As a precursor to the ESR and relaxation studies, measurements of the dielectric constants and loss for pure single crystals of calcium tungstate have been made at 1 MHz and room temperature giving values of e (_a) - 11.3 ± 0.4, e (_c) = 9.1 + 0.4 and 5 x 10 (^-3) which agree closely with Grower and Fang’s. Our measurements were extended to frequencies up to 80 MHz and to samples doped with neodymium and gadolinium. A detailed investigation has been made of the splitting of the ESR transitions in low concentration Gd (^3+) / CaWO (_4) reported first By Buckley in 1973; this has led to the proposition of an ordered oxygen vacancy model giving rise to two slightly different Gd environments in both of which Gd substitutes for Ca at calcium sites. Sources for anomalies in the ESR spectra of rare earth ions in scheelite are briefly discussed. Spin-lattice relaxation measurements for Gd (^3+) / CaWO (_4) were carried out at 37.5 GHz and in the temperature range from 4.2 K to 30 K. The relaxation in the 'direct' region agrees with preliminary measurements reported by Thorp et al, 1974, i.e. T (_1) = 5.8 m sec at 4.2 k. The change from direct to Raman behaviour occurs near 8 K, and between 8 K and 30 K a T (_1) a T (^-3) law. This behaviour in the higher temperature range is explained by the assumption of crystal imperfections. Measurements of spin-lattice relaxation were also made for Fo (^3+) / MgO in the same temperature range; here a T (^4.6) variation was found in the Raman region and the transition temperature between the direct and Raman processes was about 20 K. The data provided another example of an S-state ion behaving in the manner predicted by the present theories of relaxation. In the last chapter an account is given of the combined use of ESR and TEM (Transmission Electron Microscopy) techniques, in an investigation of the role of Impurities (mainly iron) in the growth of cavities in neutron-irradiated magnesium oxide crystals
