Theoretical calculation of the rhombohedral angle of crystals of the calcite type

Abstract

1. Calcite, one crystalline form of calcium carbonate, possesses symmetry the trigonal-scalenohedral class. It is a typical member of a well-known amorphous series, which includes the carbonates of magnesium, calcium, manganese, iron, cobalt, nickel, zinc and cadmium, as well as the double carbonate dolomite of magnesium and calcium. The crystals can be referred three equal axes making an angle α with each other, this angle α being about 2°. The cleavage takes place along the plane (100). Several of the crystals have been analysed by X-ray methods, and the arrangement of the atoms determined. The structure may be conveniently regarded as based on a ombohedral space-lattice whose axes are parallel to the edges of cleavage ombs of the crystal. Each cell of the lattice contains four CaCO 3 groups; figure illustrating the structure will be found in the paper referred to above. The crystal of calcite is composed of positive and negative ions, these being calcium ion Ca ++ and the ionized group CO 3 - - . Each calcium ion is surrounded symmetrically by six CO 3 groups, and each group by six calcium ons. The marshalling is similar to that of the positive and negative ions a simple cubic crystal of the rock-salt type, but the replacement of a spherically symmetrical ion by a flattened group such as CO 3 -- has apparently caused a distortion of the structure from a cubic to a rhombohedral form, The distortion consists in a compression of the cube along a trigonal axis, which all the CO 3 groups are perpendicular, until the edges meeting in the rigonal axis make an angle of about 102° with each other in calcite, as against 0° in rock-salt. The following table gives the molecular volume, axial ratio, hombohedral angle “α” and length of side “ b ” of the unit rhomb containing our molecules, for each member of the series.