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Optical Diffraction Patterns Produced by Bubble RaftsAuthor(s): J. DysonSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 199, No. 1056, (Oct. 7, 1949), pp. 130-139Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/98373Accessed: 13/05/2008 00:33

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130 J. Lamb and J. M. M. Pinkerton

Kneser, H. 0. 1935 Z. tech. Phys. 16, 213. Kneser, H. 0. 1938 Ann. Phys., Lpz., 32, 277. Lamb, J., Andreae, J. H. & Bird, R. I948 Nature, 162, 993. Latimer, W. M. & Rodebush, W. H. 1920 J. Amer. Chem. Soc. 42, 1419. le Fevre, R. J. W. & Vine, H. 1938 J. Chem. Soc. (II), p. 1795.

Pauling, L. & Brockway, L. 0. I934 Proc. Nat. Acad. Sci., Wash., 20, 336. Pellam, J. R. & Galt, J. K. 1946 J. Chem. Phys. 14, 608. Pinkerton, J. M. M. 1948 Nature, 162, 106. Pinkerton, J. MM. .949a Proc. Phys. Soc. B, 62, 129. Pinkerton, J. M. M. I949b Proc. Phys. Soc. B, 62, 286.

Rapuano, R. A. 1947 Phys. Rev. 72, 78. Richards, W. T. I939 Rev. Mod. Phys. 11, 36.

Riitgers, A. J. I933 Ann. Phys., Lpz., 16, 350.

Spakowski, B. I938 C.R. Acad. Sci. U.R.S.S. 18, 169. Stokes, G. G. I845 Trans. Camb. Phil. Soc. 8, 287.

Optical diffraction patterns produced by bubble rafts

BY J. DYSON Research Laboratory, Associated Electrical Industries Ltd., Aldermaston, Berks

(Communicated by T. E. Allibone, F.R.S.-Received 13 April 1949)

[Plates 2 to 7]

A method of obtaining diffraction patterns, analogous to X-ray and electron diffraction patterns, from photographs of bubble rafts is described. The results of some early experi- ments are shown, and the conditions for obtaining patterns of higher resolution and more uniform illumination are deduced. An experimental technique for realizing these conditions is described and the results are shown.

A method is described for viewing the raft in the light of a selected region of the diffraction pattern, and some results of this technique are shown.

INTRODUCTION

The ingenious bubble model illustrating the atomic pattern within crystalline materials which was developed by Bragg & Nye (I947) gives lattice structures so

closely analogous to those found in practice and illustrates effects predicted by theory so closely that it was thought that it would be useful to extend the technique to enable diffraction patterns to be obtained from the rafts which would be analo- gous to the X-ray or electron diffraction patterns produced from the crystalline material itself.

Optical analogues of X-ray or electron diffraction patterns have, of course, been produced by severalworkers (Pohl 1940; Kathavate 1945; Prins I93i; Sagani 1926), but the production of diffraction patterns by a raft of bubbles is of particular interest because the capillary forces between bubbles are analogous to inter-atomic forces, and also because of the very large number of diffracting centres which may be made to contribute to the pattern.

130 J. Lamb and J. M. M. Pinkerton

Kneser, H. 0. 1935 Z. tech. Phys. 16, 213. Kneser, H. 0. 1938 Ann. Phys., Lpz., 32, 277. Lamb, J., Andreae, J. H. & Bird, R. I948 Nature, 162, 993. Latimer, W. M. & Rodebush, W. H. 1920 J. Amer. Chem. Soc. 42, 1419. le Fevre, R. J. W. & Vine, H. 1938 J. Chem. Soc. (II), p. 1795.

Pauling, L. & Brockway, L. 0. I934 Proc. Nat. Acad. Sci., Wash., 20, 336. Pellam, J. R. & Galt, J. K. 1946 J. Chem. Phys. 14, 608. Pinkerton, J. M. M. 1948 Nature, 162, 106. Pinkerton, J. MM. .949a Proc. Phys. Soc. B, 62, 129. Pinkerton, J. M. M. I949b Proc. Phys. Soc. B, 62, 286.

Rapuano, R. A. 1947 Phys. Rev. 72, 78. Richards, W. T. I939 Rev. Mod. Phys. 11, 36.

Riitgers, A. J. I933 Ann. Phys., Lpz., 16, 350.

Spakowski, B. I938 C.R. Acad. Sci. U.R.S.S. 18, 169. Stokes, G. G. I845 Trans. Camb. Phil. Soc. 8, 287.

Optical diffraction patterns produced by bubble rafts

BY J. DYSON Research Laboratory, Associated Electrical Industries Ltd., Aldermaston, Berks

(Communicated by T. E. Allibone, F.R.S.-Received 13 April 1949)

[Plates 2 to 7]

A method of obtaining diffraction patterns, analogous to X-ray and electron diffraction patterns, from photographs of bubble rafts is described. The results of some early experi- ments are shown, and the conditions for obtaining patterns of higher resolution and more uniform illumination are deduced. An experimental technique for realizing these conditions is described and the results are shown.

A method is described for viewing the raft in the light of a selected region of the diffraction pattern, and some results of this technique are shown.

INTRODUCTION

The ingenious bubble model illustrating the atomic pattern within crystalline materials which was developed by Bragg & Nye (I947) gives lattice structures so

closely analogous to those found in practice and illustrates effects predicted by theory so closely that it was thought that it would be useful to extend the technique to enable diffraction patterns to be obtained from the rafts which would be analo- gous to the X-ray or electron diffraction patterns produced from the crystalline material itself.

Optical analogues of X-ray or electron diffraction patterns have, of course, been produced by severalworkers (Pohl 1940; Kathavate 1945; Prins I93i; Sagani 1926), but the production of diffraction patterns by a raft of bubbles is of particular interest because the capillary forces between bubbles are analogous to inter-atomic forces, and also because of the very large number of diffracting centres which may be made to contribute to the pattern.

Optical diffraction patterns produced by bubble rafts

The bubble rafts are in general only two-dimensional (although Bragg & Nye have experimented with bubble rafts two or three bubbles deep), and hence the diffraction patterns would be more analogous to those given by electron diffraction.

With this in mind, some experiments were performed with the object of obtaining optical diffraction patterns either directly from bubble rafts or from suitably pre- pared photographs.

EARLY EXPERIMENTS

The first experiment undertaken was that of obtaining diffraction from a perfect hexagonal lattice of diffracting points. Instead of a bubble raft, an assembly of about 1400 - in. bearing balls in a glass-fronted frame was used. This arrangement is due to Dr G. A. Geach of this laboratory, and has the advantage that all elements of the lattice are very accurately of the same size, and they can be manoeuvred into the correct lattice arrangement in a way scarcely possible with bubbles. The assembly was photographed on to 16 mm. film at a scale such that the distance between lattice

points was about 0*2 mm. The balls were illuminated by a single photoflood lamp in a reflector, so that each

ball was represented by a single image on a very small scale of the light source, formed

by reflexion at the convex surface of the ball. The negative was printed on to a

'photomechanical' plate by contact, giving a dark field with a small transparent spot near the centre of each ball image. The contrast was sufficiently high for the transmission of the print to be significant only in the transparent spot. The print was placed in an optical system shown in figure 1. Light from a B.T.H. type ME 250 W. mercury vapour lamp is focused on to a small pinhole and diverges to an achromatic collimator lens. The parallel light traverses the print and enters a tele-

scope lens. The (Fraunhofer) diffraction pattern is formed in the focal plane of this lens and can be examined by an eyepiece. An Ilford 'mercury-green' filter allows of

using only the green line of the mercury spectrum, together with a small part of the continuous background, which is rather high in this lamp.

plate bearing difacing structure mercury

eypic vapour lamp eyepee p_ ecf

telescope lens colimator lens pinole condenser

FIGURE 1

The resulting diffraction pattern is shown in figure 2, plate 2, and, of course, consists of a hexagonal array of spots. It can be seen that each spot has faint wings pointing in a radial direction. These are due to the continuous background and are a function of the sharpness of cut-off of the filter used. Generally, though, they are not obtrusive, and in fact are only visible around the brightest spots.

The pattern obtained bears an obvious resemblance to the electron diffraction

image obtained when electrons traverse a thin flake of mica. Such a picture, taken by 9-2

131

A. E. Ennos of this laboratory, is shown in figure 3, plate 2. The mica flake used was a number of molecules thick, and so the phenomenon of Bragg reflexion is just beginning to appear; this accounts for the fact that some of the spots are enhanced in

intensity. As the print used for the optical diffraction is a true two-dimensional array, no corresponding enhancement of intensity occurs in this case.

If the unfiltered light from the mercury vapour lamp is used, each spot becomes a radial spectrum, of length proportional to its distance from the centre, and the whole forms a beautifully symmetrical pattern of brilliant colours.

An attempt was next made to form diffraction patterns from bubble rafts. To form the pattern direct from the raft itself would be elegant and, for some purposes, desirable, but it is so difficult as to be scarcely practicable. It is difficult to produce very small bubbles of very uniform size, and so the scale of the diffraction pattern would be small, necessitating very perfect optics to attain the required definition. As the light has to traverse the raft, the liquid layer is itself a part of the optical train. The surface through the centres of the bubbles is very far from optically flat, and this would preclude the attainment of anything like the required optical per- fection. In addition, the refraction at each bubble, when considered as a negative lens, is so great that the light is spread out over a very large solid angle; hence the amount of light available to form the diffraction pattern is very small.

These considerations seemed to make the chances of success very small. Therefore it was decided to use photographs of the rafts as the diffraction gratings.

A raft was photographed on to 35 mm. film, at a scale suitable to give a bubble-

image spacing of 0-2 mm. using two photofloods in reflectors as illumination. Each

image consisted of a dark ring enclosing a transparent disk containing two minute dark spots which were the images of the lamps. The negatives were sandwiched between glass plates in Canada balsam. This was necessary as the optical quality of the film surfaces was not nearly good enough to give the required definition.

Results given by this means are shown in figures 4a to 7 b, plates 3 and 4. Figures 4a, 5a, 6a, 7 a are enlarged prints from the negatives of the bubble raft, and figures 4b, 5b, 6b and 7 b are the corresponding diffraction patterns.

Figure 4a shows a raft photographed immediately after growth. It is seen to consist of a few comparatively large crystallites in a state of considerable internal strain containing a large number of dislocations.

The corresponding diffraction image, figure 4b, consists, as might be expected, of a series of spotty rings. The individual spots are comparatively sharply defined and the regions between the rings are dark. The dislocations and strains may be

expected to scatter light outside the spots, but the definition is not good enough to show this.

Figures 5a and 5b show the same raft photographed immediately after being stirred up, with its diffraction pattern. The large crystallites have been broken up and there are areas of amorphous material and a number of small crystallites just beginning to grow.

The diffraction pattern now consists of almost smooth rings which, however, can be seen to consist of a very large number of ill-defined spots. The regions between the

rings are now filled with light scattered from the amorphous region. In taking this

132 J. Dyson

Optical diffraction patterns produced by bubble rafts

exposure an absorbing mask was placed over the centre of the diffraction pattern to reduce the intensity there. Otherwise this was so great that the halation due to the central spot obscured the first ring. As a result the background inside the first ring is darker in the photograph than that between the first and second rings.

Actually, the scattered light fell off monotonically towards the outside of the

pattern, as might be expected. Visual inspection of the pattern with an eyepiece gives an impression similar to that shown in the photograph, but this is a subjective contrast effect, caused by the proximity of the overpoweringly bright central spot. This was established by blocking out the central spot when the background intensity appears greater inside the first ring than outside it.

The diffraction pattern may be compared with the corresponding X-ray diffraction

patterns for liquids, which exhibit the same general characteristics. A diffraction figure somewhat similar to figure 5b has been given by Pohl (I940),

produced by a large number of randomly arranged apertures. The differences between this and figure 5b are due to the fact that Pohl's raft had, presumably, no trace of

crystal structure.

Figures 6 a, 7 a and 6 b, 7 b were taken from the same raft at different periods after

stirring. The amorphous regions are decreasing, and the effect of this is seen in the diffraction patterns by the clearing of the background. In addition, the crystallites are decreasing in number, and the diffraction rings are becoming more spotty.

A further effect which is very obvious in figure 7b is the appearance of six dark

spaces in each ring. The positions of these are related to each other in the same way as the spots in figure 2, and evidently indicate that a particular orientation is being avoided by the growing crystallites. This effect can also be seen in an incipient state in figure 6b. Although so prominent in the diffraction pattern, this effect is by no means obvious from inspection of the direct photographs (figure 7 a).

The four white arms radiating from the central spot in figures 4b, 5b, 6b and 7b are due to diffraction from the rectangular boundary of the diffracting negative.

DEFECTS IN THE PATTERN

These early experiments give patterns which have two outstanding defects. The resolution of the spots is poor, and there is a great concentration of light towards the centre of the pattern, especially in the central spot. Further experiments were undertaken with the object of overcoming these defects.

BRIGHTNESS AND RESOLUTION

Assume that the diffracting object consists of a square array of N2 transparent apertures in a black screen, with a linear spacing of d cm. Assume further that if the dimensions of the array be varied the size of the apertures is also varied in such a way as to keep constant the ratio of the areas of the transparent regions to the areas of the opaque regions.

Consider first the condition where the size of a spot formed by diffraction from an area of perfect lattice is determined by the size of the source, i.e. by geometrical optics. This will be the most usual case where a large number of diffracting centres

133

contribute. The angular diameter of the source is a, and the resolution of the pattern, defined as the ratio of the distance between successive rings of spots to the diameter of a spot, is k. Then

1 kact- (1)

The total amount of light collected from the source is proportional to the square of its angular diameter and to the area of the diffracting object:

total light d2a2N2. (2)

The size of the image on the photographic plate is of importance, because if it is too small the resolution will be spoiled by halation. Let the linear diameter of the first

ring be S. Then the brightness of the image will be given by

brightness d2a2N2 . (3)

N2 Substituting from (1) we get brightness k2S2 (4)

Hence, for a given resolution and image size, the brightness is dependent only on the total number of transparent diffracting areas, if their geometry is constant.

The other case is that where the spot size is fixed by diffraction phenomena, i.e. by the size of the Airy disk. Then, if the source is kept just small enough to ensure this,

aNd ~(5) The total light collected is given by

d2 N2 total light d2a2N2 - 2 d2 = constant. (6) NV2 d2

The brightness of the image is thus only dependent on its size. The resolution, how-

ever, is given by

k = N, (7) ad

as is well known from the theory of diffraction gratings. It is thus evident that the important feature is N2, the total number of diffracting

points. So far we have not considered the distribution of light among the various rings of

the pattern. This is governed by the angular distribution of light from each diffracting element. The diffracting elements in figures 4 a to 7 a consist effectively of transparent disks surrounded by thin opaque rings of diameter almost equal to the distance between centres. Such elements give an angular distribution similar to that in an

Airy disk. The angular radius of the first dark ring is given by

0-61A r , (8)

134 J. Dyson

Proc. Roy. Soc. A, volume 199, plate 2

FIGURE 2. Diffraction pattern from a perfect lattice.

FIGuRE 3. Electron diffraction pattern from a mica flake. (Facing p. 134)

Dyson

Proc. Roy. Soc. A, volume 199, plate 3

a b

FIGURE 4. a, polycrystalline raft; b, diffraction pattern.

a b

FIGuTRE 5, a, raft after stirring; b, diffraction pattern.

Dyson

Proc. Roy. Soc. A, volume 199, plate 4

a b

FIGURE 6. a, raft after 'annealing'; b, diffraction pattern.

a b

FIGURE 7. a, raft after further 'annealing'; b, diffraction pattern.

Dyson

Proc. Roy. Soc. A, volume 199, plate 5

FIGURE 8. Bubbles with back illumination. FIGURE 10. Photomicrograph of transparency for diffraction.

a b

FIGURE 11. a, polycrystalline raft with two sizes of bubbles; b, diffraction pattern.

Dyson

I

I

Proc. Roy. Soc. A, volume 199, plate 6

a b

FIGURE 12. a, stirred bubble raft; b, diffraction pattern.

a b

FIGURE 13. a, raft of large crystallites; b, diffraction pattern.

Dyson

Proc. Roy. Soc. A, volume 199, plate 7

FIGURE 14. Raft of figure 13a viewed through pinhole.

FIGURE 15. As for figure 14 but with different adjustment of pinhole,

Dyson

Optical diffraction patterns produced by bubble rafts

where r is the radius of the transparent disk. The angular radius of the first ring in the diffraction pattern is given by A

fld=, (9)

where d is the distance between centres of the transparent regions. To obtain sensibly uniform illumination up to, say, the fourth order of inter-

ference, we require that the angular radius of the first dark ring of the Airy pattern be larger than the angle corresponding to the fourth order of interference. Thus

0-61A 4A r d'

or r<0.15d. (10)

Hence to improve the uniformity of illumination it is necessary to make the

transparent spots smaller. To cut down the intensity of the central spot it is necessary to pay particular

attention to the opacity of the background, since the area of the transparent spots is a small fraction of the total area.

It may be noted that, by Babinet's principle, a similar array of small opaque spots on a transparent background will give the same diffraction pattern, but the intensity of the central spot will be very much greater.

EXPERIMENTAL TECHNIQUE

By the above analysis it is seen that what is required to obtain better patterns is to produce bubble rafts with large numbers of bubbles and to photograph these in such a way as to represent each bubble by a small circular transparent spot on an

opaque background. The requirement of a large number of bubbles depends, of course, on the particular

phenomenon under investigation. The other requirement is more under control. If the raft be illuminated by a small light source on the upper side and viewed from

the top, a small image of the source is seen by reflexion in the convex surface of each

bubble, and another in the concave surface. The predominant feature, however, is a bright ring of nearly the full diameter of the bubble. This is very much brighter than the direct image and cannot be eliminated by adjusting the angle of the light. Hence this method of illumination is of little use. If the bubbles be blown in a trans-

parent trough and a small light source placed underneath, the appearance is as shown in figure 8, plate 5. Each bubble behaves as a negative lens of focal length approxi- mately three times the radius of the bubble and so forms a small erect image of the

light source. Further images are formed by multiple reflexion at the convex surfaces of adjacent bubbles, but these are so small that they do not cause much trouble. The light source is displaced to one side away from the axis. The three-cornered areas between the bubbles then appear dark, while the direct image is still visible. It is shifted to one side, but this occurs in every bubble and so is equivalent to a slight lateral shift of the pattern.

To make use of this arrangement the bubble raft is blown in a Perspex trough about 15 x 10 cm. and about 1 cm. deep. For convenience, two front-reflexion

135

mirrors are mounted at 45? to the vertical, one above and one below the trough. The light source is a photoflood about 3 ft. from the trough, and the raft is photo- graphed by means of a camera at a distance such as to give a spacing of about 0-2 mm. between bubble images. The experimental arrangement is shown in figure 9.

45?mirror/ __

camera q Perspex

trough

o? /45?mirror photoflood

FIGURE 9

The camera lens is thrown out of focus just sufficiently to cause each image of the

light source to appear as a small round disk of the size required by equation (10). For this to be successful, the lens must be well corrected; a Goerz Doppel Anastigmat working at f/8 has been found to be satisfactory.

The plate used was Ilford Special Rapid Panchromatic, developed in I.D. 8

(maximum contrast) developer. A positive contact print is made on Ilford thin-film half-tone stripping plate, also developed in I.D. 8. The overall gamma of the double

process is of the order of 10 and is sufficiently high to suppress all detail except the circular out-of-focus disks. The result is a pattern of small circular transparent disks on an opaque background, as is shown in the photomicrograph (figure 10, plate 5). The fact that the disks have slightly soft edges is of no importance, as the effect of this is only to suppress the outer rings of the Airy pattern, leaving the central lobe almost

unchanged. The glass of a photographic plate is not of sufficiently high quality to allow of

sharp patterns being formed, so the emulsion is peeled off the stripping plates, having been cut round the required region with a knife. The emulsion is immersed in a bath of methylated spirit which has been diluted with about an equal volume of water. This enables the gelatine to take up enough water to adhere to a glass surface and yet to retain its strength. An optically flat glass plate (selected pieces of I in.

plate glass can be used) is slid under the emulsion and lifted out. Wrinkles are gently pressed out with the fingers and the plate stood on edge to dry.

When dry, a drop of Canada balsam is placed in the centre of the emulsion and another glass flat pressed down over the top. A small weight is placed thereon and the whole placed in an oven at about 50? C overnight. The balsam will spread over the whole area; the excess is wiped off at the edges and, after cooling, the resulting sandwich is rigid enough if handled carefully.

EXPERIMENTAL RESULTS

A bubble raft photographed by this technique and its diffraction pattern are shown in figures 11 a and 11 b, plate 5. This raft consisted largely of areas of almost perfect lattice, and this is reflected in the rings of sharp spots shown in the diffraction pattern.

136 J. Dyson

Optical diffraction patterns produced by bubble rafts

It will be noted that all the rings are doubled; this is because two different sizes of bubbles are present, as can be seen from close inspection of figure 11 a.

Figures 12a and 12b, plate 6, show a raft taken just after stirring, together with its diffraction pattern. The rings of diffuse spots as shown in figure 5b appear once more, but the background shown in figure 5b does not appear. The reason for this seems to be that a small delay occurred between stirring and taking the photograph in the case of figure 12a, and the amorphous regions had time to crystallize into a

large number of small crystallites. Figures 13 a and 13 b, plate 6, are of a raft consisting of only three large crystallites

and a small one. The diffraction pattern consists of only a comparatively small number of spots, but these are seen to be broken and surrounded by a diffuse nebu-

losity. This effect is evidently due to lack of perfection in the crystallites, and the question as to what form of imperfection gave rise to this phenomenon suggested the investigation described in the next section.

DIRECT OBSERVATION OF IMPERFECTIONS

An imperfect lattice such as that of figure 13a constitutes an almost periodic structure, from which a Fourier analysis gives sets of terms grouped closely around the discrete values which would represent the corresponding perfect lattice. One such set of terms gives information, generally speaking, about the broad features of the lattice, whereas the overall distribution of sets of terms contains information as to the microscopical features, such as the size and shape of the dots (see the fore- going analysis giving the relationship between the spot size and the distribution of light between the various rings).

Thus, one particular spot in the pattern, together with its associated nebulosity, can be expected to yield information about the broad features, such as shape and imperfections, of one crystallite.

The technique for applying this principle consists of mounting a thin opaque plate containing a pinhole about 0-5 mm. diameter in the focal plane of the telescope lens. The plate is mounted on centring screws so that it can be moved about to coincide with any one of the spots of the diffraction pattern. Then, with the eye- piece removed, the eye is placed close to the pinhole, when the image of the bubble raft is seen in the aperture of the telescope lens, illuminated by only the light which forms the particular spot selected.

The resulting phenomena are easier to interpret if the unfiltered light is used. Under these conditions it is possible, for certain positions of the pinhole, for the whole of the raft to be illuminated at once by light of different wave-lengths and in different orders of diffraction. Detail is then seen both by intensity and colour contrast. The resulting picture resembles the coloured counties on a map.

This may be illustrated with reference to figure 14, plate 7, which shows the raft of figure 13a viewed under these conditions. The individual bubble images cannot be distinguished, as only one diffracted beam from each area of lattice is used. Thus the experiment is a corroboration of Abbe's theory of the microscope. The grain boundaries, however, show up clearly as rows of approximately equally spaced dots.

137

By making a transparency of figure 14, to the same scale as figure 13a and super- imposing them these dots can be identified as those regions along the grain boundaries which are nearly, but not quite, large enough for the inclusion of an extra bubble.

In figure 13 a two dislocations can be seen across the waist of the central crystallite. These cause the top and bottom of the crystallite to be rotated slightly with respect to each other. This is shown clearly in figure 14, the upper region being brighter than the lower. To the naked eye, the upper region was yellow and the lower one red, the

resulting contrast being very clear. The boundary between the two regions is seen to be quite sharp, in fact as sharp as the limited resolution of the picture will allow. The two dislocations show up as dark streaks. Another boundary is shown at the

upper left of this crystallite where an 'arm' branches off to the left. The right-hand crystallite is complex in structure. There is a line of dislocations

across the upper portion shown very clearly in figure 14 as a row of 'puckers'. The

boundary between the two regions split off by the dislocations is not sharp in this case. Visually, the upper region was dark blue and the lower region light blue. To- wards the bottom ofthis crystallite is a complex structure of dislocations. The resulting pattern of boundaries was almost impossible to photograph in monochrome, but showed up visually, as a complicated pattern of green, red and light blue areas. The

dislocations, however, can be seen in figure 14 as a number of dark markings. These

give a 'plastic' appearance to the raft as if it consisted of a puckered and torn sheet of fabric. All the dislocations may be seen by close inspection of figure 13a but the boundaries between areas of perfect lattice cannot be followed so clearly.

Figure 15, plate 7, gives another view of the same raft with a different pinhole setting. Only the upper region of the central crystallite is brightly illuminated; the

boundary does not show so clearly because of scattered light, as the upper region was

over-exposed to bring out details elsewhere. The grain boundaries now show up in rows of bright dots. It should be noted that these dots represent structures of the dimensions of one bubble site, and the resolution of the picture is not sufficient to show individual bubbles; yet, as these dots indicate deviations from perfect regularity, they show up vividly both on a light and on a dark ground.

The dislocations in the right-hand crystallite now show up by themselves as

V-shaped markings. Visually they appear as bright golden yellow marks on a

'midnight blue' background, their contrast being much higher than the photograph suggests.

As the centring screws are operated the colours change in such a manner that the colour change is almost simultaneous over each area of perfect lattice. The effect is that of tilting a solid object with plane facets, each facet catching the light in turn.

Crystal boundaries appear as sharp edges, whereas the boundaries between areas in the same crystallite appear rounded to a greater or less degree. A few minutes of such observation give a much better idea of the nature of a raft than can be obtained from simple inspection, or than can easily be described in words.

138 J. Dyson

Optical diffraction patterns produced by bubble rafts

CONCLUSION

The experiments here described have two potential uses. In the first place, it

may be possible, from a study of a sufficient number of rafts and their associated diffraction patterns, to obtain some insight into the relationships between observed

phenomena in X-ray and electron diffraction and the crystal imperfections which cause them.

In the second place the method of inspection of the raft by means of the light contained in a restricted portion of diffraction pattern offers a ready method of

investigating the effects produced by dislocations on the surrounding lattice and leads to a clearer understanding of the way in which complex diffraction spots are formed.

The value of this method lies in its directness; the imperfection producing a given phenomenon in the diffraction pattern can be seen clearly without ambiguity.

A limitation to the usefulness of the analogy is imposed by the fact that only two- dimensional lattices can be treated in this way. However, this can be quite a close

approximation to conditions obtaining in electron diffraction. It was not thought worth while to try to extend the method to three-dimensional lattices, partly on account of the very great experimental difficulties, but also because it would be almost impossible to form a clear idea of the imperfections existing in a solid block of lattice.

The author wishes to thank Dr T. E. Allibone, F.R.S., for permission to publish this paper.

REFERENCES

Bragg, L. & Nye, J. F. I947 Proc. Roy. Soc. A, 190, 474. Pohl, R. W. 1940 Optik, p. 100, figure 232. Kathavate, Y. V. I945 Proc. Indian Acad. Sci. A, 21, 253. Prins, J. A. i93I Naturwissenschaften, 19, 435.

Sagani, C. M. I926 Phil. Mag. 1, 321.

139