Quantitative analysis of the electron paramagnetic resonance spectrum of a uranium(III) compound

Abstract

The fundamental formula of the EPR lineshape of field-swept spectra has been modified for the case of a broad homogeneous line. As a consequence, a new formula has been obtained for the derivative of the absorption. For the case of an inhomogeneous line, the original formula of Pilbrow holds, these formulae lay the basis for the determination of the number of spins by integration of the experimental EPR spectrum. The Pilbrow lineshape theory is then combined with the standard results for a Kramers ion having an effective spin 1/2, an anisotropic g tensor and no hyperfine interaction. The assumption is made that the linewidth in frequency units σ_ν is independent of the orientation. This assumption completes the model specifying the line position, intensity, shape and width for any given orientation. The model thus enables one to simulate a powder EPR spectrum and its derivative knowing the principal values of the g tensor and the linewidth σ_ν. The simulation entails a double integration over the spherical coordinates of the magnetic field in the frame of the principal axis of the g tensor. The number of sampling points for numerical integration is determined as a function of g_x, g_y, g_z and σ_ν. Experimentally the EPR spectrum of a coordination compound of trivalent uranium in powder form, U₃(BH₄)₉(dcc)₂, in which there are two kinds of uranium sites, has been recorded at 10.5 K in X-band. The least-squares fit between the observed and simulated spectra has been achieved using the optimisation software BSOLVE, and excellent agreement was reached with a Laplace–Gauss lineshape. The adjusted parameters for the two uraniums were confirmed by an independent fit based on the least absolute values criterion. Based on the final parameters, the EPR spectrum predicted at higher frequencies is better resolved, whereas the actual resolution of the spectrum at 16 GHz is no better. Finally, the effective magnetic moment is predicted to be slightly above 2.