Order-disorder Nature Research Articles

Microscopic Hamiltonian and chaotic behavior for Barium Titanate nanoparticles revealed by photonic tunneling model

In order to understand the microscopic properties of the ferroelectric nanoparticles, we review concepts of the attractive BaTiO3 crystals where a photon field from its constituent electrons and ions are considered. We present an associated Hamiltonian and extended potential which are the bases of the physical description of the system from certain geometry of the semiquantal space with the specific phonon mode. Furthermore, we formulate the nonlinear dynamics equation of the systems with the famous microscopic Hamiltonian and Heisenberg equation of motion. In addition, we interest ourselves to a system of BaTiO3 crystals and hypothesis leading to order-disorder nature of phase transitions. The latter are linked to the cooperative phenomenon of chains. The numerical simulations reveal that complex behaviors propagate in such system that can be useful for future application of Barium Titanate crystals in modern electronic technologies.

A first comprehensive look at the order-disorder nature of RTK KIT native and carcinogenic targets

Receptors Tyrosine Kinases (RTKs) act as sensors for extracellular ligands, the binding of which triggers dimerization, activation, and autophosphorylation of specific tyrosine (Y) residues in the Cytoplasmic Domain (CD). This leads to the recruitment and activation of multiple downstream signaling proteins, which regulate various aspects of cellular physiology.

Acoustic Anomalies and the Critical Slowing-Down Behavior of MAPbCl3 Single Crystals Studied by Brillouin Light Scattering

Inelastic light scattering spectra of organic–inorganic halide perovskite MAPbCl3 single crystals were investigated by using Brillouin spectroscopy. Sound velocities and acoustic absorption coefficients of longitudinal and transverse acoustic modes propagating along the cubic [100] direction were determined in a wide temperature range. The sound velocities exhibited softening upon cooling in the cubic phase, which was accompanied by the increasing acoustic damping. The obtained relaxation time showed a critical slowing-down behavior, revealing the order–disorder nature of the phase transition, which is consistent with the growth of strong central peaks upon cooling toward the phase transition point. The temperature dependences of the two elastic constants C11 and C44 were obtained in the cubic phase for the first time. The comparison of C11 and C44 with those of other halide perovskites showed that C11 of MAPbCl3 is larger and C44 is slightly smaller compared to the values of MAPbBr3 and MAPbI3. It suggests that MAPbCl3 has a more compact structure (smaller lattice constant) along with stronger binding forces, causing larger C11 and bulk modulus in this compound, and that the shear rigidity is exceedingly small similar to other halide perovskites. The reported elastic constants in this study may serve as a testbed for theoretical and calculational approaches for MAPbCl3.

Order-disorder nature and elastic anomaly of successive phase transition of (K0.5Na0.5)NbO3 proved by broadband Brillouin scattering

ABSTRACT The importance of the environment-friendly lead-free piezoelectric materials has attracted much attention. The (K0.5Na0.5)NbO3 (KNN) crystals with the perovskite structure undergo the cubic (C) to tetragonal (T) ferroelectric phase transition at T CT = 430 °C, and the tetragonal to monoclinic (M) structural phase transition at T TM = 190 °C. The elastic properties and relaxation process of these phase transitions of the KNN crystals have been studied by broadband Brillouin scattering. The softening of the LA and TA velocities was observed in the vicinity of T CT and T TM. The power law behavior of the velocity indicates three-dimensional fluctuations. The broadband central peak showed the critical slowing down in the vicinity of the T CT and T TM. The slowing down is attributed to the order-disorder nature of the off-center displacement of Nb in KNN.

Displacive or Order-Disorder Phase Transition? The H-bond Dynamics in Multicaloric Ammonium Sulfate

Recently, ferroic materials with giant caloric responses emerged as a possible environmental-friendly alternative for the currently used cooling devices. In our work, we have performed the Born-Oppenheimer molecular dynamics calculations for both para- and ferroelectric phases of multicaloric (NH4)2SO4. The simulations were performed in the NVT ensemble with several conditions applied for three different supercell sizes. Time and space correlations between the ion motions were analyzed using various strategies to study the interaction changes along the obtained trajectories. The investigation of thermally induced evolution of complicated H-bond system in ammonium sulfate structure was performed using calculated power spectra. The results of simulations collated with the obtained X-ray diffraction data enabled us to describe the mechanism of (NH4)2SO4 phase transition as the one of a mixed displacive and order-disorder nature. According to the origin of such structural transformation, the giant inverse barocaloric effect in ammonium sulfate is caused by the reverse H-bond system reorganization induced by hydrostatic pressure in the vicinity of the critical temperature. The spontaneous polarization observed in the ferroelectric phase is a secondary effect of symmetry change and it partially results from the disorder relaxation of both distorted NH4+ cations in low temperatures. The proposed investigation scheme should be useful in the studies of other ferrocaloric materials and H-bonded ferroelectrics.

Anomalous changes in the acoustic properties and central peak behaviors of PbxBa1−xNb2O6 single crystals with x = 0.5 studied by Brillouin spectroscopy

The acoustic properties of tetragonal PbxBa1−xNb2O6 (PBN-x) single crystals with x = 0.5 were studied by Brillouin spectroscopy over a wide temperature range from room temperature to 600 °C. Anomalous changes in the Brillouin frequency shift and the half width of acoustic waves were observed at ∼350 °C that corresponds to the ferroelectric–paraelectric phase transition temperature of PBN-0.50. The longitudinal sound velocity and its associated elastic constant (C33) showed substantial softening in the paraelectric phase when the phonon propagated along the polar c axis, while their degree of softening for the phonon along the a axis was small, revealing clear acoustic anisotropy. It was associated with the strong polarization dependence of the quasi-elastic central peak. The relaxation time derived from the central peak seemed to follow the critical slowing-down behavior indicating order–disorder nature of the phase transition. Among C44 and C66, the former displayed substantial softening in the ferroelectric phase resembling the order parameter behavior. The longitudinal sound velocity and the related acoustic damping showed significant anomalies in the ferroelectric phase of unpoled PBN-0.5, which disappeared completely under poled condition. The possible origin for these unexpected acoustic anomalies was suggested.

Thermal evolution of the crystal structure and phase transitions of KNbO3.

The thermal evolution of the crystal structure and phase transitions of KNbO3 were investigated by high-temperature powder X-ray diffraction and Rietveld refinement of the diffraction data. Two phase transitions from orthorhombic (Amm2) to tetragonal (P4mm) and from tetragonal to cubic () were confirmed, both on heating and cooling. Both phase transitions are first order based on the observed hysteresis. The mixed displacive and order–disorder nature of the tetragonal to cubic transition is argued based on symmetry and apparent divergence of the atomic positions from pseudo-cubic values. The transition between the orthorhombic and tetragonal phase shows no temperature-dependence for atomic positions and only thermal expansion of the unit cell parameters and is thus discussed in relation to a lattice dynamical instability.

Ferroelectric phase transition of Li-doped KTa1-xNbxO3 single crystals with weak random fields: Inelastic light scattering study

The broadband gigahertz dynamics of a ferroelectric phase transition of the 2.5%Li-doped KTa1-xNbxO3 crystals with x = 0.38 (KLTN/2.5/38) was investigated by inelastic light scattering. Its phase transition was found to be slightly diffused type due to weak random fields (RFs) caused by disorder in B-site of perovskite structure. The microscopic origin of the central peak (CP) and the local symmetry of the polar nanoregions (PNRs) in the cubic phase were studied by Raman scattering. In Brillouin scattering, the remarkable elastic anomaly of the longitudinal acoustic (LA) mode was observed near paraelectric cubic to ferroelectric tetragonal phase transition temperature, TC-T = 46 °C, which is attributed to the coupling between fluctuating local polarization in PNRs and the LA mode. The intermediate temperature, T* ∼ 97 °C, at which a dynamic to static transition of PNRs occurs, was determined from the significant increase of damping and intensity of the LA mode and the CP upon cooling. In the vicinity of the TC-T, a slightly stretched slowing down of the relaxation time, τCP, a feature of order-disorder nature of the ferroelectric phase transition with weak RFs, was clearly observed.

Brillouin scattering and elastic constants of relaxor ferroelectric 0.44Pb(Mg1/3Nb2/3)O3-0.56PbTiO3 single crystals

ABSTRACTElastic properties of relaxor ferroelectric 0.44Pb(Mg1/3Nb2/3)O3-0.56PbTiO3 single crystals have been studied under zero and external electric field along [100]-direction by micro-Brillouin scattering. Here we show the ability to move the ferroelectric multidomains toward a single domain state by the application of electric field. In the vicinity of TC-T = 260°C, the anomalous change of C11 in a paraelectric cubic phase was well reproduced by the power law which exhibits the three dimensional polarization fluctuations. The order-disorder nature of the ferroelectric phase transition was confirmed by the analysis of sound attenuation based on the theoretical model by Levanyuk et al.

Relaxor-like dynamics of ferroelectric K(Ta1−xNbx)O3 crystals probed by inelastic light scattering

The relaxor-like dynamics of the cubic-tetragonal ferroelectric phase transition was studied by Brillouin and Raman scattering in K(Ta1−xNbx)O3 (KTN) crystals with x = 0.40 (KTN40). The local symmetry breaking by the polar nanoregions (PNRs) was observed in a paraelectric phase by Raman scattering on the A1(z) mode of the PNRs with R3m symmetry. Upon cooling from a high temperature, the remarkable increase in the LA phonon damping starts at 45 K above the cubic-tetragonal phase transition temperature of TC-T = 308 K, which is defined as the intermediate temperature, T* ∼ 353 K, indicating the start of the rapid growth of the PNRs. The coupling between the LA mode and fluctuation of the PNRs caused a remarkable elastic anomaly in the vicinity of TC-T. The analysis of the temperature dependent central peak shows a critical slowing down towards TC-T, which is the evidence for the order-disorder nature of a ferroelectric phase transition. The evolution of the dynamic PNRs is discussed by the estimation of their length scale, and it is found that it starts to increase near T* and gradually grows towards TC-T.

Elastic anomaly and order-disorder nature of multiferroic barium sodium niobate studied by broadband brillouin scattering

The successive phase transitions of multiferroic barium sodium niobate, Ba2NaNb5O15 (BNN), were studied by Brillouin scattering. The LA, TA modes, and central peak were measured in a large temperature range from room temperature up to 750 °C. In the vicinity of a ferroelectric phase transition at about TC = 585 °C from the prototypic tetragonal 4/mmm to ferroelectric 4mm phases, elastic anomaly was observed for LA and TA modes. In addition, the order-disorder nature was observed by the temperature dependence of a central peak. For further cooling another elastic anomaly was also observed in the vicinity of a ferroelastic incommensurate phase transition at about TIC = 285 °C into orthorhombic 2mm phase with the appearance of incommensurate modulation. The large thermal hysteresis of elastic anomaly near TIC can be attributed the typical feature of the type III incommensurate phase transition predicted recently by Ishibashi and Iwata (2013 J. Phys. Soc. Jpn. 82 044703).

Raman and IR phonons in ferroelectric Sr0.35Ba0.69Nb2O6.04 single crystals

IR and Raman spectra of strontium barium niobate (SBN) with 35% of Sr were measured in a broad interval of temperatures (20–800 K). Anomalies in the frequencies and intensities of some IR and Raman active phonons were observed. These modes are presumably related to Sr and Nb–O vibrations. This brings evidence that, apart from the order–disorder nature of the ferroelectric phase transition in SBN, there could be some ferroelectricity induced by cation displacements in the low Sr content samples.

Anomalous behavior of acoustic phonon mode and central peak in Pb(Zn1/3Nb2/3)0.85Ti0.15O3 single crystal studied using Brillouin scattering

Brillouin spectroscopic measurements have been carried out on relaxor ferroelectric Pb(Zn1/3Nb2/3)0.85Ti0.15O3 single crystal over the temperature range 300–873 K. The frequency of longitudinal acoustic phonon (LA) begins to exhibit a strong decrease below the Burn's temperature TB followed by an increase in the line-width below the characteristic intermediate temperature T* ∼ 525 K. The line-width of the LA phonon mode exhibits a sharp Landau-Khalatnikov-like maximum at 463 K, the tetragonal-cubic phase transition temperature (Ttc). In addition, a broad central peak, found below T* exhibits critical slowing down upon approaching Ttc indicating an order-disorder nature of the phase transition. The relaxation time of polar nanoregions estimated from the broad central peak is found to be same as that obtained from LA phonon mode suggesting a strong coupling between strain and polarization fluctuations.

Brillouin scattering studies of acoustic phonon modes and central peak in single-crystal Pb(Sc1/2Ta1/2)O3

Brillouin spectra measurements have been carried out from 800 to 100 K for Pb(Sc${}_{1/2}$Ta${}_{1/2}$)O${}_{3}$ in back-scattering geometry. The frequency of the longitudinal acoustic (LA) phonon begins to show marked softening followed by an increase in its width below the intermediate temperature ${T}^{*}$ $=$ 450 K. The gradual increase in the width of the LA phonon below ${T}^{*}$ is attributed to the electrostrictive coupling between the local polarization and strain. The frequency of the LA phonon mode exhibits anomalous behavior around 295 K, the phase transition temperature. The width of the LA phonon exhibits a sharp Landau-Khalatnikov-like maximum at 295 K. A central peak begins to appear around ${T}^{*}$ and exhibits critical slowing down upon further cooling. The relaxation times calculated for the LA phonon and central peak indicate the order-disorder nature of the phase transition.

Why P in SrTi18O3 is Not Parallel to [100]c as Expected from the Slater Type Soft Mode?: Role of Rhombohedral Polar Clusters

In spite of a number of studies on the ferroelectricity of the isotope exchanged SrTi18O3, it has not been clarified yet why the spontaneous polarization P in the isotope exchanged SrTi18O3 is not parallel to [100] c as expected from the Slater mode but parallel to [110] c . In this paper it is shown that the dipole-dipole interaction between the rhombohedral polar clusters which exist from well above Tc is closely related to the formation of the P parallel to [110] c . The results are consistent with the appearance of the relaxational mode in the Raman spectra and suggest the existence of the order-disorder nature of this transition.

Order–disorder and displacive components in the ferroelectric–paraelectric phase transition of potassium titanyl phosphate KTiOPO4

In situ neutron powder diffraction analysis from 297 to 1358 K indicates the experimental evidence of the coexistence of order-disorder and displacive nature in the ferroelectric-paraelectric phase transition of potassium titanyl phosphate (KTiOPO(4), KTP).

Comments on Raman Spectra of SrTi18O3: Imperfect Softening and Intrinsic Inhomogeneity of the Ferroelectric Phase

A peculiar nature of the ferroelectric phase transition of isotope exchanged SrTi 18 O 3 (STO18) are discussed by comparing three independent Raman studies which have been recently published. The results reported in a paper by the present authors (Phys.Rev. B 74, 174121 (2006)) are quite different from others as follows: (a) Contrary to the report by Takesada et al. (Phys. Rev. Lett. 96 , 227602 (2006)), the perfect softening does not take place. Instead, a quasi-elastic mode appears near T c indicating the order-disorder nature of STO18; (b) Contrary to the report by Taniguchi et al. (Phys.Rev.Lett. 99 , 017602 (2007)), the ferroelectric phase of STO18 is intrinsically inhomogeneous regardless of the isotope concentration. By comparison, it is shown that the conclusions in the latter two papers are not the case. The reason is that in these papers the spectra for only a single phonon propagation direction K p were measured and analyzed without taking into account the consistency to the spectra for other K p 's. Contrary to other ordinary ferroelectric crystals, the transition in STO18 is peculiar because the ferroelectric domains are generated from the polar nano-region (PNR) and its percolation.

Origin of the Ferroelectricity in SrTi18O3 Studied by Raman Scattering

Isotope exchanged SrTi 18 O 3 (STO18) undergoes a ferroelectric transition at about T c = 24 K. Its origin and mechanism have been investigated by many authors but even the direction of spontaneous polarization has not been clarified yet. In this paper from optical and Raman scattering studies, we report that the spontaneous polarizations are parallel to [1, ± 1,0]c, which is the crystal axes of the tetragonal phase. In Raman spectra, softening of TO modes are observed but the softening is not perfect. The displacement of soft mode is not parallel to the cubic axis [1, 0, 0]ccontrary to the expectation from Slater mode. Near T c , a quasi-elastic mode appears which suggests the order-disorder nature of this transition. Although at temperatures far from T c this transition is triggered by the soft TO mode, ferroelectricity in STO18 is a result of the percolation of polar clusters which exist already above T c . The structure of STO18 below T c is inhomogeneous mixture of the orthorhombic (C2v) ferroelectric domains with / / [110] c and / / [10] c in the matrix of the tetragonal (D4h) structure.

Heat capacity and high-resolution Brillouin scattering studies of phase transitions inK2MgWO2(PO4)2: Observation of the coupled soft optic and acoustic mode

High-resolution micro-Brillouin scattering and heat capacity studies of phase transitions in ferroelectric ${\mathrm{K}}_{2}\mathrm{Mg}\mathrm{W}{\mathrm{O}}_{2}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ were performed in the temperature range $300\char21{}810\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Strong anomalies in Brillouin shift and attenuation were observed near 633, 519, and $434\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ upon cooling for the sound waves corresponding to the ${c}_{11}$ and ${c}_{33}$ elastic constants. The analysis of these anomalies and heat capacity results revealed that they correspond to second-order, typical first-order, and nearly second-order phase transitions, respectively. The highest temperature phase transition was shown to have mainly an order-disorder nature whereas the two remaining transitions may have both order-disorder and displacive nature. The obtained results revealed also very strong coupling between the ${c}_{44}$ acoustic mode and the soft optic mode of $E$ symmetry. The coupled mode model was employed to fit the experimental data. It was shown that the relaxation time of the order parameter exhibits slowing down indicating that the phase transition at $519\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is induced by instability of the $E$-symmetry soft mode. The possible microscopic origin of the soft mode is proposed.

Direct evidence of an order-disorder nature of ferroelectric phase transitions in K2MgWO2(PO4)2

K2MgWO2(PO4)2 single crystal, related to famous optical nonlinear material KTiOPO4, was investigated by micro-Brillouin scattering with a focus on the central components of the relaxation modes. A critical slowing down has been clearly observed in the vicinity of T1=436K while suppressed by the coupling with the order parameter. The temperature dependence of the relaxation time indicates that the former transition is the second order, while the latter is strongly first order. The obtained results show that disorder processes in the sublattice of potassium ions play a major role in the mechanism of these phase transitions.