Phase transition effects in polycrystalline Hg<Subscript>2</Subscript>Br<Subscript>2</Subscript> samples

The effects accompanying the ferroelastic phase transition in Hg₂Br₂ polycrystalline samples are compared in an x-ray diffraction study with similar effects observed to occur in Hg₂Br₂ single crystals. In particular, an analysis is made of the “orthorhombic” splitting of the basal plane reflections and the behavior with temperature of the Bragg and diffuse reflections from the X points of the Brillouin zone, which characterize the behavior of the order parameter and its fluctuations, respectively. Polycrystalline samples exhibit strong smearing of the phase transition effects originating from the existence of damaged surface layers and elastic and plastic strain fields which induce order parameter fluctuations over a wide temperature range.     

Order parameter and its fluctuations in Hg<Subscript>2</Subscript>Br<Subscript>2</Subscript> model ferroelastics

The Bragg and diffuse reflections from different X points of the Brillouin zone boundary of the Hg₂Br₂ crystal in the paraphase are studied. The intensities of these reflections are related to the order parameter and its fluctuations. The temperature dependence of the order parameter and its fluctuations is analyzed, and the values of the critical exponents indicating closeness of the phase transition in these crystals to the tricritical point are determined.     

X-ray study of microcrystalline Hg<Subscript>2</Subscript><Emphasis Type="Italic">Hal</Emphasis><Subscript>2</Subscript> ferroelastics

The rhombic splitting of basal plane reflections and the thermal behavior of fundamental and diffuse reflections from X-points of the Brillouin zone characterizing the behavior of an order parameter and its fluctuations, respectively, were studied in polycrystalline Hg₂Cl₂ and Hg₂Br₂ samples. In the case of polycrystalline samples, a strong broadening of phase transition effects was observed, due to damaged surface layers and elastic and plastic stress fields inducing order parameter fluctuations over a wide temperature range.     

The influence of chromium impurity centers on the critical properties of a weakly polar ferroelectric Li<Subscript>2</Subscript>Ge<Subscript>7</Subscript>O<Subscript>15</Subscript>

The Cr³⁺ EPR spectra of Li₂Ge₇O₁₅ (LGO) crystals are analyzed in the temperature range of the ferroelectric phase transition. The temperature dependence of the local order parameter is determined from the measured splittings of the EPR lines in the polar phase. The experimental critical exponent of the order parameter β=0.31 in the range from the phase transition temperature T _C to (T _C -T) ～ 40 K corresponds to the critical exponent of the three-dimensional Ising model. Analysis of the available data demonstrates that, away from the phase transition temperature T _C , the macroscopic and local properties of LGO crystals are characterized by a crossover from the fluctuation behavior to the classical behavior described in terms of the mean-field theory. The temperature dependence of the local order parameter for LGO: Cr crystals does not exhibit a crossover from the Ising behavior (β=0.31) to the classical behavior (β=0.5). This is explained by the defect nature of Cr³⁺ impurity centers, which weaken the spatial correlations in the LGO host crystal. The specific features of the critical properties of LGO: Cr³⁺ crystals are discussed within a microscopic model of structural phase transitions.     

Spectroscopic study of the behavior of the order parameter in model ferroelastic crystals of Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript>

Information is obtained about the temperature behavior of the order parameter of a phase transition by theoretical and experimental investigation of odd (acoustic and IR-active) phonons that appear in the Raman scattering spectra from the X points of the Brillouin zone (BZ) boundary in the paraphase of Hg₂Cl₂ crystals and are induced by the phase transition, unit-cell doubling, and the X → Γ folding in the BZ. The relevant critical exponents are determined, whose values are in agreement with the results of X-ray diffraction measurements and, within the Landau phenomenological theory of phase transitions, indicate that the phase transition in these crystals is close to the tricritical point.     

Spin-wave resonances in Eu<Subscript>0.8</Subscript>Ce<Subscript>0.2</Subscript>Mn<Subscript>2</Subscript>O<Subscript>5</Subscript> and EuMn<Subscript>2</Subscript>O<Subscript>5</Subscript> multiferroics

Spin-wave resonances have been observed in superlattices arising due to the phase separation and self-organization of charge carriers in Eu_0.8Ce_0.2Mn₂O₅ single crystals. The resonances are found within the 5–80 K temperature range at frequencies close to 30 GHz. Similar resonances with intensities about an order of magnitude lower are also observed in EuMn₂O₅. The latter suggests the existence of charge transfer processes between the manganese ions of different valences in EuMn₂O₅.     

Modulated magnetic structure of weak rhombohedral ferromagnets α-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>:Ga and FeBO<Subscript>3</Subscript>:Mg

The effect of diamagnetic impurities on the stability of the homogeneous magnetic state of rhombohedral antiferromagnets with weak ferromagnetism (α-Fe₂O₃:Ga and FeBO₃:Mg) is studied experimentally. It is shown that the application of an external magnetic field in the basal plane in the crystals under study in a certain temperature range induces a magnetic superstructure along the hard magnetization axis, which can be presented in the form of a ripplon phase with the azimuth of the local ferromagnetism vector oscillating about the direction of the field. The preferred orientation of the discovered modulated structures relative to crystallographic directions in the basal plane of α-Fe₂O₃:Ga and FeBO₃:Mg is studied, and the dependence of the spatial period of the superstructure on the applied magnetic field and temperature is analyzed. The magnetic-field-induced transition of the studied crystals from a homogeneous to an inhomogeneous magnetic state is described phenomenologically on the basis of the thermodynamic potential with gradient terms. In the discussion of physical reasons for magnetic order parameter modulation in weak ferromagnetic doped with diamagnetic ions, preference is given to the mechanism associated with the emergence of uniaxial magnetic centers with a random distribution of azimuths of easy axes in the basal plane of the crystal in the vicinity of impurities. A model describing the formation of a modulated magnetic state in α-Fe₂O₃:Ga and FeBO₃:Mg is proposed, according to which the competition between magnetoanisotropic and Zeeman interactions in the inhomogeneous magnetic phase of these crystals leads to periodic deviations in the direction of the local ferromagnetism vector from the direction of magnetization.     

Low-temperature Raman spectra of Hg<Subscript>2</Subscript>(Br,I)<Subscript>2</Subscript> mixed crystals

Raman spectra of Hg₂(Br,I)₂ mixed crystals were studied. The spectra revealed multimode behavior of optical vibrations, which were assigned to the existence in these crystals of molecules of three types, namely, Hg₂Br₂, Hg₂I₂, and Hg₂BrI. The spectra exhibit a manifestation of phase transition effects associated with soft modes, the density of states of IR-active vibrational branches, and of nanoclusters, whose nucleation is induced by the Br-Hg-Hg-I dipole molecules.     

Acoustic attenuation in ferroelectric Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals

The temperature and frequency dependencies of sound attenuation for the proper uniaxial ferroelectric Sn₂P₂S₆, which has a strong nonlinear interaction of the polar soft optic and fully symmetrical optic modes that is related to the triple well potential, were studied by Brillouin spectroscopy. It was found that the sound velocity anomaly is described in the Landau-Khalatnikov approximation with one relaxation time. For explanation of the observed temperature and frequency dependencies of the sound attenuation in the ferroelectrric phase, the accounting of several relaxation times is needed and, for quantitative calculations, the mode Gruneisen coefficients are more appropriate as interacting parameters than are the electrostrictive coefficients. Relaxational sound attenuation by domain walls also appears in the ferroelectric phase of Sn₂P₂S₆ crystals.     

Effect of deuteration on the thermal properties and structural parameters of the (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>WO<Subscript>2</Subscript>F<Subscript>4</Subscript> oxyfluoride

The thermal properties and structure of (ND₄)₂WO₂F₄ crystals are investigated. It is established that deuteration does not lead to a change in the symmetry of the initial phase Cmcm but considerably decreases the extent of its disordering, which, in turn, brings about a substantial decrease in the phase transition entropy. Apart from the anomalies associated with phase transitions characteristic of the protonic compound, the heat capacity exhibits two additional anomalies. Analysis of the phase diagram of the deuterated crystal reveals a triple point at a pressure p = 0.18 GPa, which is predicted for (NH₄)₂WO₂F₄ at about 0.7 GPa.     

Structural aspects of solid-state amorphization in Eu<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

X-ray diffraction studies of Eu₂(MoO₄)₃ single crystals were performed, which demonstrate that, in contrast to polycrystalline samples, these crystals do not exhibit amorphous-like diffraction patterns during the reverse transition from the high-pressure phase into the initial β phase; rather, the diffracted intensity in their diffraction patterns decreases significantly to the background. Such a diffraction pattern can be explained under the assumption that a single crystal is divided into small (nanoscopic) regions inside which the lattice parameters of the high-pressure phase and the initial β phase change continuously. The simultaneous recovery of the single-crystal state of the β phase from this intermediate state in all nanoscopic regions as the annealing temperature increases indicates that nanocrystals in this state are structurally correlated with each other. This result suggests that the halo-type diffraction patterns of polycrystalline samples reflect an intermediate state between the high-pressure phase and the β phase in every initial crystallite (as in the single crystals) rather than being caused by an amorphous structure of the sample. In this case, the total diffraction pattern of differently oriented crystallites gives an amorphous-like diffraction pattern reflecting the contributions from numerous various crystallographic planes involved in diffraction.     

Magnetic phase transitions,soliton lattices,and electric polarization in <Emphasis Type="Italic">R</Emphasis>Mn<Subscript>2</Subscript>O<Subscript>5</Subscript> multiferroics

The magnetic phase transitions in RMn₂O₅ oxides were analyzed. It was shown that the transition from the paramagnetic phase to the incommensurate phase is described by not only the basic magnetic parameter but also an associated order parameter: electric polarization along the y axis of the crystal. It was established that the antiferromagnetic-incommensurate phase transformation is a second-order phase transition, accompanied by a decrease in electric polarization.     

Electrical instability of LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> crystals

The temperature behavior of I-U curves and the field and temperature dependences of the electrical resistivity and dielectric permittivity of crystals of the LiCu₂O₂ phase have been studied. It was established that the crystals belong to p-type semiconductors and that their static resistivity in the range 80–260 K follows the Mott law ρ=Aexp(T₀/T)^1/4 describing variable-range hopping over localized states. At comparatively low electric fields, the crystals exhibit threshold switching and characteristic S-shaped I-U curves containing a region of negative differential resistivity. In the critical voltage region, jumps in the conductivity and dielectric permittivity are observed. Possible mechanisms of the disorder and electrical instability in these crystals are discussed.     

Effect of ionizing radiation on the dielectric characteristics of TlInSe<Subscript>2</Subscript> and TlGaTe<Subscript>2</Subscript> single crystals

The temperature dependences of the electrical conductivity and the permittivity of TlInSe₂ and TlGaTe₂ crystals unirradiated and irradiated with 4-MeV electrons at a doze of 10¹⁶ cm⁻² have been investigated. It has been established that electron irradiation leads to a decrease in the electrical conductivity σ and the permittivity ɛ over the entire temperature range under study (90–320 K). It has been revealed that the TlInSe₂ and TlGaTe₂ single crystals undergo a sequence of phase transitions characteristic of crystals of this type, which manifest themselves as anomalies in the temperature dependences σ = f(T) and ɛ = f(T). Electron irradiation at a doze of 10¹⁶ cm⁻² does not affect the phase transition temperatures of the crystals under investigation.     

Interrelation between the soliton lattice and electric polarization in RMn<Subscript>2</Subscript>O<Subscript>5</Subscript> oxides

Magnetic transitions from the paramagnetic state to an incommensurate magnetic structure and then to an ordered phase with long-range antiferromagnetic order in RMn₂O₅ (R is a rare-earth ion) oxides are analyzed. It is shown that a transition from the paramagnetic to the incommensurate phase is associated with exchange as well as relativistic interactions and can be described, apart from the basic magnetic order parameter, by an associated order parameter (viz., electric polarization along the y axis of the crystal). As a result of such a transition, the emergence of electric polarization in the crystal is not accompanied by a change in crystal symmetry.     

Features of the pressure-induced phase transitions in Eu<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

The structural changes induced by a 9-GPa pressure in Eu₂(MoO₄)₃ single crystals at room temperature have been studied using x-ray diffraction. It is established that a structural phase transition from the initial tetragonal phase to the new high-pressure tetragonal phase occurs rather than solid-phase amorphization that was observed previously in polycrystalline samples. The samples in the observed transition remain single-crystalline despite a significant difference (ΔV ～ 18%) between the specific volumes of the initial and final phases. It is shown that the transition from the initial state to the high-pressure phase occurs via the formation of broad transition zones featuring a continuous and smooth change of the crystal lattice parameters.     

Phase transitions in the oxyfluoride (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript>

(NH₄)₃NbOF₆ single crystals were grown, polarization-optical studies were performed, and birefringence was measured over the temperature range 90–500 K. A sequence of first-order structural phase transitions was found at temperatures T _1↓ = 259.7 K and T _2↓ = 257.7 K with temperature hysteresis δT ₁ = 0.9 K and δT ₂ = 1.9 K. The transitions are accompanied by twinning and the following change in the crystal symmetry: cubic ? tetragonal ? monoclinic. Optical second harmonic generation is found to occur at room temperature, which indicates that the cubic phase is not centrosymmetric. It is assumed that the phase transitions are ferroelastic and ferroelectric in nature.     

Electronic excitations in BeAl<Subscript>2</Subscript>O<Subscript>4</Subscript>, Be<Subscript>2</Subscript>SiO<Subscript>4</Subscript>, and Be<Subscript>3</Subscript>Al<Subscript>2</Subscript>Si<Subscript>6</Subscript>O<Subscript>18</Subscript> crystals

Low-temperature (T = 7 K) time-resolved selectively photoexcited luminescence spectra (2–6 eV) and luminescence excitation spectra (8–35 eV) of wide-bandgap chrysoberyl BeAl₂O₄, phenacite Be₂SiO₄, and beryl Be₃Al₂Si₆O₁₈ crystals have been studied using time-resolved VUV spectroscopy. Both the intrinsic luminescence of the crystals and the luminescence associated with structural defects were assigned. Energy transfer to impurity luminescence centers in alexandrite and emerald was investigated. Luminescence characteristics of stable crystal lattice defects were probed by 3.6-MeV accelerated helium ion beams.     

The Urbach tails and optical absorption in layered semiconductor TlGaSe<Subscript>2</Subscript> and TlGaS<Subscript>2</Subscript> single crystals

TlGaSe₂ and TlGaS₂ single crystals were grown by the modified Bridgman-Stockbarger method. We report the result of an experimental study of the optical absorption of TlGaSe₂ and TlGaS₂ crystals. The absorption measurements were performed in steps of 10 K. The direct and indirect band gaps for TlGaSe₂ and TlGaS₂ samples were calculated as a function of temperature. The phonon energies in TlGaSe₂ and TlGaS₂ crystals were calculated as (39±4) and (9±4) meV at 240 K, respectively. At 10 K, direct and indirect band gaps were found as 2.294 and 2.148 eV for TlGaSe₂, 2.547 and 2.521 eV for TlGaS₂ crystals, respectively. The abrupt changes were observed in the direct and indirect band gaps in the some temperature ranges. These changes were interpreted as phase transformation temperatures. The steepness parameters and Urbach energy for TlGaSe₂ and TlGaS₂ samples increased with increasing sample temperature in the range (10–320) K.