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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 structural transformation generally occurs from lower symmetric to higher symmetric structure on heating. However, the formation of locally broken asymmetric phases upon warming has been evidenced in PbQ (Q = S, Se, Te), a rare phenomenon called emphanisis, which has significant effect on their thermal transport and thermoelectric properties. (SnSe)0.5(AgSbSe2)0.5 crystallizes in rock-salt cubic average structure, with the three cations occupying the same Wycoff site (4a) and Se in the anion position (Wycoff site, 4b). Using synchrotron X-ray pair distribution function (X-PDF) analysis, herein, we show the gradual deviation of the local structure of (SnSe)0.5(AgSbSe2)0.5 from the overall cubic rock-salt structure with warming, resembling emphanisis. The local structural analysis indicates that Se atoms remain in off-centered position by a magnitude of ∼0.25 A at 300 K along the [111] direction and the magnitude of this distortion is found to increase with temperature resulting in three short and three long M-Se bonds (M = Sn/Ag/Sb) within the average rock-salt lattice. This hinders phonon propagation and lowers the lattice thermal conductivity (κlat) to 0.49-0.39 W/(m·K) in the 295-725 K range. Analysis of phonons based on density functional theory (DFT) reveals significant soft modes with high anharmonicity which involve localized Ag and Se vibrations primarily. Emphanisis induced low κlat and favorable electronic structure with multiple valence band extrema within close energy concurrently give rise to a promising thermoelectric figure of merit (zT) of 1.05 at 706 K in p-type carrier optimized Ge doped new rock-salt phase of (SnSe)0.5(AgSbSe2)0.5.

Stoichiometry, crystal compound, electronic attributes and superconductivity of compressed lithium-tin composites have been thoroughly studied using quantum mechanical genetic algorithm approach and the first principles computations based on density functional theory. Our simulations at moderate pressure (5-20 GPa) predict a complex convex hull diagram, with the following stable Li‑rich phases: I4/mmm-Li6Sn2, -Li7Sn2, -Li5Sn2, Ama2-Li4Sn2, -Li5Sn2, -Li6Sn2, C2/m-Li4Sn1, P21/m-Li6Sn2, -Li7Sn2 and Cmcm-Li4Sn2. Careful examination at their independent elastic parameters reveals sufficient mechanical stability in them. These phases are metallic system, with reasonably high electron concentration near to Fermi level or N(EF) that ranges from 0.6 to 2.4 states/eV cell. It is also interesting for us to observe soft modes and steep-flat energy bands at Fermi levels of Li6Sn2 structures which are stable throughout the pressure range. These features are prerequisites for superconducting behavior. Linear response function with Gaussian and tetrahedron methods reveals satisfactory superconducting transition temperature Tc (3.1 ~ 6.6 K) and Tc (2.1 ~ 2.4 K), respectively. Structural transition results for based elements Li and Sn agree well with literature thus signifying reliable prediction of intermediate phases.

The stability of halide perovskites has been a long-standing issue for their real-world application. Approaches to improve stability include nanostructuring, dimensionality reduction, and strain engineering, where surfaces play an important role in the formation of a stable structure. To understand the mechanism we compute the lattice dynamics of the surface of CsPbI3 using density functional theory. We demonstrate, for the first time, that CsPbI3 crystals exhibit surface phonons that are localized on the outermost layers of the slabs, and we perform a complete symmetry characterization including an identification of the Raman/IR active modes. These surface phonons are present in the optically active cubic phase but are absent in the optically inactive "yellow" phase. Furthermore, we show that the surface suppresses bulk instabilities by hardening soft modes of the bulk cubic phase, resulting in phase stabilization and quenching of dynamical disorder. This study is fundamental for understanding the structural behavior of halide perovskite materials with high surface area-to-volume ratios, and for guiding stabilization strategies.

We examine the strain effect on the dielectric permittivity of cubic SrTiO3 (STO) with Self-Consistent Phonon (SCP) theory calculations. Despite the soft mode frequency overestimation with this theory scheme and workflow, our calculations predict the correct tendency of TO1 with respect to temperature and strain. We found that a uniform tensile strain leads to softer TO1 modes. In addition, the TO1 frequency drops suddenly to zero at a specific temperature in the presence of a ferroelectric transition. The square linear relation between TO1 and temperature is used to estimate the Curie Temperature (TC), and the STO dielectric permittivity calculated with the Lyddane-Sachs-Teller relation follows the Curie-Weiss (CW) law; which can also be used to determine another TC value. Results from both approaches are in good agreement with each other and show that TC increases significantly even when the applied tensile strain is only a few percent.

GeTe that exhibits a strong anharmonicity and a ferroelectric phase transition between the rhombohedral and cubic structures has emerged as one of the leading thermoelectric materials. Herein, combining molecular dynamics simulations and inelastic neutron scattering measurements, the lattice dynamics in GeTe have been investigated to reveal the soft-mode mechanisms across the phase transition. We have constructed a first-principles-based machine-learning interatomic potential, which successfully captures the dynamical ferroelectric phase transition of GeTe by adopting the neural network technique. Although the low-energy acoustic phonons remain relatively unaffected at elevated temperatures, the high-energy optical, and longitudinal acoustic phonons demonstrate strong renormalizations as evidenced from the vibrational phonon spectra, which are attributed to the large anharmonicity accompanying the phase transition. Furthermore, our results reveal a nonmonotonic temperature dependence of the soft-modes beyond the perturbative regime. The insight provided by this work into the soft-modes may pave the way for further phonon engineering of GeTe and the related thermoelectrics.

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.

The c66E values of PZT53/47 doped with 0.6% Gd2O3 show an anomalous behavior near 132°C as a consequence of a ferroelastic transition. A non-linear fit to the experimental data of the elastic stiff...

Modified two-sublattice pseudospin lattice coupled-mode (PLCM) model Hamiltonian by adding third- and fourth-order anharmonic interactions, extra spin–lattice interactions, direct spin–spin interaction as well as external applied electric field has been considered for $$\mathrm{CsH}_{2}\mathrm{PO}_{4}$$ (abbreviated CDP) and $$\mathrm{CsD}_{2}\mathrm{PO}_{4}$$ (abbreviated DCDP) crystals. By using double-time temperature-dependent Green’s function method and Dyson’s equation, the expressions for the shift, width, soft mode frequency, dielectric constant and loss tangent have been evaluated. By fitting the model values of various physical parameters in the expressions, the thermal variations in soft mode frequency, dielectric constant and loss tangent have been calculated. Our theoretical results show good agreement with the experimental data of Levstik et al. CDP undergoes a ferroelectric phase transition at $$T_{c}=153$$ K, whereas the ferroelectric phase transition in isomorphous DCDP is $$T_{c}=267$$ K, showing a large isotope effect explains the importance of the O–H–O bonds in the phase transition mechanism.

Potassium Dihydrogen Arsenate (KH2AsO4, KDA) is an inorganic arsenate ferroelectric crystal which is a KDP-family member and undergoes a ferroelectric phase transition at 96 K. A simple pseudospin lattice coupled mode model (PLCM) with some higher order terms like direct spin–spin interaction, third and fourth-order phonon anharmonic interaction terms and external electric field term, with two-time temperature dependent Green’s function technique has been employed for the evaluation of expression of response function. We can obtain and calculate soft mode frequency ( Ω ^ ), Dielectric constant (e), and loss tangent (tanδ) expressions from response function for KDA crystal. We have shown temperature dependence of soft mode frequency ( Ω ^ ), Dielectric constant (e), and loss tangent (tanδ) in Fig. 1 , Fig. 2 , Fig. 3 . We have compared our findings, which seemed to be in fair alignment with experimental evidence.

The quite simple but relatively stable VF3-type compounds are known to be of major interest due to their building blocks – octahedra that are extremely important in perovskites as well. Here, we show that the VF6 octahedron in VF3 varies over a fairly wide pressure range (0–50 GPa), maintaining undisturbed rhombohedral crystal symmetry. Half of this pressure, VF6 rotates easily while the other undergoes strong uniaxial deformation in a “super-dense” condition. The congested sphere packing ultimately does not endure and drives the material to amorphize. We observed that the amorphous state could be quenched and acquire a transparent glass-like appearance when unloaded to ambient conditions. Dramatic, pressure-induced changes are clarified by phonon dispersion curves with the imaginary phonon mode, the so-called phonon soft mode, which indicates the structural instability. The distortion of the VF6 octahedra is attributed to the distinctive amorphization that could be further searched for throughout the whole almost identical VF3-type series providing metal trifluorides of various amorphous species.

The modified two sublattice pseudospin lattice coupled-mode model Hamiltonian by adding third- and fourth-order phonon anharmonic interactions, extra spin–lattice interactions, direct spin–spin coupling interaction and applied electric field used for the study of ferroelectric and dielectric properties of triglycine selenate (TGSe) crystal. With the help of retarded double time temperature-dependent Green’s function method, Dyson’s equation and symmetric decoupling scheme, the expressions of ferroelectric soft mode frequency, dielectric constant and dielectric tangent loss have been derived. By fitted the model values of various physical parameters in the obtained expressions, the thermal variations of soft mode frequency, dielectric constant and dielectric tangent loss have been calculated. Theoretical results were compared with experimental data reported by Bye et al.

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...

Multiferroics are materials exhibiting the coexistence of ferroelectricity and ideally ferromagnetism. Unfortunately, most known magnetoelectric multiferroics combine ferroelectricity with antiferromagnetism or with weak ferromagnetism. Here, following previous theoretical predictions, we provide clear experimental indications that ferroelectricity can be induced by epitaxial tensile strain in the ferromagnetic simple binary oxide EuO. We investigate the ferroelectric phase transition using infrared reflectance spectroscopy, finding that the frequency of the soft optical phonon reduces with increasing tensile strain and decreasing temperature. We observe such a soft mode anomaly at 100 K in (EuO)2/(BaO)2 superlattices grown epitaxially on (LaAlO3)0.29-(SrAl1/2Ta1/2O3)0.71 substrates, which is a typical signature for a displacive ferroelectric phase transition. The EuO in this superlattice is nominally subjected to 6.4% biaxial tensile strain, i.e., 50% more than believed needed from previously published calculations. We interpret our results with new first-principles density functional calculations using a hybrid functional, which provides a better quantitative agreement with experiment than the previously used local-density approximation and generalized gradient approximation functionals., Communications Materials, 1 (1), ISSN:2662-4443

[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).

Reported are the results of studying the sharp increase in the spectral intensity at the lattice soft mode near the temperature of the phase transition in the lithium tantalate crystal. The Raman scattering spectra are recorded in the x(zz)y polarization geometry corresponding to manifestation of the soft mode responsible for the ferroelectric phase transition in lithium tantalate at 898 K. The recording is performed at fixed temperatures T ( $$I(\omega {\kern 1pt} ',T)$$ , T = const) and at fixed spectrometer frequencies ( $$I(\omega {\kern 1pt} ',T)$$ , $$\omega {\kern 1pt} ' = {{\omega }_{0}} - T = {\text{const}}$$ ) under slow (1 deg./min) crystal temperature variation. Strong increase (by three orders of magnitude) is observed in the peak of the reduced spectral intensity i0(Ω) of the isofrequency temperature dependence at the fixed spectrometer frequency shift relative to the exciting radiation $$\Omega = {{\omega }_{0}} - \omega {\kern 1pt} ' = 10$$ cm–1 similar to the one earlier observed in quartz crystals.

The spectral intensity of Raman scattering in quartz crystals has been calculated in a wide temperature range including the point of the α–β phase transition. It is established that a central peak is present in the scattered radiation spectrum at different temperatures with allowance for the interaction between the fundamental soft mode and an additional low-frequency oscillator. The intensity and half-width of the central peak are calculateed in a wide temperature range.

This work is aimed at studying asymmetric BaTiO31 − xΛ/BaZrO3xΛ ((BT) 1−xΛ/(BZ)xΛ) superlattices, grown by pulsed laser deposition onto (001) MgO substrates. The thicknesses of BT (ferroelectric) and BZ (paraelectric) layers were varied so that х ranged from 0 to 1 at a modulation period Λ of about 80 Å. The films were 400 nm thick. The out-of-plane lattice parameters of constituents were assessed using X-ray diffraction. The lattice dynamic peculiarities of superlattices were probed via Raman spectroscopy; special attention is paid to the analysis of E(1TO) and A1(2TO) ferroelectric soft modes. A comparative analysis of data acquired via both experimental techniques reveals the enhancement of stress between BT and BZ layers with a decrease in symmetry from the tetragonal to a monoclinic phase due to strains induced by the lattice parameter mismatch between the constituents.

The chemical shift of the N(2)(CH3)4 ion, which has been found to exhibit the similar anomalous behavior of the monoclinic angle $\Delta \beta $ , was related to the order parameter to evaluate the temperature dependence of the linewidth (damping constant) for 14N nuclear magnetic resonance spectrum of this crystal in terms of the dynamic Ising models, namely the pseudospin-phonon-coupled (PS) and the energy fluctuation (EF) models. The results from both PS and EF models were successful to explain the abnormal behavior of the linewidth in the vicinity of the phase-transition temperature of ${T}_{C}= {287.6}$ K, when compared with the observed linewidth of the transverse acoustic soft mode in this crystal. As an extension of this work, the 14N relaxation time and the values of the activation free energy were calculated as a function of temperature. The results indicate that the ferroelastic–paraelastic phase transition in this compound is of the order–disorder type.

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...

We present a structural and optical characterization of magnetoelastic zircon-type TmVO4 at ambient pressure and under high pressure. The properties under high pressure have been determined experimentally under hydrostatic conditions and theoretically using density functional theory. By powder X-ray diffraction we show that TmVO4 undergoes a first-order irreversible phase transition to a scheelite structure above 6 GPa. We have also determined (from powder and single-crystal X-ray diffraction) the bulk moduli of both phases and found that their compressibilities are anisotropic. The band gap of TmVO4 is found to be Eg = 3.7(2) eV. Under compression the band gap opens linearly, until it undergoes a huge collapse following the structural phase transition (ΔEg = 1.15 eV). Ab initio structural and free energy calculations support our findings. Moreover, calculations of the band structure and density of states reveal that for both zircon and scheelite TmVO4 the band gap is entirely determined by the V 3d and O 2p states of the VO43– ion. The behavior of the band gap can thus be understood entirely in terms of the structural modifications of the VO4 units under compression. Additionally, we have calculated the evolution of the infrared and Raman phonons of both phases upon compression. The presence of soft modes is related to the dynamic instability of the low-pressure phase and to the phase transition.

Soft phonon modes in strongly anharmonic crystals are often neglected in calculations of phonon-related properties. Herein, we experimentally measure the temperature effects on the band gap of cubic SrTiO3, and compare with first-principles calculations by accounting for electron–phonon coupling using harmonic and anharmonic phonon modes. The harmonic phonon modes show an increase in the band gap with temperature using either Allen–Heine–Cardona theory or finite-displacement approach, and with semilocal or hybrid exchange-correlation functionals. This finding is in contrast with experimental results that show a decrease in the band gap with temperature. We show that the disagreement can be rectified by using anharmonic phonon modes that modify the contributions not only from the significantly corrected soft modes, but also from the modes that show little correction in frequencies. Our results confirm the importance of soft-phonon modes that are often neglected in the computation of phonon-related properties and particularly in electron–phonon coupling.

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 ...

By adding cubic-order and quartic-order phonon anharmonic interactions terms with spin-spin interactions terms, extra interaction term and external electric field has been considered in two-sublattice pseudospin lattice coupled mode (PLCM) model for phase transitions and dielectric properties of order-disorder Rochelle salt (RS) crystal. Using double-time temperature Green function method, we obtain the expression for Soft mode frequency, dielectric constant and tangent loss have been obtained for Rochelle salt crystal. Numerical calculations will be performed by fitting model values of various parameters in the above expressions for RS crystal. Present theoretical results agree well with experimental results of Sandy and Jones.

There was studied a jump-like deformation of AMg6 aluminum alloy at static tensile test in the soft mode of loading. The experimental methods of jump-like deformation study of this alloy are often complicated, expensive and time-consuming. Therefore, it is more effective to model the stress-strain diagram numerically. One of the promising ways to predict the stress-strain diagram of AMg6 material is based on the application of machine learning methods, in particular by neural networks, boosted trees, support-vector machines, and k - nearest neighbors. It was discovered that the method of neural networks gives the least prediction error equal to 6.9%. The errors of the methods of boosted trees, support-vector machines and k - nearest neighbours are 9.1, 7.7, and 9.4% in test sets, respectively.

Two partially fluorinated ferroelectric liquid crystals (2F3R, 3F3R) with biphenylyl benzoate core have been investigated by frequency domain dielectric spectroscopy and electro-optic metho...

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.

We report a systematic first-principles study based on density functional theory (DFT) of the structural and ferroelectric properties of the R 2 Ti2O7 perovskite-related oxides with R = La, Ce, Pr, and Nd. We show that, in all cases, the ferroelectric distortion to the ground-state polar P 2 1 structure from its parent centrosymmetric P 2 1 / m phase is driven by a single polar soft mode consisting of rotations and tilts of the TiO6 octahedra combined with displacements of the R ions. A secondary centrosymmetric distortion, which is stable in the parent structure, contributes substantially to the energy lowering of the ground state. We evaluate the trends in structure and polarization across the series as a function of R and reconcile discrepancies in reported values of polarization in the literature. Our results confirm that the family of R 2 Ti2O7 materials belong to the class of proper geometric ferroelectrics.