358 R: W. G. Wyckoff— Crystal Structures of 



those having- all odd indices would clearly exert much the 

 stronger attraction for atoms of the opposite sort than 

 those composing the plane itself. 



From these considerations, then, it should be possible 

 to arrange the possible planes of calcite in the order of 

 their tendencies to grow and hence, presumably, of their 

 relative occurrences under comparable conditions. In the 

 actual growth of crystals, other factors have been shown 

 to have very marked effects, notably the fact that the 

 faces are probably not truly plane for atomic distances 

 but may be many layers thicker at one point of a face than 

 at another, convection currents in the mother liquor, and 

 foreign substances dissolved in the mother liquor which, 

 by their presence, change the surface tension of the 

 solution with respect to the various faces. The natural 

 crystals that have been observed have come from so rela- 

 tively few localities and have grown under such uncertain 

 conditions that an arrangement in the order of the occur- 

 rence of their faces based upon any simple considerations 

 can be expected to be only roughly fulfilled. As nearly 

 as can be determined, however, the development of the 

 faces on crystals of calcite is in general agreement with 

 the point of view outlined above. A criterion is inci- 

 dentally furnished for discussing the cases of doubtful 

 planes as well as the proper set of indices to be ascribed 

 to rare planes where several sets are possible. Of course, 

 the crystallographic relationships are most conveniently 

 expressed in the Bravais-Miller indices and it may be 

 said that that plane, of several possible planes, is most 

 probable which will give upon transformation the simplest 

 Miller indices. This test is in a sense the reverse of 

 that previously used to establish the rhombohedral char- 

 acter of the fundamental lattice. It is quite as useful but 

 not, however, as sharp a test in the present case as it was 

 before, because much more complicated planes are found 

 as faces than commonly give X-ray reflections. 



In the present instance the cleavage plane (100) is the 

 one of greatest atom density. That this condition alone 

 does not determine the direction of cleavage, however, is 

 made clear by the fact that diamond and zinc sulphide, 

 both with the same crystal structures, have, one of them 

 octahedral, the other dodecahedral, cleavages. Two fac- 

 tors seem to be of importance in determining cleavage: 

 the resultant attraction at any point in the plane and the 



