W. Siegel and H. Schultz, J. Nucl. Mater. 69 & 70, 622 (1978); Phil. Msg. A, in press (1979). 6. R. W. Siegel, J. Nucl. Mater. 69 & 70. 117 (1978). 7. R. W. Balluffi in Interjacial Segregation, (edited by W. C. Johnson and J. M. Blakely) p. 193, American Society for Metals, Ohio (1979). 8. R. L. Segall, Acta Metall. 12, 117 (1964). 9. R. W. Siegel, Phil. Mag. 13, 337 (1966). 10. K. C. Jain and R. W. Siegel, Phil. Mag. 25, 105 (1972). Transmission Electron Microscopy of 11. G. Thorn= Metals, p. 162. Wiley, New York (1962). 12. R. W. Siegel, R. W. Balluffi, and L. E. Thomas, Acta Metal. 16. 7 (1968). 13. R. W. Siegel, K. C. Jain, T. Schober, R. W. BallulIi, and L. E. Thomas, Cryst. Lan. Dejects 1, 31 (1969). 14. C. P. Flynn, J. Bass, and D. Lazarus, Phil. Mag. 11, 54 (1965).

15. R. Schindler, J. E. Clemans, and R. W. Ballufi to be published. 16. S. M. Chang, M.S. Thesis, State University of New York at Stony Brook (1970). 17. D. N. Scidman and R. W. Ball&& phys. stat sol. 17, 531 (1966).

18. D. N. Seidman and R. W. Balluffi, in Lattice De/ecu and Their Interactions. (edited by R. R. Hasiguti) p. 911, Gordon & Breach. New York (1967). 19. N. Q. Lam, H. A. Hoff, P. R. Okamoto. and R. W. Siegel, Acta Merall. 27. 799 (1979). 20. T. R. Anthony, in Diffusion in Solids, (edited by A. S. Nowick and J. J. Burton) p. 353, Academic Press, New York (1975).

251

SIEGEL et 01.: VACANCY LOSS AT GRAIN BOUNDARIES 21. R. W. Balluffi. in Fundamrnral

Aspects of Radiation Durrraye irr Merols. (edited by M. T. Robinson and F. W. Young. Jr.) p. 852. National Technical Information Service. U.S. Department of Commerce, Springfield, VA 22161. (1976). 22. W. Jaeger and H. Gleiter, Scripra Met. 12, 675 (1978). 23. P. M. Morse and H. Feshbach, Methods of Theoretical Physics. p. 1237. McGraw-Hill. New York (1953).

and Feshbach [23] we have 1

c=

(A.2)

Therefore,

“‘~,,+A&__)]~ (A.3)

APPENDIX Small-anyle boundaries

as vacancy

The corresponding flux into a perfect planar sink would be sinks

Our aim is to calculate the quasi-steady state diffusion flux of vacancies to a small-angle boundary consisting of a planar array of discrete dislocations which act as perfect line sinks and to compare the result with the flux to a perfect planar sink. For this purpose we represent the boundary as a planar array of straight parallel dislocations spaced a distance d apart. Each dislocation line sink is represented by a cylinder of radius re. and since the equilibrium vacancy concentration is negligible compared to the quenched-in concentration, we take the vacancy concentration at the cylindrical surface of each dislocation to be zero. We consider the array to be embedded in a sea of supersaturated vacancies at the concentration E, and solve for the quasi-steady state current into the array under the condition that the vacancy concentration is maintained at the value E, at the distance B! Using the analogy between solutions of the Laplace equation in electrostatic and in steady state diffusion problems we may express the vacancy flux into the dislocation array as d = D&C

(A.4) and the efficiency of the dislocation array relative to the planar sink is then

The efficiency 9 deviates by more than 2Sgb from unity when

&‘n Znr, 4

b4.6)

Since W I I pm and r0 = 5 A. this occurs when d > 426OA. The corresponding angles of misorientation are then in the range 8 2 0.04”. since

02 d’

(Al)

where D, is the vacancy diffusivity, and C is the capacitance per unit area of an array of parallel wire conductors of the same geometry as the dislocation array. From Morse

1 > -. 3

( >

where b is the (b = 2.88A).

Burgers

vector

of the

dislocations