DISPERSION RELATIONS OF OPTICAL PHONONS NEAR THE CENTER OF BRILLOUIN ZONE IN CRYSTALS
Abstract
In this work we have obtained by using group-theoretical techniques, the dispersion relations of zone-center optical phonons of all thirty two point group symmetry. A dynamical matrix Hamiltonian is constructed. The LO-TO splitting is included in all cases as an empirical Hamiltonian; this is added to the dynamical matrix Hamiltonian. The dynamical matrix is expanded in power series of wavevector q. We find that linear terms (terms proportional to q) occur in E phonons of crystals belonging to point groups C(,3), D(,3), C(,4), D(,4), C(,6) and D(,6), and in F phonons of crystals belonging to T and O. These groups do not contain reflection or inversion operations. In order to calculate terms quadratic in q we have divided the 32 point groups into seven crystal systems, namely: triclinic, monoclinic, orthorhombic, trigonal, tetragonal, hexagonal and cubic systems. We have found that in the doubly degenerate E phonons of the above mentioned crystals only the component of q along the optic (Z) axis admits a linear splitting. For the triply degenerate F phonons of crystals belonging to groups T and O the linear splitting, as well as the LO-TO splitting, is isotropic. Finally, experimental studies of Raman spectra of (alpha)-quartz (D(,3) symmetry) and Bi(,12)GeO(,20) (T symmetry) are reported.
Degree
Ph.D.
Subject Area
Condensation
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