Franz Wegner 2007 J. Phys.: Condens. Matter 19 406218 doi:10.1088/0953-8984/19/40/406218
Franz Wegner
Show affiliationsThe 'rigid-unit mode' (RUM) model requires unit blocks, in our case tetrahedra of SiO4 groups, to be rigid within first order of the displacements of the oxygen ions. The wavevectors of the lattice vibrations, which obey this rigidity, are determined analytically. Lattices with inversion symmetry yield generically surfaces of RUMs in reciprocal space, whereas lattices without this symmetry yield generically lines of RUMs. Only in exceptional cases such as in β-quartz does a surface of RUMs appear, if inversion symmetry is lacking. The occurrence of planes and bending surfaces, and straight and bent lines, is discussed. Explicit calculations are performed for five polymorphs of SiO2 crystals.
63.20.-e Phonons in crystal lattices
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
Issue 40 (10 October 2007)
Received 29 March 2007, in final form 22 August 2007
Published 12 September 2007
Franz Wegner 2007 J. Phys.: Condens. Matter 19 406218
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