WycJtoff — Crystal Structure of Magnesium Oxide. 141 

 m 12 3 4 6 8 12 IG 24 32 48 04 90 192 



n 



1 liiii--------- 



2 84f2|lfi------- 



3 27 ¥ 9 ^ f ¥ f H I - - - - - 



4 64 32 -V- 16 ^2. 8 V" ^ f ^ | 1 - - 



Measurements from the (100) face of magnesium 

 oxide, using the L-series lines of tungsten, gave a value 



for ~ of 1.99. The unit cell must therefore contam 

 m 



either four or thirty-two chemical molecules of magne- 

 sium oxide.^ 



Assuming that n = 4. — (1) All four of the oxygen 

 atoms and of the magnesium atoms may be equivalent; 

 (2) conceivably there might be two sets of two equiva- 

 lent atoms; (3) three atoms might be alike and one 

 different; or (4) two alike and the other two different 

 one from the other. There seems to be no reason why 

 either of the last two should be possible physically, but 

 the second might be realized if magnesium oxide were 

 pohmierized into (MgO)2 molecules in the crystal. All 

 four possibilities will, however, be considered. 



(1) If all four atoms of the same kind are equivalent, 

 all of the space groups of the cithic system will reduce to 

 the following arrangements : 



(a) Mg: 



0, 



Hi, 



i + i, 



O: 



iih 



oii, 



iOf, 



(b) Mg: 



0, 



Hi, 



iih 



0: 



iih 



Oif, 



iOh 



J 3. i 

 2 4 4- 



4 4 ^J' 



These arrangements are obtained from the space groups 

 0'' and 0' and consequently exhibit enantiomorphic 

 hemihedry. 



(c) Mg: 0, i|0, iO i, Oih 

 O: i, I 0, 4-0, m, 



(c) can be obtained from space groups of each of the ^ve 

 classes of cubic symmetry. 



"'If the crystal had tetartohedial syiiimetiy, then the second possibility 

 could be definitely eliminated. 



