A theoretical investigation of the nuclear resonance absorption spectrum of spodumene

The interaction of nuclei of spin I>½ and non-vanishing quadrupole moment with their surroundings in a crystal consists of two parts: magnetic and electrostatic. In the absence of any external field, the interaction is mainly the quadrupole interaction of the nuclei with the electric field gradient of the crystal, since the crystalline magnetic field is often small and contributes only to the broadening of the quadrupole lines. When an external magnetic field is added, a Zeeman affect is introduced and both interactions are present at the same time. In this thesis a study is made of the resonance absorption spectrum of a nucleus subjected to both fields when the ratio of the two interaction energies assumes any given arbitrary value. After a brief survey of the theory of both interactions, and the various perturbation approximations, the problem for a nucleus of spin I= 5/2 is stated explicitly and a brief analysis shows that the solution is particularly simple in the cases where the external magnetic field coincides with one of the principal axes of the electric field gradient. For other directions of the magnetic field, the problem cannot be simplified in any obvious way and leads to much longer numerical calculations. The problem is completely solved numerically in a special case for A1²⁷ in a spodumene crystal for one particular crystal orientation, but over the entire experimentally interesting range of the external magnetic field so as to fit directly the conditions of an experiment proposed in Dr. Volkoff's laboratory in order to aid in the evaluation of its feasibility. The expected variation of the frequencies and the relative intensities of the resonance lines as a function of the applied magnetic field is exhibited in a series of graphs.Science, Faculty ofPhysics and Astronomy, Department ofGraduat