242 Wyckoff — Crystal Structure of Alahandite. 



The symmetry of this arrangement is tetartohedral. It 

 may be noted that arrangements (II) and (III) are 

 special cases of this arrangement. 



Thirty tivo Molecules in the Unit. — It has already been 

 shown in the course of the treatment of a somewhat simi- 

 lar case^ that with the present lack of precise knowledge 

 concerning the mechanism of scattering it is impossible 

 to rule out with certainty the complicated structures 

 having thirty- two molecules associated with the unit cell. 

 Such an elimination is equally impossible in the present 

 instance. It consequently becomes necessary, for the 

 present at least, to make the assumption that the 

 correct structure is simple. In this case it is to be 

 assumed that four molecules of MnS are to be associated 

 with the unit. 



The Choice of the Correct Structure for Alahandite, — 

 The expression 



I (X 





(3) 



(where I is the intensity of reflection, f{d/n) is some 

 function of the spacing between like planes of atoms, and 

 o-,. , the scattering power of the atom r for X-rays, seems 

 to be roughly proportional to the atomic number, the 

 summation is to be carried out over each of the atoms 

 (coordinates=^^^) within the unit cube), has been used 

 to obtain a measure of the intensit}^ of reflection to be 

 expected from any plane {hhl) for any conceivable 

 arrangement of atoms within the unit cell of a crystal. 



The two arrangements (II) and (III) are in a sense 

 limiting structures for the less simple ones (I) and (IV) ; 

 thus, (II) results from (I) by assigning to u and u' the 

 values 14 and % (and for convenience in computation 

 transferring the origin to the point (%%%)). Similarly 

 both (II) and (III) arise from (IV) by assigning to u 

 and u' the values and % for (II) and for (III) the 

 values and 14. These two limiting cases, (II) and (III), 

 can be most simply distinguished in their diffraction 

 effects by a consideration of the reflections from the 

 plane (111) ; the simplest plane all of whose indices are 



" Ealph W. G. Wyckofe, this Journal, 1, 138, 1921. 



