On the electrostatic potential energy, and the rhombohedral angle, of carbonate and nitrate crystals of the calcite type

Abstract

1.1. This paper is a sequel to, and an extension of, one with a somewhat similar title by W. L. Bragg and S. Chapman, in which it was shown that, on certain natural assumptions, the rhombohedral angle could be calculated for the well-known isomorphous series of carbonate crystals of the calcite type. The detailed results and the method of calculation were not described. This is done in the present paper, where also the results of a parallel calculation for a similar possible series of nitrate crystals is given; the only known nitrate crystal of this type, however, is that of sodium, the corresponding potassium salt crystallising in the aragonite form. 1.2. As the underlying principles of the method have been described in the paper cited, they need only receive brief mention here. The crystals considered are supposed to consist of positive and negative ions, namely, metallic ions (doubly charged, like Ca ++ in the carbonate series, or singly charged like Na + in the nitrate case), and ionised groups CO 3 -- ( i. e. , C ++ ++ , O -- , O -- , O -- ) or NO 3 - ( i. e. , N +++ ++ , O -- , O -- , O -- ). The detailed arrangement of these groups is described in § 2.4, but if the CO 3 or NO 3 groups are treated as wholes, the arrangement of the positive and negative ions is similar to that of the ions in a simple cubic crystal of the rock-salt type, except that the cubic lattice is contracted—into a rhombohedral lattice—parallel to one diagonal; this diagonal thus becomes the trigonal axis of the crystal. The edges meeting in the trigonal axis are inclined to one another at an angle (the “rhombohedral angle”) of about 102°, instead of 90° in the case of rock-salt.