Extra Reflexions from the Two Types of Diamond

Extra Reflexions from the Two Types of DiamondAuthor(s): Kathleen LonsdaleSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 179, No. 978 (Jan. 23, 1942), pp. 315-320Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/97612 .

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Extra reflexions from the two types of diamond*

BY KATHLEEN LONSDALE

Royal Institution

(Communicated by Sir William Bragg, F.R.S.-Received 21 October 1941)

[Plates 34-39]

New experimental facts about diamond, supported by X-ray photographs, are as follows: There are two kinds of extra reflexions to be seen on well- exposed Laue photographs. All diamonds show primary diffuse reflexions, which are temperature-sensitive but not structure-sensitive. These correspond to the diffuse reflexions observed under suitable conditions for all other substances. Type I diamonds, only, show the secondary reflexions (sharp spots, streaks and groups of spots) which have been previously described and which are not at all typical of diffuse spots in general. They are not really diffuse, they are not (or only slightly) temperature-sensitive and they are strongly structure-sensitive. Primary and secondary reflexions have been observed for many diamonds and in various orientations, associated with the {11 1} {220} {1 13} {331} Laue reflexions, using filtered and unfiltered radiation from copper and iron targets. There is as yet no explanation of the secondary reflexions which can account satisfactorily for the structure- sensitiveness, the presence of {220} spots, and the apparent incompleteness of the groups of spots actually observed.

When Sir C. V. Raman sent the preceding contribution to the discussion on diffuse reflexions of X-rays by crystals (Proc. Roy. Soc., A, 179, 1-101, 1941), he was necessarily unaware of various experimental developments, since briefly reported (Lonsdale & Smith, I941), which must have a con- siderable bearing on his, and other, theoretical arguments. These further experimental facts are as follows:

(1) Two kinds of extra reflexions. The extra reflexions given by different diamonds are not all alike. They may be divided into two classes, which we have called primary and secondary reflexions.

(2) Primary reftexions (all diamonds). nAll diamonds so far examined show the primary reflexion. This consists of a single, nearly spherical spot, which really is diffuse and which accompanies the Laue spot when the diamond orientation is not more than about + 3-5? from the Bragg position for any given plane. With the [11O] axis vertical (as it was throughout almost all

* This paper is an addition to the; series of papers published as a Discussion on 'Diffuse reflexions of X-rays by crystals' in consequence of the receipt of the pre- ceeding paper by Sir C. Venkata Raman.

315 ] 2I-2



316 K. Lonsdale

our experiments), primary reflexions have been observed for the {1 I 1} {220} {1 13} {004} {331} planes, using Cu Koc and K,8 radiations, and for the first three of these using Fe Ka and K,/ radiations. Examples of primary spots may be seen on plates 34 a-d, 35 e, f, 36 a-d, 37 a, b, d, 38 a-e, 39 a-d.

(3) Secondary reftexions (type I diamonds only). Only some diamonds show the secondary reflexions. In particular, those rare diamonds classed by

Robertson, Fox & Martin (I934, I936) as being of type II do not show them at all. [The diamonds actually tested were D 2, D 16, D 19, D 22, in their classification.*] When the [110] axis is vertical, the secondary reflexion consists of single sharp spots or of well-defined streaks (or both), or of groups of sharp spots, according to the angle and direction of incidence. These secondary spots are very persistent, being still visible even at an angle of + 120 or -8? from the Bragg angle for the (111) plane. Such secondary reflexions have been observed, using Cu Kcx and K/i radiations, for the {1 1 1} {220} {1 13} {331} planes, but not for the {004} planes; and using Fe Ka and K/S radiations, for the first three of these. Exa mples are given in plates 34 b, d, 35 b, d, ejf, 36 a, b, c, 37 a-e, 38 a-e and (very weakly) 39 a, b, c. Photographs previously reproduced in the course of this Discussion (Lons- dale & Smith, Sir W. H. Bragg, Sir C. V. Raman) have shown only {111} secondary effects.

(4) Intensity of the extra refiexions. The intensity of the primary reflexions does not vary appreciably from one diamond to another. The secondary reflexions are, however, markedly structure-sensitive. They appear strongly for som:e diamonds, weakly for others and not at all for type II diamonds. Of the diamonds examined and classed as type I by Robertson et al., the following have been examined:

D 1, a spinel twin, showed weak secondary spots and streaks from both individuals;

D 20 showed a moderate effect; D 21 and D 23 showed relatively strong effects. The most intense secondary reflexions were obtained from D (2), a small

octahedral diamond of weight 1 mg. which was found to give uniformly intense, sharp spots, streaks or groups of spots in all crystallographically equivalent orientations, that is, associated with each of the eight {1 1 1} planes, twelve {220} planes, etc. D (4), another small (slightly deformed) octahedral diamond of about the same weight, showed only extremely weak

secondary effects (plate 39 a, b, c), while D (3), a beautiful octahedral plate from Sierra Leone, 0-6 mm. thick, weight 0-047 g., and of great purity, also

* Mr Smith and I are indebted to Professor W. T. Gordon for the loan of these and all other diamonds examined.



Extra reflexions from the two types of diamond 317

gave exceedingly good secondary reflexions in the various orientations. D (2), D (3) and D (4) were not among the diamonds examined and described by Robertson et al.

(5) Intensity of normal reflexion. It was noticeable that the intensity of ordinary selective reflexion also varied greatly from one diamond to another; the more intense the secondary reflexions, the greater was the extinction of the normal reflexion. Type II diamonds, and those of type I which gave poor secondary effects, showed very little extinction and were therefore particularly fine monochromators; the normal reflexions from the {1 1 1} {220} and {1 13} planes could be seen in broad daylight on a fluor- escent screen.

(6) Position of extra reflexions. The position of the primary spots is given reasonably closely by Faxen's simple formula, and corresponds therefore to the intersections of the sphere of reflexion with an approximately spherical (and very limited) extension of reflecting power about the reciprocal lattice points. These primary reflexions became weaker and more diffuse (and therefore more difficult to measure) as the angle of missetting increases (plate 36 a, c) and soon disappear.

The position of the secondary spots and streaks corresponds geometrically, as Sir C. V. Raman has pointed out, with their being the intersections of the sphere of reflexion with cubic directions in reciprocal space (see also Lonsdale & Smith, this Discussion, p. 44). It follows that the primary reflexion lies at the centre of the triangle of secondary (111) reflexions (plates 34 b, d, 36 a, 37 a, b, etc.) or, in the alternate orientation, it forms an approximate background to the sharp secondary (111) spot from wl.ich may proceed the streaks described by Sir C. V. Raman (plates 35f, 38 d, e). In this latter orientation the primary reflexion may well be overlooked altogether, but it is most clearly seen when a small slit (0.5 mm. or less diameter) and thin crystal are used; it is, of course, quite obvious for type II diamonds, for which the sharp secondary spot and streaks are absent (plates 34 a, c, 39 d).

(7) Temperature-sensitiveness of extra reflexions. The primary reflexion is quite markedly temperature-sensitive. This has been proved beyond doubt for both types of diamond, the temperature range covered being 750 30 -1800 C for type I diamonds, and 30 - 1800 C for type II diamonds. At high temperatures, the general background is rather more intense, but the primary reflexion intensity is increased by a factor of at least three or four, relative to that at room temperatures. Even when the exposure times are varied, the primary reflexions (unlike the Laue and secondary spots) are still considerably stronger than those observed on a



318 K. Lonsdale

room-temperature photograph given double the exposure (plates 38 a, b, c, d, e, 39 a, b,,c). At liquid air temperatures the primary reflexions are weakened in intensity (plates 37 b, c, 39 d, e).

The secondary reflexions are oniy slightly temperature-sensitive. This agrees with Sir C. V. Raman's observation, although it should be noticed that there is a slight apparent increase in intensity at high temperatures and a slight diminution at low ones (plates 37 b, c, 38 a, b, c, d, e).

In the low-temperature experiments that part of the diamond under irradiation remained covered with a very thin film of liquid air, but the general excellence of the Laue photographs obtained under these conditions showed that no appreciable absorption or scattering by the liquid air itself could have affected the validity of the results. It was also found that while no ice formed on the part of the diamond in actual contact with liquid air, ice did form on the surface only 1 mm. away. This evidence of the extremely low thermal conductivity of diamond makes it doubtful whether any method which does not surround the irradiated part of the specimen with the desired temperature (that is, which depends upon conductivity for its success) can possibly be satisfactory.

(8) Extra reflexions from {1 10} planes. Sir C. V. Raman has referred specifically to the absence of any extra spots corresponding to the (110) reflexion. Diamond, crystallizing as it does in a face-centred cubic lattice, cannot of course give any first-order selective or extra reflexions from the {1 10} planes. The intensity of the (220) selective reflexion is about 46 % of that of the (111). When diamonds of type I are so orientated ([II0] vertical, angle of incidence nea-r to 37-650 for CuKac, 50.10 for FeKac radiation) as to give an (hhO) Laue reflexion near to the (220) Bragg position, strong primary and secondary reflexions may be observed with quite a short exposure (20 min. for the 5 kW tube). Diamonds of type II give only the

primary reflexion. In all orientations some 50 or less from the Bragg angle, the secondary (220) reflexion consists of a pair of sharp, inclined spots, vertically above and below the Laue spot; the primary spot is to one side and is, of course, much more diffuse in character (plate 36 b, c). Some photographs show primary and secondary reflexions from the (111) (202) (022) and (113) planes simultaneously (plate 37 a). The (202) and (022) extra reflexions seen on such photographs consist of a sharp secondary spot superposed on a more diffuse primary spot and sometimes accompanied by a sharp streak (plate 36 a).,

(9) Extra reftexions from {1 13} {331} {004} planes. The (113) secondary reflexions (in alternative orientations) are shown in plates 35 d, 37 a, d, e. The (331) secondary reflexion has also been found in both alternative orienta-



Extra reflexions from the two types of diamond 319

tions, and (131) (311) (313) (133) reflexions observed, with the [110] axis vertical.

The (004) Laue reflexion (plates 35 e, 36 d) is apparently accompanied by a primary reflexion only.- It may be pointed out, however, that any secondary reflexions corresponding to reflecting points on the [001] axis would coincide with the Laue spot in every orientation and could not therefore be observed, except by the use of strictly monochromatized radiation. This has not been attempted. Detailed contours of the reflecting regions in reciprocal space corresponding to the observed primary and secondary reflexions will be published later, but it is significant that the (220) and (113) secondary reflexions correspond to reflecting points along the [100] and [010] directions only. There are no secondary spots associated with either the (220) or the (113) reflexions which would correspond to points on the [001] axis. The (331) seondary reflexion corresponds mainly to reciprocal lattice reflecting points along the [001] direction, though there may be weak [100] [010] branches.

CONCLUSIONS

It would appear from Sir C. V. Raman's paper that the existence of the {220} extra reflexions is incompatible with his theory. We have already pointed out (Lonsdale & Smith, I94I) that the structure-sensitiveness of the secondary reflexions shows that these cannot be explained on the Faxen- Waller heat theory. Nor can the simple diffraction theory, as it stands, explain the absence of secondary spots corresponding to the [001] direction for the (220) (113) reflexions. At present these experimental facts, therefore, have received no satisfactory theoretical explanation.

On the other hand, it must be emphasized that type I diamonds are not typical, or even ideal, crystals. The primary diffuse reflexions, found for all diamonds, correspond closely to the diffuse reflexions observed under suitable conditions of orientation, wave-length and temperature for all other crystalline substances. The secondary reflexions are quite different in character, and indeed, as Sir C.V. Raman has insisted, are not diffuse reflexions at all. They are analogous in some respects to the sharp spots or scratches which are occasionally observed, superposed on the ordinary diffuse spots, in the case of cleaved or cold-worked crystals (Lonsdale & Smith; this Discussion, p. 26). Examples of these 'strain' spots have even been found on some photographs of type II diamonds with worked faces, but they disappear when the diamond is shifted slightly. They are not temperature- sensitive (plate 39 d, e).

If the secondary diamond reflexions are to be explained on the basis of



320 K. Lonsdale

strain, however, it must be a strain which is cubic in symmetry and inherent in the majority of diamonds, although in differing degree. The interdepend- ence of secondary effects and extinction, and their variation with the diamond examined, make it obvious that intensity measurements, whether relative or absolute, will apply only to the particular diamonds used, and cannot be used for purposes of generalization.

Mr H. Smith has been associated with me throughout the entire course of this research. We are indebted to SirW. H. Bragg and to colleagues both in the Davy Faraday Laboratory and elsewhere for much help and interested encouragement.

REFERENCES

Lonsdale & Smith 1941 a Nature, Lond., 148, 112, 257. Lonsdale & Smith 194I b Proc. Phys. Soc. 53, 529. Robertson, Fox & Martin 1934 Phil. Trans. A, 232, 463. Robertson, Fox & Martin 1936 Proc. Roy. Soc. A, 157, 579.

Di:ffCuse scattering of X-rays by crystals

The Faxen-Waller theory and the surfaces of isodiffusion for cubic crystals

BY H. A. JAHN

Davy Faraday Laboratory, Royal Institution

(Communicated by Sir William Bragg, F.R.S.-Received 5 July 1941)

An elementary derivation is given of the Fax6n-Waller formula for the diffuse scattering of X-rays by thermally excited lattice vibrations and the shapes of the surfaces of isodiffusion in reciprocal space for cubic crystals investigated. It is shown that for substances with high elastic anisotropy large deviations from spherical character are to be expected for the surfaces of isodiffusion belonging to each of the individual lattice planes and, more- over, marked differences in shape between surfaces belonging to different lattice planes. The theory is illustrated by calculations made for a single crystal of sodium.

Recent experimental work (Laval 1939; Preston I939; Raman and Nilakantan I940; Lonsdale, Knaggs and Smith 1940; Siegel and Zachariasen I940; Jauncey and Baltzer I94I) has brought added interest to the funda- mental theoretical work of Faxen (1923) and Waller (I925) on the effect of



Lonsdale Proc. Roy. Soc., A, volume 179, plate 34

202 9 1202 ao

Ct, clt a : 1 1 b

022 0 2 022 116

Cu unfiltered radiation, 0911 =-23 8?. Film normal at 680 to undeviated incident beam; 0 Laue spot, G primary, 0 secondary spot. a, D 16, type II diamond showing no secondary reflexions: b, D (2), type I diamond showing strong secondary reflexions.

202 202 00

Laue +13 Laue-4-/? 4 black paper rings"

c A lil 1 - l 1 G P*111Il d

Laue a Lu-~

022 022 *

Cu unfiltered radiation, 011= -200. Film normal at 680 to undeviated incident beam; ellipses around 202, 022 Laue spots (in c) are due to reflexion of intense Cu K,/ beam by black paper covering film-holder; c, D 22, type II diamond; d, D (3), type I diamond.

[11()] vertical in all photographs. Film distance, 2-85 -- 4-15cm. No intensifying screens we?re used, as these would have spoilt the definition of the photographs.




Fe unfiltered radiation, 0111 = + 28.350. Film normal at 56 LI to undeviated incident beam. a, D22, type II; b, D(2), type I.

Fe unfiltered radiation, 0113= + 64.20. Film normal at 800 to undeviated incident beam. c, D 22; d, D (2), showing secondary streaks. The ellipses on c and d and the circles on a and b are due to Fe Ka reflexion by the black paper of the film-holder (see Lonsdale and Smith I94i b).

I %:; ~313

-f

e 004 #7

111

133 Lu

e, D(2), Cu, 000,=504'. Film parallel f, D(2), Fe, 0111= +26.850. to undeviated incident beam. Film normal at 56-10 to un-

deviated incident beam.




ct D (2), Cu radiation, 0111 = -27o. Film normal at 440 to undeviated incidentbeam. Differentialprint-

_- 202 ing adopted to bring out detail of film.

_~~~~~~~ 0

a 0 ̂ * Iil 0

022

___________________________ | D (2), Cu radiation, 6.10 = 39.75?. Film normal at 75.30 to un-

- o deviated incident beam.

/t~~~~~~~~~~~~~~~~~~~ bS !

22 0 Ja,Iwt'

D (2), Fe radiation, Oio= 46. 1?. Film normal at 80? to undeviated incident beam.

c ~~~~~~~~~~~~~~~0 - ~~~~~ ~~~~~~~~~/3 * a

22 _ ~~~~~~~~~~2210 Laue

_D(2), Cu radiation, Ooo0=61-70. *; Film normal at 800 to undeviated * *.

8i;it incident beam. No secondary, d1 :1 only primary(Cu Ka) diffuse spot

_: 4 just by 004 Laue.




i X 202 0-:

III 13 113 a

022

a, D (2), Cu radiation (partly filtered); 0111 =18 1?. Film normal at 80' to undeviated incident beam. Room temperature.

I) C c

D(3), Cu unfiltered radiation, 0m11=-18.60. Film normal at 68 50 to undeviated incident beam. b, 300 C, 9 min.; c, - 1800 C, 15 min.

D(2), Fe unfiltered radiation. Film parallel to undeviated incident beam. d, 0113 =-62 75?; e, 0113 =-66 75? (Bragg angle 64.20).




U c

b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

11 113

D (2), Cu unfiltered radiation, 011 =-180. Film normal at 69? to undeviated incident beam. a, 30? C, 10 min.; b, 6500 C, 10 min.; c, 6500 C, 5 min.

d et?P-

~~~~~~~~~~~~~111

* Laue spot primary spot

O secondary spot / secondary streak

e _

D (2), Cu unfiltered radiation, 0111 = + 21-20. Film normal at 600 to undeviated incident beam. d, 250 C, 30min.; e, 6500 C, 30 min. D (2) is a type I diamond, giving strong secondary effects.




a

! am i

b

D (4), type I diamond, giving very weak secondary effects. Cu unfiltered radiation, p111 = - 19'. Film normal at 680 to undeviated incident beam. a, 25?C, 10mi1in.; b, 6500C, 5min.; c, 650?C, 10min.

d e

Laue ct

D 2, type Il diamond giving no secondary effects. Cu unfiltered radiation, 0111 = - 200. Film normal at 680 to undeviated incident beam. d, 250 C, 5 min.; e, -180? C, 10 min.



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Extra Reflexions from the Two Types of Diamond