Wychoff — Crystal Structure of Alabandite, 243 



odd. Writing A for the evaluation of the cosine terms 

 and B for the corresponding sine terms, the application 

 of expression (3) to these two possible arrangements 

 leads to the following: 

 Arrangement (II) : 



I oc/(c0z)X (A+B^). 

 When the indices are two odd and one even: 



A = 0, when n = odd, 



A =4Mn + 4S, when n — even, 



B = always. 

 When the indices are two even and one odd: 



A = 0. when )i = odd, 





A 



= 4Mn + 48, 



when 



n 



= even, 





B 



= always. 









When 



the ir 



idices are all odd: 









A 



= 4M^ - 4S, 



when 



n 



= odd. 





A 



= 4Mn 4- 48, 



when 



n 



= even, 





B 



= always. 









Arrangement (III) : 



I<x/(d/n)x (A-' + B'). 

 When the indices are two odd and one even: 



A = 0, W'hen n = odd, 



A = 4Mn + 48, when n = even, 



B = always. 

 When the indices are two even and one odd: 



A = 0, when n = odd, 



A = 4Mn =F 48, — when 7i = 2, + when 7i = 4, 



B = always. 

 When the indices are all odd: 



A = 4Mn, B = 48, when ?i = odd, 



A = 4Mn =F 48, — when n = 2, + when n = 4, B = 0. 



From these two sets of expressions it is evident that if the 

 arrangement of the atoms of alabandite is that of (II) or 

 is an arrangement of (I) lying close to (II) then the 

 first order reflection from the (111) plane must be weak; 

 if on the other hand the grouping is that of, or approaches 

 close to that of, (III) then this reflection must be great. 

 Hence a study of the relative intensity of this reflection 

 and of the reflections from other strongly reflecting planes 

 will serve to distinguish between these limiting cases 



