150 Wyckoif — Crystal Structure of Magnesium Oxide, 



available. The arrangement that would result if u and v 

 were both nearly equal to 14 (or %) is scarcely feasible 

 from a physical standpoint. Thus {j) furnishes a 

 possible arrangement for the atoms in magnesium oxide. 



Possible arrangement (k). 

 This must be treated in a similar fashion to the 

 preceding. Thus the reflection term from the (100) 

 face is 



A=:Mg|8cos2 7r?iz^-|-8cos7r;i {l-\-2u)-\-^cos Trn (.J- — 2^/) 



-|-8cos7^?^ (i+2i«)}-|-0 {a similar term \x\ v\. 

 B=0. 

 When n = l,2 and 3, A = for all values of u and v. 

 Plane (110). 



A=Mg-| 8H-8cos4 TT nu-\-^Qo^ -n- ^i-j-Scos ir 7i (1 — 4i<) } 



-j-O'a similar term in i;}. 

 B=0. 

 When n = l or 3, A = 0. 

 For 71 = 2: 



A=Mg ; I6 + COS8 TT ?^H- 1 16 + 16cos8 nv]. 



Plane (111). 



A=Mg {4:Gos6 TT ?iu -\-'\2cos2 TT 7iu -\-12sin2 TT 72U— 4:sinQ -w ini\ 

 -j-OJa similar term in v]. 



B = — A. For the present qualitative uses it may, 

 therefore, be neglected. 



It can be shown by a treatment similar to that applied 

 to {j) that when u^ = % and U2 =% (for these particular 

 values of u, the thirty-two equivalent positions each 

 reduce to sixteen) and v = Yg, there is complete agree- 

 ment with experiment. Except for the fact that the 

 element whose parameters are represented by 1*1 and Uo 

 will be of two sorts (all of the atoms of the other kind 

 will be alike), this particular arrangement is simply a 

 twice-scale (c) grouping. If, however, u and v had 

 values close to % and %, the differences in the reflections 

 would be so slight as to escape detection. Arrangement 

 (k) thus becomes a possibility. 



Grouping (c), the ''sodium chloride arrangement'' 

 has now been shown to be the only simple structure which 

 explains the experimental data, if the arrangement of the 

 atoms in magnesium oxide is really holohedral. The 

 tetartohedral grouping (/), however, can be made to fit 



