weak beam microscopy of grain boundaries

A. R. JONES et al.: Weak Beam Microscopy of Grain Boundaries

phys. stat. sol. (a) 88, 107 (1976)

Subject clessificcrtion: 1.4; 21.1.1

Department o/ Welcrllurgy and Yakriala Science. Univcra’ty o/ Cambridge

107

Weak Beam Microscopy of Grain Boundaries BY

A. K. Joxes, P. R. HOWELL, and B. RALPH

The use. and unefulneea of the weak beam technique in studies of defect structuree at grain boundariee is diecueeed. The localization of strain contraet, in this imaging mode, at dielocatione makes their detection eaeier than in conventional imaging mcdee. A h , the reduction in extinction distance can lead to a fine graticule of extinction contours on which topographical discontinuities may be “mapped”.

Es wird der Gebrauch und die Niitzlichkeit von Elektronenmikroekopie mit suhwachem Strahl bei Unternuchungcn der Defektetruktur bei Korngrenzen diekutiert. Die Lokeli- eiorung dea Spennungekontrastee bei dieser Abbildungsmode macht deren Nachweie leich- tar ale bei konventionellen Abbildungemoden. Die Verringerung dee Extinktionssbetands kann auch zu einer feinen Raeterung der Extinktionekonturen fiihren. wodurch t o p - graphische Diskontinuititen ,.abgebildet“ werden konnen.

1. Introduction

This paper shows how the technique of weak beam transmission electron microscopy has been applied to the study of high angle grain boundaries in a commercial dispersion hardened austenitic stainless steel.

The observations outlined in the following sections relate to a variety of grain boundary structurea ( I ] some of which may be characterised in terms of their strain fields (e.g. intrinsic and extrinsic grain boundary dislocations and certain topographical discontinuities), while others may be considered as more or less strain free (e.g. boundary curvature around pinning precipitates, certain steps and ledges etc.).

Full details of the alloy used and the heat treatments given, may be found elsewhere [2 to 41.

1.1 Weak beam electron microseopg of intragronuhr defects

Weak beam electron microscopy has been used extensively in the study of intragranular defects in the last few years (5 to 81.

The technique is relatively simple, involving the manipulation of diffraction conditions in one reciprocal lattice zone, when only one reciprocal lattice zone is exhibiting strong hffraction. Initially, an area of crystal including the defect which is to be analysed is set up in two-beam diffracting conditions. From this situation, one method of obtaining a weak beam image of the defect is to tilt the crystal such that the excesa Kikuchi line for the operating reflection is driven out beyond the higher order reflections in the reciprocal lattice zone (usually a t least as far as the third order reflection, and sometimes further) ; in a centred dark field image formed from the f i rs t order reflection, diffracted intensity is localised to either one side or the other of the core of the defect by the local distortion of the crystal lattice in the vicinity of the defect. The image width of the

108 A. R. JONES, P. R. HOWELL, and B. RALPH

defect is much narrower than it would be under normal two-beam diffracting conditiom; an increase in.effective resolution is obtained.

The following sections show that , while the above technique of weak beam microscopy gives rise to basically similar results when applied to the analysis of high angle grain boundary defect structures, certain aspects of diffraction contrast a t inclined interfaces, combined with the individual and structurally complex nature of grain boundaries, lead to individual and additional contrast behaviour in weak beam images.

12 The &led popuhtion at groin boundaries

It has been shown that periodic arrays of intrineic dislocations form the major “equilibrium defect” component of a percentage of grain boundaries [I] . These intrinsic dislocations tend to have small Burger’s: vectors which are partials in the nearest coincidence site lattice. For a planar section of boundary they are periodically spaced, leading to extensive mutual cancellation of long range strain fields. These defects, and others which are part of the “non-equilibrium” component of the boundary, exist in a region where the elastic constants are ill defined.

The “non-equilibrium” components of grain boundaries comprise extrinsic dislocations (formed due to interaction and dissociation of matrix dislocations) and topographical discontinuitiee. When present, extrinsic dislocations (which have similar Burgers vectors to the underlying intrinsic structure) will perturb the periodic and mutually reduced strain fields of the intrinsic dislocation structure and, thus, will have longer range strain fields. Topographical discontinuities (ledges, steps, boundary junctions and curvature) may be associated with long range strain fields or may be essentially strain free.

2. Weak Beam Microscopy 01 Intergranular Defects

Two basic features of the technique of weak beam electron microscopy com- mend i t to the study of grain boundaries. Theae are:

1. the localisation of strain contrast to a region close to the core of a defect; this feature of weak beam electron microscopy allows closely spaced intrinsic defect arrays to be resolved more readily than under conventional two-beam imaging conditions. The interaction of matrix dislocations with boundaries to form extrinsic dislocations by dissociation may also be studied more readily using this technique.

It should be noted that when analysing intragranular defects the crystallo- graphically limited range of possible Burgers vectors results in certain diffraction zones being more suitable than others for use in forming weak beam images. However, the wide variety of Burgers vectors of grain boundary dislocations mitigates against any such simple and prior selection of “suitable” diffracting zones.

2. a reduction in the extinction distance ; the reduced extinction distance which accompanies the formation of weak beam images results in a considerable increase in the number of thickness extinction contours projected onto an in- c h e d boundary plane (compare Fig. la with l b and Fig. 2a with 2b). The increased nuwber and decreased width of the extinction contours in a weak beam image provides a fine scale projected “graticule” which can be used to provide more precise measurements of small changes in boundary topography.

Weak Beam Microscopy of Grain Boundaries 109

Fig. 1. a) Weak beam image of a grain boundary, g :: [200]. S, = 0.13 nm-1. Extrinsic dislocations are present in the boundary at A, B and C; note the change in contrast along the line of the dislocation a t B. Bright contrast is continuous at X along B, whereas, at Y, bright contrast is segmented and restricted to the intersection of tho dislocation line with the extinction contours. b) The two-beam dark field image. 9, = 0. A set of intrinsic dislocations which are clearly visible at D and E in a) (and see insert to (a)) are only barely

visible at D in this image

This point. is amply illustrated in Fig. 2a, where an abrupt change in boundary plane is clearly seen along A T , and a series of fine steps are resolved a t C ; these featurea are hardly apparent in the bright field two-beam image shown in Fig. 2 b.

Anomalous absorption of the diffracted intensity is an important factor affecting the visibility of grain boundary dislocation structures in weak beam images. A comparison of Fig. l a (weak beam) with Fig. 1 b (two-beam dark field) show8 that in weak beam imaging conditions the clear contrast of the thickness extinction contours becomes faint and is smeared into the background contrast a t smaller depths into the wedge of diffracting crystal than when imaging conditions are strongly two-beam. It is obvious from Fig. 1 a and b that , apart from the more

110 A. K. JONES, P. R. HOWELL. and B. KALPR

a

0

Fig. 2. a) A weak beam image of a grain boundary, with g = [111], 8, = 0.23 nm-1. b) Two-beam bright field image, 8, = 0, of area shown in a). A change in boundary plane along AB and steps at C are clearly ieen in

the weak beam image

highly localised nature of the strain contrast a t the extrinsic dislocations in the weak beam image, the nature of the strain contrast along the line of each defect depends on the degree of anomalous absorption of the overall diffracted intensity. Hence, the bright contrast of thc extrinsic dislocation a t B in the weak beam image is less pcrturbcd along its line a t X than a t Y. A t position Y , where the extinction contours are still visible, the contraat at the extrinsic dislocation is strongly modulated. However, a t X, the strain contrast from the defect is continuous and is superimpos- ed on the uniformly low contrast background which results from anomalous absorption of the weak diffracted intensitv.

In addition, anomalous absorption of the diffracted intensity in the weak beam image results in the resolution of the weak strain contrast of a set of faint intrinsic dislocation images (at D and E in Fig. l a , and enlarged in insert); these defects are only barely visible in the two-beam dark field image at I) (Fig. 1 b).

From Fig. 1 and 2, the major advantages of weak beam microscopy over conventional two-beam bright or dark field microscopy of grain boundaries can be seen to arise in terms of an increase in resolution and definition of dislocation defects and an improved resolution of small “strain free” topographical defects.

The information contained in Fig. 1 and 2 implies that in a single weak beam image of a grain boundary, the improved resolution of both intrinsic grain boundary dislocations and topographical defects will occur under conditions which are to some extent mutually exclusive, viz. the visibility of thickness extinction contours projected onto the grain boundary plane is essential for topographical defect resolution, but deleterious to the resolution of the weak strain contrast of dislocation images. These features of the weak beam technique arc

110 A. K. JONES, P. R. HOWELL. and B. KALPR

a

0

Fig. 2. a) A weak beam image of a grain boundary, with g = [111], 8, = 0.23 nm-1. b) Two-beam bright field image, 8, = 0, of area shown in a). A change in boundary plane along AB and steps at C are clearly ieen in

the weak beam image

highly localised nature of the strain contrast a t the extrinsic dislocations in the weak beam image, the nature of the strain contrast along the line of each defect depends on the degree of anomalous absorption of the overall diffracted intensity. Hence, the bright contrast of thc extrinsic dislocation a t B in the weak beam image is less pcrturbcd along its line a t X than a t Y. A t position Y , where the extinction contours are still visible, the contraat at the extrinsic dislocation is strongly modulated. However, a t X, the strain contrast from the defect is continuous and is superimpos- ed on the uniformly low contrast background which results from anomalous absorption of the weak diffracted intensitv.

In addition, anomalous absorption of the diffracted intensity in the weak beam image results in the resolution of the weak strain contrast of a set of faint intrinsic dislocation images (at D and E in Fig. l a , and enlarged in insert); these defects are only barely visible in the two-beam dark field image at I) (Fig. 1 b).

From Fig. 1 and 2, the major advantages of weak beam microscopy over conventional two-beam bright or dark field microscopy of grain boundaries can be seen to arise in terms of an increase in resolution and definition of dislocation defects and an improved resolution of small “strain free” topographical defects.

The information contained in Fig. 1 and 2 implies that in a single weak beam image of a grain boundary, the improved resolution of both intrinsic grain boundary dislocations and topographical defects will occur under conditions which are to some extent mutually exclusive, viz. the visibility of thickness extinction contours projected onto the grain boundary plane is essential for topographical defect resolution, but deleterious to the resolution of the weak strain contrast of dislocation images. These features of the weak beam technique arc

Weak Beam Microecopy of Grain Boundariee 111

discussed later. The next section will discuss in more detail the application of weak beam microscopy to the various types of grain boundary defect structures encountered in the polycrystalline samples of the commercial stainless steel examined.

3. Contrast from Dielocations 3.2 hitrinsic dbloat ions

The weak beam image of a grain boundary shown in Fig. 3 illustrates the interaction of a set of widely spaced intrinsic dislocations with thickness extinction contours projected onto the grain boundary plane ; where anomalous absorption “washes out” the contra& of the extinction contours, the strain contrast. of the intrinsic dislocations becomes more prominent and is continuous along the line of each defect. This contrast is similar to that exhibited by the intrinsic dislocations in the thicker parts of the wedge crystal shown in Fig. l a , a t D and E. Fig. 3 adds weight to the evidence that where thickness extinction contours exhibit strong contrast in the weak beam image i.e. in the thin regions of what is, essentially, a wedge crystal, the contraat from the intrinsic dislocations is less well defined. In fact, in the thin regions of the diffracting wedge, the presence of the intrinsic dislocations is only registered by a periodic perturbation of the bright contrast of the extinction contours.

Fig. 4a to d are a series of 111 centred dark field micrographs showing the same stepped and dislocated grain boundary, lying a t a very low angle to the foil surface. The deviation parameter, S, increases from S = 0 in Fig. 4u to S 0.16nm-1 in Fig. 4d. Strain contrast from the intrinsic dislocations (arrowed) on facet A , can be seen to become increasingly localised as the deviation parameter increases to S = 0.1 nm-l (Fig. 4c). As S is increased further, th i s contrast becomes increasingly localised to the intersection of the dislocation line with the thickness extinction contours. A t S = 0.16 nm-I (Fig. 4d), the intrinsic dislocations appear as less sharply defined periodic perturbations in the continu- ity and contrast of the extinction contours. Thus, the optimum weak beam condi- tione for the observation of those defects shown on facet A of micrographs 4a to d occurs at a deviation from exact two beam diffraction conditions of S < 0.16 nm-1 (and w < 5). A weak beam analysis of intragranular defects usually involves the use of deviation parameters >0.2 nm-l. Generally, the only

Fig. 3. A set of intrineic dielocations in a weak beam image of a grain boundary. g = [420], S, = 0.1 nm-1. The contrast from the intrinsic dialocations ie more readily apparent where

the contrast from the extinction contours is faint

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factor which mitigates againat the use of very large..deviation parameters in such analyses is the limitation dictated by microscope stability during the long exposure times necessary to produce an image.

However, in the present case, i.e. the weak beam analysis of grain boundary dislocations, i t seems likely that other limitations may dictate the diffraction conditions utilised to obtain optimum weak beam images. Apart from any interaction between the contrnst arising from intrinsic grain boundary dislocations and that due to projected thickness extinction contours, the actual magnitude of the strain field of intrinsic dislocations is likely to be less than that associated with an intragranular dislocation [9]. Thus, weak beam imaging conditions which would prove suitable for the analysis of intragranular dislocations, where the effective deviation parameter can be close to zero to one side or the other of the dislocation core could, in the case of intrinaic grain boundary dislocations, be sufficiently weak to preclude the resolution of any visible strain contrast.

In addition, the boundary specific nature of intrinsic grain boundary dislocations makes i t impossible to predict either reciprocal lattice reflections or suitable deviation parameters with which to form the best grain boundary weak beam dislocation images, without prior knowledge of grain boundary parameters ; a situation rarely encountered in practice (a notable exception to this situation is the case of specially prepared bi-crystal specimens).

33 Extrinsic dislocaiions

Fig. 5 a and b are two-beam dark field and weak beam images, respectively, of extrinsic grain boundary dislocations. In the weak beam image of the grain boundary, the strain contrast of the extrinsic dislocations a t A and B can be

Fig. 5. Extrinsic dielocations in a grain boundary. a) The two-beam dark field image, g = [200], 8,, = 0. b) The week beam image of tho area of grain boundary shown in a), S, SL 0.14 nm-1. In the weak beam image. extrinsic dielocations at A and B show changes in contrast along their lines e.g. for A, localiced and perturbed bright contraet at X. con-

tinuous bright contrast at Y, while extrinsic dislocations C and D are barely visible

8 phyBlCb (a) SS/1

114 A. R. JONES, P. R. HOWELL, and B. RALPH

Been to be more highly localised than in the two-beam dark field image. However, another eet of extrinsic dislocations (at C and D) which exhibited rather weaker strain contrast in the two beam dark field image, has been put out of contrast by the tilt introduced to effect weak beam imaging conditions. It is interesting t o note that although the extinction contours in the weak beam image are visible acrom the whole width of the grain boundary plane, the contrast along the line of the extrinsic dislocations a t A and B can be seen to be affected by anomalous absorption. The contrast of each of these extrinsic dislocations varies across the boundary plane, changing from separated segments of bright contrast (e.g. a t X along A) to a'perturbed tbough continuous line of bright contrast (at k- along A). These contraat effects are similar to thoee affecting the extrinsic dislocations shown in Fig. l a , where anomalous absorption of the diffracted intensity was more obviously apparent.

A faint set of intrinsic dislocations is also visible in Fig. Sa ; the line vectors of these dislocations are nearly parallel to the line vectors of extrinsic dislocations A and B. In Fig. Sb, these dislocations are only visible as a faint perturbation of the bright contrast of the extinction contours.

At sufficiently large deviations from exact two beam diffraction conditions, the presence of an extrinsic dislocation in a weak beam image is usually only registered by a distortion of the extinction contours which cross its line. How- ever, there may be some residual difference in intensity of the extinction contours on either side of the dislocation line. Such an intensity variation is caused by a slight change in the deviation parameter across the dislocation line. This change in deviation parameter is introducted by the strain field associated with the line defect. In Fig. 6, the weak beam contrast of the extrinsic disloca-

Fig. 0. Extrinsic dislocations are present in this weak beam image (g = [200], S, = = 0.2 nm-l) at A, B, C, and D. Extinction contours are distorted where they cross the line vectors of these dielocations. The intensity of the extinction contours is different on either side of the line of each of these dislocations. This intensity variation is due to a change, AS, in deviation parameter introduced on crossing each dislocation line. Elsewhere in the boundary, an extinction contour is Been to terminate where a matrix dielocation joins the boundary

plane (arrowed)


tiona a t A, B, C, and D can be M n have certain of the characteristics outlined above.

Recently, Schapink [ 101 examined the interaction of the strain contrast of dislocations lying parallel to the surface of wedge shaped crystals with the projected contrast of thickness extinction contours in weak beam images. It was suggested that the sense of curvature introduced into extinction contours which crow a dislocation line will be reversed for a reversal in the direction of the Bur- gers vector of the dislocation. Although extrinsic dislocations Ue in a region of anisotropic elasticity and run from the top to the bottom surface of a thin foil, certain aspects of the contrast and interaction of the extrinsic dislocations a t A and B in Fig. 8 suggest that there might be close parallels between the behaviour in weak beam images of extrinsic dislocations at grain boundaries and the behaviour of intragranular dislocations as outlined by Schapink. It can be seen that the sense of curvature of the extinction contours crossing the extrinsic dislocations a t A and B is in opposite directions a t each defect. Extending the analysis of Schapink to the present example would suggest that the extrinsic dislocations a t A and B have Burgers vectors of substantially opposite character. If this were the case, then the slight change in deviation parameter across each defect would be in opposite directions. It can be seen that the contrast of the extinction contours inside the “wedge” of crystal defined by A, B, and X, is enhanced with respect to the contrast of the extinction contours immediately to either side of this “wedge”, (this observation is most clearly apparent close to X,). Inside the “wedge” of crystal defined by X,, Y, and Z, where the line vectors of the two extrinsic dislocations have become crossed, an opposite change in contrast behaviour can be seen, i.e. the intensity of the thickness extinction contours is weaker inside than immediately outside of this “wedge”. Such contrast variations support the proposal that the extrinsic dislocations have Burgere vectors of substantially opposed character. Further weight is lent to the above argument by the fact that where the line vectors of the extrinsic dislocations a t A and B, merge, along X,X,, perturbation and contrast changes in the thickness extinction contours which cross this line are minimal, suggesting a substantial mutual cancellation of the strain fields of t h e dislocations.

A further feature of interest, illustrated in Fig. 6, is the termination of a thicli- ness extinction contour a t the point of intersection of each intragranular dislocation with the grain boundary plane (e.g. arrowed). An analysis involving a simple calculation of the tilt occurring across the line of an 4 2 (110) dislocation a t various depths in a thin foil (e.g. see reference [ I l l ) indicates that it is possible for such a line defect to introduce R change in the deviation parameter of sufficient magnitude to terminate a n extinction contour “in the grain boundary plane”. (A knowledge of the direction froiii which such an extinction contour terminates can give information on the sense of the Burgers vector of the intragranular dislocation.)

4. Qrain Boundary Topography An example of the way in which a weak beam image of a grain boundary

can increase the resolution of topographical defects, is shown in Fig. 7 a and b. The grain boundary shown in Fig. 7 separates two grains which are related to each other by a misorientation characteristic of a primary annealing twin. The increased reeolution of the grain boundary topography in the weak beam image (Fig. 7a) is quite marked.

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8.

116 A. R. JONES, P. R. HOWELL, and 3. RALPH

Fig. 7. The finer apacing of the extinction contours in the weak beam image of t h e grain boundary increaees the reeolution of topographical defects, when compared to the two-beam

dark field image. a) g 7 [l l l] , S, = 0.11 nm-1; b) S,, = 0

It should be appreciated that in a weak beam analysis of a grain boundary, where the principal aim of the investigation is simply to increase the resolution of strain free topographical defects, certain reflections are more suitable than others for use in forming the image. Low index reciprocal lattice reflections carry a strong diffracted intensity and also have the shortest extinction distances. Hence, in a weak beam analysis, where i t is desired to provide a “fine scale graticule” of extinction contours to improve the resolution of topographical defects, it is better to form an image using low index reflections rather than high index reflections. It should also be appreciated that weak beam electron microscopy which is used for improving the resolution of topographical defects is only possible in quite thin crystals, or in the thinner regions of thick crystals. Fig. 1 a showed that anomalous absorption of the weak intensity of a diffracted beam can completely “wash out” the contrast of extinction contours. Thus, in the first instance, the extent to which topographical defects in a grain boundary may be successfully examined by this technique will be a function of the local foil thickness and the intensity of the diffracted beam. It should, perhaps, be noted that care must be taken not to incorrectly identify the distortion introduced into thickness extinction contours by the strain field associated with grain boundary dislocations as being attributable to distortion due to small scale boundary steps. In general, i t should be possible to distinguish between these two types of defect by virtue of the type of contrast variations each will exhibit in the image. How- ever, it is possible, for grain boundary steps to have associated strain fields; it would prove difficult to positively identify small steps of such mixed character on the basis of image contrast alone.


Recently, stepped grain boundaries were investigated in bi-crystal specimens of gold [ 121. These stepped boundaries were examined in non-weak beam imaging conditions using the projected contrast of thickness extinction contours. The examination of similar aluminium specimens would be difficult, i t was claimed, due to the large extinction distance of even the lowest index reflecting planes in this material. In fact, stepped grain boundaries in polycrystalline aluminium specimens have been brought into contrast by using the above simple method, involving weak beam microscopy, to decreaee extinction distances [ 131.

6. Discussion and Conclusions This paper has shown how i t is possible to apply weak beam microscopy to the

The main conclusions which can be drawn from the preceeding sections are: 1. A weak beam analysis of grain boundary dislocation defect structures will

not normally involve production of the same diffraction conditions which would be utilised in a weak beam analysis of intragranular dislocation structures.

2. There are no reciprocal lattice reflections which can be generally thought of as being “ideal” for the analysis of grain boundary dislocations.

3. Strain contrast associated with intrinsic grain boundary dislocations is more clearly apparent in weak beam images in the presence of strong anomalous absorption of the diffracted intensity.

4. The interaction of extrinsic grain boundary dislocations with thickness extinction contours in weak beam images appears to be closely comparable to the interaction of intragranular dislocations with thickness extinction contours in wedge shaped crystals.

6. Improved resolution of grain boundary topographical defects in weak beam images can only be achieved in the absence of strong anomalous absorption of the diffracted intensity.

Acknowledgemmis

The authors are grateful to Prof. R. W. I<. Honeycombe for the provision of laboratory facilities. Financial support from the Science Reaearch Council and the Harwell and Springfield laboratories of the United Kingdom Atomic Energy Authority is gratefully acknowledged.

References [l] P. R. HOWELL, A. R. JONES, and B. RALPH, J. Meter. Sci. 10. 1351 (1976). [2] A. R. JONES, P. R. HOWELL, T. F. PAOE, and B. RALPH, IV. Bolton Landing Cod.

Grain Boundaries in Engineering Materia~s. AIME/ASM, Ed. J. L. WALTER, J. H. WESTBROOK, end 0. A.-WOODFORD, Claitor. New York 1975 (p. 629).

study of grain boundary defect populations.

[3] A. R. JONES, Ph.D. Thesis, Cambridge University 1974. [4] A. H. JONKS, and B. RALPH, Act8 metall. 23, 366 (1975). [6] A. HOWIE and Z. S. BASINSKI, Phil. Mag. 17, 1039 (1968). [6] D . J . H. C~CKAYNE, I. L. F. RAY, and M. J. WHEELAN. Phil. Mag. 20, 1265 (1969). [7] I. L. F. RAY and D. J. H. COCKAYNK, J. Microscopy 98, 170 (1973). [8] D. J. H. C ~ C K A Y X E , J. Microscopy ‘38, 116 (1973). [9] W. BOLLYANN, Crystal Defecta and Crystalline Interfaces, Springer Verlag, Berlin/

Gottingen/Heidelberg/New York 1970. [lo] F. W. SCHAPIHK. phys. stet. sol. (a) 26, K95 (1974). [ll] R. SIEMS, P. DPLAVIONETTE, and S. AYELINCXX, phys. stat. sol. 3.874 (1963). 1121 W. R. WAONER, T. Y. TAN, and R. W. BALLUFFI, Phil. Mag. 29, 885 (1974). [I31 B. RALPH, unpublished.

( R a i d September 29, 1975)

weak beam microscopy of grain boundaries

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