UBC Theses and Dissertations
Some experimental and theoretical studies of magnetic properties.of solids Wong, Samuel Kim Po
This thesis is concerned with three aspects of magnetic properties in solids. 1. The mean square value <I(I + 1)> of the proton angular momentum per molecule has been measured to be 3.73 ± 0.18 in solid CH₄ at 4.2 K . The experiment was done by measuring the ratio of the proton magnetic resonance free induction decay signal to that of ¹³C at the same frequency in a sample containing 53% ¹³CH₄ . The measured value of <I(I + 1)> differs appreciably from the high temperature value of <I(I + 1)> =3 and from the value of <I(I + 1)> = 6 when all the molecules are converted into the A spin symmetry species. Experiments at lower temperatures using a sample containing 0.002% O₂ impurity indicated that there may be a slight increase in the value of <I(I + 1)> between 4.2 K and 2.45 K . The presence of 0.05% O₂ impurity shortened the time constant for conversion of CH₄ between different symmetry species. The interpretation of measurements of <I(I + 1)> in the presence of large amounts of O₂ impurities is complicated by changes in the NMR line shapes. These complications are discussed in terms of the theoretical results obtained in the second part of the thesis. 2. The NMR line shape inhomogeneously broadened by paramagnetic impurities in solids was investigated theoretically using the statistical method of Margenau. The general expression for the Fourier transform of the line shape function was derived. The lattice can be divided into an inner spherical cut-off region and its complement. Impurities inside the cut-off region give rise to satellite lines and impurities outside determine the shape of the main line and satellite lines. Detailed numerical calculations were performed for a f.c.c. lattice when the impurities are (a) classical magnetic dipoles, (b) spin 1/2 systems and (c) spin 1 systems. An asymmetry in the line shape is predicted at finite temperatures. The peak intensity is shifted from the centre by an amount linear in the impurity concentration and in the magnitude of the magnetic moment and the overall line shape adjusts itself in such a way to give a vanishing first moment about the centre. The line shape is always Lorentzian at the centre and Gaussian in the wings. It depends on the impurity concentration. At low concentrations, the main line and the satellite lines have the same shape which is predominantly Lorentzian. The shape of a powdered sample is also discussed. 3. General expressions are derived for the first two terms in the expansion of the specific heat of a paramagnetic salt in powers of T⁻¹. It is assumed that the interaction between the paramagnetic ions consists of magnetic dipole and isotropic exchange interactions, and that the g-tensor of each ion is axial and has the same orientation for all ions. The general formulae are evaluated numerically for cerium magnesium nitrate. Comparison with the experimental data of Mess and coworkers indicated that the exchange parameter corresponds to a ferromagnetic interaction.
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