156 



gram. The number of molecules NaCl in the cube with its edge of 



58 5 

 3,00 cm. is therefore: ^ Q . ' | Q _ 24 = 0,610 X 10 24 , or 1,22 x 



10 24 atoms. On every edge of the cube there are as a consequence: 

 7,07 x 10 8 atoms, their mutual distance, therefore, being: -*-f\T~ fns 



cm. = 2,8 x io~~ 8 cm. 



The spacing of the layers parallel to (1 10) or (1 1 1) is then easily 

 calculated from this number, while that of the consecutive layers 

 of KCl parallel to (100), is of course: j,/5 X 10 8 cm.; etc. 



26. The cases of sodium-, and potassiumchloride, discussed more 

 in detail, may give an idea of the general method of reasoning 

 followed by Bragg to try to find out the internal structure of crys- 

 talline substances. The study of the relative intensities of the spectra 

 of the first, second, third order, etc., and of other peculiarities of 

 them, as for instance in the case of diamond, where the second spec- 

 trum was completely cut out, requires a number of conditions 

 to be fulfilled, before the arrangement adopted really explains the 

 diffraction-phenomena observed in every special case. l ) 



More particularly the face-centred space-lattice of cubic symmetry, 

 so closely related to the most closely packed arrangement, appears to 

 be of high importance for the internal structure of cubic crystals. Thus 

 in the case of zinc-sulphide, the zinc-atoms are arranged in such a face- 

 centred cubic lattice, while the sulfur-atoms are disposed through 

 the system in such a way that they occupy the centres of half the 

 number of the eight smaller cubes in which the greater face-centred 

 cubes of the zinc-atoms may be imagined to be subdivided; in this 

 case two of these smaller cubes must never be adjacent to each other. 



When the zinc- and the sulphur-atoms in ZnS are all substituted 

 by carbon-atoms, the structure of diamond is obtained, such as it 

 must be with respect to the experimental results met with in the 

 study of its crystals. That there, contrarily to what was observed 

 in the case of ZnS, the spectre of the second order (f = 2 x 2?r) 

 is completely cut out in the reflection at the octahedron-faces, is 

 explained by the fact that the alternating layers all consist of identical 

 atoms, the amplitudes a and a' of both oppositely directed secondary 



*) The question may be raised: can the supposed structures be the only true 

 ones, excluding every other possible arrangement? According to Barlow (Proc. 

 Roy. Soc. London, 91, 1, (1915), the possibility of other explanations as given 

 by Bragg, seems to be undeniable. 



