PROF. W. H. BRAGG ON X-RAYS AND CRYSTAL STRUCTURE. 



255 



C 



Fig. 3. Arrangement of atoms 

 in any plane in rock salt 

 which is parallel to a cube 

 face. Blank circles repre- 

 sent sodium atoms ; the 

 others chlorine, or fin vtrsA. 



The atoms of the crystals may be considered as arranged in a series of planes which 

 are perpendicular to the paper and cut it in lines parallel to AB. These planes all 

 contain equal numbers of Na and Cl atoms and are all 

 alike. The spacing is 2'81 A.U. (10~ 8 cm.). 



On the other hand, we may think of the atoms as lying 

 on sets of planes which are perpendicular to the paper 

 and intersect it in lines parallel to BC. These planes 

 are also all alike, containing equal numbers of Na and Cl 

 atoms, although the atoms lying along the lines of inter- 

 section with the paper are all of one or of the other kind. 



/ 



The spacing is very nearly 2 A.U., being \/2 times less 



than the former spacing. 



Again, if we proceed in a direction parallel to a cube- 

 diagonal of rock salt, we encounter alternately planes 

 containing nothing but Na atoms, and planes containing 

 nothing but 01 atoms. The periodicity now has a spacing 



o 



3 '24 A.U. ; extending, say, from one Cl plane to the next. 



If we pass a pencil of X-rays of wave-length X through a piece of rock salt, there 

 will be a reflection in the planes parallel to a cube face if the rays make with those 

 planes an angle 9 where sin 6 = A/5 '62, in the planes perpendicular to a face-diagonal 

 if the angle made with these planes is given by sin 9 = X/4, and in the planes 

 perpendicular to the cube-diagonal if the angle made with such planes is given by 

 sin 9 = X/6'48. Of course it is extremely unlikely, though quite possible, that more 

 than one of these conditions can be satisfied at one time by the same set of 

 homogeneous rays. But if the pencil of X-rays contains rays of a great range of 

 wave-lengths various constituents may be found to satisfy the condition of reflection 

 not only by these but by many other planes, or by many others and not by these. 

 In this way a number of different constituents of the original pencil may be reflected 

 in different directions, which will have an ordered arrangement dependent on the 

 symmetry of the crystal. This is the explanation of the photographs first obtained 

 by FRIEDEICH and KNIPPING as the result of the brilliant suggestions of LAUE.* 



The X-rays usually penetrate such a little distance into a crystal that the reflection 

 seems to occur at the face of the crystal in the ordinary way. It is usual though not 

 always possible to cut the crystal so that the surface is parallel to the set of planes 

 to be considered, unless a natural face is available. - If the crystal is cut imperfectly 

 so that the face is not parallel to the planes, the angle between the incident and 

 reflected rays is not affected thereby, because the reflection is truly related to the set 

 of the planes and ignores the face. Moreover it is just as sharp where the face is 

 rough as when it is smooth, so long as the crystal is uniform. 



* The explanation was given in . this simple and complete form by W. L. BRAGG, ' Proc. Camb. Phil. 

 Soc.,' vol. xvii., Pt. I., p. 43. 



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