Diffuse Reflection of X-Rays by Single Crystals

Lonsdale, Kathleen; Knaggs, I. Ellie; Smith, H. W.

doi:10.1038/146332a0

Cited by 19 publications

(9 citation statements)

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“…While this explanation may be plausible for electron-diffraction photographs, the sharpness of the lines on X-ray photographs shows th at here we are dealing with much bigger crystals. Taylor & Laidler (1940) suggested th at the extra lines may be another mani festation of the 'diffuse' reflexion of X-rays, but Lonsdale, Knaggs & Smith (1940) showed that this cannot be so. Edwards & Lipson (1942) thought that they may be due to defects in the graphite structure similar to those found in cobalt (Edwards, Lipson & Wilson 1941), but occurring at regular intervals.…”

Section: Introductionmentioning

confidence: 99%

“…These lines have attracted attention because of their very general occurrence; they are given by graphites of many different origins, natural and artificial. For instance, they occur on a photograph that Rooksby (1940) gives as typical of natural graphite, and Taylor & Laidler (1940) found th at they are given by graphite crystallized in an arc. Purification of the specimens does not remove the lines, but they do disappear after long periods of digestion with a mixture of concentrated sulphuric and nitric acids.…”

Section: Introductionmentioning

confidence: 99%

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The structure of graphite

Lipson

Stokes

1942

Proc. R. Soc. Lond. A

225

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The structure of graphite

Lipson

Stokes

1942

Proc. R. Soc. Lond. A

225

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“…9 Both derivations, however, depend on the assumption of spherical equi-scattering surfaces surrounding the hkl reciprocal lattice point. The experimental work of Laval with monochromatic rays has been confirmed by Preston, 10 Siegel and Zachariasen, 11 Raman and Nilakantan, [12][13][14] Lonsdale, Knaggs and Smith, 15 Jauncey and Baltzer, 16 and Siegel. 17 Raman and Nilakantan's results have been discussed by Zachariasen.…”

Section: Introductionmentioning

confidence: 89%

Non-Laue Maxima in the Diffraction of X-Rays from Rocksalt—Equatorial Maxima

Jauncey

Baltzer

1941

Phys. Rev.

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The existence of non-Laue maxima in the diffraction of x-rays was first recognized in 1938 by Wadlund for a continuous spectrum of x-rays and by Laval for monochromatic x-rays. A brief description of Laval's exhaustive work is given. The main points of the theories of Zachariasen, of Raman, Nilakantan and Nath, and of Preston, Bragg and Jauncey are also described. In the authors' experiments CuKa, CuKp, or MoKa x-rays with a weak background of continuous radiation were diffracted from an etched cleavage face of a thick rocksalt crystal. With the crystal face set to give the 200 reflection of CuKai a total divergence of 1.6' was found in the reflected beam, indicating very little warping in the layers near the crystal surface. With the crystal face turned by steps of 1° from a glancing angle of 45°07' to 28 c 07' the positions of the non-Laue maxima associated with the 400 and 620 Bragg reflections were found. The non-Laue spots are called associated Bragg spots. All photographs showed a shift of the maxi-mum intensity of the associated Bragg spot from the position of the corresponding Bragg spectrum line which is greater than zero. This result differs from that of Raman and Nilakantan, who report zero shift with rocksalt. The observed shift is always less than Zachariasen's theoretical value for a given A, the angle by which the crystal is set away from the position for a Bragg reflection. Possibly for A< 1° the Zachariasen formula holds. From the value of A at which the associated Bragg spots disappear the shortest effective wave-lengths of the elastic waves concerned are about 13A to 17A. These are between 2 and 3 times the minimum wave-length in Debye's specific heat theory. On the Preston-Bragg-Jauncey view a shift less than the Zachariasen value implies that the groups of atoms which give rise to the associate Bragg spots are considerably larger than an atom plus its 12 nearest neighbors as supposed by Preston.1

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“…Recent experimental work Preston 1939; R am an and Nilakantan 1940;Lonsdale, Knaggs and Smith 1940;Siegel and Zachariasen 1940;Jauncey and Baltzer 1941) has brought added interest to the funda mental theoretical work of Faxen (1923) and Waller (1925) on the effect of on May 12, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from 321 thermally excited lattice vibrations on the scattering of X-rays by crystals. This theory of Faxen and Waller has been recapitulated recently by Zachariasen (1940), who has shown th a t it is capable of giving general agreement with the experimental results.…”

Section: Davy Faraday Laboratory Royal Institution ( Communicated Bymentioning

confidence: 99%

“…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 Preston 1939; R am an and Nilakantan 1940;Lonsdale, Knaggs and Smith 1940;Siegel and Zachariasen 1940;Jauncey and Baltzer 1941) has brought added interest to the funda mental theoretical work of Faxen (1923) and Waller (1925) on the effect of on May 12, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from 321 thermally excited lattice vibrations on the scattering of X-rays by crystals. This theory of Faxen and Waller has been recapitulated recently by Zachariasen (1940), who has shown th a t it is capable of giving general agreement with the experimental results.…”

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confidence: 99%

Diffuse scattering of X-rays by crystals - The Faxén-Waller theory and the surfaces of isodiffusion for cubic crystals

Jahn

Bragg²

1942

Proc. R. Soc. Lond. A

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strain, however, it m ust be a strain which is cubic in symmetry and inherent in the m ajority of diamonds, although in differing degree. The interdepend ence of secondary effects and extinction, and their variation with the diamond examined, make it obvious th a t 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 Sir W. H. Bragg and to colleagues both in the Davy Faraday Laboratory and elsewhere for much help and interested encouragement. D iffu se s c a tte r in g o f X -r a y s b y c r y s ta ls T h e F a x e n -W a lle r t h e o r y a n d th e s u r f a c e s o f is o d iffu s io n fo r c u b ic c r y s ta ls By H. A. J ahn Davy Faraday Laboratory, Royal Institution ( Communicated by Sir William Bragg, F.R.S.-Received 5 J u ly 1941)An elementary derivation is given of the Faxen-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 Preston 1939; R am an and Nilakantan 1940;Lonsdale, Knaggs and Smith 1940;Siegel and Zachariasen 1940;Jauncey and Baltzer 1941) has brought added interest to the funda mental theoretical work of Faxen (1923) and Waller (1925) on the effect of on May 12, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from 321 thermally excited lattice vibrations on the scattering of X-rays by crystals. This theory of Faxen and Waller has been recapitulated recently by Zachariasen (1940), who has shown th a t it is capable of giving general agreement with the experimental results. Zachariasen used, however, a less general expression than the complete Faxen-Waller formula, his final formula not taking into account the full elastic anisotropy of the crystal. I t is the purpose of this paper to deduce from the general expression given by both Faxen and Waller the manner in which the shape of the surfaces of isodiffusion discussed by depend upon the three fundamental elastic constants of a cubic crystal. I t is found th a t for substances with high elastic anisotropy such as sodium, large deviations from spherical character are to be expected for the surfaces of isodiffusion belonging to each of the individual lattice planes and, moreover, marked differences in shape between surfaces belonging to different lattice planes. Theoretically, therefore, the diffuse scattering phenomenon is capable of being developed into a method of determining the elast...

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Diffuse Reflection of X-Rays by Single Crystals

Cited by 19 publications

References 2 publications

The structure of graphite

The structure of graphite

Non-Laue Maxima in the Diffraction of X-Rays from Rocksalt—Equatorial Maxima

Diffuse scattering of X-rays by crystals - The Faxén-Waller theory and the surfaces of isodiffusion for cubic crystals

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