Wyckoff — Crystal Structure of Silver Oxide. 185 



same value of m/n z , where n may be chosen as any integer, 

 it is evident that m for Ag 2 can just as well be equal 

 to 16. 



Table 1. Measurements upon two Silver Oxide Films. 



Distance of line from 



central 



image 



dtki/n in A. U. 



hkl 



d 100 in 



A.U. 



Film 1. 



Film 2. 



Film 1. 



Film 2. 





Film 1. 



Film 2. 



2.86 cm. 



2.85 cm. 



2.75 3 



2.75 s 



111(1) 



4.775 



4.779 



3.30 5 



3.30 5 



2.38 5 



2.38 5 



100(2) 



4.770 



4.770 



4.72 5 



4.73 5 



1.67 3 



1.67° 



110(2) 



4.758 



4.752 



5.55 



5.54 5 



1.42 6 



1.42 7 



113(1) 



4.768 



4.770 



Mean 4.768 4.768 



The value d 100 is of course the length of the side of the unit cube. 



The Possible Structures for Silver Oxide. — If m = 2 : 

 There is but one way of arranging two molecules of Ag 2 

 within a unit cell so that the resulting structure will have 

 any form of cubic symmetry. 4 It is as follows : 

 Arrangement (a) : Oxygen atoms at 

 000; Ui- 



Silver atoms at 



111. 133 . 313. 331 

 444) 444 5 444) 444' 



This grouping can be deduced from the space groups 

 Th 2 ,0 2 or Oh 4 . 



If m = 16 : If the two silver atoms in the molecule of 

 Ag 2 are chemically (and hence crystallographically) 

 alike, there are three ways of arranging sixteen molecules 

 of Ag 2 in a unit cube so that the resulting structure has 

 cubic symmetry. 5 They are : 



Arrangement (b) : In this arrangement, which can be 

 deduced from the space groups Th 4 ,0 4 and Oh 7 , the six- 

 teen oxygen atoms lie in unique positions ; the thirty-two 

 silver atoms possess one variable parameter and are upon 

 trigonal axes. 



4 These results are taken from tables which form a portion of a book 

 entitled "An Analytical Representation of the Theory of Space Groups' ; 

 which is shortly to be published by the Carnegie Institution of Washington. 

 Some of them are also given in P. Niggli, Geometrische Krystallographie des 

 Discontinuums (Leipzig, 1919). 



5 If it were assumed that the two silver atoms could be different, then the 

 several space groups having as special cases sixteen equivalent positions with 

 one variable parameter would introduce additional possibilities. Such an 

 assumption finds no justification from the chemistry of the compound and 

 would run counter to the general trend of crystal structure determinations 

 thus far made. 



