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The structural and electronic properties of buckled antimonene have been analysed using density functional theory based ab-initio approach. Geometrical parameters in terms of bond length and bond angle are found close to the single ruffle mono-layer of rhombohedral antimony. Inter-frontier orbital analyses suggest localization of lone pair electrons at each atomic centre. Phonon dispersion along with high symmetry point of Brillouin zone does not signify any soft mode. With an electronic band gap of 1.8eV, the quasi-2D nano-surface has been further explored for NH3/NO2 molecules sensing and qualities of interaction between NH3/NO2 gas and antimonene scrutinized in terms of electronic charges transfer. A current-voltage characteristic has also been analysed, using Non Equilibrium Green's function (NEGF), for antimonene, in presence of incoming NH3/NO2 molecules.

This paper presents a survey of soft modes and their relationship to structural phase transitions. After introducing the concept of a soft mode, the origin of softening is considered from a lattice-dynamical point. The Landau theory approach to structural transitions is then discussed, followed by a generalization of the soft-mode concept through the use of the dynamic order-parameter susceptibility. The hyper-Raman spectra in the cubic phase of (Ba0.8Sr0.2)Ti0.95(Zn1/3Nb2/3)0.05O3 are studied with special emphasis on the lowest-frequency phonon mode. The spectral structure is found to change above the Curie temperature (303–873 K). Soft modes were put forward by Cochran and Anderson about 50 years ago as an explanation of structural phase transitions. Extending Landau's theory of phase transitions, their prediction was that the square of the frequency of the soft mode was proportional to ω 0 ( T ) = C T − T C where Tc is the transition temperature.

We model the superfluid properties of a trapped exciton–polariton condensate under non-resonant excitation subjected to a rotating defect. With increasing the linear velocity of rotating defect, the density modulation can be classified into superfluid-like regime, parabolic-like regime, Cherenkov regime and over-Cherenkov regime. The threshold-like behavior of drag force and the onset of turbulent fringes can define the critical velocity for the superfluidity. Based on the perturbative drag force in the Bogoliubov-type analysis, the rigid modes with gapped excitation spectrum have higher critical velocity than that of the soft modes.

First-principles calculations on AlPO4 predicted the stability of a stishovite-like phase and the existence of a ferroelastic phase transition between this phase and m-CaCl2 phase. The ferroelastic phase transition is consistently supported from the point view of energy, spontaneous strain, tilt angles of octahedra, and behaviour of soft-modes. The soft modes are B 1 g in stishovite-like phase and Ag in m-CaCl2 phase. The static transition occurs at pressure 45.3 GPa, which was judged from the character of soft modes, and phase stability fields were investigated up to high temperatures. For computational methods, this study calculated total energies with density functional theory (DFT), phonon properties with density functional perturbation theory (DFPT), and high-pressure high-temperature phase boundaries within quasiharmonic approximation (QHA).

A self-consistent Landau phenomenological approach has been used to study the ferroelectric transition in films in the presence of various surface effects such as depolarization and strain. The polarization distribution of the film is computed and its variation with respect to temperature, thickness and strain is determined. The gradual decrease in polarization across the transition shows the diffusive behavior which is confirmed from the soft mode and the dielectric susceptibility analysis. The critical thickness below which ferroelectricity disappears is also computed. The degree of diffuseness in the transition is obtained from the susceptibility exponent which shows more and more diffusive behavior for smaller and smaller film thickness.

We have studied the detailed mechanism of epitaxial strain induced ferroelectricity in rocksalt binary compound by ab initio calculation and soft mode group theory analysis. By applying compressive strain, cubic binary rocksalt (Fm3m) transforms into tetragonal (I4/mmm) structure. With increasing compressive strain, tetragonal structure becomes unstable against spontaneous transformation to lower symmetry tetragonal structure (I4/mm), evident both from ab initio calculation and from soft mode group theory analysis. For the tensile strain, phase transition sequence can be cubic binary rocksalt to tetragonal (I4/mmm) and to orthorhombic structure (Im2m). From ab initio calculation and space group analysis, we propose that the epitaxial strain induced ferroelectricity of rocksalt binary compound is the generic property.

We address the dielectric behavior in a free standing spherical particle using the phenomenological Landau theory. Considering the equations of motion and small perturbation against uniform polarization, we obtain the size driven ferroelectricity. The size driven polarization is shown to diverge at a new correlation length which turns out to be the extrapolation length. Mode analysis in such systems is carried out and it is found that the size driven ferroelectricity is associated with a soft mode which takes a minimum value at the new transition temperature similar to that of the bulk system. We suggested that such a mode can be tested in Raman measurement.

Bismuth titanate nanocrystals with grain size from 25 to 83 nm were synthesized by chemical coprecipitation via heat treatment. Lattice structures of the nanocrystals were determined by X-ray diffraction and refined by using the Rietveld method. An empirical relationship a / b ∼ 1 − e − d is established between the orthorhombic distortion ratio a / b and the grain size d , from which a critical grain size d c for vanishing of ferroelectricity of bismuth titanate nanocrystals was found to be 38 nm. Low-frequency Raman spectra were investigated at various grain sizes in the nanocrystals. The results show that the soft mode obviously softens and ferroelectricity weakens with decrease in the grain size. An empirical formula ω 2 = ω 0 2 ( 1 − d 0 / d ) is found to describe the relationship between the soft-mode frequency ω and the grain size d with two fitting parameters ω 0 = 29 cm − 1 and d 0 = 23 nm.

Ab initio calculations based on the density functional theory are performed to investigate the pressure-induced rutile–CaCl2 phase transition in MgF2. The phase transition is characterized as a second-order nature by evidence of the continuous changes of the cell volume and lattice constants at the transition, consistent with the experimental observation. Under compression, the B 1 g Raman active mode in the rutile phase is predicted to soften, signifying the dynamical instability. The softening of shear modulus C s with increasing pressure is also identified through the elastic constants calculation. The transition pressures derived from the free energy, soft mode, and elastic constants calculations are in satisfactory agreement with the experimental value. The current calculations have demonstrated that the rutile–CaCl2 phase transition is driven by the coupling between the Raman active B 1 g mode and shear modulus C s .

The dielectric properties of the [4-NH2C5H4NH] SbCl4 (abbreviated as 4-APCA) crystal were investigated under hydrostatic pressure up to 300 Mpa. The pressure–temperature phase diagram was given. The paraelectric–ferroelectric phase transition (II→III) temperature (Tc) increases linearly with increasing pressure with a slope dTc/dp=21×10−2 K/MPa. The pressure dependence of Curie–Weiss constants has been evaluated also. In the paraelectric phase (II) the Curie constant (C+) was pressure dependent whereas the C− constant over the ferroelectric phase (III) was almost constant. The results are interpreted in terms of improper and displacive type phase transition model with a soft phonon at a zone boundary.

The temperature dependences of internal friction and modulus were measured for the Fe–Mn–Si–Cr– x N alloys. A stable modulus softening of parent was newly observed to associate with the γ→e martensitic transformation in the alloys containing certain amount (e.g. >0.086 mass%) of nitrogen, although the rather strong softening has been always recognized to occur during its reverse transformation. The enhanced strength and the increased stacking fault energy of γ matrix by nitrogen alloying are suggested to make contribution to the soft mode.

Diamagnetic phase transition is shown to be associated with the instability of the three-dimensional electron gas against a temperature dependent magnon soft mode whose frequency vanishes at the phase transition point. Temperature and sample size softening of the magnon mode of an orbital nature is considered at quantizing magnetic fields under conditions of the non-linear de Haas-van Alphen effect in bulk metals and confined metallic samples.

Phase transitions in a recently discovered class of hydrogen-bonded organic crystals are analyzed by Landau theory. It is shown that the transitions are ferroelastic. Two types of transition, orthorhombic-to-monoclinic and monoclinic-to-triclinic, are analysed using an expansion of the free energy in symmetry-allowed powers of the strain components. For three examples, new data are presented for the crystallographic parameters in a range of temperature including the phase transition point Tc. These data show that the transitions are second order and the temperature dependences are consistent with the mean-field analysis. We propose that the making and breaking of the hydrogen bond interactions with variation of temperature accounts for these reversible ferroelastic phase transitions. Expressions are derived for the entropy and the specific-heat discontinuity at Tc. It is pointed out that the transitions should be accompanied by ‘soft-mode’ behavior in a phonon of appropriate symmetry.

Temperature dependent EPR measurements on copper doped Rb2ZnCl4 single crystals allowed us to evidence and study the P21cn↔C1c1 structural phase transition that takes place in this compound at 74.6 K. From the two types of Cu2+ centers localized at different anionic sites, called Cu2+(I) and Cu2+(II), which are formed in this compound, only the Cu2+(II) centers exhibit observable changes in their EPR spectra, attributable to the symmetry lowering. The observed changes have been related to the soft-mode responsible for the structural phase transition.

We conducted theoretical studies of the properties of solid halogens (iodine, bromine and chlorine) under pressure, employing the full potential linear muffin–tin orbital method with the local density approximation. From the electronic dispersion curves, we estimated the metallization pressures as 10, 35 and 100 GPa for iodine, bromine and chlorine, respectively. We also examined the pressure dependence of frequencies of Raman-active A g modes using the frozen-phonon method, and found that there was good agreement with experimental data. We found frequency softening in iodine and bromine, and consider this as not only a precursor of molecular dissociation, but also a consequence of metallization. We examined the scaling rules, and found that these agreed with the band-theoretical results.

We apply the Heisenberg model for antiferromagnetic interaction and Diffour model for ferroelectric interaction to analyze the magnetic, electric, magnetoelectric property in the system with the spontaneous coexistence of the ferroelectric and antiferromagnetic orders below a certain temperature. The soft mode theory is used to calculate the on-site polarization and mean field theory is applied to deal with the on-site magnetization. We also present the perpendicular magnetoelectric susceptibility χ me ⊥ , polarization susceptibility χ p as a function of temperature, and discuss the effect of the inherent magnetoelectric coupling on them. In addition, it is found that an anomaly appears in the curve of the polarization susceptibility due to the coupling between the ferroelectric and antiferromagnetic orders.

An atomistic simulation based on the Buckingham potential is investigated in order to describe the phonon behaviour in the wurtzite, zinc-blende, rocksalt and NiAs structures in gallium nitride. The obtained results show the presence of soft modes in the wurtzite structure, with a negative pressure coefficient of the E2 (low) mode, in good agreement with experimental results. Our calculations are extended to predict the dynamical properties of the zinc-blende, rocksalt and NiAs phases such as the evaluation of the pressure coefficient and the Gruneisen parameter for each mode.

Dielectric dispersion is shown to occur at microwave frequencies in single crystals of PbCo1/2W1/2O3 in the frequency range of 0.5–500 GHz. The frequency dependence of this dispersion can be explained in terms of a strongly damped ferroelectric soft mode occurring in the incommensurate phase and near each of the paraelectric–incommensurate and incommensurate–ferroelectric transitions.

The isotope exchange effect on the stability of the paraelectric phase and on the Curie temperature in displacive ferroelectrics is considered. It is shown that ferroelectric (FE) lattice instability induced by the isotope exchange is the anharmonic and quantum effect and the associated FE phase transition is the result of the suppression of the zero-point atomic motion due to the enhancement of atomic masses caused by the substitution of a heavy isotope for a light one. A criterion for the low-temperature isotopically induced ferroelectricity is formulated. It is found that only in quantum paraelectrics with nearly complete compensation of the harmonic contribution into FE soft mode frequency by the zero-point motion contribution this isotope effect may occur. The isotope effect in SrTi(16O1−x18Ox)3 discovered recently is explained. The influence of 105 K antiferrodistortive phase transition in SrTiO3 on the FE isotope effect is discussed. It is shown that unlike SrTiO3 the stability of the paraelectric phase of KTaO3 is scarcely affected by oxygen isotope exchange. Thus, no ferroelectricity induced by such a mechanism must be observed in KTaO3.

The temperature dependence of the unpolarized Raman spectra from 1T-TaS2 has been measured between 297 K and 48 K. The present work demonstrates that the three Raman modes observed above 220 cm−1 (high frequency region) at room temperature exhibit remarkable frequency changes toward low wavenumbers in the vicinity of 200 K, where 1T-TaS2 undergoes a first-order transition of the charge density wave (CDW) from nearly commensurate to a commensurate state. The monotonic line-broadening and intensity reduction with temperature has been identified for these Raman modes. In contrast, the behavior observed in the low frequency region (less than 200 cm−1), suggested that the soft phonons are less likely to be involved in the temperature dependence of the high frequency Raman modes.

Zr doping in ceria (CeO2) results in enhanced static dielectric response compared to pure ceria. On the other hand, Ti doping in ceria keeps its dielectric constant unchanged. We use first-principles density functional theory calculations based on pseudopotentials and a plane wave basis to determine electronic properties and dielectric response of Zr/Ti-doped and oxygen-vacancy-introduced ceria. Softening of phonon modes is responsible for the enhancement in dielectric response of Zr-doped ceria compared to that of pure ceria. The ceria-zirconia mixed oxides should have potential use as high-k materials in the semiconductor industry. (c) 2010 Elsevier Ltd. All rights reserved.

Russian Foundation for Basic Research Grant (99-02-18316); NSF Grant (DMR-9805272); ISSEP Grant

The pressure dependence of the phonons in GaPO4 has been investigated up to 18 GPa using Raman spectroscopy. The existence of sharp Raman lines above the phase transition at approximately 11 GPa is a clear indication that the high-pressure phase is crystalline and not amorphous. Two phonons in the low-pressure phase exhibit soft mode behavior.

Dielectric response of the ammonium hydrogen bis-chloroacetate, NH 4 H(ClCH 2 COO) 2 (AHCA), in the frequency range from 100 Hz to 10 GHz has been studied. In the temperature range close to the phase transition a two-relaxator dielectric behaviour was found. The high frequency (∼1 GHz) relaxator has properties of ferroelectric relaxational soft mode. The low frequency (∼10–100 MHz) relaxator displays properties common to the domain dielectric contribution known for some other ferroelectrics. The coexistence of the two dielectric relaxators in the vicinity of the phase transition is discussed using a conception of the free and pinned order clusters.

Vibrational properties of NaV2O5 under pressures up to 33 GPa have been studied by Raman spectroscopy ( T=300 K ). Up to 10 GPa the phonon frequencies exhibit pronounced nonlinear pressure dependences which can be correlated with distinct structural changes. Increasing layer interaction causes a major softening of the VO1 out-of-plane stretching mode. The phonon-electronic-excitation coupled mode at 453 cm−1 was found to be particularly sensitive to structural changes. A phase transition from the layered towards a three-dimensionally linked structure starts near 25 GPa. The transition pressure is significantly reduced under non-hydrostatic pressure conditions. The intercalation of Na stabilizes the low-pressure phase of NaV2O5 in comparison to V2O5.

Dielectric measurements were performed in CaTiO3 ceramic samples at frequencies from 10 Hz–1 MHz and at temperatures between 4.2 and 300 K. The dielectric constant increases with decreasing temperature and saturates at low temperatures. According to this behavior, CaTiO3 has been classified as an incipient ferroelectric or a quantum paraelectric similar to SrTiO3, KTaO3 and TiO2.

Cataloged from PDF version of article. The temperature dependence of the Raman-active mode frequencies in indium sulfide was measured in the range from 10 to 300 K. The analysis of the temperature dependence of the A(g) intralayer optical modes show that Raman frequency shift results from the change of harmonic frequency with volume expansion and anharmonic coupling to phonons of other branches. The pure-temperature contribution (phonon-phonon coupling) is due to three- and four-phonon processes. (C) 1999 Elsevier Science Ltd. All rights reserved.

Structural optimizations were performed for all previously predicted phases of SrHfO3, using density functional theory. The phonon dispersion relations of cubic P m 3 ¯ m phase of SrHfO3 have been calculated within density functional perturbation theory. Instabilities have been observed along the M – Γ – R – M line in the Brillouin zone. Based on the soft mode frequencies and calculated ground state energies we conclude that the I m m a , I 4 / m c m and P b n m phases are likely to exist, while P 4 m m and C m c m phases are not likely to occur.

The ferroelectric soft modes of KDP (KH2PO4) and the 90% deuterated compound (K(H0.1D0.9)2PO4) have been excited coherently by impulsive stimulated Raman scattering. The observed time dependence of the excited modes shows a complete single exponential time decay after an electronic response at its time origin. The temperature dependence of the relaxation time τ of the modes shows clearly a critical slowing down in paraelectric phase, τ = τ 0 T 0 (T−T 0 ) , where T0 is the phase transition point of the clamped crystal. The isotope effect on τ is well confirmed as τ0 is 0.11×10−12s for KDP and τ0 is 0.82×10−12s for K(H0.1D0.9)2PO4.

Here we present a microscopic theory to explain different Raman phonon modes of the cuprates in normal state. We used the electronic Hamiltonian of Fulde in presence of anti-ferromagnetism. We added phonon interaction to the hybridisation between the conduction electrons of the system and the f-electrons. The spectral density is calculated by the Green function technique of Zubarev at zero wave vector and low temperature limit. The spectral density is studied in detail by varying model parameters like position of f-level (ϵf), the effective electron-phonon coupling strength (g), the staggered magnetic field (h) and the hybridisation parameter (V). Four Raman active modes are observed in addition to the original phonon peak. Then their softening and hardening behaviour and change in peak height are studied. These parameters influence the Raman modes substantially.

Data on the calorimetric, dielectric and infrared properties of a molecular crystal cyclohexane-1,1′-diacetic acid around its 397 K ferroelectric phase transition are presented and discussed. The DSC experiments confirm the first order character of the phase transition and the dielectric measurements reveal a relaxation soft mode in an unusually low frequency region 10 3 –10 4 Hz. Detailed analysis of the possible nature of the pseudoproper ferroelectric phase transition is based on the symmetry aspects.

The vibrational spectra of insulating pressure polymerised C 60 and conducting o -RbC 60 polymers are studied by Raman and neutron spectroscopy. Model calculations give detailed informations on particular excitations and restoring forces as well. A pronounced anomalous phonon softening present in the conducting polymer is not found in the neutral compound. The breaking up of polymer chains in pressure polymerized C 60 is followed with temperature.

Series of charge-compensated solid solutions of n = 2 and 3 Aurivillius phases with structures derived from the Bi 2 A n −1 B n O 3 n +3 by fractional substitution in the (Bi 2 O 2 ) 2+ blocks as well as in the perovskite-type blocks ( A n −1 B n O 3 n +1 ) 2− have been prepared by solid state reaction. Raman spectra of two series Bi 2− x Pb x Sr 1− x Nd x Nb 2 O 9 and Bi 4− x Pb x Ti 3− x Nb x O 12 for 0 ≤ x ≤ 1 were obtained in the range of 15–200 cm −1 at room temperature. Significant changes with composition are observed only for the low Raman shift features assigned to soft modes and can be related to the ferroelectric to paraelectric phase transition in these materials.

We present a model of ferroelectrics which takes into account the softening of a transverse optical mode, the existence of dynamical spontaneous off-center displacements and their interaction with each other. In this paper we confine ourselves to temperatures above T c . The model is quantitatively compared with experimental results in two very different materials, PbTiO 3 and KNbO 3 . The results show that the existence of off-center displacements and their interaction with the soft mode play a crucial role in explaining the properties of ferroelectric phase transitions in perovskite crystals and possibly other crystal families.

An X-ray study of the effect of pressure and electric field on the incommensurate phase transition in ZrTiO4 was performed in order to obtain the information concerning the nature of the competing forces that give rise to a structural instability at a general wave-vector. It was found not only that an increase in pressure lowers the transition temperature ( d T i d P i ≅ −6.9 K kbar −1 ), but also that an increase in d.c. electric field shifts the transition temperature ( d T i d E i ≅ +1.7 deg cm kV −1 ) to a higher. The pressure and electric field dependence of the incommensurate to commensurate transition were also investigated ( d T c d P c ≅ −9.0 K kbar −1 ) and ( d T c d E c ≅ +1.5 deg cm kV −1 ), respectively.

Lattice-dynamical calculation results are presented in which YBa2Cu3O7−δ (δ = 1.0) lattices become unstable at high hydrostatic compression. For YBa2Cu3O1, an incommensurate instability is predicted via the vanishing of the A′ mode near the (0.2, 0.2, 0.2) point of the Brillouin zone. For YBa2Cu3O7, the prognosticated destabilization is found to be associated with the softening of a whole dispersionless phonon branch corresponding to zig-zag vibrations of the CuOCu chain.

A microscopic theory for the central peak in H-bonded ferroelectrics is given. We obtain three different mechanisms for the formation of the central peak: a relaxation mechanism, i.e. the transverse soft mode is coupled to the longitudinal mode; an oscillatory mechanism, i.e. the transverse soft mode is coupled to the phonon mode; the third mechanism can be treated as an effective coupling between the phonon and the longitudinal modes.

Temperature-dependent Raman spectra are recorded in order to investigate the stability of the room temperature orthorhombic D2h13 structure of CsInF4. The appearance of new lines as well as a soft-like mode below 283 K is observed. These new features indicate that the D2h13(Pmmn) phase undergoes a structural modification for temperatures T

The Landau model for structural, displacive transitions has been widely used. When specifically applied to second orde (only!) transitions, the lattice becomes dynamically unstable for infinitesimal displacements at the critical temperature T c ; above the frequency of the critical soft mode behaves as ω 2 ∞(T-T c ). Without justification, the so-called “soft mode” theory has then been vaguely and uncritically applied to both the design and interpretation of experiments on any displacive transformation. In fact, however, second order transitions are the exception rather than the rule. Landau models for the much more common first-order transitions are presented, and the secondary role of mode softening is clarified. In contrast to ideal second-order transitions, first-order transitions are not accompanied by dynamic instabilities, rather, they are thermodynamically unstable .

On deuteration (NH 4 ) 2 TeCl 6 undergoes two additional structural phase transformations at T c 2 ( x ) and T c 3 ( x ) which are investigated as a function of the deuteron concentration x by Raman scattering. T c 2 decreases monotonously from 48 K at x = 1 to 13 K at x c 2 = 0.15 and T c 3 is reduced from 28 K at x = 1 to 20 K at x c 3 = 0.85. For deuterium contents smaller than the critical concentrations x c 3 and x c 2 the third and second transition are suppressed. Two low energy soft modes are observed below T c 2 ( x ) in the partially deuterated crystals.

The existence of a martensitic transformation in off-stoichiometric Ti 50− x Ni 50+ x compounds is accompanied by a peak occurring in the density of states at the Fermi level and by a minimum of the Debye temperature θ D corresponding to a minimum of martensitic transition temperature as a function of x . By doping TiNi with Os or Fe soft mode effects are observed in the specific heat behaviour.

The softening of phonons can be driven by the appearance of another superconducting state in a superconducting state. Such a transition of the second order is possible in multilayered CuO 2 superconductors. The soft mode must be an optical mode which vibrates CuO 2 planes out of phase. The softening can explain a tiny but sharp anomaly of the transverse nuclear quadrupole relaxation rate around T =35 K in double-layered YBa 2 Cu 3 O 7− δ with critical temperature T c ≈92K. However, the present theory predicts the absence of anomalies in single-layered compounds such as La 2− x Sr x CuO 4 .

Using synchrotron radiation we have performed a high wavevector resolution study of the X-ray critical scattering above the cubic-to-tetragonal structural phase transition in SrTiO 3 . The high incident X-ray flux enabled us to follow the thermal evolution of the critical scattering up to approximately T c + 10 K, whereas previous high-resolution studies using a rotating anode X-ray source were restricted to working within 2 K of T c . In contrast to earlier studies, our results show that even when using high resolution there are two length scales in the observed critical scattering: one diffuse component associated with the R -point soft mode; and a second sharper component which has a Lorentzian-squared line shape, isotropic in wavevector, and a width which narrows to the instrumental resolution as T → T c . These qualitative features of the second component are consistent with the calculated effect of random fields on a weakly first-order transition.

Inelastic neutron scattering on deuterated BCCD revealed a transverse acoustic branch of Λ3 symmetry coupled to a soft polarisation branch Py(k) of same symmetry. As the transition to the incommensurate state is approached from above (T>T1 = 164 K), the lowest-frequency branch develops a broad dispersion minimum near k =0.32c ∗ . The soft mode is observed as an underdamped excitation down to 170K. The present results establish the displacive nature of the phase transition at T1 and the P y- symmetry of the primary order parameter. A semi-quantitative scheme for the 14 lowest phonon branches along the c∗ direction, in the normal phase, is suggested, based on the available neutron-scattering, infrared, Raman, and acoustic data.

Motional correlation times for the fluctuations of the heavy cation 133Cs are reported in CsH2AsO4 in the range 260–320 K using EPR of the AsO44− center, ENDOR of 133Cs and 1H, and computer calculations based on the modified Bloch equations. It is further shown that the fluctuations involving relative motions of the 133Cs, 75As and 1H nuclei are correlated and although two-three orders of magnitude slower they imply a motion analogous to that of the soft mode.

Paraelectric soft mode behaviour in TSCC was reinvestigated using near-millimetre dielectric spectroscopy and compared with low-frequency dielectric data. Farther above Tc the classical displacive mean-field behaviour was observed with the extrapolated Curie temperature ≌ 2.6 K above Tc. Closer to Tc deviations from Cochran law as well as appearence of the central mode are correlated with deviations from the Curie-Weiss law for the low-frequency permittivity. The central mode is assigned to critical cluster dynamics.

The frequency dependence of the dielectric response deduced from the analysis of infrared reflection spectra of the BaTaO2N perovskite is reported. The results are compared with those of barium titanate and discussed. It is concluded that the substitution of one nitrogen for oxygen — together with replacement of Ti+IV by Ta+V to ensure the proper charge balance — appears to cancel the possibility offered by some oxidic perovskites to observe very high dielectric constants since here no soft mode behaviour is found.

A soft mode have been observed in the Raman spectra of SrBi 2 Nb 2 O 9 . The frequency of the soft mode decreases and the soft mode becomes overdamped on approaching the Curie point. Its linewidth diverges as Γ (T)=Γ (0)[(T c −T)/T c ] −1 . The soft mode seems to be associated with the ferro- to para- electric phase transition.

It is suggested that the superconducting fluctuations observed by Coleman et al. just above the Peierls soft mode instability in psuedo one-dimensional organic solids is a reflection of Frohlich's one-dimensional model in which superconductivity arises from a coupling of the electrons with moving lattice waves rather than from a BCS type pairing.

The thermal conductivity of KH2PO4 (Potassium Dihydrogen Phosphate, KDP) single crystal under dc bias fields up to 2 kV/cm was measured using a novel technique called the 3ω method. Without a bias field, a small but definite discontinuity was observed at the Curie temperature (Tc = 123 K), indicating the first-order nature of the transition. The value of the thermal conductivity was very small due to the protonic scattering of phonons. The dc bias field tended to increase the thermal conductivity of KDP only in the vicinity of Tc and round the discontinuity at the same time. These results clearly demonstrate the coupling between the heat carrying phonons and the soft mode associated with the ferroelectric transition.