Raman scattering and lattice-dynamical calculations of crystalline KNO3.

The Raman spectrum of a KNO3 single crystal was measured at both room and liquid-nitrogen temperatures. Lattice-dynamical calculations, based on the rigid-ion approximation and empirical potentials, were performed. The possibility of a phase transition at 217 K was investigated by measuring the temperature dependence of the Raman spectrum. ©1992 The American Physical Society. Used by permission. URL: http://link.aps.org/doi/10.1103/PhysRevB.45.2142 DOI: 10.1103/PhysRevB.45.2142 PHYSICAL REVIEW B VOLUME 45, NUMBER 5 1 FEBRUARY 1992-1 Raman scattering and lattice-dynamical calculations of crystalline KN03 D. Liu The Center for Electro-Optics, 248 WSEC, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 F. G. Ullman Behlen Laboratory of Physics and the Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 J. R. Hardy Behlen Laboratory of Physics and the Center for Electro-Optics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (Received 19 August 1991) The Raman spectrum of a KNO, single crystal was measured at both room and liquid-nitrogen temperatures. Lattice-dynamical calculations, based on the rigid-ion approximation and empirical potentials, were performed. The possibility of a phase transition at 217 K was investigated by measuring the temperature dependence of the Raman spectrum. The potassium nitrate crystal demonstrates strongly anharmonicity and dynamical disorder in its latticedynamical properties. Below 384 K, potassium nitrate is in so-called phase 11, which has Dig symmetry.' Above 403 K, it is designated in phase I, which is believed to have D& symmetry. It has a ferroelectric phase (phase 111) between 384 and 398 K. Balkanski, Teng, and Nusimovicil reported Raman scattering at room and several higher temperatures. At room temperature, 12 of the 30 Raman active modes allowed by the symmetry-selection rules for phase I1 were observed. Two lines at 50 and 83 cm-' had very strong intensities. Later Raman scattering work on KNO, was done by ~ r o o k e r * ~ and Akiyama, Morioka, and ~ a k a ~ a w a . ' Brooker measured the Raman spectra of single-crystal KNO, at both room and liquid-nitrogen temperatures. He observed a broad asymmetry on the low-frequency side of the lattice mode at 52 cm-I for the (ac) scattering configuration at room temperature. He associated this mode with the translational motion of K + ions against the NO3 ions and interpreted the asymmetry as arising from the large amplitude of the motion and associated anharmonicity. Fermor and ~ j e k s h u s ~ performed electrical-resistivity and dielectricconstant measurements on K N 0 3 at low temperature. They reported an anomaly at about 217 K and suggested that there is another phase transition at this low temperature. Lattice-dynamical calculations on KN03 were done by Rao et al.',' and Akiyama, Morioka, and ~ a k a ~ a w a . ' The former used a rigid-body approximation for the NO,molecular ions. The values of their calculated frequencies were not reported. The latter was done by direct least-squares fitting of the force constants to the measured Raman frequencies. There still remains much to be learned about the lattice-dynamical properties of KNO,, such as the symmetry assignments of many lattice modes and further information about the anharmonicity and dynamical disorder. Also, a lattice-dynamical calculation based on analytical inter-ion potentials would be desirable, because it would provide a more physical description of the crystal, free of the kind of errors of numerical fitting of vibrational frequencies, which result from the uncertainty of the vibrational-mode assignments. In this paper we report experimental and theoretical studies of the latticedynamical properties of phase I1 of KNO,. Raman spectra were measured at both room and liquid-nitrogen temperatures. Lattice-dynamical calculations were made, based on the rigid-ion approximation with empirical potentials. The force constants within the molecular group NO,were obtained by numerical fitting of the internal vibrational frequencies. Since the internal modes of NO3are well known, the numerical fits of these modes are free of the uncertainty of the mode assignments. Raman spectra in the lattice-mode region in the (ac) scattering configuration were measured at a series of temperatures to investigate the possibility of a phase transition at 217 K. 11. CRYSTAL STRUCTURE Phase I1 of KNO, was determined by Nimmo and Lucas9 to have an aragonite structure of Dig orthorhombic symmetry. The lattice constants are az5.4142, b=9.1659, and c=6.4309. As shown in Fig. 1, it has four molecules per unit cell and the negative nitrate ions stack directly above each other. The three oxygens in the nitrate ion are not exactly in a plane, and there is a slight bending of the ion. The coordinates of atoms in the unit cell9 are listed in Table I. A complete symmetry analysis was given by ~us imov ic i . ' ~ 111. EXPERIMENTAL APPARATUS AND CALCULATION METHOD Single crystals of KNO, were grown from an aqueous solution by slow cooling. The orientations of the crystal45 2142 @ 1992 The American Physical Society RAMAN SCATTERING AND LATTICE-DYNAMICAL . . . c or °1' 1 A , . y.. = A