Soft TO Mode Research Articles

Potency of Extended X-ray Absorption Fine Structure Spectroscopy toward the Determination of Individual Bond Grüneisen Parameter for High Thermoelectric Performance

Si–Ge is a well-known disordered alloy exhibiting high anharmonicity. These two features, disorder and anharmonicity, arise due to the unique nature of bonding instead of structural complexity and are beneficial as they limit the thermal conduction and are widely used in high-temperature thermoelectric applications. In this regard, a comprehensive understanding of the nature of interatomic bonds and the calculation of the Grüneisen parameter, which is a characteristic metric of anharmonicity, of the individual bond are essential to design a crystalline solid along with the development of a high-throughput thermoelectric alloy exhibiting ultralow lattice thermal conductivity. Here, we demonstrate the origin of the low lattice thermal conductivity, κl, of ∼0.8 and 0.4 Wm–1 K–1 for the transition-metal (Ni and Cr)-doped Si–Ge alloy, respectively, due to the difference in the anharmonic pair potential achieved using synchrotron-based X-ray absorption fine structure spectroscopy. The technique enables the determination of the Grüneisen parameter of the individual bond in the alloy and thus reveals the unpaired electron-induced bond anharmonicities and bonding heterogeneity. The technique also determines the bond Grüneisen parameter more precisely in comparison to the values obtained from the speed of sound, as the latter neglects the existence of the soft TO mode, which also contributes to lattice dynamics. Thus, the synergistic presence of (i) heteroatoms as point scatters (mass contrast), (ii) bonding anharmonicities, and (iii) electron–phonon scattering suppresses the lattice thermal conductivity beyond the theoretical alloy limit. Furthermore, the analysis imparts a conception for the estimation of the bond Grüneisen parameter through the acquisition and analysis of extended X-ray analysis of fine structure (EXAFS) spectra.

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.

Mode coupling and polar nanoregions in the relaxor ferroelectricPb(Mg1/3Nb2/3)O3

We present a quantitative analysis of the phonon line shapes obtained by neutron inelastic scattering methods in the relaxor ferroelectric $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ (PMN). Differences in the shapes and apparent positions of the transverse acoustic-- (TA) and transverse optic-- (TO) phonon peaks measured in the (300) and (200) Brillouin zones at 690 K are well described by a simple model that couples the TA and soft TO modes in which the primary parameter is the wave vector and temperature-dependent TO linewidth $\ensuremath{\Gamma}(q,T).$ This mode-coupling picture provides a natural explanation for the uniform displacements of the polar nanoregions (PNR's), discovered by Hirota et al. as the PNR result from the condensation of a soft TO mode that also contains a large acoustic component.

Nature of low frequency dielectric permittivity behaviour in weakly and moderate concentrated KTaO3:Li

The low frequency complex dielectric permittivity (′’ and ″) have been studied in the frequency-temperature region 100 Hz - 1 MHz and 5 K - 300 K in weakly (x <0.01) and moderatly (x < 0.1) concentrated K1-xLix TaO3 (KLT). The ″'(T) dependencies reveal one or two well-pronounced temperature maxima depending on the Li concentration. Only one maximum in the ″'(T) and ″ (T) behaviour is present in the weakly doped KLT, whose magnitude strongly depends on frequency. For the moderatly Li concentration an additional relaxation temperature maximum emerges with a larger potential barrier of the dipolar reorientation. In both cases the magnitudes of the permittivity maxima with temperature appear to be very large, which can not be explained only by the Li+ off-centre reorientations themselves. We present a theory, which considers two types of the Li+ related relaxors coupled to the soft TO mode that describes quantitatively the phenomena observed.

Electric field dependence of the thermal conductivity of quantum paraelectrics

Thermal conductivity measurements have been carried out on single crystals of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{KTaO}}_{3}$ in the presence of electric fields applied either perpendicular or parallel to the heat current. In the case of ${\mathrm{SrTiO}}_{3},$ the response is surprisingly large: a 7 kV/cm parallel field increases the thermal conductivity by up to $400%.$ A pronounced anisotropy in both materials, which becomes apparent above nearly the same temperature, is also observed. These effects can be interpreted qualitatively using a simple model in which TA phonons in an energy band near the soft TO mode scatter off of either impurities, ferroelectric microregions, or quantum ferroelectric fluctuations.

Possible role of charge transfer vibronic excitons in light induced change of polarizability in ferroelectric solid solutions KTa1-xNbxO3

The charge transfer vibronic excitons (CTVE) induced by two-photon absorption within the pulsed degenerate four-wave mixing (DFWM) study of ferroelectric solid solution KTa1-xNbxO3 is considered as an origin of the transient optical response. The CTVE are created by charge transfer between oxygen and tantalum, or oxygen and niobium ions with appearance of O−—Ta4+ or O−—Nb4+ pairs accompanied by self-consistent lattice distortion. This lattice distortion is caused mainly by strengthening of the vibronic interaction in final recharged ion states of CTVE. Dipole—soft TO-phonon interaction as well as Jahn-Teller interaction are effective here. The electron-hole “negative-” effect plays important role in CTVE formation in addition. As a result, the changes in dielectric polarizability induced by optical pumping and correspondent CTVE creation increase the initial polarizability due to the interaction of CTVE reoriented dipole moments with soft TO-mode. The latter leads to critical increase of light induced change in polarizability (LICP) and thus it is connected with critical increase of DFWM absolute diffraction efficiency (ADE) in accord with experimental concentration dependence of DFWM for KTa1-xNbxO3.

Light-induced charge transfer and kinetics of the NIR absorption of Nb 4+ polarons in SBN crystals at low temperatures

Sr1-xBaxNb2O6 (SBN) crystals with open tungsten-bronze structure show enhanced photorefractive properties with doping of impurities such as Ce, Cr, Rh etc. Under illumination with Kr+ laser (647 nm) or Ar+ laser light (488 nm or 514 nm) or UV light at low temperature, pure and doped SBN crystals show a broad polaron absorption band around 0.7 eV (6000 cm-1). The first step of a theoretical model involves the excitation of electrons by illumination from Cr3+/Ce3+ to higher excited states or the conduction band. The excited electrons can then be trapped by Nb5+ to form Nb4+ polarons and further on can directly tunnel through or hop over the potential barrier (with a value Δ≈0.15±0.02 eV) to recombine with Cr4+/Ce4+ ions. The experimental intensity dependence, temperature dependence, and decay process of the light-induced Nb4+ polarons can be fitted with the help of this model. Small, but systematic, differences lead to the additional assumption of different recombination rates of polarons at distinct distances from the Cr4+/Ce4+ recombination centers and therefore many parallel decay channels are active where each decay channel obeys a monoexponential decay law. A stretched exponential decay function is employed to fit in this case the decay process of the Nb4+ polarons at different temperatures and under illumination with different intensities. Due to the high dielectric constant value (e33 and e11 have values in the 102-103 range) at low temperature, the long range Coulomb attraction (to Ce3+ Sr/Ba) or repulsion (from Cr3+ Nb) of the electronic polaron is suppressed. The leading role in the attraction and the following trapping of the electronic Jahn–Teller polaron, both on Cr3+ Nb and Ce3+ Sr/Ba centers, is played by the indirect dipole–dipole interaction via the soft TO-mode.

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn2P2S6 is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a*-c* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (Px), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn2P2Se6, a strong coupling between the TO(Px) and TA(uxz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(Px) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(Px) dispersion in the a*-b* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(uyx) and LA(uxx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed.

Vibronic charge-transfer excitons: Possible nature of the unusual properties of virtual perovskitelike ferroelectrics

A vibronic charge-transfer exciton, which is a pair of Jahn-Teller electron and hole polarons, is considered as a possible cause of the appearance of the Muller phase in the virtual ferroelectric SrTiO3 and the “green” luminescence in the virtual ferroelectric KTaO3. The two “green” luminescence bands can be associated with emission from two states of a typical intrinsic defect, viz., a vibronic charge-transfer exciton trapped by an oxygen vacancy and an isolated vibronic charge-transfer exciton. In both cases the “green” luminescence corresponds to the recombination of the electron and the hole in the vibronic charge-transfer exciton, which is accompanied by the emission of light. The properties of the Muller phase can be attributed to mixing of the normal state and states of the vibronic charge-transfer exciton phase when they interact with polarization in the soft SrTiO3 matrix under the conditions of a pseudo-Jahn-Teller (pseudo-JT) effect on a soft TO mode of the displacement type. In this case the vibronic charge-transfer exciton phase forming the low-lying excited states has “order-disorder” degrees of freedom and exists at temperatures significantly below the point of the order-disorder ferroelectric transition in SrTiO3 at T=T Q≈37 K. The corresponding lowering of the symmetry of the vibronic charge-transfer exciton phase to polar symmetry leads to the possibility of a long-period incommensurate phase in such excited states, which arises as a result of the appearance of a Lifshitz invariant. The valence-band state making the largest contribution of the pseudo-JT effect corresponds to a wave vector equal to the critical wave vector of the incommensurate vibronic charge-transfer exciton phase. When the temperature is lowered, the pseudo-JT distortion increases down to ∼T Q and subsequently saturates in accordance with the saturation of the dielectric constant. The basic assumption in the model is that the temperature T=T Q corresponds to the narrow temperature range for the transition from an intermediate to a strong pseudo-JT effect under the conditions for the realization of polarization tunneling states. The appearance of a significant admixture of states of the modulated ferroelectric vibronic charge-transfer exciton phase to the ground state under the conditions for the realization of polarization tunneling states at low temperatures provides an explanation for the principal properties of the Muller phase.

Charge transfer vibronic excitons as an origin of a new quantum paraelectric regime (Müller phase) and of polar microdomains in incipient perovskite-like ferroelectrics

The unified mechanism of a new quantum paraelectric regime (Müller phase) as well as of polar microdomain forming in incipient perovskite-like ferroelectrics is considered. Müller phase (MP) is formed by charge-transfer vibronic excitons (CTVE) with intrinsic elastic and electric dipole moments. CTVE form order-disorder clusters with co-operative lowering of energy due to charge transfer ordering. Such CTVE clusters are characterized by long life time and can be considered as proper defects. The transition to MP (T = TQ ≈ 37 K in SrTiO3) corresponds to local ferroelectric-type transition in such CTVE-clusters. This local ferroelectric transition is induced by interaction between lattice soft TO-mode and soft polarization mode of CTVE cluster. This is the mechanism of polar microdomain appearing. Simultaneously the model gives a new explanation of soft TO-mode stabilization as a result of repulsion from local polarization modes of CTVE clusters. The coexistence of order-disorder and displacive type behaviour in incipient perovskite-type ferroelectrics also find the explanation. The latter is based on the existence of order-disorder degrees of freedom of CTVE-clusters. The relaxationtype fluctuations of dipole moments of CTVE and CTVE-clusters also interact with TO- and E g soft lattice modes and create the central peak phenomena. The theoretical model is in agreement with experimental results.

Giant LO-TO splittings in perovskite ferroelectrics.

We perform a first-principles investigation of the role of Coulomb interactions in eight AB${\mathrm{O}}_{3}$ cubic perovskite compounds. The predicted spontaneous polarization and the LO and TO phonon frequencies are found to be in good agreement with experiment. Anomalously large dynamical effective charges give rise to very strong mixing of the mode eigenvectors on going from the TO to the LO case, resulting in a ``giant LO-TO splitting'' in the sense that the soft TO mode is most closely related to the hardest LO modes. The results help explain the extreme sensitivity of these compounds to electrostatic boundary conditions.

Elastic and Dielectric Studies on the Phase Transition of Ferroelectric LiTlC4H4O6·H2O

Elastic and dielectric properties of ferroelectric LiTlC 4 H 4 O 6 ·H 2 O (LTT) were studied in the paraelectric phase. The Curie-Weiss type anomalies were observed in the elastic stiffness constant at constant electric field, the free dielectric constant and the clamped dielectric constant, while no definite anomaly was found in the elastic stiffness constant at constant electric displacement. The phase transition of LTT is proper ferroelectric, in contrast to the case of isomorphic LiNH 4 C 4 H 4 O 6 ·H 2 O (LAT) known as proper ferroelastic. The dielectric instability in LTT is consistently explained by the low-lying soft TO mode reported previously.

Quantum effects and glass-like behavior in ferroelectric oxides

Quantum fluctuations, or zero-point motions, can strongly influence the low temperature response of a system near a structural phase transition. Among the manifestations of quantum fluctuations at ferroelectric phase transitions are different critical exponents, the suppression of the transition temperature, T c, below its classical value and the development of a quantum paraelectric state. To study these quantum effects as well as the crossover from the classical to the quantum regime, it is necessary to shift T c continuously from high to low temperatures. Hydrostatic pressure is an excellent variable for doing so. Results on the mixed oxides K 1− y Na y TaO 3 and KTa 1− x Nb x O 3 for fixed y and x will be summarized and discussed to illustrate some of the essential features. Some of these mixed oxides, as well as simpler oxides, exhibit short-range dipolar correlations and glass-like responses. An important current debate is centered around the question of whether or not the low temperature phase of these systems results from the freezing in of short-range order. Results on KTa 1− x Nb x O 3 oxides will be discussed and contrasted with other oxides. A novel pressure-induced crossover from normal ferroelectric ordering to dipolar glass behavior in soft TO mode systems with dilute impurities will be discussed, and possible experimental evidence for such a phenomenon will be presented.

Critical quasielastic light scattering in KTa0.968Nb0.032O3.

Intense quasielastic light scattering is observed in potassium tantalate niobate at temperatures near the ferroelectric transition at ${T}_{c}$\ensuremath{\sim}40 K. The central peak (CP) has a non-Lorentzian shape and consists of a sharp component with a broad tail. Near ${T}_{c}$, the sharp component narrows to 1.5 GHz (half-width at half maximum) which is close to the limit of resolution achievable when using an ${\mathrm{I}}_{2}$ vapor filter to eliminate elastically scattered light. It is, therefore, possible that the CP has a much narrower distribution than that of the renormalized Fabry-Perot data. Spectra obtained over a range of frequency shifts including the Raman scattering from the soft TO mode have been fitted by a coupled-mode formalism in which it is assumed that the CP derives all of its intensity from the coupling to the TO phonon. This model accounts reasonably well for the relative intensities of the CP and phonon and the large renormalized frequency of the phonon near ${T}_{c}$. The integrated intensity of the CP has a temperature dependence which is singular at ${T}_{c}$, whereas that of the TO phonon is close to a step-function increase at ${T}_{c}$. Although ordinary two-phonon difference (phonon-density-fluctuations) scattering cannot be excluded as a possible origin of the observed quasielastic scattering, several properties of the quasielastic and Raman spectra, as well as other recent experimental results, suggest a mechanism involving fluctuations due to the disorder in the polarizabilities and force constants introduced by the Nb substitution.

Nature of the Phase Transition in KTaO3 with Random Site Impurities

Recent results, including high pressure data, on the low temperature properties of KTa1-xNbxO3 (KTN) are presented and discussed. Most of the emphasis is on the question of whether the low temperature polar phase in dilute KTN (x≈0.02) arises from the spontaneous displacement of ions below Tc (i.e. a static structural phase transition) or from the freezing of impurity-induced dipolar motion. Much of the evidence argues against a bulk equilibrium phase transition and suggests the coexistence of random dipole freezing and slowly relaxing ordered clusters which grow with decreasing T. The likelihood of a pressure-induced crossover from normal ferroelectric ordering to dipolar glass behavior in soft TO mode systems is discussed and possible evidence for such a phenomenon is presented.

The Oscillator Strength of the Soft Mode in Li2Ge7O15

The temperature dependences or the soft TO mode and the associated LO mode in Li 2 Ge 7 O 15 have been measured by Raman scattering technique in the ferroelectric phase. The frequency of the LO mode decreases as T c is approached from below. The LO-TO splitting of the soft mode was observed to be smaller than 1 cm -1 . The results are discussed in the relationship with those obtained through measurements of dielectric constant. The oscillator strength for the polar soft mode in the paraelectric phase is expected to be very small.

Infrared dispersion in SrTiO3at high temperature

Infrared reflection spectra of strontium titanate are reported as obtained with a scanning interferometer from room temperature up to 1200 K. A fit of the factorized form of the dielectric function to reflectivity data yields the temperature dependence of TO and LO frequencies, dampings, and TO oscillator strengths. The soft TO mode is found to be coupled with the next TO mode. A significant deviation of the soft-mode behavior from the Curie law is evidenced above 400 K. The temperature dependence of the soft-mode damping is discussed.

Field-dependent specific heats and soft modes in KTaO3and SrTiO3at low temperatures

Measurements of the electric-field dependence of the specific heats of a KTa${\mathrm{O}}_{3}$ crystal (up to 16 kV/cm) and of a SrTi${\mathrm{O}}_{3}$ ceramic (up to 22 kV/cm) at temperatures below 10 K are reported. The specific heat of both materials decreases with applied field, and the data are analyzed assuming this decrease is due to the hardening and splitting of the soft TO mode frequency. The field dependence of the soft mode is described using a Lyddane-Sachs-Teller-Devonshire formalism, and the soft-mode contribution to the specific heat is described by appropriate Einstein terms. Good agreement with the experimental data is obtained.

Specific heat and electrocaloric properties of a SrTiO3 ceramic at low temperatures

Specific heat data (at zero field and 21.7 kV/cm) and electrocaloric data (field strengths up to 23.5 kV/cm) were measured on the same sample of a carefully prepared SrTiO3 ceramic between 2-30 K. A field-dependent maximum in CT-3 at 23 K is due primarily to a large density of acoustic phonons at 70 cm-1 and to the field induced splitting and hardening of the soft TO mode at low temperatures. A combination of the thermodynamic TdS equation and the Gibbs free energy expansion describes the reversible electrocaloric data very well using the measured specific heat data. The nonlinear Gibbs coefficients ζ and ζ are determined between 8-30 K: ζ has a slight temperature dependence, ζ = 4.73 × 10-14 (T + 15.6) and ζ is constant, 2.96 × 10-21 (cgs units). An irreversible electrocaloric effect occurs in the ceramic, and the unusual temperature dependence of this effect indicates state switching at the large field strengths used.

An acoustic anomaly at the phase transition in GeTeSnTe alloy single crystals

The ultrasonic wave velocities and attenuation have been measured in single crystals of 20 mole.% GeTeSnTe alloys between 90 and 373°K. The ultrasound velocities and thus the elastic constants show a step-like behaviour, which is accompanied by a peak in the attenuation, at the cubic to rhombohedral transformation temperature (240°K). In the vicinity of the transition a strong interaction occurs between the acoustic phonon modes and the soft TO mode.