1920] on Crystal Structure 199 



centres in zinc oxide, we see that each of the atoms appears to occupy 

 a space of the same dimensions in all these crystals, sulphur in pyrites 

 and zinc sulphide, zinc in zinc sulphide, oxide, and carbonate, oxygen 

 in zinc oxide and carbonate, carbon in the carbonate and in diamond. 



7. This will illustrate the manner in which the atomic diameters 

 shown in the diagram (Fig. 3) have been calculated. The results 

 may be summarized by saying that the distance between two 

 neighbouring atoms in a crystal structure is equal to the sum of two 

 constants characteristic of the atoms. We can therefore picture the 

 atoms as a set of spheres packed together so that they are in contact, 

 by taking these constants to be the radii of the spheres, and the 

 models which illustrate this lecture have been built up in this way. 



In the figure the elements are arranged in the order of their 

 atomic numbers, and the ordinates represent the diameters of the 

 corresponding spheres, measured in Angstrom Units. A comparison 

 of the distances found between the atoms in these structures which 

 have so far been determined, with the distance calculated by adding 

 the "atomic radii," shows that the average discrepancy between the 



o 



two is 0*06 A, or between two and three per cent. 



It will be seen that the atomic diameters lie on a series of regular 

 curves which show very strongly the periodic arrangement of the 

 elements. The monovalent electropositive elements have the greatest 

 diameters, the divalent metals the next greatest, and passing along- 

 each period the diameter diminishes steadily until it approaches a 

 lower limit for the electronegative elements at the end of the period. 

 In the case of two of the elements, chromium and manganese, it 

 is necessary to suppose that the atom has a smaller diameter when 

 functioning as an electronegative element than as an electropositive 

 one. 



The curve may be compared to Lothar Meyer's curve of atomic 

 volumes, but in the case considered above the volume is that occupied 

 by the atom in all the compounds into which it enters, so that the 

 curve has a wider application. The molecular volume of a com- 

 pound often differs very greatly from the volume obtained by adding 

 the atomic volumes of its constituents, but if the crystalline struc- 

 ture is taken into account, this generalization shows that the space 

 occupied by each atom is approximately constant. 



In some cases the distances between atoms do not agree with 

 those calculated from the diameters ; for example, this is the case for 

 many of the elements. In spite of this, the analysis of a complicated 

 crystal is greatly helped by this way of regarding the atomic arrange- 

 ment. When marshalling the atoms together in trying to find some 

 arrangements which account for the diffraction effects, the necessity 

 of allowing each atom a certain space in the structure limits the 

 variable parameters to a small range and so simplifies the analysis. 



8. The physical interpretation of these empirical relations must 

 be sought for in the structure of the atom, and in fact that theory of 



