146 Wyckoff — Crystal Structure of Magnesium Oxide. 



Possible arrangement (c), 

 A = Mg [l-f-cosTT ?i {h-{-k)-\-cos'7r7i {h-{-l)-{-cos7rn {k-{-l)} 



+ {cOSTT7ll-\-GOS7r9lk-\-COS7r7lh-^COS7r7l {/l-{-k-\-l)] . 



B = 0. Mg and O represent the scattering powers of magnesium 

 and of oxygen respectively. 



In case A, /v, and I are all odd : 



When n = l, A = 4"Mg-40; when ^ = 2, A = 4Mg + 40. 

 In case the indices are tioo of them odd and 07ie eve7i: 



When n=l, Ad:0; when 7i = 2, A = 4Mg4-4 0. 

 In case the indices are two eveyi and 07ie odd : 



AVhen n = l, A = 0; when n = 2, A = 4Mg+4 0. 



The results from the arrangement, which is the 

 ^'sodium chloride arrangement," are seen to be in 

 complete agreement with the experimental data as 

 obtained from the Laue photographs and illustrated in 

 figure 6. 



Possible arrangement (d). 



The calculations show that this arrangement also would 

 have first order reflections only from planes with indices 

 that are all odd. The second of such planes is in this 

 case weaker than the first — a fact which is contrary to 

 the experiment. Grouping (d) consequently must be 

 ruled out of consideration. 



Possible arrangement (e). 



This and the next arrangement, (/), are most simply 

 tested by comparison with the spacing measurements 

 from simple faces (the results to be obtained with the 

 spectrometer or by photographing the spectra). Trial 

 was made by seeing whether values of u and v could be 

 chosen so as to give results which would be in close 

 agreement with those from {c). The reflections to be 

 obtained from the (110) faces serve to eliminate (e). 

 According to the experimental results— from the spectrum 

 measurements and presumably also from the powder 

 photographs— the intensity of the first order reflection 

 from (110) is zero or practically zero. If u and v are 

 the variable parameters for magnesium and for oxygen 

 respectively, then the calculated first order from (110) 

 may be represented by: 



A=Mg{2-f2cos47r2^}+0 j2+2cos4 7rv|-. 

 B=0. 



