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BELL SYSTEM TECHNICAL JOURNAL 



"cell"; hence the most populous of all the planes traversing the 

 crystal. I have spoken above of the "important" strata of the 

 crystal, meaning those which are likely to be parallel to facets. The 

 word "important" is vague, and it is better that it should remain 

 somewhat vague ; but, in a rough way, the more populous a stratum 

 is the more likely it is to be "important" in that sense, and also in 

 the sense that it produces strong diffraction-spots. We will therefore 

 consider chiefly the planes, which cut through the unit cube in such 

 a way as to traverse three or four of the atom-groups. Put the origin 

 of coordinates at A, the x, y, z axes through C, 5, D respectively. 



Fig. 21 — Illustrating the cubic lattice. 



Commence with the plane containing BCD, normal to the direction 

 AE which is one of the principal diagonals of the cube. We wish a 

 symbol for this plane that shall describe its orientation, which is its 

 important feature, — a symbol that shall denote not only the plane 

 BCD, but equally all those which are parallel to it, such as FGH 

 and the parallel planes through A and E and other unit cells. We 

 might use the three direction-cosines of the normal to this family 

 of planes; or we might use the three intercepts of BCD on the three 

 coordinate-axes, multiplied by an arbitrary factor to convert them 

 into convenient integers and show that we are not more concerned 

 with BCD than with any other member of the family; or we might 

 use the reciprocals of these three intercepts, also multiplied by some 

 convenient arbitrary factors. The last choice is the standard one. 

 The three intercepts are a, a, a; their reciprocals are \Ja, 1/a, 1/a; 

 we multiply these by a and obtain (1, 1, 1) as the symbol for not only 

 the plane or stratum BCD, but all the strata parallel to it, including 

 for example any facets that may be formed upon such strata. The 

 reader will easily identify three other families of planes for which the 

 symbols are (—1, 1, 1); (1, —1, 1); and (1, 1, —1). Some substances 

 with cubic lattices form crystals in the shape of octahedra; the surfaces 

 of these are strata with such symbols. Usually the commas are left 

 out of the symbols, and the minus signs printed over the digits. 



