Diamagnetic anisotrophy of crystals in relation to their molecular structure

Abstract

In order to determine the fine structure of molecular crystals by means of a Fourier analysis of X-ray data, it is usually necessary that the configuration and orientation of the molecules should be known with considerable accuracy. Only in a few cases can this information be obtained directly from the X-ray data. Typical examples of crystals for which this has been done are hexamethylbenzene and cyanuric triazide, both layer lattice structures, and hexamethylene tetramine in the crystal of which the molecule itself possesses high symmetry. In other cases, e. g ., anthracene, naphthalene, etc., the “trial and error” structure has been obtained by an intensive study of the X-ray data, a difficult problem involving much expenditure of time and trouble. Any independent physical methods which indicate the approximate orientation of the molecules in the crystals are therefore greatly to be welcomed. Krishnan and his collaborators, in a series of recent papers, have emphasized the fact that a knowledge of the optical and diamagnetic anisotrophy of the crystal may, in favourable cases, give very direct information concerning the shape and orientation of the molecules. They point out also that, given the diamagnetic anisotrophy of the crystal and the accurate orientation of the molecules in the crystal, the principal diamagnetic susceptibilities of a single molecule can be directly calculated. It is important, therefore, that the exact mathematical relationship between the crystal and molecular diamagnetic susceptibilities and the molecular orientations relative to the crystal axes should be correctly formulated. Triclinic System The triclinic system is in one sense the most complicated and in another the simplest of all the classes. The directions of the three principal diamagnetic susceptibilities, x 1 , x 2 , x 3 , do not bear any simple relationship to the crystal axes and must therefore be located by experimental investigation; but, on the other hand, since the unit cell contains but one or perhaps two molecules centrosymmetrically arranged, the connexion between molecular and crystal anisotrophy is a very simple one.