196 Professor W. Lawrence Bragg [^ay 28, 



threefold axis passes through every corner, and the necessary propor- 

 tion of two sulphur atoms to one iron atom is realized. 



On the conception of the crystal as a set of spheres packed 

 together, it will be seen that there are two possible positions for the 

 sulphur atom. It may lie at the centre of the cube, where it is 

 surrounded by the four iron atoms at A, C, H, and F, an arrange- 

 ment which exists in the structure of fluor spar, CaF 2 . Alternatively, 

 it may move along the axis to a position G 2 on the other side of the 

 plane HFC, where it will be packed between the three iron atoms at 

 H, C and F, and the corresponding sulphur atom at So. 



If the size of the sphere representing the iron atom is known, 

 geometrical considerations fix the centre of the sulphur atom touching 

 the iron atoms and the other sulphur atom. As a first approximation 

 to the size of the iron sphere, the distance between atomic centres in 

 metallic iron, first analysed by Hull, may be taken. This distance is 

 2 '47 x 10~ 8 cm., or 2*47 Angstrom Units. Using this value, the 

 ratio S X G/AG is found to be equal to 0*22. The author originally 

 deduced the value 0"20 for this parameter, and a more exact 

 determination by Ewald gave it as 0'226, so it will be seen that the 

 conception of the atoms as a set of spheres packed together leads to 

 a determination of the parameter very near the true one. Further, 

 the diameter of the sphere representing the sulphur atom follows to 



o 



be 2*05 A. Fig. 2 will illustrate the manner in which this result 

 is arrived at. 



6. The structure of zinc sulphide, and therefore the distance 

 between the zinc and sulphur atomic centres, is known : it is illustrated 

 by Plate II., fig. a. Taking the diameter of the sulphur sphere to be 



o o 



2*05 A, that of the zinc sphere touching it is found to be 2 '65 A. 

 From the zinc oxide structure the dimensions of the oxygen sphere 



o 



can be calculated; its diameter is found to be 1*30 A. This 

 difference of 0*75 A between the diameters of the oxygen and 

 sulphur spheres is also found to exist in a number of other crystals. 



The rhombohedral carbonates typified by calcite, CaC0 3 , provide 

 a check on these figures. We have seen that the oxygen sphere has 

 a diameter of 1 ■ 30 A. In the diamond the distance between the 



o 



carbon centres is 1 • 54 A, and this may be taken to be the diameter 

 of the carbon sphere. Every carbon atom in the carbonates is closely 

 surrounded by three oxygen atoms, and we should therefore expect 

 the distance between carbon and oxygen centres to be J (1*54 + 



o o 



1'30)A, or 1*42 A. As a matter of fact the X-ray measurements 



o 



show it to be 1 * 47 A, which is in fair agreement with the calculated 

 value. Further, in zinc carbonate the zinc atom is surrounded by six 



oxygen atoms, the distance between the centres being 1*99 A. 



Comparing this with the distance 1*97 A between zinc and oxygen 



