On the form and energy of crystalline sodium nitrate

Abstract
This paper is a continuation of a former paper, in which the electrostatic potential energy of the carbonate and nitrate crystals of the calcite type was calculated, for a series of values of two parameters which determine the size and shape of the unit crystal cell. In addition to the electrostatic forces of attraction and repulsion between the atomic ions of which these crystals are supposed to consist, there are certain other repulsive forces which will be distinguished by the term “intrinsic.” Since the former paper was written, data concerning these repulsive forces have been published by Lennard-Jones and his collaborators, for many of the ions included in the crystals referred to. The part of the crystal energy which corresponds to these forces can therefore now be calculated in many cases, and, in particular, for the crystals CaCO 3 , MgCO 3 , and NaNO 3 . By mutual arrangement, our values of the electrostatic potential energy for carbonate crystals of the calcite type were communicated to Dr. Lennard-Jones before publication, and he, with Miss Dent, calculated the energy corresponding to the repulsive forces for the series of values of the parameters which we had used. It was thus possible to determine the whole energy of the crystals of CaCO 3 and MgCO 3 , measured relatively to a state of infinite dispersion of the metallic ions and the ionic groups CO 3 – – (as wholes); such values of the energy were found for various configurations, and the stable configuration of minimum energy could be shown to lie on a certain linear series of configurations. The stable configuration cannot be found completely at present owing to lack of knowledge of the forces determining the size of the CO 3 ionic group itself. The parameter in the series of configurations just mentioned is the size of the CO 3 group, as measured by the distance ( b ) from the C to the O ion. The series as determined by Lennard-Jones and Dent did not include the actual measured configuration, but the difference between the measured and nearest calculated configurations was not great, and afforded an estimate of the distance b , viz.. 1·08 Å. In our previous paper we attempted to deduce the value of b without a knowledge of the repulsive forces, by finding the configuration of minimum electrostatic energy in a virtual displacement of the crystal chosen so as to eliminate, as far as possible, any change in the energy corresponding to the repulsive forces. The CO 3 ion was maintained of constant size, and the distance between each oxygen ion and the nearest metallic ion was also kept constant. For such a displacement there will be no change in the energy due to the repulsive force between nearest neighbours among the ions, and since the repulsive forces vary according to a high inverse power of the distance, it was assumed that there would be no change in the total energy of the repulsive forces. The value of b deduced on this assumption was 0·92 Å. The slight difference between this and the value found by Lennard-Jones and Dent is investigated, for the parallel case of NaNO 3 , in 6 of this paper, and found to be due to a slight variation, during the above virtual displacement, in the energy of the repulsive forces between oxygen ions not of the same CO 3 group.

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