Theoretical and experimental studies in electron paramagnetic resonance II : an investigation of the ground state splitting of the Gd3+[4f7, 8S7/2] ion in lanthanide ethylsulphates and the design of l-8GHz coaxial electron paramagnetic resonance spectrome
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1972
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Abstract
Consistently normalized tensor operators T(J) expressed in terms of the angular momentum i are introduced to facilitate the analysis of EPR spectra. The various mathematical relationships involving these tensor operators necessary for their application in EPR spectral analyses are derived and tabulated. The tensor operator techniques of Racah (1942) were also employed to calculate the matrix elements of various interactions including the spin-orbit coupling in a crystalline electric field. These matrix element calculations facilitate theoretical investigations of the ground state splitting of Gd 3 in crystalline electric fields. An iterative, convergent computing procedure has been developed for determining from experimental EPR spectra the best-fit parameters in a generalized spin-Hamiltonian of arbitrary complexity. This procedure requires a high-speed digital computer and employs a least-square fit criterion and exact diagonalization of the spin-Hamiltonian secular matrix. The 1-8GHz, 10GHz and 35GHz EPR spectrometers employed to perform the measurements reported in this thesis are described. The 1-2GHz and 2-4GHz coaxial EPR spectrometers were designed for the direct determination of the ground state splitting of Gd 3+ in the ethylsulphate lattice and involved unique features. The ground state splitting of the Gd 3 {4f 7,8S712 } ion in the ethyl sulphate lattice has been investigated systematically using both conventional and weak magnetic field-sweep variable-frequency EPR spectroscopy. This splitting has also been calculated theoretically using various mechanisms based on the ionic model. The results of these studies showed that all these perturbation mechanisms are inadequate to explain this splitting. The generalized spin-Hamiltonian parameters of Gd 3 in lanthanum ethyisulphate (LaES) were determined from 290K, 35GHz EPR spectra. The parameters associated with a third- or higher-rank spin tensor operator are found to be six orders of magnitude smaller than the g-factor. Precision measurements and analyses have been made of 290.5K, 10GHz EPR spectra of the Gd 3 ion dilutely substituted ( 5:l0) into the C 3 site symmetry of the lanthanide host lattices Ln(C 2H5SO 4 )3.9H 20 where Ln La, Ce, Pr, Nd, Sm, Eu, Tb, Ho, Er, Tm, Yb and Lu as well as Y which is chemically lanthanide-like. It is found that empirical linear relationships exist between the spin-Hamiltonian parameter B1320 of Gd 3+ . and (i) the ionic radius of the lanthanide host; (ii) the unit cell dimensions of the host lattice; (iii) the molar volume of the host lattice; and (iv) the estimated crystal field parameter A<r 2>Gd . A similar linear relationship is found between the ionic radius of the lanthanide host and the spin-Hamiltonian parameter B60 , but not B40 . The 8s71.2 ground state splittings of Gd 3 in LaES have been determined directly using weak magnetic field-sweep variable-frequency EPR spectroscopy. These directly determined splittings were measured in single crystals of LaES doped with 0.5 and l.0(at)% Gd 3 impurity at 290.5 and 77K to a high accuracy of ± 0.1MHz. It is discovered that the J± ½> doublet of the 8S 7 /2 state of Gd 3+ in LaES sp lits anomialously n zero external magnetic fields. This anomalous splitting is found to be (16.60 ± l.0)MHz at 290.5K and (11.15 ± l.0)MHz at 77K. It is shown that spin-spin interaction can produce this type of splitting.
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Bibliography: p. 157-165.
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Shing, Y. H. (1972). Theoretical and experimental studies in electron paramagnetic resonance II : an investigation of the ground state splitting of the Gd3+[4f7, 8S7/2] ion in lanthanide ethylsulphates and the design of l-8GHz coaxial electron paramagnetic resonance spectrome (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/19704