Symmetry of Energy States in α-LiIO3 Crystals Taking Time-Inversion Invariance into Account
DOI:
https://doi.org/10.15407/ujpe68.6.397Keywords:
crystal lattice dynamics, Brillouin zone, Jones zone, Raman spectroscopy, lithium iodateAbstract
Using the theory of the projective representations of groups, the non-degenerate representations of the wave vector groups at points Г, Δ, and А of the Brillouin zone for the α-LiIO3 crystal have been constructed, and their compatibility conditions have been found. The energy states of the α-LiIO3 crystal at those points are classified taking the time-inversion invariance into account, and their corresponding classification in the large (Jones) zone is provided. Based on experimentally measured first-order Raman spectra, the dispersion curves of phonon branches in the Г−А direction are plotted. Contributions of overtones and components at points Г and А to experimentally recorded second-order Raman spectrum have been discussed; their role in the second-order spectrum formation is associated with the considered features in the phonon state density at those points and the vibrational states of other critical points in the Brillouin zone. It has been concluded that the application of the quasi-molecular approximation is valid, when considering the lattice dynamics of α-LiIO3 crystals.
References
W. Otaguro, E. Wiener-Avnear, C.A. Arguello, S.P.S. Porto. Phonons, polaritons, and oblique phonons in LiIO3 by Raman scattering and infrared reflection. Phys. Rev. B 4, 4542 (1971).
https://doi.org/10.1103/PhysRevB.4.4542
F.E.A. Melo, F. Cardeira, V. Lemos. Raman scattering from three phases in LiIO3. Solid State Commun. 41, 281 (1982).
https://doi.org/10.1016/0038-1098(82)90375-1
D.F. Baisa, O.I. Barabash, V.P. Demyanenko, O.K. Zavadiyeva, G.O. Puchkovska, Yu.O. Frolkov, I.S. Rez. Study of spectral characteristics of hexagonal and tetragonal modifications of lithium iodide. Ukr. Fiz. Zh. 18, 1610 (1973) (in Ukrainian).
K.E. Haller, E.M. Jarvekyulg, L.A. Rebane. Raman spectra and phase transitions in lithium iodate. Fiz. Tverd. Tela 18, 1409 (1976) (in Russian).
Yu.N. Polivanov. Raman scattering of light by polaritons. Usp. Fiz. Nauk 126, 185 (1978) (in Russian).
https://doi.org/10.3367/UFNr.0126.197810a.0185
A. Rozenzweig, B. Morosin. A reinvestigation of the crystsl structure of LiIO3. Acta Crystallogr. 20, 758 (1966).
https://doi.org/10.1107/S0365110X66001804
J.L. de Boer, F. van Bolhuis, R. Olthof-Hazkamp, A. Vos. A reinvestigation of the crystsl structure of lithium iodate. Acta Crystallogr. 21, 841 (1966).
https://doi.org/10.1107/S0365110X66004031
A. Emiraliev, A.G. Kocharov, I.I. Yamzin, V.A. Lyubimtsev. Neurodiffraction refinement of the α-LiIO3 structure. Krystallografiya 18, 1177 (1973) (in Russian).
A. Emiraliev, A.G. Kocharov, I.I. Yamzin, V.A. Lyubimtsev. Thermal parameters of atoms in α-LiIO3. Krystallografiya 21, 391 (1976) (in Russian).
T. Hahn. International Tables for Crystallography. Vol. A. Space Group Symmetry (Reidel, 1983).
V.O. Gubanov, A.P. Naumenko. Forms of normal vibrations of pyramidal molecules and 3 ions. Visn. Kyiv. Univ. Ser. Fiz. Mat. Nauky 4, 342 (1997) (in Ukrainian).
G.L. Bir, G.E. Pikus. Symmetry and Strain-Induced Effects in Semiconductors (Wiley, 1974).
L.D. Landau, E.M. Lifshitz. Quantum Mechanics. NonRelativistic Theory (Pergamon Press, 1981).
M. Hamermesh. Group Theory and Its Application to Physical Problems (Dover Publications, 1989).
G.F. Koster, J.O. Dimmock, R.C. Wheeler, H. Statz. Properties of the Thirty-Two Point Groups (MIT Press, 1966).
H. Poulet, J.P. Mathieu. Vibration Spectra and Symmetry of Crystals (Gordon and Breach, 1976).
S.L. Mayants. Theory and Calculation of Molecular Vibrations (Izd. Akad. Nauk SSSR, 1960) (in Russian).
C. Herring. Character tables for two space groups. J. Franklin Inst. 233. 525 (1942).
https://doi.org/10.1016/S0016-0032(42)90462-9
D.S. Balchuk, M.M. Bilyi, V.P. Gryshchuk, V.O. Gubanov, V.K. Kononov. Symmetry of vibrational modes, timeinversion invariance of energy states, and Raman light scattering in 4h- and 6h-SiC crystals. 1. Classification of energy states in Brillouin zones. Ukr. Fiz. Zh. 41, 146 (1996) (in Ukrainian).
H. Jones. The Theory of Brillouin Zones and Electronic States in Crystals (North-Holland Publishing, 1960).
J.J. Sullivan. Lattice vibrations of wurtzite structure crystals. J. Phys. Chem. Solids 25, 1039 (1964).
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