142 Wyckoff — Crystal Structure of Magnesium Oxide. 



1 1 



2" 2"- 



(d)Mg: 0, iiO, iOi, 



O: iii, if f, f if, f f i. 



(d) results from groups having tetartoliedral and tetra- 

 liedral symmetry. 



(e) Mg : II u u^ u u u^ u u ii, u u u. 



0\ V V v^ V V I), V V V, V V V. 



This arrangement also possesses either tetartohedral 

 or tetrahedral symmetry. 



(y) M^' : u u u ; u -\- ^, ^ — u, u ; ic, u -\- ^, ^ — ii ; 

 ^ — w, It, i( -{- ^. 

 O : V V v; v -{- ^, ^ — v, v; v, v -\- ^, ^ — v; 

 ^ — V, V, V -}- ^. 



(/) has tetartohedral symmietry. 



There are no space groups which can be specialized to 

 give four sets of two like atoms and consequently (2) is 

 impossible. For a similar reason (4) must be eliminated. 

 There are two ways of meeting (3) : 



(g)Mg:0 0; and ^ ^ 0, 10^,0^^. 



O: ^J-l; and 0^, 4-0 0, i 0. 



(A) Mg: m; and ^ ^ 0, i i, O^h 



O: 0; and i, i 0, 4-0. 



(g) is seen to be identical in position with (c). Both 

 (g) and (h) can be derived from groups of any class of 

 symmetry. 



Assuming that n = 32. — There seems to be no method 

 of deciding between the two possible values of n except 

 one of trial. There are three different ways of arranging 

 thirty-two molecules of magnesium oxide in the unit cell 

 if all of the magnesium atoms are alike and if all of the 

 oxygen atoms are also alike. If some of the chemically 

 lilce atoms are assumed to be different crystallographi- 

 cally, as was just done when n was treated as equal to 

 four, so large a number of possibilities arises that it is 

 not feasible to consider each one in detail. Such arrange- 

 ments are, however, highly improbable. The possible 

 -arrangements corresponding to (1) are as follows: 



