CONTEMPORARY ADVANCES IN PHYSICS 427 



I remarked near the beginning of the article that while it would be 

 the simplest possible thing to suppose that the particles arranged in a 

 cubic lattice have full spherical symmetry, yet this supposition is as a 

 rule too simple for the facts. In particular it is too restricted to ex- 

 plain the diffraction-pattern of any one of the numerous elements which 

 crystallize on cubic lattices. One might then be forced to assume that 

 the atoms themselves do not have spherical symmetry. But luckily 

 this is unnecessary; for it happens that if with each lattice-point of the 

 cubic lattice we associate a properly-spaced and properly-oriented 

 group of spherical atoms — in some elements a pair, in other elements 

 a group of four — the difficulties vanish. The diffraction-patterns are 

 explained, and there is no outstanding conflict with the data assembled 

 by the crystallographers; for both of these arrangements, like that in 

 which each lattice-point is occupied by a single spherical atom, possess 

 full cubic or isometric symmetry in the crystallographic sense of those 

 words. 



In the first of these permitted arrangements, the two atoms as- 

 sociated with each lattice-point are so placed and so spaced, that if we 

 label them, say, A and B, the atoms A by themselves form one single 

 cubic array, and the atoms B by themselves form another simple cubic 

 array with an atom B in the very centre of each cube composed by 

 atoms A — and vice versa. This is the "body-centred cubic" arrange- 

 ment. It is depicted in the middle drawing of Fig. 21. The atom 

 at the centre of the cube may be associated with any one of the eight 

 corner atoms to form a pair; this pair is then repeated over and over 

 again on the cubic lattice to form the crystal. The alkali metals, iron, 

 and several other elements are addicted to this arrangement. 



In the second of the arrangements, the four atoms forming a group 

 are so placed and so spaced that if we call them A, B, C, and D, the 

 atoms of each letter form a cubic array; and these four cubic arrays are 

 interlocked in such a fashion, that the cubes of any one of these 

 arrays have in the centres of all their faces atoms belonging to the 

 others. Thus in the righthand sketch of Fig. 21 the atom at any corner 

 may be associated with the atoms in the centres of the three faces 

 which meet at that corner, and these four form the atom-group which 

 is repeated over and over again on the cubic lattice to build the crystal. 

 Many of the metallic elements have adopted this "face-centred cubic" 

 arrangement, the noble metals for example, and argon also. 



How does one recognize from the diffraction pattern which of these 

 arrangements exists in a cubic lattice? At this point I will not give 

 an exact answer: but the principle is simple. Even as on an earlier 

 page it was shown that for certain directions of diffraction adjacent 



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