V3 Mode Research Articles

Structural characteristics of Mg-doped (1-x)(K0.5Na0.5)NbO3–xLiSbO3 lead-free ceramics as revealed by Raman spectroscopy

This paper presents a Raman spectroscopic study of compositional-change-induced structure variation and of the related mechanism of Mg doping in LiSbO3 (LS)-modified (K0.5Na0.5)NbO3 (KNN) ceramics. With increasing LS content from 0 to 0.06, a discontinuous shift towards higher wavenumbers was found for the band position of the A1g(v1) stretching mode of KNN, accompanied by a clearly nonlinear broadening of this band and a decrease in its intensity. Such morphological changes in the Raman spectrum result from two factors: (i) changes in polarizability/binding strength of the O–Nb–O vibration upon incorporation of Li ions in the KNN perovskitic structure and (ii) a polymorphic phase transition (PPT) from orthorhombic to tetragonal (O → T) phase at x > 0.04. Upon increasing the amount, w, of Mg dopant incorporated into the (1-x)KNN–xLS ceramic structure, the intensity of the Raman bands are enhanced, while the peak position and the full width at half maximum of the A1g(v1) mode was found to experience a clear dependence on both w and x. Raman characterization revealed that the mechanism of Mg doping is strongly correlated with the concentration of Li in the perovskite structure: Mg2+ ions will preferentially replace Li+ ions for low Mg doping while replace K/Na ions for higher doping of Mg. The PPT O → T was also found to be altered by the introduction of Mg and the critical value of LS concentration, xO−T, for incipient O → T transition in the KNN–xLS–wMT system was strongly dependent on Mg content, with xO → T being roughly equal to 0.04 + 2w, for the case of dilute Mg alloying.

Vibrationally quantum-state-specific dynamics of the reactions of CN radicals with organic molecules in solution

The dynamics of reactions of CN radicals with cyclohexane, d(12)-cyclohexane, and tetramethylsilane have been studied in solutions of chloroform, dichloromethane, and the deuterated variants of these solvents using ultraviolet photolysis of ICN to initiate a reaction. The H(D)-atom abstraction reactions produce HCN (DCN) that is probed in absorption with sub-picosecond time resolution using ∼500 cm(-1) bandwidth infrared (IR) pulses in the spectral regions corresponding to C-H (or C-D) and C≡N stretching mode fundamental and hot bands. Equivalent IR spectra were obtained for the reactions of CN radicals with the pure solvents. In all cases, the reaction products are formed at early times with a strong propensity for vibrational excitation of the C-H (or C-D) stretching (v(3)) and H-C-N (D-C-N) bending (v(2)) modes, and for DCN products there is also evidence of vibrational excitation of the v(1) mode, which involves stretching of the C≡N bond. The vibrationally excited products relax to the ground vibrational level of HCN (DCN) with time constants of ∼130-270 ps (depending on molecule and solvent), and the majority of the HCN (DCN) in this ground level is formed by vibrational relaxation, instead of directly from the chemical reaction. The time-dependence of reactive production of HCN (DCN) and vibrational relaxation is analysed using a vibrationally quantum-state specific kinetic model. The experimental outcomes are indicative of dynamics of exothermic reactions over an energy surface with an early transition state. Although the presence of the chlorinated solvent may reduce the extent of vibrational excitation of the nascent products, the early-time chemical reaction dynamics in these liquid solvents are deduced to be very similar to those for isolated collisions in the gas phase. The transient IR spectra show additional spectroscopic absorption features centered at 2037 cm(-1) and 2065 cm(-1) (in CHCl(3)) that are assigned, respectively, to CN-solvent complexes and recombination of I atoms with CN radicals to form INC molecules. These products build up rapidly, with respective time constants of 8-26 and 11-22 ps. A further, slower rise in the INC absorption signal (with time constant >500 ps) is attributed to diffusive recombination after escape from the initial solvent cage and accounts for more than 2/3 of the observed INC.

Extremely slow intramolecular vibrational redistribution: Direct observation by time-resolved raman spectroscopy in trifluoropropyne

We have studied the dynamics of intramolecular vibrational redistribution (IVR) from the initially excited mode v1 ≈ 3330 cm−1 (acetylene-type H-C bond) in H-C≡C-CF3 molecules in the gaseous phase by means of anti-Stokes spontaneous Raman scattering. The time constant of this process is estimated as 2.3 ns—this is the slowest IVR time reported so far for the room-temperature gases. It is suggested that so long IVR time with respect to the other propyne derivatives can be explained by a larger defect, in this case, of the Fermi resonance of v1 with v2 + 2v7—the most probable doorway state leading to IVR from v1 to the bath of all vibrational-rotational states with the close energies. In addition, it is shown that the observed dynamics is in agreement with a theoretical model assuming strong vibrational-rotational mixing.

A computational study on the ring stretching modes of halogen‐substituted pyridine involved in H‐bonding

AbstractDensity functional method B3LYP plus the AUG‐cc‐pVDZ and AUG‐cc‐pVTZ basis sets is used to investigate ring normal modes of halogen‐substituted pyridines involved in the N···HX H‐bonds with HX (X = F, Cl). The results demonstrated that the formation of hydrogen bond leads to an increase in the frequencies of the ring breathing mode v1, the N‐para‐C stretching mode v6a and the meta‐CC stretching mode v8a, whereas there is no change in the triangle mode v12 for free pyridine and a smaller blue shift for substituted pyridines. There is a strong coupling between the CY stretching vibration and the triangle mode (ortho‐ and para‐substituted) or the breathing mode (meta‐substituted) in substituted pyridines, which leads to the frequency decrease in the triangle or breathing modes. The natural bond orbital analysis suggests that electrostatic interaction and charge transfer caused by the intermolecular and intramolecular hyperconjugations are the origin of the frequency blue shift in the ring stretching modes. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Rovibrational state specific scattering distributions of the O(1D) + CD4→ OD + CD3 (v1, v2, N) reaction

The rovibrational state distributions and state-resolved scattering distributions of CD(3) radicals produced by the reaction O((1)D) + CD(4) were investigated by crossed molecular beam ion imaging. The rotational structure of the resonance-enhanced multiphoton ionization spectrum of CD(3) in the ground vibrational state indicates that the low K rotational states of CD(3) radicals are preferentially populated. The state-resolved scattering distributions of CD(3) (v = 0) and those of the excited states of the out-of-plane bending (v(2)) mode exhibit a structureless forward-scattering component due to an insertion pathway and a structured backward-scattering component due to an abstraction path. The scattering distributions of CD(3) in the excited state of the C-D symmetric stretch (v(1)) do not exhibit the abstraction component. The scattering distribution of the abstraction component gradually extends in the forward direction with increasing intensity as the v(2) vibration becomes more strongly excited. This suggests that abstraction with a larger impact parameter results in stronger excitation of v(2).

Optimization of the infrared multiple-photon dissociation of SiF4 to increase the isotopic selectivity

The influence of laser fluence and wavelength as well as of the sample pressure on the infrared multiple-photon dissociation (IRMPD) of SiF4 and H2 mixtures has been studied. Different lines of the 9.4 μm emission band of a TEA CO2 laser have been used as excitation sources. A power law dependence of the fraction of molecules dissociated per pulse on the laser fluence was found. The optimization of the IRMPD of silicon tetrafluoride was performed by varying both SiF4 and H2 pressures. The IRMPD spectrum exhibits a red shift of ~ 12 cm−1 produced by the anharmonicity of the molecular vibrations. Moreover, the isotopic selectivity of the IRMPD of SiF4 has been determined with wavelengths shifted to the red and the blue of the 9P(36) line which is quasi-resonant with the v3 mode of 28SiF4. The maximum values were obtained with the 9P(32) emission line which has the least overlap with the absorption bands of the less abundant species.

An Application of near Infrared and Mid-Infrared Spectroscopy to the Study of Natural Halotrichites: Halotrichite, Apjohnite and Wupatkiite

Near infrared (NIR) and Fourier transform infrared (FT-IR) spectroscopy have been used to determine the mineralogical character of isomorphic substitutions for Mg2* by divalent transition metals Fe, Mn, Co and Ni in natural halotrichite series. The minerals are characterised by d→ d transitions in the NIR region 12,000–7500 cm−1. The NIR spectrum of halotrichite reveals broad features from 12,000 cm−1 to 7500 cm−1 with a splitting of two bands resulting from ferrous ion transition 5T2g→5Eg. The presence of overtones of OH− fundamentals near 7000 cm−1 confirms molecular water in the mineral structure of the halotrichite series. The appearance of the most intense peak at around 5132 cm−1 is a common feature in the three minerals and is derived from a combination of OH− vibrations of water molecules and v2 water-bending modes. The influence of cations such as Mg2+, Fe2+, Mn2+, Co2+ and Ni2+ shows on the spectra of halotrichites, especially for wupatkiite-OH stretching vibrations in which bands are distorted conspicuously to low wave numbers at 3270 cm−1, 2904 cm−1 and 2454 cm−1. The observation of a high-frequency v2 mode in the infrared spectrum at 1640 cm−1 indicates that the coordination of water molecules is strongly hydrogen bonded in natural halotrichites. The splitting of bands in v3 and v4 (SO4)2− stretching regions may be attributed to the reduction of symmetry from T d to C2 v for sulphate ion. This work has shown the usefulness of NIR spectroscopy for the rapid identification and classification of the halotrichite minerals.

Theoretical study on effects of hydrogen bonding on the ring stretching modes of pyridine

Pyridine generally acts as the proton acceptors in the hydrogen bonding interaction by using its lone pair n(N) or pi-electrons. Some previous research indicated that for the N-type H-bond, the ring breathing mode v(1), the N-para-C stretching mode v(6a) and the meta-CC stretching mode v(8a) of pyridine showed a frequency blueshift but the triangle mode v(12) had no change in frequency. Both electrostatic interaction and charge transfer caused by intermolecular hyperconjugation n(N)-->sigma( *)(HX) have contributions to the frequency blue shifts, while charge transfer is predominant at equilibrium intermolecular distance. An intramolecular hyperconjugation between the lone pair n(N) and the two sigma( *)(meta-CC) orbitals in the pyridine ring provides a reasonable interpretation for the effect of charge transfer on the ring stretching modes upon formation of the N-type H-bonding.

Phase Transition in CCl4 under Pressure: a Raman Spectroscopic Study

High-pressure Raman studies at room temperature are performed on CCl4 up to 13 GPa. The Raman bands of the internal modes (v2, v4 and v1) show entirely positive pressure dependence. The slopes dω/dP of the internal modes exhibit two sudden changes at 0.73 GPa and 7.13 GPa, respectively. A new lower frequency mode (225 cm−1) appears at 3.03 GPa, and the splitting of v2, v3 and v4 occurs at about 7.13 GPa. Moreover, Raman spectra of Fermi resonance show that the relative position of the v1 + v4 combination and the v3 fundamental firstly interchanges corresponding to that at ambient pressure, then the v1 + v4 combination disappears in the gradual process of compression. It is indicated that the pressure-induced phase transition from CCl4 II to CCl4 III occurs at 0.73 GPa, and CCl4 III undergoes a transition to CCl4 IV below 3.03 GPa. Further CCl4 IV transforms in a new high-pressure phase at about 7.13 GPa, and the symmetry of the new high-pressure phase is lower than that of CCl4 IV. All the transitions are reversible during decompression.

Phase coexistence and high electrical properties in (KxNa0.96−xLi0.04)(Nb0.85Ta0.15)O3 piezoelectric ceramics

( K x Na 0.96 − x Li 0.04 ) ( Nb 0.85 Ta 0.15 ) O 3 lead-free piezoelectric ceramics were produced by conventional solid-state reaction method. The effects of K/Na ratio on the phase transitional behavior, Raman spectrum, microstructure, and dielectric, piezoelectric, and ferroelectric properties of the ceramics have been investigated. The phase structure of the ceramics undergoes a transition from orthorhombic to tetragonal phase with increasing x. A double-degenerate symmetric O–Nb–O stretching vibration v1 and a triply degenerate symmetric O–Nb–O bending vibration v5 are detected as relatively strong scattering in the Raman spectra. The peak shifts of v5 and v1 modes all have a discontinuity with x between 0.42 and 0.46, which may suggest the coexistence of orthorhombic and tetragonal phases in this range. Properly modifying x reduces the sintering temperature, promotes the grain growth behavior, and improves the density of the ceramics. The polymorphic phase transition (at To-t) is shifted to near room temperature by increasing x to 0.44 (K/Na ratio of about 0.85:1), and the coexistence of orthorhombic and tetragonal phases in the ceramics at x=0.44 results in the optimized electrical properties (d33=291 pC/N, kp=0.54, εr=1167, tan δ=0.018, To-t=35 °C, TC=351 °C, Pr=27.65 μC/cm2, and Ec=8.63 kV/cm). The results show that the equal K/Na ratio is not an essential condition in obtaining optimized electrical properties in (KxNa0.96−xLi0.04)(Nb0.85Ta0.15)O3 ceramics.

Conformational Heterogeneity of Cytochrome c Probed by Resonance Raman Spectroscopy as a function of pH and Temperature

The oxidized state of cytochrome c is a subject of continuous interest due to the multitude of conformations the protein adopts. Despite numerous studies, native and non-native states of ferricytochrome c have not been comprehensively analyzed regarding the influence of solvent conditions on structure, function, and thermodynamic equilibrium. Compared to the oxidized state, the reduced state of cytochrome c is rather stable since it adopts one conformation over a broad pH (2-12) and temperature (∼100°C) range. In the current study, we have analyzed the high frequency (1200-1800cm−1) Soret and Q-band resonance Raman spectra of oxidized and reduced horse heart cytochrome c (hhc) in terms of depolarization ratios and normalized Raman intensities, as a function of increasing pH and temperature. Initial analysis of our data collected for the Soret band resonance indicates that the depolarization ratios of A1g modes v2, v3, and v4 of the native state III and the alkaline state IV are practically identical. They deviate from the respective D4h-value, indicating that B1g (triclinic) or B2g (rhombic) type distortions affect the Raman tensor. For state III, the depolarization ratios of B1g modes v10, v11, and v13 deviate substantially from the expectation value indicating that these modes are affected by a large B1g type distortion. The alkaline III-> IV transition moves the depolarization ratios of these B1g modes closer to their D4h-value of 0.75, indicating a substantial decrease of the rhombic B1g-type deformation. Data from pH 12, which favor the population of the V-state, suggest a substantial increase of rhombic deformations, apparently caused by the replacement of a lysine by a hydroxyl ligand. Currently we are analyzing the depolarization ratios for the Q band resonance and the high temperature data for both resonances.

The Transformation of Nesquehonite to Hydromagnesite in the System CaO-MgO-H2O-CO2: An Experimental Spectroscopic Study

ABSTRACT This study reports the nature of the nesquehonite-to-hydromagnesite transition at 52°C in an aqueous medium hosting magnesian calcite and nesquehonite. The latter mineral occurs with abundant calcite at the floor of the experimental chamber (substrate) and as a film of needles at the interface between the mother liquor and the atmosphere (surface film). The experimental vessel was held at 52°C for 336 h and at 60°C for a further 192 h. Precipitates were analyzed by Fourier transform (FT)–Raman, augmented by FT-infrared and x-ray diffraction. At 52°C, hydromagnesite and dypingite occur with abundant quantities of a hitherto unreported transitory magnesium hydrate carbonate (TMHC), together with huntite, magnesian calcite, and traces of nesquehonite and monohydrocalcite. The FT-Raman spectra of the first-formed hydromagnesite crystals contain the Raman-forbidden v2 mode, interpreted to indicate a relaxation in selection rules, caused by rapid precipitation. Hydromagnesite growth at the expense of T...

Forced Resonant Oscillations as a Response to Periodic Winds in a Stratified Reservoir

The response of the Sau reservoir to a wind field characterized by having marked periodicities of 12 h and 24 h has been studied. Measurements of temperature, with a thermistor string, and currents, with an acoustic Doppler current meter, show that the reservoir also responds with the same water periodicities. During certain times of the stratified period, some of the natural oscillation modes of the reservoir are close to these forcing wind periods. In particular, in mid-July the vertical Mode V2 is close to 12 h and in mid- to end of September the vertical Mode V3 is close to 24 h. In these situations, these modes are selected out of the spectrum of possible internal waves and the reservoir behaves as a forced oscillator in resonance with the wind. The structure and the period of these vertical modes have been elucidated by using the 3D model ELCOM. Both modes are affected by the Earth's rotation at the widest part of the reservoir.

Chemical Enhancement Effects in SERS Spectra: A Quantum Chemical Study of Pyridine Interacting with Copper, Silver, Gold and Platinum Metals

Using density functional theory, we have studied the interactions between pyridine (Py) and coinage metals (silver, copper, and gold) as well as the transition metal platinum. We present here a detailed analysis of the influence of chemical enhancement effects on the SERS signals. We analyze the differential Raman scattering cross sections of the a1 vibrational modes related to Py. The results show that the relative Raman intensities of SERS spectra depend strongly on the binding interaction between Py and the SERS active centers, the electronic property of metal materials, and the incident wavelengths. When the bonding between Py and a SERS site is very weak, analogous to physical adsorption, the Raman spectra of the adsorbed Py are similar to that of free Py. For Py interacting strongly with copper, gold, and platinum clusters, we find that the Raman intensities of the v1, v6a, v9a, and v8a modes of Py are enhanced, whereas the intensity of the v12 mode decreases. To check the enhancement effect of the charge-transfer mechanism, we calculate the preresonance Raman spectra. For Py interacting with silver, copper, and gold clusters, the low-lying charge transfer states are formed from the valence shell s orbital of metal to the unoccupied π*-type orbitals (b1 and a2) of the Py ring; whereas for Py adsorbed on platinum clusters, the low-lying charge transfer states are formed due to the transitions from some d orbitals of the metal clusters to the two unoccupied π*-type orbitals of Py. The results show that the Raman spectral property depends strongly on the property of these excited states and the electronic structures of the metal materials.

The influence of temperature on Raman modes in YVO4 and GdVO4 crystals

Frequency shift and line broadening of Raman laser active Ag(V1) vibronic modes in yttrium and gallium vanadate crystals are investigated in the 15-300 K temperature range. It was found that the vibronic mode frequency is reduced in both crystals with the temperature increase that can be ascribed to the thermal expansion of the crystal lattice. The values of the frequency shift derivative with respect to the temperature in YVO4 and GdVO4 crystals were measured to be -0.023 and -0.018 (cm⋅grad)-1. The temperature broadening dependencies of Ag(v1) modes exhibited a complex behavior. At about room temperature they obey a linear dependencies with the slope 0.013 and 0.008 (cm⋅grad)1, correspondingly.

The seasonal evolution of high vertical‐mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoir are examined through the analysis of field observations and numerical techniques. The study period extends from the onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing was periodic, with a period of 24 h (typical of land‐sea breezes), and the thermal structure in the lake was characterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to medium sized reservoirs with deep outtakes. Basin‐scale internal seiches of high vertical mode (ranging from mode V3 to V5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed as stratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local wind forcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 became dominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing.

Low-energy electron collisions with CH3Br: the dependence of elastic scattering, vibrational excitation, and dissociative attachment on the initial vibrational energy

Using the laser photoelectron attachment (LPA) method at an energy width of 1–2 meV, the Br− yield due to dissociative electron attachment to the molecule CH3Br has been measured over the energy range 1–180 meV at a gas temperature of 600 K. The data clearly exhibit the vibrational Feshbach resonance predicted by Wilde et al (2000 J. Phys. B: At. Mol. Opt. Phys. 33 5479) and associated with the v3 = 4 vibrational level of the C–Br stretch mode in the neutral molecule. We also report the dependence of the rate coefficient for Rydberg electron attachment (measured at high principal quantum numbers n ≈ 150) on gas temperature and find an Arrhenius-type behaviour compatible with the results of R-matrix calculations and with earlier findings of electron swarm experiments. With the aim to stimulate experiments, we report absolute cross sections for elastic scattering and vibrationally inelastic scattering involving the C–Br stretch mode v3 of CH3Br for several initial vibrational levels in the range v3 = 0–4; they were obtained with R-matrix calculations based on the same potential input as that involved in the computations of the cross sections for dissociative attachment.

Rotationally Resolved Optical Rotation and Circular Dichroism Effects for Symmetric Top Molecules Induced by a Resonant Circularly Polarized Pumping Optical Field

The rotationally resolved laser-induced optical activity including the laser-induced optical rotation (LIOR) and laser-induced circular dichroism (LICD) effects of an IR probing light pumped by a collinear intense resonant circularly polarized light dependent on the third-order susceptibility due to the pure electric dipole interaction for achiral symmetric top molecules in the gas phase is discussed theoretically. The laser-induced optical activity contains four distinct contributions named A, B, C, and D terms: the B term of the LIOR and LICD arising from the rotational wave function perturbed by the pumping light is deduced using the semiclassical perturbation theory, and the expressions for A, C, and D terms, respectively, due to the ac Stark effect, the Boltzmann statistical redistribution, and the alteration of occupation polability, are obtained from previous results [Zheng, R.-H.; Chen, D.-M.; Wei, W.-M.; He, T.-J.; Liu, F.-C. J. Chem. Phys. 2004, 121, 6835]. The microwave-IR double resonant spectrum is proposed to detect the LIOR and LICD effects. As an example, the LIOR and LICD for the HCF(3) molecules in the conditions of 298.15 K and 0.3 Torr when the IR probing light sweeps over the rotational-vibrational transition of the v(5) and v(1) modes and the right circularly polarized microwave pumping light with the intensity of 1 kW cm(-2) at the resonant frequency 40.84 GHz are calculated on the basis of the B3LYP/6-311++G* computations. The theoretical results indicate that the B term can be of the same order of magnitude as the A and D terms, and the LIOR and LICD can be measurable in comparison to the rotationally resolved MVCD. The laser-induced optical activity may provide useful new information and form a basis for a different kind of optical activity spectroscopy.

Coupling Among CH Stretching, Bending and Rocking Vibrational Modes in CH2Cl2

Infrared absorption spectra of gaseous CH2Cl2 in the regions of 120012000 cm1 were measured using a Bruker IFS 120HR Fourier transform spectrometer in conjunction with a multipass cell. 47 vibrational levels of overtone and combinational spectral lines of the CH stretching (v1, v6), bending (v2), and rocking (v8) modes were analyzed and assigned. Utilizing the normal mode model and considering the coupling among CH stretching, bending and rocking vibrations, values of the harmonic frequency i, the anharmonic constant xij, and the coefficients of Fermi and the Darling-Dennison resonances of v1, v6, v2 and v8 modes were also determined from experimental spectral data with nonlinear least-square fitting. These spectral constants reproduced the experimental levels very well. These results showed that Fermi resonance between CH stretching and rocking vibrations (k188 = 254.63 cm1) is stronger than that between CH stretching and bending vibrations (k122 = 54.87 cm1); and that Darling-Dennison resonances between CH stretching and bending vibrations (k1166 = 215.28 cm1) is also much stronger than that between CH bending and rocking vibrations (k2288 = 5.72 cm1).

Raman Scattering Study of Piezoelectric (Na0.5K0.5)NbO3-LiNbO3 Ceramics

A Raman scattering study of (Na0.5K0.5)NbO3 (NKN)-LiNbO3 (LN) lead-free piezoceramics has been carried out on nominal compositions of (1-x)NKN-xLN (0 ≤x ≤0.70). The Raman spectra demonstrated a variety of changes with x, mainly classified as lattice translations involving motions of the alkaline cations and internal modes of NbO6 octahedra. At 0.05 ≤x ≤0.07, the broadening of the scattering peaks corresponding to the internal modes of the NbO6 octahedra occurred preferably, which is consistent with the evidence for a morphotropic phase boundary (MPB). Furthermore, an abrupt shift was observed in the peak position of the symmetric stretching mode v1 to a higher frequency, resulting from the distortion of O-Nb-O angles caused by incorporating small Li ions into the perovskite units. This is considered to be a prologue for the structural transformation in the NKN-LN solid solution from orthorhombic to tetragonal symmetry. At compositions in which x increases above the MPB, the translational mode of the Li+ cation emerged clearly, and the overall scattering pattern gradually changed to complex patterns caused by the formation of a tungsten-bronze K3Li2Nb5O15 (KLN) secondary phase and an increase in the number of distorted LiNbO3-type crystal units.