18& R. W. G. Wychoff — Cryst alio graphic and 



lated for the simple body-centered arrangement, (1), it 

 would be anticipated that the correct structure approxi- 

 mates it quite closely. Inspection, however, shows that 

 none of the arrangements can be made to approach this 

 grouping of atoms. To discuss satisfactorily the diffrac- 

 tion effects from each of these possibilities it is necessary 

 to assign to each of the variable parameters a range of 

 values covering the entire unit cell and to calculate there- 

 from the intensities of reflection from various planes. 

 These rather laborious calculations can be carried out 

 with the aid of a graphical method which is an obvious 

 extension of that one previously used in discussing the 

 various possible arrangements for the atoms in periclase 

 (MgO). 8 A rigorous treatment of these arrangements is 

 scarcely attainable because of the somewhat qualitative 

 character of diffraction data and of the assumptions upon 

 which their discussion is based. It can, however, be 

 shown that none of these arrangements will furnish rea- 

 sonable structures which can account for the observed 

 diffractions. 



Such, then, are the results which lead to the impasse 

 outlined in the introduction to this paper. The simple 

 structure which is in agreement with the X-ray data is 

 possessed of a tetrahedral hemihedral symmetry while the 

 crystallographic information points to an enantiomorphic 

 hemihedry. There is, furthermore, no chemically per- 

 missible arrangement of atoms, no matter how compli- 

 cated we may wish to choose it, which will account for 

 these diffraction data and will be capable of possessing in 

 any way an enantiomorphic hemihedry. 9 



The issue thus appears to be sharply drawn. If pre- 

 vious observations upon crystals of ammonium chloride 

 are correct in giving it pentagonal icositetrahedral faces, 

 there seems to arise some uncertainty as to the value of 

 the symmetry assignments commonly made by crystal - 

 lographers upon their interpretations of face develop- 

 ment. The more or less obvious interpretation of the 

 sides of etch-figures as solution faces upon a crystal leads, 

 in its application to the present case, to the same con- 

 clusion. An attempt to account for this discrepancy by 



8 Kalph W. G. Wyckoff, this Journal, 1, 138, 1921. 



e This statement is true no matter what symmetry characteristics may be 

 assigned to the constituent atoms. 



