some 



Carbonates of the Calcite Group. 357 



according to the probability of their occurrences. 41 A 

 knowledge of the crystal structure of a substance fur- 

 nishes the basis for the same sort of discussion. 



Evidence has been adduced to show that the carbon and 

 oxygen atoms in calcite act together in single unit groups 

 and that these groups and the calcium atoms are ar- 

 ranged, as are the atoms in sodium chloride, alternately 

 throughout the entire mass of the crystal. This is the 

 arrangement to be expected if the calcium atoms and car- 

 bonate groups attract one another and at the same time 

 repel like atoms or groups. 



Any plane containing either carbon atoms (as centers 

 of carbonate groups) or calcium atoms, or both, is the 

 plane of a possible crystal face. In general, however, 

 the forces tending to draw a calcium or carbonate particle 

 down upon a face will be greatest for planes that are 

 thickly studded with atoms so that such faces will have 

 the greatest tendency to grow and will, if enough crystals 

 are considered, have the commonest occurrence. 



Those planes having the greatest relative spacing 

 will contain the greatest number of points of the lat- 

 tice. This spacing and consequently the relative density 

 (in atoms) of the various kinds of faces of calcite can be 

 simply obtained by assuming half the points of a rhombo- 

 hedral lattice occupied by carbon, as center of the car- 

 bonate group, and the other half by calcium, by using the 

 kind of expression previously used in the determination 

 of the crystal structures. 42 It can be roughly stated that 

 the simpler the Miller indices of a face, the more atoms it 

 contains per unit area. 



Planes in calcite are of two kinds : some will contain 

 either all calcium or all carbon atoms (that is, carbonate 

 groups), the others will contain both calcium and carbon 

 atoms. Those planes all of whose indices are odd (using 

 the ordinary crystallographic axes) are of the first kind, 

 all others are of the second sort. The essential factor, 

 other conditions being equal, in determining the develop- 

 ment of a face is what seems commonly to have been 

 termed the "pulling down force", that is, the resultant 

 attraction at a point exerted in a direction normal to the 

 plane and towards the face. For planes of the same rel- 

 ative spacing and consequently of the same atom density, 



41 H. P. Whitlock, Proc. Am. Acad. Sci., 50, 289, 1915. 



42 A. W. Hull, op. cit. 



