Abstract
Starting from a sterical hindrance potential for the motion of the NO2-molecular group in the deformable cage of neighbouring Na-ions, we derive a microscopic model for the NaNO2 crystal in the paraelectric phase. The dynamical variables are the translational displacements of both the NO2-groups and the Na-ions, and the reorientations of the NO2-groups. Reorientations are described by means of symmetry adapted functions. From a numerical study of the model, we conclude that reorientations of the NO2-groups take place essentially through rotations about the crystallographicc-axis. The model explains why optical experiments have led to the incorrect conclusion of reorientations about thea-axis. By studying the symmetry properties of the bilinear coupling of translations and rotations, we separate optical and acoustical displacements. Only the former couple to the order parameter in the long wavelength limit. Therefore there is no acoustical soft mode at the ferroelectric phase transitions. The bilinear coupling leads to an effective lattice mediated interaction among reorienting NO2-groups.
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References
Sawada, S., Nomura, S., Fuji, S., Yoshida, Y.: Phys. Rev. Lett.1, 320 (1958)
Lines, M.E., Glass, A.M.: Principles and applications of ferroelectrics and related materials. Oxford: Clarendon Press 1977
Tanisaki, S.: J. Phys. Soc. Jpn16, 579 (1961)
Yamada, Y., Shibuya, L., Hoshino, S.: J. Phys. Soc. Jpn18, 1594 (1963)
Hoshino, S., Motegi, H.: Jpn J. Appl. Phys.6, 708 (1967)
Janssen, T., Janner, A.: Ferroeleclrics24, 11 (1980)
Kucharczyk, D., Pietraszko, A., Lukaszewicz, K.: Ferroelectrics21, 445 (1978)
Böhm, H.: Z. Kristallogr. Mineral.148, 207 (1978)
Yamada, Y., Yamada, T.: J. Phys. Soc. Jpn21, 2167 (1966)
Dolling, G., Sakurai, J., Cowley, R.A.: J. Phys. Soc. Jpn28, Supplement, 258 (1970)
Sakurai, J., Cowley, R.A., Dolling, G.: J. Phys. Soc. Jpn28, 1426 (1970)
Cochran, W.: Adv. Phys.9, 387 (1960)
Cowley, R.A.: Phys. Rev. Lett.9, 159 (1963)
Vogt, H., Happ, H.: Phys. Status Solidi16, 711 (1966)
Axe, J.D.: Phys. Rev.167, 573 (1968)
Barnoski, M.K., Ballantyne, J.M.: Phys. Rev.174, 946 (1968)
Hatta, I., Sakudo, T., Sawada, S.: J. Phys. Soc. Jpn21, 2162 (1966)
Michel, K.H., Naudts, J.: Phys. Rev. Lett.39, 212 (1977); J. Chem. Phys.67, 547 (1977)
Press, W., Hüller, A.: In: Anharmonic Lattices, Structural Transitions and Melting. Riste, T. (ed.) Leiden: Noordhoff 1974
Pick, R.M.: In: Vibrational Spectroscopy of Molecular Liquids and Solids. Bratos, S., Pick, R.M. (eds.). New York, London: Plenum 1980, p. 305
Michel, K.H.: ibidem, p. 263
Ziegler, G.E.: Phys. Rev.38, 1040 (1931)
Carpenter, G.B.: Acta Crystallogr.5, 132 (1952)
Kay, M.I.: Ferroelectrics4, 235 (1972)
Nomura, S.: J. Phys. Soc. Jpn16, 2440 (1961)
Chisler, E.V., Shur, M.S.: Phys. Status Solidi17, 173 (1966); idem Fiz Tverd. Tela9, 1015 [Sov. Phys. Solid State9, 796 (1967)]
Born, M., Mayer, J.: Z. Phys.75, 1 (1932)
Shibuya, I., Iwata, Y., Koyano, N., Fukui, S., Mitani, S., Tokunaga, M.: J. Phys. Soc. Jpn28, Supplement, 281 (1970)
We follow the potations and conventions of Bradley, C.J., Cracknell, A.P.: The mathematical theory of symmetry in solids. Oxford: Clarendon 1972
The elastic properties and further consequences of the present model will be published in a following paper by the present authors
Ota, K., Ishibashi, Y., Takagi, Y.: J. Phys. Soc. Jpn.29, 1545 (1970)
Hauret, G., Gharbi, A.: C. R. Acad. Sci. (Paris)271B 1072 (1970)
Hatta, I., Shimizu, Y., Hamano, K.: J. Phys. Soc. Jpn.44, 1887 (1978)
Haussühl, S.: Solid State Commun.13, 147 (1973)
Krasser, W., Buchenau, U., Haussühl, S.:idem18, 287 (1976)
Boissier, M., Vacher, R., Fontaine, D., Pick, R.: J. Phys.39, 205 (1978)
Rowe, J.M., Rush, J.J., Vagelators, N., Price, D.L., Hinks, D.G., Susman, S.: J. Chem. Phys.62, 4551 (1975)
Rowe, J.M., Rush, J.J., Chesser, N.J., Michel, K.H., Naudts, J.: Phys. Rev. Lett.40, 455 (1978)
Yamada, Y., Takatera, H., Huber, D.L.: J. Phys. Soc. Jpn.36, 641 (1974)
Michel, K.H., Naudts, J.: J. Chem. Phys.68, 216 (1978)
For a review, see Cochran, W.: CRC Crit. Rev. Solid State Sci.2, 1 (1971)
Strauch, D., Schröder, U., Bauernfeind, W.: Solid State Commun.30, 559 (1979)
Ehrhardt, K.-D., Press, W., Lefebvre, J., Haussühl, S.: Solid State Commun.34, 591 (1980)
See e.g. Maradudin, A.A.: In: Dynamical Properties of Solids, Vol. 1, p. 61, Horton, G.K., Maradudin, A.A. (eds.). Amsterdam: North-Holland 1974
Wagner, H., Horner, H.: Adv. Phys.23, 587 (1974)
Kanamori, J.: J. Appl. Phys.31 (Supplement), 14S (1960)
Elliott, R.J., Harley, R.T., Hayes, W., Smith, S.P.R.: Proc. R. Soc. (Lond.) A328, 217 (1972)
Salamon, M.B.: Phys. Rev. B15, 2936 (1977)
Lam, L., Bunde, A.: Z. Physik B30, 65 (1978)
Harada, M., Koyano, N., Mitani, S., Iwata, Y., Shibuya, I.: Ann. Res. Report Reactor Inst. Kyoto Univ.12, 1 (1979)
Denoyer, F.: private communication
Sato, Y., Gesi, K., Takagi, Y.: J. Phys. Soc. Jpn.16, 2172 (1961)
Sawada, S., Tokygawa, Y.: J. Phys. Soc. Jpn19, 2105 (1964)
Hartwig, C.M., Wiener-Avnear, E., Porto, S.P.S.: Phys. Rev. B5, 79 (1972)
Vogt, H., Happ, H.: Phys. Status Solidi B44, 207 (1971)
Betsuyaku, H.: J. Phys. Soc. Jpn21, 187 (1966)
Iwaizumi, M., Kobuta, S., Isobe, T.: Bull. Chem. Soc. Jpn.44, 3227 (1971)
Sing, S., Singh, K.: J. Phys. Soc. Jpn36, 1588 (1974)
Suzuki, S., Takagi, M.: J. Phys. Soc. Jpn30, 188 (1971); idem J. Phys. Soc. Jpn.32, 1302 (1972)
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Ehrhardt, K.D., Michel, K.H. Microscopic model of NaNO2 in the paraelectric phase. Z. Physik B - Condensed Matter 41, 329–339 (1981). https://doi.org/10.1007/BF01307322
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DOI: https://doi.org/10.1007/BF01307322