Dispersion Relations of Optical Phonons Near the Center of Brillouin Zone in Crystals.
Abstract
In this work we have obtained by using grouptheoretical techniques, the dispersion relations of zonecenter optical phonons of all thirty two point group symmetry. A dynamical matrix Hamiltonian is constructed. The LOTO 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT.......139B
 Keywords:

 Physics: Condensed Matter