Exact analytical solution for the powder pattern of orthorhombic-g systems. Predicted EPR powder spectrum and application to powder TiO2 : Cr3+ in the rutile phase

Abstract

An exact analytical solution for the powder pattern of an ion with orthorhombic effective g factor is found by use of the isotimic method. Theoretical first-derivative powder EPR spectra are obtained by convoluting the product of the analytic powder pattern and the transition probability, at the sites of the main spectral features, with first-derivative Lorentzian lineshape functions of constant-in-field and constant-in-frequency widths. The calculation is made in a PC capable of handling the MATHEMATICA program. The EPR spectrum of powder TiO₂ : Cr³⁺ in the rutile phase, which is assumed to be composed of two orthorhombic g spectra, is interpreted through these results. Unambiguous assignments of five of the six anisotropic g parameters are made from the five features composing the observed orthorhomic g powder spectrum. These are g_z= 5.04, g_y= 2.63, g_x= 1.64 and g′_z= 5.82, g′_y= 1.33. The value of g′_x= 1.14 which corresponds to a spectral feature not yet observed in the spectrum is deduced from the others by means of the existing theory for g values arising from Kramers doublets. Boltzmann factors of the populations giving rise to the two spectra are deduced from line-intensity measurements. Theoretical powder EPR spectra of the two orthorhombic-g systems calculated with the above six g values and Boltzmann factors are compared with experiment for the different kinds of Lorentzian lineshape functions employed. This suggests that a broadening of the elementary lineshape function is responsible for the dissapearance of the feature at H(g′_x)= 597 mT.