Space Group of a Cubic Crystal. 185 



It will be observed that a number of space groups give 

 rise to diffraction effects which are different from those 

 resulting from anv other space group. These unique 

 space groups are * T h 2 ,T h 6 ,O h 2 ,O h 4 ,T h 4 ,(V ,O h s ,T h 7 ,T d 6 ,O h 10 ; 

 and, less certainly because they depend upon the presence 

 or absence of planes of the single form 100; T 4 ,0 2 ,0 6 and 

 7 ,O,0 s . The symmetry of a crystal corresponding to 

 any one of these space groups can consequently be deter- 

 mined with complete certainty without any reference to 

 face development, etch-figure symmetry or any other of 

 the customary methods of crystallography. A possible 

 experimental method is thus furnished for finding out 

 what relations exist between the symmetry assigned to a 

 crystal by studies of its external appearance and the sym- 

 metry of the arrangement of its atoms. 



The experimental establishment of the space group of 

 a particular crystal is simple and can be carried out by 

 the procedure common in crystal structure determination 

 of taking one or more Laue photographs about some con- 

 venient orientation, determining the indices of the various 

 diffraction spots by the usual methods of projection and 

 finding the wave-lengths of the X-rays producing these 

 spots with the aid of a measurement of the dimensions of 

 the unit cell through a reflection spectrum measurement 

 from some convenient crystal face. 9 Then if the voltage 

 applied to the X-ray tube in producing the photographs 

 is known, the range of the spectrum in which there will be 

 only first-order reflections can immediately be told. It 

 happens that in all cases where it is necessary to go to the 

 second-order region to distinguish between space groups, 

 first-order reflections from the planes involved are also 

 missing. No ambiguity is therefore introduced concern- 

 ing the order of reflection of diffraction spots lying in the 

 region of strong second-order effects. Reflections from 

 faces of the form {100} are as a rule more readily 

 obtained by reflection spectrum measurements than from 

 Laue photographs. It is desirable to reemphasize that, 

 for the reasons already given, only the appearance and 

 not the absence of {100} reflections can necessarily 

 furnish conclusive evidence upon which to base assign- 

 ments to particular space groups. 



In certain of the cases where the diffraction data are 



9 Ralph W. G. Wyckoff, this Journal, 50, 317, 1920. 



