140 Wyckoff — Crystal Structure of Magnesium Oxide. 



chemical molecules that it is possible to place in the unit 

 cell is limited by the symmetry of the crystal. In the 

 case of the normal cubic symmetry (holohedry) the 

 greatest number of equivalent points (and equivalent 

 atoms) to be expected in a unit cell is 192, since there are 

 48 equivalent points in the corresponding point group 

 and there may be four points of the lattice associated with 

 the unit of structure. Fewer than this number of mole- 

 cules in the unit will result from atoms taking up special 

 positions so that two or more of the equivalent positions 

 coincide, and will consequently be whole numbers obtained 

 by dividing 192 by tw^o, three, or four, or by products 







Figure 3. 





+ 400 



\ v^ 



..^ 





_^ / 



+ 200 



vx^ 



_^v 



^^ 



-^J 







x"\> 



v.^^ 



■^ ^y 



y/ 



^\ 



'^'"''''^v 



y ^- 



^u^^^^ y 



-200 



\ V 



1 I 



^x^ 



1 /\ 



I i r 



.-400 



T^X r- 



of two, three, or four, into themselves or each other.^ 

 Possible values of the ratio — are listed in the following 

 table : 



^ The holohedral structure contains p'aiies of s mmetry and two-, three-, 

 and four-fold axes of symmetry. If a special position lies in a plane of sym- 

 metry, or on a two-fold axis, the number of equivalent positions wdll be re- 

 duced to one-half; if it lies on a three- or a four-fold axis, three or four 

 equivalent points will occupy the same position. 



