178 R. W. G. Wychoff — Determination of the 



be obtained from atoms arranged according to the 

 general positions of any one of the space groups can be 

 readily calculated with the aid of the customary intensity 

 expression : 



I OC / (^\[A*+B*l where 



A = ^d [<r m co&%irn(hx m +ki/ m -\-lz m )], [1] 



m 



and B is a similar sine term. In this expression 8 1 is the 

 intensity and n is the order of reflection from a plane 

 whose Miller indices are (hM) ; x m ,y m ,z m are the coordi- 

 nate positions of each of the m atoms (within the unit) 

 over which the summation is to be extended and o- m is the 

 scattering power of the atom m. The value of 



/fir) 



where d hkl is the spacing of the plane (hhl), need not be 

 evaluated for the present purposes. If these diffraction 

 effects are calculated for each of the space groups it 

 is found that for some of them reflections from certain 

 classes of planes in some orders will be entirely absent. 

 Such a complete absence of definite classes of pLanes, 

 different for different space groups, makes it possible to 

 distinguish between these groups. 



As an example of the mode of procedure a common 

 space group, T h 6 , the sixth group having paramorphic 

 hemihedral (pyritohedral) symmetry, will be considered 

 in detail. The coordinates of the most generally placed 

 equivalent points within a unit cube for this space group 

 are 



xyz; x + %, \—y , z; x,y+i, \—z\ i—x, y, z+\ 

 zxy; z, a?+£, |— y; %—z, x, y+$; z + i, \—x, y 

 yzx; %—y, z, x + %; y + i, £— «, as; y, £+^, \—x 

 xyz; \—x, y+i, z\ x, $ — y, z+i; x+%, y, \—z 

 zxy; z, i—x, y+i; z+i, x, \ — y; \—z, x+\, y 

 yzx; y+i, z, \—x\ f— y, z + $, x) y, \—z, x+\. 



Taking for the present purposes the scattering power 

 (o-) of atoms in these general positions as unity and divid- 



8 Kalph W. G. Wyckoff, this Journal, 50, 317, 1920. 



