THE 



AMERICAN JOURNAL OF SCIENCE 



[FIFTH SERIES.] 



Aet. XVII. — The Determination of the Space Group of a 

 Cubic Crystal; by Ralph W. G. Wyckoff. 



Introduction. 



The theory of space groups presumably defines all of 

 the ways in which elements of symmetry may be distri- 

 buted in space so that their aggregates will possess 

 crystallographic symmetry. 1 A knowledge of the space 

 group to which a particular crystal should be assigned 

 thus describes completely its characteristics of symme- 

 try, and forms thereby one of the principal goals of 

 descriptive crystallography. On the basis of direct 

 experimental evidence it has hitherto been impossible to 

 carry crystallographic description so far ; only in a few 

 isolated cases could the appropriate space groups be 

 inferred. 2 Use of the diffraction effects resulting from 

 the action of X-rays upon crystals offers, however, the 

 opportunity in many cases of determining experimentally 

 the space group corresponding to a crystal. 



The crystal symmetry which is deduced by the use of 

 X-ray methods of study is the symmetry of the arrange- 

 ment of the atoms of which the crystal is composed. The 

 identification of this internal symmetry with the external 

 crystal symmetry, obtained from studies of face-develop- 

 ment and the like, requires an assumption equivalent to 

 one that states that the external symmetry of a crystal is 

 consistent with the arrangement of its constituent atoms. 

 Not only does it appear natural to relate them thus but 

 the generally satisfactory agreement between the exter- 

 nal symmetries and the symmetries of the crystal models 

 of those crystals whose structures have thus far been 

 studied with X-rays points to the correctness of this 

 assumption. 



1 A. Schoenflies, Krystallsysteme und Krystallstructur, Leipzig, 189L 



2 For instance, C. Viola, Z. Kryst., 28, 225, 1897; L. Sohncke and E. Fed- 

 erov have made similar assignments. 



Am. Jour. Sci. — Fifth Series, Vol. IV, No. 21. — September, 1922. 

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