First Advisor

Jack S. Semura

Term of Graduation

Spring 1975

Date of Publication


Document Type


Degree Name

Master of Science (M.S.) in Physics






Crystals -- Defects



Physical Description

1 online resource (ix, 80 pages)


We examine the problem of the dynamics of a hexagonal close packed crystal with a single substitutional impurity. The effects of the mass and the force constant changes due to the introduction of the impurity atom are taken into account assuming nearest neighbor interactions under the harmonic approximation. Using Green’s function and group theoretical methods, the equations of motion for the perturbed normal modes are obtained in an exact form. The calculations are performed by allowing for very general force constant changes which can have noncentral as well as central contributions. Further, by assuming central forces, we simplify the equations of motion for the nondegenerate perturbed normal modes in which the impurity atom participates and obtain the condition for the occurrence of a resonance or a localized mode, the defect amplitude of vibration, and the defect mean square displacement. The analytical expressions obtained in the central force approximation are of the same forms as those expressions obtained by Mannheim and Cohen for cubic systems.


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