The Effect of Crystalline Electric Fields on the Paramagnetic Susceptibility of Cupric Salts

The paramagnetic susceptibility of the cupric ion in the hexahydrate sulphates Cu${\left(\mathrm{N}{\mathrm{H}}_4\right)}_2$ ${\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$: 6${\mathrm{H}}_2$O and Cu${\mathrm{K}}_2$ ${\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$: 6${\mathrm{H}}_2$O has been computed on the assumption that the crystalline field has monoclinic symmetry but deviates only slightly from cubic symmetry. The computed variation of the magnitudes of the principal susceptibilities with temperature agrees with the data over the limited range of experimental measurements. The mean susceptibility should follow quite closely the simple formula $\chi =\frac{A}{T}+B$, even if the individual susceptibilities do not. This agrees very well with the observations of de Haas and Gorter on the mean susceptibility of CuS${\mathrm{O}}_4$: 5${\mathrm{H}}_2$O for the temperature range 14°K to 290°K. In a rhombic field, such as was previously used by Schlapp and Penney for calculations on ${\mathrm{Co}}^{++}$ and ${\mathrm{Ni}}^{++}$, the directions of the principal magnetic axes are independent of temperature, while the more general monoclinic field gives a rotation of the magnetic axes as the temperature is varied. The calculated variation of the direction of the principal axes with temperature in ${\mathrm{Cu}}^{++}$ is in qualitative accord with the observations of Bartlett, but the numerical agreement is not very good. The introduction of an exceedingly asymmetrical diamagnetic correction greatly improves the agreement for the potassium salt, but more likely, the large rotations observed by Bartlett are due to allotropic changes, since the temperature range is not far below the temperatures at which dehydration and decomposition take place. From the choice of parameters which give agreement with the magnetic data, conclusions are drawn about the structures of these crystals.