342 R. W. G. Wyckoff— Crystal Structures of 



Space Group D 5 3d . 



(a) Ca == u 3 n 3 u 3 and u 3 u 3 u 3 . 



C — u' u u' and u' u' u' . 



O — u u 0, u w, u w, u u 0, u w, u u. 



(b) Ca and C same as (a). 



O = u u 1/2, u 1/2 u, 1/2 u u, u u 1/2, 

 u 1/2 w, 1/2 w u. 



(c) Ca and C same as (a). 



O = u u v, u v u, v u u, u u v , u v w, v u u. 



(d) Ca and C same as (a) 



u"u"u" , u"u"n" ; u x u x u x , ufauj u 2 u 2 u„ ufifi^ 



(e) Ca and C same as (a). 



O - 1/2, 1/2 0, 1/2 0; 1/2 1/2, 

 1/2 1/2 0, 1/2 1/2. 



Space Group D 6 3d . 

 (/) Ca = 1/4 1/4 1/4, 3/4 3/4 3/4, or 0. 1/2 1/2 1/2. 

 C = , 1/2 1/2 1/2, or 1/4 1/4 1/4, 3/4 3/4 3/1. 

 O = 1/4 3/4 3/4, 3/4 3/4 1/4, 3/4 1/43/4, 1/4 3/4 1/4, 

 3/4 1/4 1/4, 1/4 1/4 3/4. 

 (g) Ca and C as in (f). 



O = u u 0; u u\ u u\ 1/2 — u, w + 1/2, 1/2; 

 u + 1/2, 1/2, 1/2-w; 1/2, J/2-w, w+1/2. 

 (h) Ca and C as in (f ). 



O = u u 1/2; u 1/2 u; 1/2 u u\ 1/2- w, w + l/2, 0; 

 w + 1/2, 0, 1/2-w; 0, 1/2-w, w+1/2. 



All but a very few of the planes that are reflecting in 

 the first order have indices that are two odd and one even. 

 This fact points clearly to a body-centered structure for 

 calcium carbonate. None of the arrangements developed 

 from the space group D ft 3d is body-centered. Also any ar- 

 rangement which might conceivably be built up from D a 3d 

 to contain the necessary mass would give reflections from 

 different planes which would be strongly affected by the 

 value of h + Jc + I ; such a state of affairs is contrary to 

 experimental results. Consequently it may be concluded 

 that the space group of calcite is D\ . 



The intensity of reflection by a plane whose Miller in- 

 dices are h, h, I can be represented as proportional to the 

 following expression: 



1 



Intensity x /(^ « 



p m cos 2irn (hx m + 7cy m + ls m ) + 



J 



p m sin 2t™ (hx m +ky m + lz m ) 



