Space Group of a Cubic Crystal. 177 



have been established for other than cubic crystals, 

 although their application to specific instances is not so 

 straightforward. Some discrimination among the 

 special cases where one or more of the coordinates of 

 position are defined by considerations of symmetry can 

 likewise be made. 



Means of distinguishing between cubic space groups as 

 an aid to studies of crystal structure by reflection spec- 

 trum observations of the relative spacings against the 

 (100), (110) and (111) faces have already been given. 4 

 For a variety of reasons, however, this method is of little 

 •certain value in actual practice. 



A study of the Laue photographs taken in a single 

 direction through a crystal distinguishes as far as possi- 

 ble between the various space groups. Because of the 

 much larger mass of data with which they deal, space 

 group determinations based upon Laue photographic 

 studies are not' open to the same measure of uncertainty 

 as those derived from reflection spectrum measurements. 



It will be seen from the criteria to be discussed that 

 many of the space groups give diffraction effects which 

 are different from those given by any other space group 

 and thus a method is established for deducing completely 

 and uniquely the (internal) symmetry of a crystal with- 

 out recourse to methods of studying external symmetry, 

 such as those of face-development and etch-figure forma- 

 tion. 



These space group criteria have already been used 

 upon a number of crystals of rather complicated chemical 

 compositions. Of these, studies of nickel nitrate hexam- 

 monate 5 and of sodium hydrogen acetate 6 have either 

 been published or are in the course of publication; the 

 determination of the symmetry and structure of zinc 

 bromate hexahydrate, published elsewhere in this 

 Journal, 7 has been written primarily to serve as an illus- 

 tration of the application of these criteria. 



Methods of Distinguishing between the Cubic Space Groups. 

 The general characteristics of the diffraction effects to 



4 P. Xiggli, Geometrische Kiystallographie des Discontirimims, p. 492, 

 Leipzig, 1919. 



5 Ralph W. G. Wvekoff, Jour. Am. Chem. Soc, June, 1922. 



6 Ralph W. G. Wvekoff, see the third article in this number of this Journal. 



7 See the following article in this number. 



