Comparative investigation of LiNbO3 crystals Raman spectra in the temperature range 100–400 K

Accepted Manuscript Title: comparative investigation of LiNbO3 crystals Raman spectra in the temperature range 100–400K Authors: Nikolay Sidorov, Alexander Yanichev, Mikhail Palatnikov, Diana Manukovskaya PII: DOI: Reference:

S0924-2031(17)30230-8 https://doi.org/10.1016/j.vibspec.2018.02.005 VIBSPE 2774

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11-8-2017 15-2-2018 18-2-2018

Please cite this article as: Sidorov N, Yanichev A, Palatnikov M, Manukovskaya D, comparative investigation of LiNbO3 crystals Raman spectra in the temperature range 100–400K, Vibrational Spectroscopy (2010), https://doi.org/10.1016/j.vibspec.2018.02.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

COMPARATIVE INVESTIGATION OF LiNbO3 CRYSTALS RAMAN SPECTRA IN THE TEMPERATURE RANGE 100-400 K Nikolay Sidorov1, Alexander Yanichev1, Mikhail Palatnikov1, Diana Manukovskaya1 1 I.V. Tananaev Institute of Chemistry and Technology of Rare Elements and Mineral Raw Materials, Kola Science Center, Russian Academy of Sciences, Apatity, Murmansk region, Russian Federation, 184209. Highlights Lithium niobate stoichiometric Raman spectra contain only fundamental bands. Lithium niobate congruent Raman spectra contain low intensity extra bands. The anharmonicity of Nb5- vibrations along the polar axis is stronger compared to that of Li+. Fundamental bands intensity depends on temperature nonmonotonically, extra bands – linearly.

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Abstract. We have investigated Raman spectra of congruent and stoichiometric LiNbO3 crystals in the temperature range 100–450 K. Slope gradient is greater for the temperature dependence of band width associated with Nb5+ ions vibrations than that associated with Li+ ions vibrations in a lithium niobate crystal structure. This fact indicates that the anharmonicity of Nb5+ ions vibrations along the polar axis is greater compared to Li+ ions vibrations. It is likely that O2– ions contribute to this anharmonicity. The O2– ions vibrations are characterized by an anharmonic potential in the LiNbO3 crystal structure. The O2– ions vibrations according to ab initio calculations strongly interact with vibrations of Nb5+ ions. We have found that the temperature dependence of the fundamental bands intensity is nonmonotonic and the “extra bands” intensity is strictly linear. Keywords: lithium niobate crystal; Raman spectroscopy; temperature dependence; extra Raman band; cation sublattice order. 1. INTRODUCTION

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A ferroelectric lithium niobate (LiNbO3) crystal is one of the most demanded nonlinear optical materials for recording, transformation, and processing of optical information [1–4]. Investigation of the structural perfection of normally pure (with different ratio R = Li/Nb) and doped LiNbO3 crystals in relation to the method of synthesis is also of considerable interest [5, 6]. Raman spectra of nominally pure congruent (LiNbO3congr) and stoichiometric (LiNbO3stoich) lithium niobate crystals were previously investigated [3, 7-27]. The rhombohedral unit cell of the LiNbO3 crystal ferroelectric phase belongs to the C3V6 (R3c) space symmetry group and contains two formula units [3, 4]. The phonon dispersion curve has 30 vibrational branches: 27 optic and 3 acoustic [3, 10, 11]. The optical vibrations are a family Γ = 4A1 + 5A2 + 9E [3, 10, 11]. Since the inversion point is absent at the lithium niobate structure, optical vibrations that are active in the Raman scattering should also appear in the IR absorption. At k = 0 (in the center of the Brillouin zone), there are 4A1 + 9E dipole fundamental active vibrations in the Raman scattering and IR absorption spectra [3, 11]. Due to the polar nature of all optical vibrations (except for A 2), they split in the crystal into longitudinal (LO) and transverse (TO) vibrations. The vibrations of А2 symmetry type are not dipole active and their LO-TO splitting in the crystal does not occure [11]. Therefore, taking into account the LO–TO splitting, 26 bands, which correspond to fundamental phonons, should appear in the Raman scattering spectrum [3, 11]. In addition, there are 2А1 + Е acoustic and 5А2 optically inactive fundamental vibrations, which are not supposed to appear in the Raman scattering and the IR absorption spectra [2, 11]. However, since real lithium niobate crystals have a complex defect structure and possess the photorefractive effect [3, 9, 10], optically inactive А2 symmetry vibrations can be active in the spectrum. This can be caused by the fact that

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structure defects, microstructures and clusters (which are characteristic of LiNbO3 crystals) lead to local changes in the microsymmetry of the ferroelectric crystal [2, 3, 9, 23, 25]. Polarized Raman spectra of LiNbO3congr crystal (R [Li/Nb] = 0.946) measured in different scattering geometries exhibit a series of low-intensity (“extra”) bands, which do not belong to fundamental vibrations of the crystal lattice [3, 7–12, 16-19, 22-27]. Reasons for the appearance of extra bands in the Raman spectrum of the LiNbO3 crystal are the subject of the discussion [3, 9, 10, 13, 20, 22-27]. Previously [9, 10] attention has been drawn the fact that extra bands in the LiNbO3 crystal Raman spectrum can be caused by small features in the cation sublattice order along the polar axis. Extra bands were found to be mainly observed in scattering geometries in which manifest А1(ТО) symmetry type totally symmetric cation vibrations along the polar axis. At the same time, extra bands were not observed in the spectra that were recorded in scattering geometries in which E(TO, LO) symmetry cation vibrations manifest. These vibrations occur perpendicularly to the polar axis of the crystal. This fact means that the structure units order in the cation sublattice along the polar axis plays a significant role in the formation of features of the crystal vibrational spectrum. Note that the cations order along the polar axis forms a spontaneous polarization of the LiNbO3 crystal [3, 4] and, consequently, its ferroelectric and nonlinear optical characteristics. In order to evaluate the degree of structural perfection of LiNbO3 crystals, it is important to study not only their Raman spectra in relation to the crystal composition, but also the temperature behavior of spectra of crystals of different compositions. In this paper, we comparatively investigate the temperature behavior of the main parameters of bands in the Raman spectra of a stoichiometric LiNbO3 single crystal (LiNbO3stoich, R=1; there are no extra bands) and of a congruent single crystal (LiNbO3congr, R = 0.946), in the spectrum of which, apart from fundamental bands, extra bands are reliably observed. 2. MATERIAL AND METHODS LiNbO3stoich and LiNbO3congr crystals were grown in air atmosphere by the Czochralski method on a Crystal-2 setup from a melt of Li2O–Nb2O5 with 58.6 mol % of Li2O and from a congruent melt, respectively. The charge preparation technique and growth of crystals is described in more detail in [5, 28]. The samples for investigations of Raman spectra were cut in the shape of parallelepipeds ~7 × 6 × 5 mm with the edges parallel to the crystallographic axes X, Y, and Z (Z is the polar axis of the crystal). Faces of parallelepipeds were thoroughly polished. Raman spectra were excited by radiation 514.5 nm of an argon-ion laser (Spectra Physics, 2018RM) and were registered with a resolution of 1 cm–1 on a Horiba Jobin Yvon T64000 spectrograph, which was equipped with a confocal microscope. In order to eliminate the influence of the photorefractive effect on the Raman spectrum, the spectra were excited by low power radiation (3 mW). Processing of spectra was performed using the programs Horiba Lab Spec 5.0 and Origin 8.1. The errors of the band frequency and the bandwidth were ±1.0 and ±3.0 cm–1, respectively, while that for the intensity was 5%. 3. RESULTS AND DISCUSSION Fig. 1a demonstrates temperature dependences of the LiNbO3congr crystal Raman spectra in the Y(ZZ)Y and Y(ZX)Y scattering geometries. The temperature dependences of the LiNbO3stoich crystals spectra have a similar shape, thus we found its demonstration unneccecary. Fig. 1b demonstrates detailed fragments of spectra measured at different temperatures, in which extra bands can be clearly seen, and temperature dependences of widths and intensities of extra bands are presented. Figure 1 should be somewhere here Table 1 should be somewhere here Table 1 summarizes the main parameters of Raman bands of LiNbO3stoich and LiNbO3congr crystals at 100 K in the Y(ZZ)Y and Y(ZX)Y scattering geometries (vibrations of the A1(TO) and E(TO) symmetry are active) and their assignment, as well as calculations from the literature. The cation sublattice of LiNbO3stoich is more ordered compared to that of the LiNbO3congr. Table 1

demonstrates that bands in the spectrum of the LiNbO3stoich are much narrower than of the LiNbO3congr. In addition, we have detected no extra bands in the LiNbO3stoich spectrum. Our experimental data also demonstrate that frequencies of Raman fundamental vibrations bands of LiNbO3stoich and LiNbO3congr coincide well within the error. Table 2 should be somewhere here

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The lattice dynamics of the LiNbO3 crystal has been analyzed both by ab initio methods [29, 30] and in the valence force field [14]. Ab initio calculations of vibrations frequencies and shapes, atoms coordinates, and unit cell parameters proved to be most close to the experiment [29, 30]. Frequencies of fundamental A1(TO), E(TO), and A2(TO) symmetry types vibrations in the center of the Brillouin and fequencies calculated in [29, 30] ab initio are demonstrated in Table 1 and 2. Frequencies of A2 symmetry vibrations calculated in [29, 30] are marked in Table 1 with the upper index (2). Unfortunately, it is impossible to calculate A2 symmetry vibrations frequencies (forbidden by selection rules) in the valence force field [14]. In accordance with calculations of vibrations bands shapes [29, 30], certain ions shift predominantly contribute to fundamental lattice vibrations of the A1(TO) and E(TO) symmetry. Thus, the 1A1(TO) vibration with a frequency 239 cm–1 (Table 1) predominantly involves shift of Nb5+ and O2– ions in opposite directions along the Z axis. The 2A1(TO) vibration with a frequency 320 cm–1 (Table 1) predominantly involves Li+ and Nb5+ ions shift along the Z axis. The A1(TO) vibrations with frequencies 381 and 607 cm–1, respectively (Table 1), predominantly involves O2– ions shift in the plane perpendicular to the Z axis [14, 29, 30]. Note that, in accordance with the calculations in [14], vibrations of E(TO) symmetry are much more mixed than vibrations of the A1(TO) symmetry. The spectra of LiNbO3congr crystal were registered in the Y(ZZ)Y scattering geometry (vibrations of the A1(TO) symmetry are active). They differ from the calculated spectrum. The difference is in the range of extra bands frequencies (Table 1). In the LiNbO3stoich Raman spectra we have revealed all four A1(TO) fundamental vibrations and all nine E(TO) fundamental vibrations allowed by the selection rules (Table 1, 2). In spectra of highly ordered LiNbO3stoich crystal we have detected low-intensity bands with frequencies 610 and 180 cm–1 (Table 2, Fig. 2). The band 177 cm-1 previously was observed in IR spectrum in paper [31]. Bands with frequencies 177.3 and 609.8 cm-1 were observed in paper [7] in Raman spectrum of stoichiometric lithium niobate crystal. These bands lie among very intense bands and correspond to the E(TO) fundamental vibrations. In Raman spectra of LiNbO3congr crystal the 610 and 180 cm–1 low-intensity bands are masked by structural disorder effects and stay hidden. At the same time, the LiNbO3congr spectra measured in the polarization geometries (where only the A1(TO) fundamental vibrations should be observed) exhibit much more bands than is allowed.

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Apart from the fundamental bands in the LiNbO3congr spectrum measured at T = 293 K different authors in different scattering geometries [3, 7–12, 15-19] reliably observed low-intensity extra bands with frequencies 85, 92, 103, 117, 187, 305, 331, 412, 477, 535, 605, 668, 690, 739, 743 and 825 cm–1. In particular, near intence 632 cm–1 band (4A1(TO), Table 1), we reliably observed a low-intensity band with a frequency of 694 cm–1 (Fig. 1, Table 1) in the LiNbO3congr spectrum. Its interpretation is contradictory and is still discussed in the literature [3, 9-11, 20]. In addition, a low-intensity band with a frequency 330 cm–1 is observed at low temperatures (100 K) near the 333 cm–1 band with a frequency (3A1(TO), Table 1). The 330 cm–1 band does not belong to fundamental vibrations. It is masked by structural disorder effects at higher temperatures (Fig. 1, b). In a low-frequency range, the LiNbO3cong Raman spectrum (Fig. 1, b) exhibits a low-intensity 120 cm–1 band, which corresponds to vibrations of quasi-particles: two-particle states of acoustic phonons with a zero total wave vector [3].

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The appearance of extra bands in the Raman spectrum can be caused by the fact that Nb Li defects randomly violate an ideal order of cation sublattice structure along the polar axis. Under certain conditions local distortion of the nonstoichiometric crystals structure by NbLi defects can cause lowering of the vibration symmetry [21, 32]. In this case, the entire spectrum of fundamental vibrations broadens and deforms. This indeed is observed at the ratio R = Li/Nb value decrease. (Table 1). Raman bands in the stoichiometric LiNbO3 crystal are narrower than the bands in the congruent crystal. The stoichiometric crystal is characterized by the absence of Nb Li defects and by much ordered cation sublattice than the congruent crystal. At the same time the spectrum stays unchanged (Table 1). Random violations of structural order caused by Nb Li defects can lead to dephasing of crystal vibrations [32]: corresponding atoms of each unit cell cease to vibrate in phase. Statistically, the random phonons dephasing by defects can be described by spatially damping waves with damping factor χ = 1/l, where l is the average distance between defects [32]. The damping leads to a broadening of bands in the spectrum due to the violation of the radiation interference conditions in the crystal along the scattering direction. At higher concentrations of randomly arranged NbLi defects, the Brillouin zone “unfolds”. Thus not only limiting (k = 0) frequencies of optical branches are observed (with intensities proportional to the defects concentration), but also other frequencies, which are determined by the scatter of the wave vector |Δk| ~ 2π/l [32]. Taking into account small dispersion of optical branches [3], rather narrow additional (extra) bands appear in the spectrum. The bands should be absent due to selection rules for the given space group of the crystal. We have measured the temperature dependences of frequencies, widths, and intensities of experimentally observed bands (fundamental and extra). For extra bands, we succeeded to measure correct main parameters of bands with frequencies 104, 120, 330, and 694 cm–1 (Table 1, Fig.3). It appeared that the frequencies and widths of all the bands (fundamental and extra) experience no anomalies and depend linearly on temperature in the examined temperature range (100–450 K). In this case, temperature dependences of fundamental vibrations frequencies are identical for LiNbO3stoich and LiNbO3congr.

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Attention should be drawn to the fact that the temperature dependences of 1A1(TO) and 2A1(TO) bands widths (Table 1) are noticeably different (Fig. 4). The 2A1(TO) band in accordance with calculations of [29, 30] is attributed to vibrations with predominant participation of Li+ ions along the Z axis. Extraordinarily, the 2A1(TO) band width depends on temperature much weaker than the 1A1(TO) and 4A1(TO) bands widths. 1A1(TO) and 4A1(TO) bands refer, respectively, to vibrations that involve a predominant participation of Nb5+ ions along the polar axis and to totally symmetric vibrations of О2– ions of oxygen octahedra perpendicularly to the polar axis. This fact indicates that the anharmonicity of both vibrations is considerably stronger than that of vibrations of Li+ ions along the polar axis. Thus, vibrations of heavy Nb5+ cations in the oxygen octahedra are more anharmonic than are vibrations of light Li+ ions, which is rather unusual. It is likely that О2- ions appreciably contribute to the anharmonicity of 1A1(TO) vibrations. These vibrations involve the predominant participation of Nb5+ ions. Ab initio calculations have demonstrated that Nb5+ and О2– ions vibrations strongly interact. This can mainly be caused by an anharmonic potential of oxygen atoms vibrations in the crystal. The anharmonicity of the vibrations associated with О2– ions is confirmed by an exponential themperature dependence of the width of the band that is attributed to 4A1(TO) vibrations of О2– ions perpendicularly to the polar axis. This dependence is similar to the temperature dependence of the 1A1(TO) band width (Fig. 4). Furthermore, the slope gradient for the temperature dependence of the 1A1(TO) and 4A1(TO) bands widths for the LiNbO3stoich is smaller than that for the LiNbO3congr (0.64 and 0.86, respectively). At the same time, the slope angle tangent for the temperature dependences of

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the bands widths that correspond to the E(TO) symmetry fundamental vibrations are roughly the same for all bands. A predominant broadening of the 1A1(TO) and 4A1(TO) bands (they correspond to vibrations with a predominant participation of Nb5+ ions along the polar axis and totally symmetric vibrations of О2– ions of the A1(TO) symmetry perpendicularly to the polar axis) indicates that, with an increase in temperature, the unit cell expands predominantly in the direction of the polar axis, which consistent with X-ray data. Namely, the parameter c of the unit cell of the LiNbO3congr is greater than that of the LiNbO3stoich [3, 4]. Remarkably, the intensity of extra bands of the spectrum increases simultaneously with the broadening of Raman bands that correspond to A1(TO) symmetry fundamental vibrations of ions (with increasing degree of disorder in the cationic sublattice), Fig.3. Figure 5 should be somewhere here

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An unusual temperature behavior is observed for the intensities of Raman fundamental bands of LiNbO3stoich and LiNbO3congr (Fig. 5). Most of the fundamental bands intensities depend on temperature nonmonotonically. At the same time, the temperature dependence of extra bands intensities is strictly linear (Fig. 3). This behavior of fundamental bands intensities is apparently related to the clusters and microstructures in the crystal volume. Clusters inevitably exist in the ferroelectric LiNbO3 crystal because it is a phase of a variable composition [3, 4, 22, 33]. Boundaries and the structure of clusters and microstructures deformate during changes in temperature and composition. In particular, clusters and microstructures can be reliably confirmed in LiNbO3 crystals of different compositions by the laser conoscopy method [34, 35]. Clusters and microstructures, including laser induced ones, are an important kind of defects in the ferroelectric LiNbO3 crystal. Electrons in nominally pure crystals localize precisely on these defects, therefore, they play an extremely important role in the formation of the photorefractive effect [3, 36]. In [33, 37], computer simulation demonstrated that during formation of a cluster in a LiNbO3 crystal, a crystal structure considerably rearranges not only inside the cluster, but also in the crystal matrix at rather long distances away from the cluster. In this case, ions occupy low-symmetry positions, which leads to the appearance of dipole moments and to a change in the spontaneous polarization. In addition, this can give rise to the appearance of A2 symmetry bands forbidden by selection rules. Nonmonotonic temperature behavior of LiNbO3stoich and LiNbO3congr Raman bands may be also caused by temperature features of photorefraction in lithium niobate. Photorefractive LiNbO3 contains a large number of structural microscopic inhomogeneities (defects) that confidently manifest in Raman spectra [3, 9, 10, 23, 25]. Electrons localize on these defects [3]. The number of structural microscopic inhomogeneities with localized electrons is maximal at low temperatures (~ 196K) [2, 3]. Thus, in a photorefractive crystal only a part of the light excites atoms vibrations in the crystal lattice. Microscopic inhomogeneities with localized electrons scatter the rest of the energy. Temperature decrease leads to decrease in the number of microscopic inhomogeneities, and thereby the effect of refraction reduces. Since the photorefractive effect is greatest at low temperatures, the photoinduced light scattering (PILS) also has the maximum value. At temperatures above 393 K, the effect of photorefraction is absent [3]. As the temperature increases photorefraction mechanisms gradually switch off (thermal annealing of defects and the "healing" of defects occur), which reduces the scattered laser radiation. The consequence of reducing of the scattering is the increase in the energy that goes directly to the excitation of lattice vibrations. As a result the intensity of the Raman fundamental bands grows, and the intensity of the PILS conversely decreases. From this point of view, a difference in the temperature dependence of the Raman bands intensities of LiNbO3stoich and LiNbO3congr crystals becomes clear. It is well known [36, 38] that PILS (due to fewer number of defects with localized electrons) in LiNbO3congr is significantly less than in LiNbO3stoich. Thus such a significant change of the Raman band intensities with the changes in temperature is observed for LiNbO3stoich, but not for LiNbO3congr.

4. CONCLUSION

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In the spectrum of the LiNbO3stoich crystal, we have observed only fundamental bands allowed by selection rules for the space group C3V (R3c), Z = 2. In the spectrum of the LiNbO3congr crystal, apart from fundamental bands, we have observed low-intensity extra bands, which correspond to forbidden vibrations of the A2 symmetry and two-particle states of acoustic phonons with the zero total wave vector. The Raman bands frequencies and widths depend linearly on temperature in the range 100– 450 K. The width of the 2A1(TO) band, which corresponds to vibrations of Li+ ions along the polar axis, depends much more weakly on temperature than the width of the 1A1(TO) band, which correspond to vibrations of Nb5+ ions along the polar axis. Thus the anharmonicity of Nb5+ ions vibrations along the polar axis is much stronger compared to that of Li+ ions. It is likely that the anharmonicity of 1A1(TO) vibrations is appreciably contributed by О2– ions, which are characterized by an anharmonic potential. Also vibrations of О2– ions, according to ab initio calculations, are mixed with Nb5+ ions vibrations. The anharmonicity of O2– ions vibrations is evidenced by a strong temperature dependence of the width of the band that refers to 4A1(TO) vibrations of О2– ions perpendicularly to the polar axis. Thus this dependence is close to the temperature dependence of the width of the 1A1(TO) band. We have revealed that the intensity of fundamental bands depends nonmonotonically on the temperature. At the same time, the temperature dependence of the extra bands intensity is strictly linear.

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FUNDING SOURCES This work was supported by RFBR grants № 15-02-04261 and 15-03-03372.

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FIGURE CAPTIONS Fig. 1. Temperature changes in the Raman spectrum of a congruent LiNbO 3 crystal, extra bands are indicated by arrows. Left of (a): A1(TO) vibrations measured in the Y(ZZ)Y scattering geometry; right of (a): E(TO) vibrations measured in the Y(ZX)Y scattering geometry. A1(T) vibrations measured in the Y(ZZ)Y scattering geometry along with a extra E(TO) band at 151 cm– 1 are demonstrated on (b).

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Fig. 2. Raman spectra of LiNbO3:Y(0.46 wt.%) (1), congruent LiNbO3 crystal (2), stoichiometric LiNbO3 crystal (3) in the frequency range 60-180 and 300-360 cm–1 Fig. 3. Temperature dependences of widths (S) and intensities of extra bands at 694, 330, 120, and 104 cm–1 measured in the Y(ZZ)Y scattering geometry.

SC R

Fig. 4. Temperature dependences of widths (S) of bands that correspond to fundamental lattice vibrations in the Raman spectra of (a) congruent and (b) stoichiometric LiNbO3 crystals.

A

CC E

PT

ED

M

A

N

U

Fig. 5. Temperature dependencies of intensities of Raman bands that correspond to fundamental lattice vibrations in the spectra of (a) congruent and (b) stoichiometric LiNbO3 crystals.

A ED

PT

CC E

IP T

SC R

U

N

A

M

Figr-1

A ED

PT

CC E

IP T

SC R

U

N

A

M

Figr-2

A ED

PT

CC E

IP T

SC R

U

N

A

M

Figr-3

A ED

PT

CC E

IP T

SC R

U

N

A

M

Figr-4

A ED

PT

CC E

IP T

SC R

U

N

A

M

Figr-5

Tables: Table 1. Main parameters of bands (frequency ν, cm-1; width S, cm-1) in Raman spectra of congruent (congr.) and stoichiometric (stoich.) LiNbO3 crystals that correspond to vibrations of the A1(TO) and А2 symmetry types at T = 100 K. Experimentally observed frequencies of extra bands are marked by the upper index 1, and calculated frequencies of “forbidden” vibrations of the A2 symmetry type are marked by the upper index 2. А1(ТО) and А2 phonons 2A1 (TO)

256

275

254

276

3301

10,0

7,2

19.0

12,6

9,4

21,6

2202

239

320

3212

1532

208

279

1041

congr . S, сm-1

1201

stoic h. congr .

25,9

34,4

Calculations, [29]

239

2872

271

4A2

4A1 (TO)

5A2

630

333

632

5,1

16,3

6,9

21,4

69 41

8801

35, 8

381

4322

4622

607

8932

344

4172

4392

583

8832

328

633

ED

M

[14]

3A2

335

A

ν,сm-1 [30]

3A1 (TO)

SC R

stoic h.

2A2

IP T

1A1 (TO )

U

ν, сm-1

1А2

N

Experiment, this work

PT

Table 2. Main parameters of bands (frequency ν, cm-1; width S, cm-1) in Raman spectra of congruent (congr.) and stoichiometric (stoich.) LiNbO3 crystals that correspond to vibrations of the E(TO) symmetry type at T = 100 K. Experiment, this work

E(TO) phonons 4E(TO) 5E(TO) 6E(TO)

1E(TO)

2E(TO)

3E(TO)

stoich.

152

180

237

262

322

congr.

151

235

264

stoich.

6,1

6,3

congr.

7,6

Calculations, [29]

157

[30] [14]

CC E

ν,сm-1

A

S, сm-1

ν,сm-1

7E(TO)

8E(TO)

9E(TO)

368

435

579

610

320

370

430

581

8,3

8,5

18,2

7,6

14,6

7,7

10,6

9,7

20,7

9,9

16,8

214

269

349

419

423

446

605

690

151

167

236

307

334

352

432

526

617

163

200

249

267

324

372

424

572

619