148 WycJcoff — Crystal Structure of Magnesium Oxide, 



reflection from sucli a plane unless u and v have values 

 such that the arrangement becomes identical with {c). 

 If, however, u and v have values close to, but not equalling 

 the coordinate positions of (c), then the intensity of 

 reflection in this type of plane would be small enough to 

 escape detection with the insensitive methods of obser- 

 vation that are now available. There is, consequently, 

 no way to rule this arrangement completely out of consid- 

 eration. It is, however, improbable because magnesium 

 oxide itself gives no indications of tetartohedral sym- 

 metry. 



Possible arrayigement (g). 



Since the positions of the atoms are the same as in the 

 case of (c), it also fits the X-ray data. 



Possible arrangement (h). 



The reflections from planes all of whose indices are 

 odd and from those having one even and two odd indices 

 as calculated from this grouping are in agreement with 

 the experimental results. The amplitude of the reflection 

 in the first order for the planes having one odd and two 

 even indices is not, however, equal to zero for this 

 arrangement. 



A=:20- 2Mg, B = o. 



Since no such planes are found in the first order region 

 from the Laue photographs, this grouping may be 

 eliminated. 



Possible arrangement (i). 



If the origin is moved to the point (Vg Vs Vs), this 

 arrangement is seen to be identical in the present instance 

 with (c). 



Possible arrangement (j). 

 Writing a = h^h^l, b=h-k-l, c=k-h-l, d=l-h-k, then 



A = Mg52cos27rm^a-{-2cos27rr<w^-j-2cos27rnwc+2co827r>zw(? 

 -f2cos2 7^?^ [wa+i (A+^-)] -f2cos2 7rn [ub-^^ (A+A;)] 

 +2cos2 7r?i [wc + l {h-]-k)] -f2cos2 7r7z [ud-\-^ (A+/;)] 

 + 2cos2 7r/z [ua^\ (^+0] +2cos2 7r?i [ub^^ {h-\-l)'] 

 + 2cos2 7rn \itc-\-^ [f^-^iy] +2cos2 7r72 \ud-\-\ {h^l)'] 

 +2cos2 TT/i [iia^\ (^+0] +2cos2 7r72 \:itb-\-^ (^'+0] 

 + 2cos2 7r?i [iic-\-^ (^+0] H-3cos2 7r?i [ud-^^ {>^+^)] 

 + 0{a similar term in v]. 

 B = in the cases to be considered. 



