July 17, 1913] 



NATURE 



5i9 



ways orientated) atoms in the crystal that are produc- 

 ing- the reflections ; in other words, the planes of the 

 space-lattice. 



At first Laue, who published a separate memoir on 

 the theory of the experiments, considered that it was 

 the space-lattice due to similarly situated zinc atoms 

 which afforded the spot patterns, as he had been 

 engaged with Prof. Summerfeld in experiments relat- 

 ing to the action of zinc on X-rays. But there appears 

 no reason why the sulphur atoms should not be simi- 

 larly capable of producing reflections of these extremely 

 fine vibrations of corpuscles, and as the space-lattice 

 is the same for both elements, according to all ver- 

 sions of the geometrical theory of crystal structure, 

 there is really no reason why we should not consider 

 the reflection's as due to the general space-lattice of 

 zinc blende. Laue considered the "molecules" of the 

 crystal to form a three-dimensional grating — that is, a 

 Raumgitter — and that each molecule is capable of 

 emitting secondary vibrations when struck by incident 

 electromagnetic waves from the X-ray bulb ; also that 

 the molecules are arranged according to the simple 

 cube space-lattice (No. ij. The incident waves being 

 propagated parallel to one of the cube axes (edges), 

 the wave-surfaces will be parallel to the plane of the 

 other two cube edges. He then considers the spots 

 to be interference maxima of the waves scattered by 

 the orderly arrangement of the molecules in the 

 crystal. The equations of condition were next found 

 for interference maxima of direction cosines a, 0, 7, 

 and for incident wave-length *■, and from the position 

 of each spot the direction cosine of the pencil of rays 

 which formed it was calculated, assuming all the 

 transmitted pencils to come from the centre of the 

 crvstal. Thirteen spots in each quadrant were inves- 

 tigated, and in every case Laue's equations were 

 satisfied; hence, the conclusion that the spots are due 

 to interference of secondary Rontgen radiation appears 

 to agree with the positions of the soots, provided only 

 radiations of certain definite wave-lengths are present 

 in the incident rays. 



The lecturer pointed out, in an article in Nature 

 of November 14, 1912, that the structure of zinc 

 blende was probably not so simple as had been 

 assumed by Laue, and that the space-lattice with a 

 point at the centre of each side of the cube (No. 3) 

 was the more probable one, the structure being that 

 assigned to it by Barlow and Pope, as already de- 

 scribed in this lecture. 



A satisfactorv explanation has since been advanced 

 bv W. L. Bragg, which does accord with this struc- 

 ture and with other essential conditions referred to 

 by the lecturer, altogether avoids the assump- 

 tion of only a few wave-lengths, and agrees 

 with a simple reflection of unchanged X-ravs from the 

 planes of points of the general space-lattice of zinc 

 blende. He regards the incident radiation as com- 

 posed of a series of independent pulses, which, falling 

 on a number of atoms definitely scattered in a plane, 

 are separately reflected, each atom acting as a centre 

 of a secondary wave, and the whole building up a 

 wave-front. The interference maximum is thus due 

 to the reflection of the incident pulses from a system 

 of parallel planes of similar atoms, that is, from one of 

 the parallel series of planes of the space-lattice. Now 

 besides the principal planes of the space-lattice, the 

 cube planes, the points of the space-lattice also lie in a 

 considerable number of other planes, all of which are 

 possible crystal faces corresponding to rational indices. 

 For instance, the octahedral planes are verv easily 

 traced, as also those of the rhombic dodecahedron. 

 A minute fraction of the energy of a pulse traversing 

 the crystal will be reflected from each parallel plane 

 in succession, and the corresponding interference 

 NO. 228l, VOL. 91] 



maximum will be produced by a train of reflected 

 pulses. The crystal thus actually manufactures rays 

 of definite wave-lengths, just as a diffraction grating 

 does, the only difference being here in the extremely 

 short length of the waves, which is the very reason 

 why X-rays can penetrate in this manner into the 

 Raumgitter structure. Each incident pulse produces 

 a train of pulses, resolvable into a series of wave- 

 lengths, \ *-/j, a,,X/ 4 , &c, where a. = 2<2 cos 0, d being 

 the shortest distance between successive identical 

 parallel planes in the crystal, and the angle of inci- 

 dence of the primary X-rays on the plane of points 

 of the space-lattice. The intensity of any spot de- 

 pends on the energy in the spectrum of the incident 

 radiation characteristic of the corresponding wave- 

 length, and this varies considerably so that certain 

 parts of the spectrum are much more pronounced than 

 others. Also it depends on the number of reflecting 

 atoms in the plane — that is, on the reticular density 

 of the possible crystal face corresponding to the plane. 

 Hence, the greater the reticular density, the more- 

 intense the spot produced in the photograph. As 

 reticular density is also proportional to importance of 

 face, the primary faces having the greatest reticular 

 density, it follows that the most important facial 

 planes reflect the intensest spots, a fact which may 

 prove of great value in enabling us to discover the 

 real primary planes in doubtful cases. Each spot 

 reflected by a plane (considered as passing through 

 the origin and two other points) lies at the inter- 

 section of two ellipses, and the figure on the screen, 

 showing an analysis of one of the spot photographs, 

 exhibits this clearly. Indeed, the plane of atoms 

 corresponding to any spot can be found from the two 

 ellipses ; for each ellipse is the section of a cone by 

 the plane of the photographic plate, the axis of the 

 cone being the line joining the origin (centre of the 

 triaxial system, and considered as one of the three 

 points determining the plane) and the particular atom 

 (the second or third point of the three, of definite 

 coordinates), and the generator of the cone being the 

 incident beam. 



The interesting results of Bragg are in full accord 

 with the assumption of the centred-face cubic space- 

 lattice (No. 3), but not with either the simple-cube 

 or the centred-cube space-lattice (Nos. 1 and 2). They 

 also account for the elliptical shape of the spots. The 

 amount of ellipticity depends on the distance of the 

 photographic plate from the crystal. When the two 

 are very close the spots are round, but they become 

 more and more elliptical as the plate is receded (com- 

 pare Figs. 9 and 10). The phenomenon is due to the 

 fact that the initial rays are not strictly parallel, and 

 the effect will be clear from the next slide. The vertic- 

 ally diverging rays striking the reflecting planes of 

 the upper part of the crystal meet them at a less angle 

 of incidence than those of the lower part, and so the 

 reflected ravs converge. Horizontally diverging rays, 

 however, diverge still more on reflection. Hence the 

 section of the reflected beam is an ellipse with major 

 axis horizontal. 



It is of importance to note that the centred-face 

 cubic space-lattice is characteristic both of the arrange- 

 ment of identically (sameways) orientated and en- 

 vironed atoms of the same element, zinc or sulphur, 

 and of the atoms of both elements regarded as equal 

 spheres in contact. In the slide already shown 

 (Fig. 5), of Barlow and Pope's model, the spheres 

 of sulphur are coloured vellow to distinguish them 

 from the grey-coloured spheres of zinc. If we ignore 

 the colour and consider them as similar spheres, we 

 see that thev form the centred-face cubic arrangement. 

 The hemihedral nature of zinc blende is, however, 

 verv likelv connected with some real difference of 



