Abstract
The recent demonstration, by the application of X-rays to the study of crystal structure, that the dimensions of atoms remain fairly constant and definite from one crystalline compound to another appears to necessitate a revision of the current views of isomorphism. To make this evident it is only necessary to list the volumes which atoms of some of the elements have been found by various workers (especially W. L. Bragg) to occupy, and, assuming crystals to be essentially close-packed structures, to consider the consequences of the relations brought out. The results of X-ray measurements are usually reported in terms of atomic diameters, but they may be transformed into volumes by using the approximate formula: V = 4.2 (d/2)3, the unit becoming 10−24 cc. The elements vary in volume more or less—perhaps ±30% of the mean value—from one mode of combination to another. The mean values which seem most likely to be represented in the silicates, estimated from the data available, are given here in increasing order:
