34S R. W. G. Wyckoff — Crystal Structures of 



The conditions of symmetry permit the placing of the 

 carbon atoms either at the corners and center of the nnit 

 or along* the diagonal at u = 14 and u = %, and the con- 

 siderations thus far advanced do not distinguish between 

 these two possible arrangements. This choice cannot be 

 made withont the nse of the relation between mass and 

 scattering power. Bnt by nsing snch a relation and by 

 making photometric measurements of two planes, reflect- 

 ing the same wave length and having the same relative 

 spacing, one plane having h-k + l divisible by four so 

 that the calcium term is added to the carbon term and 

 the other plane having h + ti+l divisible only by two 

 so that the two amplitudes are opposite in sign, the 

 carbon and calcium atoms could be placed with respect to 

 the oxygen atoms. Or planes having the same kind of a 

 sum (h + k + l) but different values of the difference be- 

 tween the two odd indices, that is, divisible by four or two 

 only, might be compared. The same result, however, can 

 be very simply obtained with the spectrometer. This of 

 course has already been done, 27 and, as would be expected 

 from the fact that the forces operating between carbon 

 and oxygen seem much stronger than those between cal- 

 cium and oxygen, the oxygen atoms lie closer to the car- 

 bon atoms. This arrangement was assumed in writing 

 the expressions for amplitude. 



The arrangement of the atoms in the unit of structure 

 (fig. 13) of calcite must consequently be as follows : 



Ca = 1/4 1/4 1/4 ; 3/4 3/4 3/4. 



C =0 0; 1/2 1/2 1/2. 



= u u ; u u ; u u; 1/2 — u, u + 1/2, 1/2 ; u + 1/2, 



1/2, 1/2 — u ; 1/2, 1/2 — u, u + 1/2, where u has a value 

 very close to one-fourth and probably lying somewhere be- 

 tween 0.24 and 0.26. The angle between the axes of this 

 simplest unit is 46° 6' and the length of the side of the 

 unit of structure is 6.16 A. U. 



The unit which has previously been figured 2S is not the 

 simplest unit of structure. Calculations, like those which 

 have just been made, on the basis of such a unit, would 

 have been much more complicated and could not have been 

 carried out so as to place the oxygen atoms uniquely with- 

 out the aid of those uncertain assumptions commonly 



27 W. L. Bragg, op. eit. 



