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Transition metal carbides are candidates for high-temperature structural ceramics because of their high melting point, high hardness, and high strength. However, one challenge is overcoming their high intrinsic brittleness. In this study, we investigated a new class of (Fe, Mo, W)6C carbides, which have three Wyckoff positions for metallic atoms (16d, 32e, and 48f) and one Wyckoff position for carbon (16c). These different Wyckoff positions provide a great opportunity to optimize the mechanical properties by the partial replacement of atoms at each Wyckoff position to obtain high-entropy carbides. The current results show that the phonon spectra have no imaginary frequency when Fe occupies the 16d or 32e positions, but a soft mode is observed when Fe occupies 48f. (Fe, Mo, W)6C η carbides have a higher fracture toughness compared with those of M3C and MC carbides owing to their low carbon content (14.3 at.%). The mechanical anisotropy of (Fe, Mo, W)6C is weak, which is beneficial for increasing the damage tolerance. The thermal expansion coefficients of the (Fe, Mo, W)6C η carbides are predicted to be approximately (8.5–9.5) × 10−6 K−1 at 1400 K.

The statistical retarded double-time temperature-dependent Green’s function method and modified two sublattice pseudospin lattice coupled mode model Hamiltonian by adding phonon anharmonic interactions, extra spin–lattice interactions, direct spin–spin interaction and as well as an electric field terms have been used for the study of phase transition mechanism in PbHPO4-type crystals. The expressions for soft mode frequency, dielectric permittivity and dielectric loss tangent are derived for PbHPO4-type crystals. The modelled values of different physical parameters are fitted in the obtained theoretical expressions. The temperature dependence of soft mode frequency, dielectric permittivity and loss tangent are obtained for PbHPO4, PbHAsO4, BaHPO4 and CaHPO4 crystals. Present results are in good agreement with experimental data for dielectric permittivity reported by Arend et al. The modified model Hamiltonian is suitable to explain transitions in PbHPO4-type crystals.

Ferroelectric materials with high Curie temperatures, TC, and tuning of the TC over a large temperature range are very important for the basic sciences and engineering. This paper reviews the vario...

We studied the bilayer heterostructures with the different consequence of the Ba0.4Sr0.6TiO3 and Ba0.8Sr0.2TiO3 layers grown on the single-crystal MgO and Si substrates. The thermodynamic theory fo...

[EN] We report high-pressure Raman spectroscopy studies of Fe(IO3)(3) up to nearly 21 GPa that have been interpreted with the help of density functional theory calculations, which include the calculation of phonon dispersion curves and elastic constants at different pressures. Zero-pressure Raman-active mode frequencies and their pressure dependences have been determined. Modes have been assigned and correlated to atomic movements with the help of calculations. Interestingly, in the high-frequency region, there are several modes that soften under compression. These modes have been identified as internal vibrations of the IO3 coordination polyhedron. Their unusual behavior is a consequence of the changes induced by pressure in the coordination sphere of iodine, which gradually change from a threefold coordination to an almost sixfold coordination under compression. The coordination change is favored by the decrease of the stereoactivity of the iodine lone electron pair so that likely a real sixfold coordination is attained after a first-order phase transition previously reported to occur above 21 GPa. The strong nonlinear behavior found in Raman-active modes as well as in theoretically calculated elastic constants has been discovered to be related to the occurrence of two previously unreported isostructural phase transitions at 1.5-2.0 and 5.7-6.0 GPa as shown by dynamic instabilities close to the Brillouin zone center., This work was supported by the Spanish Ministry of Science, Innovation and Universities, the Spanish Research Agency (AEI), the European Fund for Regional Development (ERDF, FEDER) under grants MAT2016-75586-C4-1/2/3-P, PID2019-106383GB-C41/42/43, and RED2018-102612-T (MALTA Consolider-Team Network), and the Generalitat Valenciana under grant Prometeo/2018/123 (EFIMAT). A.L. and D.E. would like to thank the Generalitat Valenciana for the Ph.D. fellowship GRISOLIAP/2019/025).

A theoretical analysis of the features of first-order structural and magnetostructural transitions in magnetocaloric helimagnetic alloys of the Mn1 – xCrxNiGe system is performed. The observed structural transitions of the displacement type hex(P63/mmc) ↔ orth(Pnma) are described using the local soft mode model in the approximation of a displaced harmonic oscillator. In the absence of a magnetic field, the emergence of a helimagnetic order as a structurally induced second-order transition is described within the Heisenberg model with allowance for the dependence of the exchange integrals on the structural order parameters and elastic strains. In the presence of a magnetic field, it was found that the mutual approach of the characteristic temperatures for the helimagnetic state (HM(Pnma)) and the lability temperatures of the hexagonal paramagnetic state (PM(P63/mmc)), due to the action of the magnetic field, leads to the appearance of previously unexplored peripheral first-order magnetostructural transitions with insignificant magnetization jumps, increasing with increasing magnetic induction field. In this case, as the pressure increases to 4 kbar with a constant magnetic induction field, the peripheral transitions are transformed into reversible first-order magnetostructural transitions and, at even higher pressures (10–14 kbar), into full-scale first-order magnetostructural transitions with magnetization jumps comparable with the maximum magnetization. Experimental baric studies of the temperature dependences of the magnetization in static magnetic fields with an induction up to 1 T and pressure up to 14 kbar confirm the theoretical results.

Comparison of isotemperature and isofrequency temperature dependences was used for revealing the soft mode behavior near phase transition points in ferroelectric and ferro-structural phase transiti...

The condensation of two soft modes has been found when studying the Raman spectra of the solid solution HoFe2.5Ga0.5(BO3)4 in the temperature range from 7 to 350 K. The first high-temperature soft ...

The frequencies of lattice vibrations in the RFe3(BO3)4 (R = Pr, Nd, Tb, Dy, or Ho) crystals in the high-temperature R32 phase and their temperature dependence have been calculated using the quasi-harmonic approximation. It has been found that, at the boundary point Λ of the Brillouin zone, the frequency of the unstable vibration mode the structural phase transition R32 → P3121 is related to strong changes with temperature in the TbFe3(BO3)4, DyFe3(BO3)4, and HoFe3(BO3)4 crystals. With increasing temperature, the frequency of the soft mode stabilizes and takes a real value. No significant changes in the phonon spectra, including the boundary point Λ, with increasing temperature for the PrFe3(BO3)4 and NdFe3(BO3)4 crystals have been observed.

The effect of hydrostatic pressure on phase transitions in lead hafnate (PbHfO3) has been studied by the methods of X-ray diffraction and X-ray diffuse scattering. The measurements were performed in the temperature range of 182 < T < 316°C and the pressure range of 1.6 < P < 2.6 GPa. Four regions characterized by different X-ray diffraction patterns and corresponding to an antiferroelectric phase, phases with a long-wavelength modulation of the lead sublattice, and phases with different distortions of the oxygen sublattice are identified. In the temperature region immediately above the region of phases with a long-wavelength modulation, a temperature-dependent maximum in the distribution of diffuse scattering was detected, which means that such a modulation is formed due to condensation of an incommensurate soft mode.

First-principles (FP) calculations and first-principles molecular dynamics (FPMD) simulations for Cu4SnS4 were performed to clarify the origin of the structural phase transition at 232 K between the high-temperature phase (HP) and low-temperature phase (LP), which leads to an experimentally measured drastic change in the transport properties of Cu4SnS4. The results of the FP and PFMD calculations indicated that, rather than being caused by the so-called freezing of soft modes, the key driving force behind the phase transition in Cu4SnS4 is a large-scale displacement of the Cu atoms located at particular sites due to thermal vibration. In fact, tetrahedrally coordinated CuS4 is stabilized by the effect of the thermal vibration of Cu atoms in the HP whereas CuS3, which is in a trigonal planar environment, is stabilized in the LP.

Raman spectra of Hg2Br2 model improper ferroelastic crystals have been investigated in a wide range of high hydrostatic pressures. Baric dependences of the phonon frequencies have been obtained; of greatest interest are the observed soft mode originating from the slowest TA1 acoustic branch at the Brillouin zone boundary (X point) of the tetragonal phase and the anomalous behavior of this mode. In the ferroelastic phase spectra, the ignition of the second acoustic TA2 from the same point has also been detected and its baric behavior has been studied. Under sufficiently high pressures, splitting of doubly degenerate phonons with the Eg symmetry has been observed and explained. The parameters of the Gruneisen constants have been determined from the baric dependences of the phonon frequencies and discussed.

The lattice instability of lead-free potassium sodium niobate, (K0.5Na0.5) NbO3 (KNN50) piezoelectric crystals were studied by Raman scattering in the temperature range between 20 and 550 °C. The KNN50 undergoes the cubic to tetragonal ferroelectric phase transition at TC = 430 °C, and the tetragonal to monoclinic structural phase transition at Ttr = 190 °C. In the monoclinic phase, the lowest frequency mode at 68 cm−1, which is related to the soft mode of KNbO3, is clearly observed at room temperature. On heating from room temperature it shows noticeable softening towards Ttr and becomes overdamped. For further heating, the intense central peak (CP) appears in the tetragonal phase just above Ttr, and the CP intensity shows a peak at TC. The relaxation time determined from the CP width shows the critical slowing down towards TC.

The structure in real planar samples of ferroelectric liquid crystals as well as the collective modes characterizing these structures, are strongly affected by surface anchoring of molecules. This is reflected in dielectric properties, which become significantly dependent on the sample thickness. The dielectric strength and the relaxation frequency of the characteristic modes (pinned Goldstone mode for the thick samples and twisted mode for the thin ones) are determined and found that for both types of structures the dielectric strength increases and the relaxation frequency decreases with increasing the sample thickness. We proved theoretically predicted thickness dependences of various physical parameters for new ferroelectric liquid crystalline compound. We concluded the experimental results are in accordance with the theory taking into account the real structure of the samples.

Recently we have demonstrated that out-of-plane dielectric properties of polycrystalline SrTiO3 (ST) films depend on the strain/stress induced by the substrates due to thermal expansion misfit. Here, we present a complementary infra-red (IR) spectroscopy investigation of the role of Al2O3 and MgO substrates on the lattice dynamics and in-plane dielectric properties of ST thin films also prepared by sol-gel. We verify that ST films deposited on Al2O3 substrates, being under a tensile stress, present the soft mode behaviour similar to that of ST single crystals, deviating just below 150 K. In contrast, ST films deposited on MgO substrates, being under compressive stress, have higher soft mode frequency from 10 to 300 K. It is thus proved that for polycrystalline ST films the intrinsic in-plane relative permittivity may be tuned through an induced stress state.

The Raman spectra of novel ferroelectric ceramics SnxSr1-xTiO3 (x = 0.1, 0.05 and 0.02) were obtained to clarify the mechanism of their ferroelectric phase transitions. Two transverse-optic modes in the ferroelectric phase showed softening toward the ferroelectric transition temperature. A comparison of the spectra obtained for SnxSr1-xTiO3 with the spectrum of PbxSr1-xTiO3 facilitated the assignment of the observed modes under the assumption of the ferroelectric phase in C4v1 symmetry. However, several peaks violating the Raman selection rules were observed, suggesting the emergence and growth of polar regions even in the paraelectric phase.

Controversial views of the Raman spectrum related to the mechanism of the ferroelectric phase transition of KDP (KH2PO4) are discussed. In the model proposed by Tominaga etal. (Solid St. Commun. 48 (1983) 265), it was concluded that PO4 tetrahedra are distorted to polar C2 symmetry already above Tc. Here, it is shown that the C2 symmetry is simply that of a local H2PO4− ion. Therefore, the Raman spectra do not give any evidence of the "PO4 orientational order-disorder model" in which protons are not involved at all in the phase transition. The assignment of the overdamped soft mode in this model is also discussed.

The $$ {\hbox{Ba}}_{0.7} {\hbox{Sr}}_{0.3} {\hbox{TiO}}_{3} $$ (BST) thin film (30.3 nm) deposited on a $$ {\hbox{SrTiO}}_{3} $$ (STO) film/silicon substrate sample was modulated by 532 nm continuous-wave laser in the range of 0.2–1 THz at room temperature. The refractive index variation was observed to linearly increase at the highest 3.48 for 0.5 THz with the pump power increasing to 400 mW. It was also found that the BST/STO sample had a larger refractive index variation and was more sensitive to the external optical field than a BST monolayer due to the epitaxial strain induced by the STO film. The electric displacement–electric field loops results revealed that the increasing spontaneous polarization with the STO film that was induced was responsible for the larger refractive index variation of the BST/STO sample. In addition, the real and imaginary part of the permittivity were observed increasing along with the external field increasing, due to the soft mode hardening.

Three orthogonal smectic phases (SmE*, SmB*hex and SmA*) have been identified in a biphenylyl chiral compound from optical polarizing microscopy, synchrotron X-ray diffraction and dielectric spectroscopy studies. SmB*hex phase exhibits two variants – the lower temperature one is more ordered. All the phases are found to be partially bi-layer type, observed first time in a chiral system without any cyano terminal group. Long range ordering is revealed in both the in-plane and across the plane correlations. Cell parameters of the herringbone like structures of higher ordered smectic phases have been determined and are found to be densely packed. Transitions from SmE* to SmB*hex and within the two SmB*hex variants are of displacive type. Dielectric spectroscopy reveals Maxwell Wagner relaxation in all the phases, however, flip-flop mode relaxation about molecular short axis has been observed in the higher ordered smectic phases only. Absence of short axis relaxation mode as well as soft mode in SmA* phase has been explained.

Using GW approximation + Bethe-Salpeter equation, we study optical and electronic responses of three fluorinated structures of GeC namely, F - GeC - F , F - GeC and GeC - F and compare our results with other fluorinated 2D materials. The absence of soft modes demonstrates stability of the three structures. The band gaps were determined in presence and absence of quasiparticle correction. The results show that fluorination tunes the gap but its nature remains the same. Effect of polarization direction and local field on imaginary part of macroscopic dielectric function were also reported. Optical properties investigated through analysing absorption spectra reveals a weak electron-hole interaction for GeC-F where Bohr radius of exciton is 8.64 A. However, a strong electron-hole interaction in the two others fluorinated structures leads to the appearance of small radius of excitons with spatially separated electron and hole, which are localized out of plane and in plane, respectively. The presence of such bounded excitons in the studied structures makes them good candidates for optoelectronic applications and quantum information technologies.

Herein we reported structural stability, vibrational and thermal properties of K2Ce[PO4]2, a relatively underexplored complex phosphate of tetravalent Ce4+ from in situ high-pressure Raman spectroscopic investigations up to ~ 28 GPa using a diamond anvil cell. The studies identified the soft phonons that lead to a reversible phase transformation above 8 GPa, and a phase coexistence of ambient (PI) and high pressure (PII) phases in a wider pressure region 6–11 GPa. From a visual representation of the computed eigen vector displacements, the Ag soft mode at 82 cm−1 is assigned as a lattice mode of K+ cation. Pressure-induced positional disorder is apparent from the substantial broadening of internal modes and the disappearance of low frequency lattice and external modes in phase PII above 18 GPa. Isothermal mode Gruneisen parameters γi of the various phonon modes are calculated and compared for several modes. Using these values, thermal properties such as average Gruneisen parameter, and thermal expansion coefficient are estimated as 0.47, and 2.5 × 10−6 K−1, respectively. The specific heat value was estimated from all optical modes obtained from DFT calculations as 314 J-mol−1 K−1. Our earlier reported temperature dependence of phonon frequencies is used to decouple the “true anharmonic” (explicit contribution at constant volume) and “quasi harmonic” (implicit contribution brought out by volume change) contributions from the total anharmonicity. In addition to the 81 cm−1 Ag lattice mode, several other lattice and external modes of PO43- ions are found to be strongly anharmonic.

To better understand the electronic, optical, and thermodynamic behaviors of lanthanum doped strontium titanate (La-STO) with different doping levels at high temperature, ab initio thermodynamics have been employed to investigate their electronic structures and thermodynamic evolutions versus temperatures. The results show that with increasing La-doping level, the corresponding structures of La-STO become less stable with an increasing number of phonon soft modes. The calculated thermodynamic properties show that with increasing La-doping levels, the free energy and enthalpy changes of La-STOs are decreased at given temperature. For all La-STOs with different La-doping levels investigated, we found that in three cases doping with 25%, 37.5% and 75% La substituted for Sr, the diagonal elements of their dielectric constant matrix are not all equal, which means these crystal structures are uniaxial and anisotropic. Our results indicate that doping La into STO could alter the optical properties of pure STO to be birefringent.

Frequencies, damping constants and the relaxation times of some Raman modes including the two soft modes are calculated as a function of pressure near the tetragonal-cubic transition in PbTiO 3 . Calculation of the Raman frequencies is performed using the observed volume data from the literature by means of the mode Gruneisen parameter at various pressures. Pressure dependence of the damping constant and the relaxation time is predicted using the pseudospin-phonon coupled model and the energy fluctuation model by considering that the Raman frequency can be taken as the order parameter (spontaneous polarization) for the tetragonal-cubic transition in PbTiO 3 . Expressions from both models for the damping constants are fitted to the observed Raman linewidths of the two soft modes and for the other Raman modes the damping constant and the relaxation time are predicted close to the transition. We find that damping constants diverge and the inverse relaxation time decreases for the soft modes with increasing pressure near the critical pressure (P C ∼ 11 GPa). The other Raman modes exhibit unusual critical behavior. Our results indicate that the observed behavior of the Raman frequencies can be predicted from the volume data through the mode Gruneisen parameter for the tetragonal-cubic transition in PbTiO 3 . The damping constant and the relaxation time for the Raman modes can also be predicted adequately using the pseudospin-phonon coupled model and the energy fluctuation model to explain the mechanism of the phase transition between the tetragonal and cubic phases in PbTiO 3 .

A biocompatible Aurivillius-like layered ferroelectric that was designed by first-principles analysis and its thin film fabricated using radio frequency magnetron sputtering has been utilized for sensors of biomedical microelectromechanical systems. Aurivillius ferroelectrics have superior characteristics such as ferroelectric anisotropies and high Curie temperatures, and are widely used for sensors and memories. However, they contain the bio-toxic element, bismuth. In this study, we designed and fabricated a new biocompatible Aurivillius-like ferroelectric. SrBi 2 Ta 2 O 9 was subjected to first-principles calculation for validation. Lattice parameters of SrBi 2 Ta 2 O 9 in each phase and the spontaneous polarization value were in good agreement with the experimental reports. Subsequently, the prediction of Aurivillius-like materials and generation of its thin films were performed. During the design of the new molecule, 37 candidates were obtained by including constraint conditions such as the tolerance factor. We carried out the first-principles calculations for the structure optimization, determination of the band gap (for insulation), the soft mode (for ferroelectric phase transition), and the ferroelectric properties. The spontaneous polarization of BaIn 2 Ta 2 O 9 was calculated as 7.95 nC/cm 2 . Next, a BaIn 2 Ta 2 O 9 thin film was generated. Through the experimental design procedure using an L 27 orthogonal array, we determined the sputtering conditions. Introducing the post-annealing process, the polarization-electric field hysteresis loop was obtained and its remnant polarization was calculated to be 15 nC/cm 2 . The x-ray diffraction pattern predicted the crystal structure of SrBi 2 Ta 2 O 9 -type materials. These results show the possible formation of the biocompatible Aurivillius-like ferroelectric material, BaIn 2 Ta 2 O 9 .

The lattice instability and elastic anomaly of a ferroelectric and incommensurate (IC) phase transitions of Sr2(Nb1-xTax)2O7 single crystals with x = 0.20 and 0.40 were studied by Raman and Brillou...

The 180° Raman scattering experiment has been performed in Bi4-xGdxTi3O12 (x = 0, 0.1, 0.28, and 0.36) and Bi4-xLaxTi3O12 (x = 0, 0.17, and 0.31) single crystals. The materials of x ≠ 0 are known to undergo successive phase transitions at TH and TL (

We investigated the tunability of the dielectric characterization spectra of the Ferroelectric Barium Strontium Titanate (Ba0.5Sr0.5TiO3) thin films in an external optical field through the terahertz time-domain spectroscopy. The real part of the permittivity reached up to 22% when we applied the optical field up to 600mW/cm2 and the imaginary part is not really obvious. And the results are attributed to the soft mode harden caused by the excited optical field.

We calculate the order parameter (spontaneous polarization) and the inverse dielectric susceptibility at various temperatures in the ferroelectric phase of LiNbO3 for its ferroelectric-paraelectric phase transition (TC = 1260 K) using the Landau phenomenological model. For this calculation, the Raman frequencies of the soft optic mode (TO1) are used as the order parameter and the fitting procedure is employed for both the order parameter and the inverse dielectric susceptibility by means of the observed data from the literature. The temperature dependences of the damping constant and the inverse relaxation time are also computed using the pseudospin-phonon coupled model and the energy fluctuation model for the ferroelectric phase of LiNbO3. The activation energy is deduced from the damping constant for both models studied and compared with the k B T C value of LiNbO3. We find that the order parameter (Raman frequency of the TO1 mode) and the inverse dielectric susceptibility decrease with increasing temperature, as expected from the mean field model. We also find that the damping constant and the inverse relaxation time of this soft mode increases and decreases, respectively, with increasing temperature on the basis of the two models studied in the ferroelectric phase of LiNbO3. This indicates that our method of calculation is satisfactory to describe the observed behaviour of the ferroelectric-paraelectric phase transition in LiNbO3.

We investigate the low-frequency spin wave dynamics involved in the magnetization reversal of a Penrose P2 tiling using the dynamical matrix method. This system consists of a two-dimensional, connected wire network of elongated thin-film segments, whose complete reversal occurs as a cascade of successive local segment reversals. Using soft mode theory, we interpret the reversal of an individual segment as a first order magnetic transition, in which magnetization curve of the system suffers a small discontinuity. Near this discontinuity a specific mode of the spin wave spectrum goes soft (i.e., its frequency goes to zero), triggering a local instability of the magnetization. We show that this mode is localized, and is at the origin of the local reversal. We discuss the correlation of the mode spatial profile with the “reversal mechanism”, which is the passage of a domain wall through the segment. This process differs from reversal in periodic square or honeycomb artificial spin ices, where a cascade of reversing segments (e.g., “Dirac string”) follows an extended (though irregular) path across the sample; here the spatial distribution of successive segment reversals is discontinuous, but strictly associated with the area where a soft mode is localized. The migration of the localization area across the P2 tiling (during reversal in decreasing applied fields) depends on changes in the internal effective field map. We discuss these results in the context of spin wave localization due to the unique topology of the P2 tiling.

Below a threshold magnetic field, domain structures in ferromagnetic samples may start to nucleate from the initially saturated state via either continuous or discontinuous phase transitions. Such processes are usually accompanied by the occurrence of soft spin-wave modes at the critical point. In this paper, we present a theoretical study on the critical phenomena of uniform soft modes in a macrospin model and spatially non-uniform ones in ferromagnetic thin films. The critical exponents of the mode frequency and its polarization are derived. The value is found to be equal to one half, which is directly related to the breaking of a reflection-symmetry in the phase transition. At the critical point, the soft mode becomes linearly polarized, which provides an additional measurable effect of the critical phenomena.

The sequence of phase transitions \(P\overline 3 m1 \to {{C2} \mathord{\left/ {\vphantom {{C2} m}} \right. \kern-\nulldelimiterspace} m} \to {{C2} \mathord{\left/ {\vphantom {{C2} c}} \right. \kern-\nulldelimiterspace} c}\) in K3Na(CrO4)2 crystals and existence of the intermediate phase have been studied both experimentally by the Raman scattering method and theoretically by programs and retrieval tools of the Bilbao Crystallographic Server. A zone-edge soft mode responsible for a transition from the intermediate C2/m to a low-symmetry C2/c phase at T = 210 K has been discovered experimentally for the first time. The symmetry of the soft mode has been established theoretically to be A2+. The temperature interval of the intermediate monoclinic phase has been determined to be 239–210 K.

The temperature dependence of the phonon frequency ω p h and of the damping constant Γ s p due to pseudospin-phonon coupling of the lowest-frequency soft mode is calculated in the ferroelectric phase near the transition temperature (TC = 196 K) in Cd2Nb2O7. Raman frequency of the soft mode is used as an order parameter which is calculated from the molecular field theory. On that basis, the damping constant is calculated by fitting the expressions from the pseudospin-phonon coupled model and the energy fluctuation model to the observed linewidth from the literature below TC in Cd2Nb2O7. From our analysis, we find that the molecular field theory is adequate for the soft mode behaviour and that both models are also satisfactory for the divergence behaviour of the damping constant as TC is approached from the ferroelectric phase in Cd2Nb2O7. Values of the activation energy U are extracted from the temperature dependence of the damping constant (HWHM) of the soft mode in the ferroelectric phase of this crystal. Also, the inverse relaxation time is predicted using the Raman frequency and damping constant close to the TC in the ferroelectric phase of Cd2Nb2O7, which increases considerably as TC is approached from the ferroelectric phase, as observed experimentally.

Far-infrared and terahertz spectroscopy of ferroelectric soft and central modes in thin films on substrates is reviewed. In addition to classical displacive proper ferroelectrics, also incipient and relaxor ferroelectrics and multiferroics are discussed. Special attention is paid to differences between the soft-mode behavior in thin films and bulk materials (ceramics and single crystals) and their influence on the low-frequency permittivity. Particularly the effects of the thin film strains and depolarizing electric fields of the probing waves on the grain boundaries are emphasized. The soft-mode spectroscopy is shown to be a very sensitive tool to reveal the thin film quality., This review was submitted to Ferroelectrics

A comparative study of the lattice dynamic upon phase transitions in a polycrystalline Ba0.8Sr0.2TiO3 (BST) film on a Pt substrate and in epitaxial BST films grown on various sections of an MgO substrate has been performed by Raman spectroscopy. It has been found that different sequences of phase transitions take place in these films. The BST/Pt films demonstrate the same sequence of phase transitions that is observed in the bulk ceramics. The hardening of a soft mode in BST/(001)MgO and BST/Pt films shows that the transition from the tetragonal ferroelectric phase to the paraelectric phase has features of the displacement-type phase transition and also the order–disorder phase transition. When approaching the ferroelectric transition temperature, the soft mode in the BST/(111)MgO film is softened, following the Cockran law, which indicates the displacement-type phase transition.

The ferroelastic phase transition in LiCsSO4 crystal is vividly shown by the change of slowness surfaces between 293 K and 202 K. The soft mode theory is used to investigate the phase transition. The pure shear mode which is corresponding to the elastic constant c66 starts softening at 206 K and softens completely at 202 K. According to the elastic constitutive relations and the Curie principle, LiCsSO4 crystal is in the same symmetry between 202 K and 206 K. There isn't an intermediate phase during the phase transition.

Three dimensional slowness surfaces are used to study ferroelastic phase transitions of hexagonal crystals. The most prominent softening direction and the soft mode have been determined by the maximum slowness. For hexagonal crystals, the components of the elastic stiffness coefficients c44 or c66 has direct relationship with ferroelastic phase transitions. The spontaneous strains are calculated by using the elastic constitutive relation. The symmetry of ferroelastic phases are determined by using the Curie principle.

The structural instability of Cd2Ta2O7 (CTO) is studied by first-principles calculations. All of the zone-center phonons for the cubic CTO with symmetry have real frequencies. However, one soft mode at the X-point with an imaginary frequency of 17.5 cm−1 is found. By freezing in this soft mode we obtain an energetically favorable structure with Pnma symmetry. The Pnma phase is centrosymmetric and thus is not ferroelectric. Detailed analysis indicates that the Pnma phase CTO is antiferroelectric. Thus our results approve that the phase transition reported experimentally is an antiferroelectric transition.

The recent progress of Terahertz Time-Domain Spectroscopy (THz-TDS) using a coherent terahertz radiation enables the accurate and reliable measurements of dielectric properties in comparison with t...

The structural, electronic, and optical properties of Be2B and its ternary compounds XBeB (X = Al, Na, and Mg) have been calculated using the full-potential linearized augmented plane wave (FP_LAPW) method, which is based on the first-principles method with the generalized gradient approximation (GGA) and the local density approximation (LDA). While, the lattice dynamical and thermodynamic properties were performed using the density functional perturbation theory (DFPT). The calculated lattice constants are in good agreement with the available theoretical and experimental values. The partial density of states (PDOS), and phonon dispersion curves have been obtained and compared with previous works. An accurate calculation of the dielectric function, refractive index, reflectivity, optical conductivity, absorption spectra, extinction coefficient, and energy-loss spectrum were performed. The first time calculated optical properties suggest that AlBeB can be used as possible shields for UV radiations. The phonon dispersion results of the investigated compounds confirm the dynamical stability of both structures Be2B and AlBeB. However the soft modes are observed for both compounds MgBeB and NaBeB, indicating their dynamical instability. Finally, the first time calculated thermodynamic properties showed clearly the thermodynamic instability of NaBeB compound.

The effect of hydrophobic aerosil nanoparticles on the dynamics of the soft mode and the Goldstone mode near the SmA*–SmC* phase transition in the ferroelectric liquid crystal (S)-2-methylbutyl 4-n-nonanoyloxybiphenyl-4′-carboxylate has been investigated by means of broadband dielectric spectroscopy. The obtained results for hydrophobic aerosil composites exhibit some differences in the dynamics of the collective processes as compared with dielectric measurements for hydrophilic aerosil dispersions. The observed changes in dynamics of the collective modes near the SmA*–SmC* phase transition were explained taking into account differences in surface treatment of the aerosil nanoparticles and effect of random disorder.

The reflection and transmission spectra of ceramic samples of SrTiO3–SrMg1/3Nb2/3O3 solid solutions have been measured in the frequency range of 5–5000 cm–1 and in the temperature range of 5–370 K. Based on these spectra, the spectra of the real e'(ν) and imaginary e''(ν) parts of the complex permittivity e*(ν) have been simulated by the method of dispersion analysis. It has been found that the temperature evolution of the dielectric constant is entirely determined by the behavior of the soft mode.

The mechanical properties of a MIL-53(Al) and H2O composite (MIL-53(Al)⊃H2O) in the narrow pore (np) phase were addressed using density functional theory. The tensorial analysis of the elastic constants in the np phase provides a further support of adsorption induced stress mechanism of the breathing effect in MIL-53 and the practical mechanical properties of MIL-53(Al) in humidity condition. The adsorption of water molecules in MIL-53(Al) forms a reinforced wine-rack topological structure. The stable structure in the np phase eliminates the high anisotropy and anomalously low Young and shear moduli of the large pore phase. In addition, new soft modes which indicate the evolving path back to the large pore phase were found in the np phase.

A strong increase in the spectral intensity of Raman scattering (Raman opalescence effect) at the polar soft mode, responsible for the instability of the crystalline lattice, near ferroelectric phase transition points in the barium sodium niobate (BSN) crystal was found. Raman opalescence is explained as a consequence of a sharp increase in the amplitude of the transverse A1(Z; TO) polar optical soft mode near the temperature of the ferroelectric phase transition in BSN (Tc = 830 K). Experimental results were obtained using a new experimental technique, based on the construction of isofrequency temperature dependences, when registering the spectral intensity of Raman scattering at fixed frequencies of the spectrometer, near the frequency of the exciting line, for certain polarization geometry. The conditions for observing the effects of Hyper Raman opalescence near the phase transition temperature in the BSN are established.

Two antiferroelectric liquid crystals of different fluorinated chain length have been studied. Although both exhibit antiferroelectric (SmCA*), ferroelectric (SmC*) and paraelectric (SmA*) phases, melting point decreases with increasing achiral chain length but clearing point shows opposite trend. Thermal ranges of SmCA* and SmC* phases exhibit odd-even effect like the dipole moments and spontaneous polarization. Layer spacings, average intermolecular distances and correlation lengths across the smectic planes also increase with chain length. Temperature dependence of layer spacings, x-ray tilt, optical tilt and spontaneous polarization suggest tricritical nature of SmC*–SmA* transition. Dielectric increments decrease with increased achiral chain. Both soft mode and Goldstone mode critical frequencies decrease with decreasing temperature in the lower derivative but opposite behaviour is observed in the higher derivative. Both the compounds show Curie–Weiss behaviour in soft mode near SmC*–SmA* transition temperature (Tc). Goldstone mode critical frequency is much higher in the higher derivative. Both in-phase and anti-phase antiferroelectric modes are observed in SmCA* phase in the higher derivative but in the lower derivative only anti-phase antiferroelectric mode is observed. Optical tilts suggest orthoconic nature of the SmCA* phase of both the compounds. Ferroelectric-antiferroelectric transition temperature decreases with increasing ac field in both compounds.

The structural phase transition in the Pr3Sb5O12 crystal has been studied using Raman spectroscopy. The phase transition is accompanied by the recovery of the soft mode below T = 735 K, which is associated with the displacements of the oxygen and antimony atoms.

Raman spectroscopy investigation of phase transition in Pr3Sb5O12 crystal is reported. Spectra were obtained in temperature range from 300 to 800 K. Soft mode restoration has been found below 735 K, that allows to attribute structural phase transition as displacive.

Based on Raman spectra, we have studied structural ordering processes in ceramics of ferroelectromagnetics Bi1–x La x FeO3 (x = 0.075–0.20). It has been found that the structure of Bi1–x La x FeO3 is close to the structure of the crystal BiFeO3. However, lines in Raman spectra of Bi1–x La x FeO3 are considerably broadened compared to lines in the Raman spectrum of the BiFeO3 single crystal, which indicates that the structure of solid solutions is much more disordered. In Raman spectra of Bi1–x La x FeO3, in the range of librational vibrations of octahedra as a whole (50–90 cm–1), several groups of lines are observed in frequency ranges 59–69, 72–77, and 86–92 cm–1 (depending on the composition of solid solution). This confirms X-ray data that examined solid solutions are not single-phase. At a La content x = 0.120, Raman lines in the low-frequency spectral range narrow, which indicates that the ordering of structural units in cationic sublattices somewhat increases. Upon an increase in the content of La in the Bi1–x La x FeO3 structure, no unambiguous dependence of parameters of spectral lines is observed. It is likely that this is explained by the fact that, as the value of x increases, the character of the incorporation of La into the structure of the solid solution changes.

In this work the semi-microscopic vibronic theory of quantum paraelectrics and ferroelectrics of oxide perovskites (SrTi16O3, CaTiO3, SrTi(18Ox16O1-x)3, KTaO3 etc.) has been developed further. It is shown that the electron-lattice couplings of the filled A1g and empty F1u electronic states of the BO6 cluster in ABO3 perovskite-oxides with the potential ferroelectric soft mode F1u (Γ15) and the zone-boundary phonon mode F2u (Γ25) lead to the antiferrodistortive phase transition at Ta = 105 K in SrTiO3. The vibronic interaction causes the softening of the ferroelectric F1u mode in the antiferrodistortive phase with the D4h symmetry. The electron-lattice coupling-hybridizations of the 1A1g and F1u electronic states by the F1u and R-corner F2u modes lead to the splitting of the F1u mode frequencies ωf (in the cubic phase) into the frequencies ωf,c and ωf,a, respectively, in the phase D4h. The Helmholtz free energies of such quantum paraelectrics and ferroelectrics are obtained.