Abstract Generated abstract
This paper examines the origin of complex infrared absorption bands in sodium nitrate, especially whether they should be attributed to librations of nitrate ions or to combinations of internal and external lattice vibrations. Polarized infrared spectra of oriented single crystals were measured from 700 to 1300 cm⁻¹ over 80 to 560 K, and the bands were interpreted using factor-group selection rules and known lattice-vibration symmetries. The analysis assigns many observed features to combination transitions involving internal nitrate vibrations and external modes, including acoustic contributions near the Brillouin-zone boundary, and finds little support for an interpretation based primarily on librations about the trigonal axis. Temperature-dependent broadening, shifts, and intensity changes are related to lattice expansion, ion mobility, and orientational disordering near the high-temperature phase transition.
Full Text
UDC 548.0:535.343
PHYSICS
S. V. KARPOV, A. A. SHULTIN
INFRARED SPECTRUM AND LATTICE VIBRATIONS OF A SODIUM NITRATE CRYSTAL
(Presented by Academician A. A. Lebedev, July 5, 1967)
Since the discovery of the complex structure of the infrared absorption spectrum in the vicinity of the fundamental stretching vibration of the OH ion in the crystal brucite, Mg(OH)\(_2\), and also in Ca(OH)\(_2\) and LiOH crystals, a discussion has arisen in the literature about the nature of these absorption bands. According to one point of view (\(^1\)), this structure is due to coupling of the stretching vibration of the OH ion with localized librations of noninteracting hydroxyl ions. Another point of view (\(^2\)) relates the observed picture to combinations of internal and external vibrations of the crystal lattice of Mg(OH)\(_2\), Ca(OH)\(_2\), and LiOH. In the opinion of Dows (\(^3\)), the librational theory has indicated the path toward understanding the phenomenon, but at present it is necessary to conclude that the idea of stronger interaction apparently can better explain the complex spectra of these crystals in the near infrared region.
Table 1
Selection rules for the IR spectrum of a NaNO\(_3\) crystal
| Symmetry | Normal coord. | Fundamental freq. | Polarization | Combination | Polarization | Combination | Polarization |
|---|---|---|---|---|---|---|---|
| \(A_{1g}\) | \(Q_1\) | \(\nu_1\) | inactive | \(\nu_1 \pm \nu_L\ (A_{1u})\) | inactive | \(\nu_2' + \nu_L\ (A_{1u})\) | inactive |
| \(A_{1u}\) | \(Q_1'\) | \(\nu_1'\) | inactive | \(\nu_1 \pm \nu_L\ (E_u)\) | \(x, y\) | \(\nu_2' \pm \nu_L\ (E_u)\) | inactive |
| \(A_{2g}\) | \(Q_2\) | \(\nu_2\) | inactive | \(\nu_1 \pm \nu_L\ (E_g)\) | inactive | \(\nu_2' \pm \nu_L\ (E_g)\) | \(x, y\) |
| \(A_{2u}\) | \(Q_2'\) | \(\nu_2'\) | \(z\) | \(\nu_1 \pm \nu_L\ (A_{2u})\) | \(z\) | \(\nu_2' \pm \nu_L\ (A_{2u})\) | inactive |
| \(E_g\) | \(Q_3, Q_4\) | \(\nu_4\) | inactive | \(\nu_1 \pm \nu_L\ (A_{2g})\) | inactive | \(\nu_2' \pm \nu_L\ (A_{2g})\) | inactive |
| \(E_u\) | \(Q_3', Q_4'\) | \(\nu_4'\) | \(x, y\) | \(\nu_1' \pm \nu_L\ (A_{1u})\) | inactive | \(\nu_4 \pm \nu_L\ (A_{1u})\) | \(x, y\) |
| \(A_{1u}\) | \(Q_7\) | \(\nu_7\) | inactive | \(\nu_1' \pm \nu_L\ (E_u)\) | inactive | \(\nu_4 \pm \nu_L\ (E_u)\) | \(x, y, z\) |
| \(E_u\) | \(Q_{10}, Q_{11}\) | \(\nu_{10}\) | \(x, y\) | \(\nu_1' \pm \nu_L\ (E_g)\) | \(x, y\) | \(\nu_4 \pm \nu_L\ (E_g)\) | inactive |
| \(E_u\) | \(Q_{12}, Q_{13}\) | \(\nu_{12}\) | \(x, y\) | \(\nu_1' \pm \nu_L\ (A_{2u})\) | inactive | \(\nu_4 \pm \nu_L\ (A_{2u})\) | \(x, y\) |
| \(E_u\) | \(Q_{14}, Q_{15}\) | \(\nu_{14}\) | \(x, y\) | \(\nu_1' \pm \nu_L\ (A_{2g})\) | \(z\) | \(\nu_4 \pm \nu_L\ (A_{2g})\) | inactive |
| \(E_g\) | \(Q_{16}, Q_{17}\) | \(\nu_{16}\) | inactive | \(\nu_2 \pm \nu_L\ (A_{1u})\) | \(z\) | \(\nu_4' \pm \nu_L\ (A_{1u})\) | inactive |
| \(E_g\) | \(Q_{18}, Q_{19}\) | \(\nu_{18}\) | inactive | \(\nu_2 \pm \nu_L\ (E_u)\) | \(x, y\) | \(\nu_4' \pm \nu_L\ (E_u)\) | inactive |
| \(A_{2u}\) | \(Q_{21}\) | \(\nu_{21}\) | \(z\) | \(\nu_2 \pm \nu_L\ (E_g)\) | inactive | \(\nu_4' \pm \nu_L\ (E_g)\) | \(x, y, z\) |
| \(A_{2u}\) | \(Q_{22}\) | \(\nu_{22}\) | \(z\) | \(\nu_2 \pm \nu_L\ (A_{2u})\) | inactive | \(\nu_4' \pm \nu_L\ (A_{2u})\) | inactive |
| \(A_{2g}\) | \(Q_{23}\) | \(\nu_{23}\) | inactive | \(\nu_2 \pm \nu_L\ (A_{2g})\) | inactive | \(\nu_4' \pm \nu_L\ (A_{2g})\) | \(x, y\) |
| \(A_{2g}\) | \(Q_{24}\) | \(\nu_{24}\) | inactive | \(\nu_2 \pm \nu_L\ (A_{2g})\) | inactive | \(\nu_4' \pm \nu_L\ (A_{2g})\) | \(x, y\) |
Note. inactive — not active. The vibration of the nitrate ion \(\nu_3\) and its combinations with lattice vibrations are not considered in the present work.
Recently, the complex structure of the IR spectra of a number of nitrate and carbonate crystals in the region of the fundamental internal vibrations of the \(\mathrm{NO_3^-}\) and \(\mathrm{CO_3^{2-}}\) ions was interpreted (\(^4\)) on the basis of the idea of librations of these ions about the trigonal axis. In light of the preliminary results of the discussion mentioned above, such an interpretation of the spectral structure of crystalline nitrates and carbonates is doubtful; and to assess its reliability, studies (\(^5\)) of the dispersion of the branches of external vibrations, knowledge of the special points of the Brillouin zone, and also a more careful study of the IR spectra are necessary. Since one of the most characteristic spectra presented in that work pertains to sodium nitrate, we
an attempt was undertaken at a more detailed study of the IR spectrum of oriented single-crystal samples of NaNO\(_3\) in polarized light in the region 700–1300 cm\(^{-1}\) at temperatures of 80–560° K.
The NaNO\(_3\) lattice has a calcite-type structure. The space group is \(D_{3d}^{6} — R\bar{3}c\); the rhombohedral unit cell contains 2 “molecules” and has dimensions \(a = 6.313\) Å, \(\alpha = 47^\circ 15'\) at 18° C \((^6)\). On heating above 200° C, NaNO\(_3\) undergoes a second-order phase transition, which is completed at 276° C \((^7)\) and, according to present-day data \((^{8,9})\), is associated with orientational disordering of the anions and an increase in the migration rate of sodium ions.
The normal vibrations of the unit cell of the low-temperature phase of NaNO\(_3\) were analyzed in \((^{10,11})\). Kastler showed \((^{12})\) that the real lattice vibrations are a superposition of translational and rotational vibrations belonging to the same symmetry type (Fig. 1).
Fig. 1. External normal vibrations of the unit cell of a sodium nitrate crystal
The spectroscopic selection rules (in the factor-group approximation) are given in Table 1. The internal vibrations of the nitrate ion have the following frequencies:
\[ \nu_1(A_{1g}) = 1068\ \text{cm}^{-1}; \]
\[ \nu_2'(A_{2u}) = 838\ \text{cm}^{-1}; \]
\[ \nu_3(E_g) = 1385\ \text{cm}^{-1}; \]
\[ \nu_3'(E_u) = 1385\ \text{cm}^{-1}; \]
\[ \nu_4(E_g) = 720\ \text{cm}^{-1}, \]
\[ \nu_4'(E_u) = 726\ \text{cm}^{-1}. \]
Despite the splitting of the internal vibrational terms into two components, in the IR spectra and in the spectra of combinational scattering (c.s.) of the crystal there is no change in the number of the corresponding bands. The calculation carried out showed that the splitting of the components \(\nu_2(A_{2g})\) and \(\nu_2'(A_{2u})\) (according to \((^{13})\), for this vibration the derivative of the dipole moment with respect to the coordinate is \(\partial \mu/\partial q = 1.6\) debye per 1 Å), taking into account the interaction of the 80 nearest ions, does not exceed 0.5 cm\(^{-1}\).
Experimental investigations of the c.s. of the NaNO\(_3\) crystal have been carried out many times (see, for example, \((^{14})\)). In the low-frequency region of the spectrum there are 2 lines of type \(E_g\) with frequencies 98 and 185 cm\(^{-1}\), and their intensities are approximately in the ratio 1 : 3. Since the librational motion of the nitrate ions is accompanied by a strong change in the polarizability of the cell, the ratio of the intensities of these lines can serve as a measure of the participation of such motion in each of the two real vibrations.
The available information on the IR spectrum of NaNO\(_3\) in the region of external vibrations is poorer and less reliable. From the reflection spectrum of a single crystal, Liebisch and Rubens \((^{15})\) give for the \(E_u\) ensemble the frequencies 71, 133, and 217 cm\(^{-1}\), and for the \(A_{2u}\) ensemble the frequencies 71 and 217 cm\(^{-1}\). In \((^{16})\), for a polycrystalline sample the frequencies 89, 173, and 217 cm\(^{-1}\) were obtained.
Absorption of NaNO\(_3\) in the near IR region has been studied repeatedly (see, for example, \((^{17,18})\)); however, most of the results refer either to polycrystalline layers or to mica plates (plane \(10\bar{1}1\)). The spectra obtained in the present work are shown in Fig. 2,
from which it is seen that all absorption bands are sharply polarized. This fact makes it possible to assume that the selection rules for combination bands, derived in the factor-group approximation, are valid, at least, for part of each of the bands (19). In view of the fact that the available information on lattice vibrations pertains to \(T = 300^\circ\text{K}\), it is natural to begin the discussion with spectrum 3 (Fig. 2). In the polarization \(\mathbf{E}\perp c\), the selection rules allow combination absorption with the participation of external vibrations of the types \(E_g\) and \(E_u\). Therefore the bands 1004 and 926 cm\(^{-1}\) should be assigned to combinations \(\nu_2'\) with the ensemble of external vibrations \(E_g\), the first of which can be predominantly associated with the motion \(\nu_{18}\) (Fig. 1). Similar combinations of \(\nu_2\) with the ensemble \(E_u\) give rise to the appearance of bands 1048, 978, and 954 cm\(^{-1}\). Since librations of nitrate ions about the \(c_2\) axes in antiphase should have a higher frequency than in librations in phase, the band 1048 cm\(^{-1}\) can be predominantly associated with the motion \(\nu_{14}\).
Fig. 2. Infrared absorption spectra of a NaNO\(_3\) crystal. 1 — \(\mathbf{E}\perp c\), 560°K; 2 — \(\mathbf{E}\perp c\), 385°K; 3 — \(\mathbf{E}\perp c\), 293°K; 4 — \(\mathbf{E}\perp c\), 80°K; 5 — \(\mathbf{E}\parallel c\), 293°K; 6 — \(\mathbf{E}\perp c\), 80°K; (Spectra 1–4 were obtained on a sample cut perpendicular to the optical axis, spectra 5 and 6 on one cut parallel to it.)
The region of combination transitions of the internal vibration \(\nu_1\) becomes sufficiently transparent only when the sample is cooled. At \(T = 80^\circ\text{K}\) in this range (4 in Fig. 2) about 10 absorption maxima can be distinguished. The maxima 1167 and 1254 cm\(^{-1}\) should be assigned to combination transitions with external vibrations of the \(E_g\) ensemble, and the bands 1220–1229 cm\(^{-1}\) and 1189–1200 cm\(^{-1}\) to combination transitions with external vibrations of the \(E_u\) ensemble. The region corresponding to the 954 cm\(^{-1}\) band (spectrum 3), upon cooling, reveals a more complex structure. In this case the maximum 963 cm\(^{-1}\) can be interpreted as \(\nu_2 + 115\) cm\(^{-1}\) \((E_u)\), and the maximum 952 as \(\nu_1 - 116\) cm\(^{-1}\) \((E_u)\). The absorption bands 788 and 893 cm\(^{-1}\), located in all spectra 1–4 symmetrically with respect to the band of the vibration \(\nu_2\), are apparently caused by combinations of this vibration with acoustic lattice vibrations of type \(E_u\), whose density of frequencies is maximal near the boundary of the Brillouin zone. Librations of nitrate ions about the trigonal axis together with translations along this axis form the ensembles \(A_{2g}\) and \(A_{2u}\), which in the approximation considered do not give IR-active combination bands with the vibrations \(\nu_2\) and \(\nu_2'\). The possibility of combination absorption in the region of the vibration \(\nu_1\) (or \(\nu_1'\)) with these ensembles can be realized only in the region of weak absorption 1140 cm\(^{-1}\) (\(\mathbf{E}\parallel c\), spectrum 6). Therefore the argu-
the arguments presented in work (4) in favor of the librational concept seem unconvincing to us. The most probable interpretation of the remaining bands is given in Table 2. It may be noted that the inactive fundamental lattice vibration \(\nu_7(A_{1u})\), according to spectra 5 and 6, has a frequency of about \(175\ \mathrm{cm}^{-1}\).
On cooling, many bands of combination absorption show splitting. However, because of the lack of sufficient information concerning the dispersion of the vibrational branches and the number of critical points in the Brillouin zone, it is difficult to indicate the actual cause of this.
Table 2
Frequencies of the bands of the IR spectrum of NaNO\(_3\)
| 80° K | 300° K | Polarization | Assignment | 80° K | 300° K | Polarization | Assignment | 80° K | 300°K | Polarization | Assignment |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 727 | 726 | \(x, y\) | \(\nu_4'\) | 946 | 927 | \(z\) | \(\nu_4+\nu_{14}\) | 1050 | \(x, y\) | \(\nu_2+\nu_{14}\) | |
| 790 | 788 | \(x, y\) | \(\nu_2-\) acoustic | 952 | \(x, y\) | \(\nu_1-\nu_{10}\) | 1066 | 1048 | \(x, y\) | \(\nu_2+\nu_{14}\) | |
| 815 | 815 | \(z\) | \(\nu_2(\mathrm{N}^{18}\mathrm{O}_3^-)\) | 963 | 954 | \(x, y\) | \(\nu_2+\nu_{10}\) | 1141 | \(z\) | \(\nu_1+(A_{2u},\,A_{2g})\) | |
| 826 | 825 | \(x, y\) | \(\nu_4'+\nu_{16}\) | 981 | \(x, y\) | \(\nu_2+\nu_{11}\) | 1154 | \(x, y\) | \(\nu_1'+\nu_{16}\) | ||
| 838 | 838 | \(z\) | \(\nu_2'\) | 987 | 978 | \(x, y\) | \(\nu_2+\nu_{12}\) | 1167 | \(x, y\) | \(\nu_1'+\nu_{16}\) | |
| 840 | 840 | \(x, y\) | \(\nu_2'\) | 1014 | \(x, y\) | \(\nu_2'+\nu_{18}\) | 1189 | 1185 | \(x, y\) | \(\nu_1+\nu_{10}\) | |
| 873 | \(z\) | \(\nu_4+\nu_{12}\) | 1023 | 1004 | \(x, y\) | \(\nu_2'+\nu_{18}\) | 1200 | \(x, y\) | \(\nu_1+\nu_{10}\) | ||
| 893 | 889 | \(x, y\) | \(\nu_2+\) acoustic | 1035 | 1010 | \(z\) | \(\nu_2+\nu_7\) | 1220 | \(x, y\) | \(\nu_1+\nu_{11}\) | |
| 906 | \(z\) | \(\nu_4+\nu_{18}\) | 1229 | \(x, y\) | \(\nu_1+\nu_{11}\) | ||||||
| 930 | 926 | \(x, y\) | \(\nu_2'+\nu_{16}\) | 1254 | \(x, y\) | \(\nu_1'+\nu_{18}\) | |||||
| 937 | \(x, y\) | \(\nu_2'+\nu_{16}\) | 1265 | \(x, y\) | \(\nu_1+\nu_{14}\) |
Heating the sample leads to broadening of the bands and their shift (for some, up to \(0.1\ \mathrm{cm}^{-1}/\mathrm{deg}\)) toward lower frequencies. The intensity of the \(1066\ \mathrm{cm}^{-1}\) band decreases noticeably already at \(T=385^\circ\mathrm{K}\). If it belongs to the \(E_u\) ensemble and, basically, corresponds to librations of nitrate ions about the \(c_2\) axes (motion \(\nu_{14}\), Fig. 1), then this behavior reflects a decrease in the magnitude of the coupling of the vibrations within this ensemble as a result of the strongly anisotropic expansion of the crystal lattice on heating (20). With further heating, orientational disordering of the nitrate ions makes meaningless the choice of a cell with two “molecules.” In view of the lowering of the site symmetry of the nitrate ions in a layer, the \(\nu_1\) band begins to appear in absorption (21).
The increase in the intensity of the combination bands in the region of 800 and \(875\ \mathrm{cm}^{-1}\) is apparently due to an increase in the mobility of the ions in directions perpendicular to the trigonal axis.
Leningrad State University
named after A. A. Zhdanov
Received
2 VII 1967
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