The cubic-to-monoclinic phase transition in (NH4)3ScF6 cryolite: A Raman scattering study

This paper reports on a Raman study of the cubic-to-monoclinic phase transition in (NH₄)₃ScF₆ cryolite. We observed sharp anomalies in the frequencies and half-widths of the Raman lines corresponding to internal vibrations of the ScF ₆ ³⁺ ions and to lattice vibrations; no soft lattice mode condensation was revealed. It is concluded that the phase transition studied is related primarily to the orientational ordering of these ions.     

Structure and lattice dynamics of the high-pressure phase in the ScF3 crystal

The high-pressure phase of the ScF₃ crystal has been studied using synchrotron radiation diffraction and Raman scattering. This phase existing in the pressure range 0.6–3.2 GPa is optically anisotropic: its structure is described by space group R $ \bar 3 $ \bar 3 c, Z = 2, and the transition is associated with the rotation of ScF6 octahedra around the threefold axis. The pressure dependences of the lattice parameters and the rotation angle have been determined. The number of lines in the Raman spectrum corresponds to the expected number for this structure; the recovery of soft modes has been observed above the phase transition.     

Lattice dynamics and the phase transition from the cubic phase to the tetragonal phase in the LaMnO<Subscript>3</Subscript> crystal within the polarizable-ion model

The paper reports on the results of ab initio calculations of the static and dynamic properties of the LaMnO₃ crystal with a perovskite structure in the cubic, rhombohedral, and orthorhombic phases. The calculations are performed within the ionic crystal model, which takes into account the deformability and polarizability of the ions. It is revealed that the spectrum of lattice vibrations in the cubic phase contains unstable vibrational modes, which occupy the phase space in the entire Brillouin zone. The eigenvectors of the softest mode at the boundary point R of the Brillouin zone are associated with the displacements of the oxygen ions and correspond to the “rotation” of the MnO₆ octahedron. The condensation of one, two, and three components of this mode leads to the tetragonal, orthorhombic, and rhombohedral distortions of the structure. The structural phase transition is described in terms of the local mode approximation with the use of the double perovskite unit cell, in which the MnO₆ octahedron is explicitly separated. The parameters of the model Hamiltonian are determined. The static properties are investigated by the Monte Carlo method. The calculated temperature of the phase transition from the cubic phase (9800 K) is considerably higher than the melting temperature of the crystal under investigation. The calculated frequencies of long-wavelength lattice vibrations in the experimentally observed orthorhombic and rhombohedral phases are in reasonable agreement with experimental data.     

Pressure-induced phase transition in the cubic ScF<Subscript>3</Subscript> crystal

Pressure-induced phase transitions in the ScF₃ crystal were studied using synchrotron radiation diffraction, polarization microscopy, and Raman spectroscopy. The phase existing in the range 0.6–3.0 GPa is optically anisotropic; its structure is described by space group R ₃ c (Z = 2), and the transition is due to rotation of ScF₆ octahedra around a threefold axis. The pressure dependence of the structural parameters and angle of rotation are determined. The number of Raman spectral lines corresponds to that expected for this structure; above the phase transition point, a recovery of soft modes takes place. At a pressure of 3.0 GPa, a transition occurs to a new phase, which remains metastable as the pressure decreases. The results are interpreted using an ab initio method based on the Gordon-Kim approach.     

Raman scattering investigation of ferroelastic Sb5O7I crystals

Sb₅O₇I undergoes a displacive phase transition at 481 K where the symmetry is changed fromC _6h ² toC _2h ⁵ . In the low temperature monoclinic phase the crystal is ferroelastic. The polarized Raman spectra of Sb₅O₇I have been measured at various temperatures below and above the phase transition. The frequencies and symmetries of most of the theoretically expected Raman active phonons in the ferroelastic phase have been determined. The observation of a soft mode in the ferroelastic phase which disappears above the phase transition together with the fact that the unit cell of the ferroelastic phase is twice as large as that of the paraelastic structure permits the conclusion that the phase transition results from a phonon instability at the Brillouin zone boundaryM-point of the hexagonal phase. The temperature dependent splittings and intensity changes of several Raman lines are discussed with respect to the ferroelastic property of the crystal and the phase transition.     

Lattice dynamics of BiFeO<Subscript>3</Subscript> under hydrostatic pressure

The vibrational frequencies of the BiFeO₃ crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm^?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure.     

Lattice dynamics of BiFeO<Subscript>3</Subscript>: The untypical behavior of the ferroelectric instability under hydrostatic pressure

Within a nonempirical model of an ionic crystal with the inclusion of the dipole and quadrupole ion polarizations, the lattice vibrational frequencies, high-frequency dielectric constant, Born dynamic charges, and the elasticity moduli of the BiFeO₃ crystal have been calculated and their dependencies on the hydrostatic pressure in the cubic, rhombic, and rhombohedral phases have been determined. The results indicate the presence of the ferroelectric instability, which depends weakly on the pressure in all of the phases investigated. The dependence of the crystal lattice dynamics on the applied pressure for the cubic phases of BiAlO₃, BaTiO₃, and PbTiO₃ has been calculated for comparison.     

Structural aspects of the antiferroelectric-paraelectric phase transition in double perovskite Pb2MgWO6 at high pressures and temperatures

The crystal structure of antiferroelectric Pb₂MgWO₆ has been studied using neutron diffraction at high pressures to 5.4 GPa at room temperature and energy-dispersive X-ray diffraction at high pressures to 4 GPa in the temperature range 300–400 K. At normal conditions, in Pb₂MgWO₆, there is an antiferroelectric phase with the crystal structure described by the orthorhombic symmetry with space group Pnma. At temperature T = 313 K and normal pressure or at room temperature and pressure P ～ 0.9 GPa, the crystal under-goes a structural phase transition to the cubic phase with space group $Fm\bar 3m$ (paraelectric phase). The temperature and pressure dependences of the lattice parameters, unit cell volume, and interatomic bond lengths have been obtained, and the thermal expansion coefficients and the bulk moduli have been calculated for the antiferroelectric and paraelectric phases of Pb₂MgWO₆.     

Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice

In this paper, the propagation of acoustic waves in the phononic crystal of 3D with rhombohedral(I) lattice is studied theoretically. The crystal composite constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of Brillouin zone. In the present work, we have investigated the effect of lattice angle on the band structure and width of the band gap rhombohedral(I) lattice in the irreducible part of the first Brillouin zone and its planes separately. The results show that more than one complete band gape are formed in the four planes of the irreducible part. The most complete band gaps are formed in the (111) plane and the widest complete band gap in (443) with an angle greater than 80 \(^{\circ }\) . So, if the sound passes through the (111) and (443) planes for the lattice angle close to 90 \(^{\circ }\) , the crystal phononic displays the excellent insulation behavior. Moreover, in the other planes, the lattice angle does not affect on the width and the number of band gaps. Also, for the filling fraction 5 %, the widest complete band gap is formed. These results are consistent with the effect of symmetry on the band gap width, because the (111) plane has the most symmetry.     

Lattice dynamics of a Rb2KScF6 crystal in unstable cubic and tetragonal phases and in a stable monoclinic phase

The results of a nonempirical calculation of the static and dynamic properties of a Rb₂KScF₆ crystal with elpasolite structure in cubic, tetragonal, and monoclinic phases are presented. The calculation is performed on the basis of a microscopic model of an ionic crystal that takes account of the deformability and polarizability of the ions. The deformability parameters of the ions are determined from the condition that the total energy of the crystal is minimum. The computational results for the equilibrium lattice parameters are in satisfactory agreement with experimental data. Unstable vibrational modes are found in the vibrational spectrum of the lattice in the cubic and tetragonal phases. These modes occupy the phase space throughout the entire Brillouin zone. The characteristic vectors of the most unstable mode at the center of the Brillouin zone of the cubic phase are related to the displacements of the fluorine ions and correspond to rotation of ScF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In the tetragonal phase the most unstable mode belongs to the boundary point of the Brillouin zone and condensation of this mode leads to monoclinic distortion with doubling of the unit-cell volume. In the monoclinic phase unstable modes are absent in the vibrational spectrum of the lattice. Fiz. Tverd. Tela (St. Petersburg) 41, 1297–1305 (July 1999)     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

Crystal structure phase separation in anion-deficient La0.70Sr0.30MnO3 − δ manganite system

The crystal structure of anion-deficient La_0.70Sr_0.30MnO_{3 ? δ} manganite powders (δ = 0, 0.10, 0.15, 0.20) has been investigated at room temperature by the neutron diffraction method using a high-resolution Fourier diffractometer. The structure data have been refined by the Rietveld method. The crystal structures of the stoichiometric La_0.70Sr_0.30MnO₃ and anion-deficient La_0.70Sr_0.30MnO_2.90 manganites are satisfactorily described by the rhombohedral space group R $\bar 3$ c. A small amount of the non-perovskite MnO phase (space group Fm $\bar 3$ m) has been found for the anion-deficient La_0.70Sr_0.30MnO_2.90 sample. It has been found that the anion-deficient La_0.70Sr_0.30MnO_2.85 sample consists of two perovskite phases described by space groups R $\bar 3$ c and I4/mcm and the MnO phase (space group Fm $\bar 3$ m). The crystal structure of the anion-deficient La_0.70Sr_0.30MnO_2.80 sample is described by one perovskite phase with space group I4/mcm. The volume fraction of the MnO phase is ?1% for all anion-deficient samples. Oxygen vacancies in the anion-deficient La_0.70Sr_0.30MnO_{3 ? δ} manganite system stimulate the structure phase separation at 293 K.     

Lattice dynamics and Raman scattering spectrum of elpasolite Rb<Subscript>2</Subscript>KScF<Subscript>6</Subscript>: Comparative analysis

Raman scattering spectra of elpasolite Rb₂KScF₆ are studied in a wide temperature range including two phase transitions: from the cubic to the tetragonal phase and then to the monoclinic phase. The experimental Raman scattering spectrum is compared with the lattice vibration spectra of these phases calculated using an ab initio approach. A number of anomalies (caused by structural rearrangement during the phase transitions) are revealed and quantitatively analyzed in the ranges of both the intramolecular vibrations of the octahedron molecular ScF₆ ions and low-frequency intermolecular lattice vibrations. The interaction between low-frequency intramolecular vibrations and the intermolecular modes is found to be significant, and strong resonance interaction of the rotational soft modes (which are recovered below the phase transition points) with hard low-frequency vibrations of the rubidium ion sublattice is detected. These interactions are shown to substantially complicate the spectra.     

Concentration-dependent structural transition in the La0.70Sr0.30MnO3−δ system

The crystal structure of anion-deficient La_0.70Sr_0.30MnO_3?δ manganites (δ = 0, 0.10, 0.15, and 0.20) has been studied by powder neutron diffraction at room temperature. The crystal structures of the stoichiometric La_0.70Sr_0.30MnO₃ and anion-deficient La_0.70Sr_0.30MnO_2.90 samples are satisfactorily described by the rhombohedral R $\bar 3$ c space group. The anion-deficient La_0.70Sr_0.30MnO_2.85 sample separates into two perovskite phases with the R $\bar 3$ c and I4/mcm space groups. The crystal structure of La_0.70Sr_0.30MnO_2.80 cannot be described by a single perovskite phase in the I4/mcm space group. It is found that the clustering of oxygen vacancies is the cause of structural phase separation at 293 K in anion-deficient La_0.70Sr_0.30MnO_3?δ manganites.     

A polarized micro-Raman study of a 0.65PbMg1/3Nb2/3O3 - 0.35PbTiO3 single crystal

Polarized micro-Raman spectra of a 0.65PbMg_1/3Nb_2/3O₃-0.35PbTiO₃ (0.65PMN-0.35PT) single crystal poled in the [001] direction are obtained in a wide frequency range (50-2000 cm^-1) at different temperatures. The best fit to the Raman spectrum at 77 K is achieved using 17 Lorenzians to convolute into it, and this is proved to be a reasonable fit. According to the group theory and selection rules of overtone and combinational modes, apart from the seven Raman modes that are from first-order Raman scattering, the remaining ones are attributed to being from second-order Raman scattering. A comparison between the experimental results and theoretical predictions shows that they are in satisfactory agreement with each other. Our results indicate that at 77 K the sample belongs to the rhombohedral symmetry with the C_3v⁵ (R3m) space group (Z=1). In our study, on heating, the 0.65PMN-0.35PT single crystal undergoes a rhombohedral to tetragonal to cubic phase transition sequence. The two phase transitions occur at 340 and 440 K, which correspond to the disappearance of the soft mode near 106 cm^-1 recorded in VV polarization and the vanishing of the band around 780 cm^-1 in VH polarization, respectively.     

Structural heterogeneities in the cubic ZnS crystal doped with Fe2+ ions

The structural state of the cubic Zn_0.999Fe_0.001S single crystal grown by the chemical transport method has been investigated using thermal neutron diffraction at 300 K for the first time. It has been found that the diffraction patterns of the crystal contain diffuse scattering regions with wave vectors q = 0 and $q = (\bar 1/3, 1/3 , 0)2\pi /a$ . The experimental results have been discussed in the context of the available information on neutron diffraction in the Zn_0.999Fe_0.001Se compound. It has been shown that the effects of diffuse scattering are caused by local shear deformations of the metastable cubic lattice of the compound under investigation.     

Effects of the phase transition in Hg2(Br,I)2 crystals

The effects of the phase transition in Hg₂(Br,I)₂ crystals have been investigated over a wide range of temperatures by the Raman scattering spectroscopy and X-ray diffraction analysis. The overtones (at the X point of the Brillouin zone boundary) and the fundamental tones (at the center of Brillouin zone) of soft modes are found in the Raman spectra of these crystals and studied in detail. The density of one-phonon states of the soft TA branch manifests itself in the Raman spectra of mixed crystals. The potentialities of the soft-mode spectroscopy are realized in full measure. Analysis of the ratio between intensities of overtones and fundamental tones of the soft modes has demonstrated the applicability of the Landau phenomenological theory of phase transitions. The orthorhombic splitting of the reflections corresponding to the basal plane is revealed in the X-ray diffraction patterns and thoroughly explored. The temperature dependences of the isotropic and shear spontaneous strains are obtained. It is shown that the shear spontaneous strain plays a decisive role. The critical indices are determined and the model of the improper ferroelastic phase transition D _4h ¹⁷ → D _2h ¹⁷ in the vicinity of the tricritical point is corroborated.     

Twinning and short-range order in ordered titanium monoxide

Electron diffraction was used to study the annealed titanium monoxide TiO_1.087 containing the monoclinic ordered phase Ti₅O₅. The diffraction pattern of titanium monoxide in the (112)* _B1 plane of the reciprocal lattice of the parent B1 cubic structure contains not only structural, superstructural, and additional reflections but also a system of planar diffuse strips. It has been established that part of the additional reflections are twins of the superstructure reflections of the monoclinic ordered phase; the twinning plane is the ( $\overline 1 \overline 1 1$ ) plane of the reciprocal lattice of the parent cubic phase. The diffuse scattering contours cover finite plane areas in the reciprocal space characterized by the wave vectors K ₁₀₀ ～ ± (h + 0.07)k ₁₀₀, K ₀₁₀ ～ ±(k + 0.07)k ₀₁₀, and K ₀₀₁ ～ ±(l + 0.07)k ₀₀₁ in the B1 structure. The diffuse scattering is caused by short-range displacement order. Short-range substitution order and the corresponding diffuse scattering are absent.     

Phase transition in the layered perovskite CsScF4 induced by hydrostatic pressure

Using polarization microscopy and Raman scattering, we have discovered a new phase transition in the layered perovskite crystal CsScF₄ under a hydrostatic pressure around 6 GPa. The proposed space group of the high-pressure phase is C _2h ² , Z=4. Fiz. Tverd. Tela (St. Petersburg) 41, 1683–1685 (September 1999)     

Synthesis, crystal structure, and spectroscopic study of K0.92(2) Zn0.08(2) H1.92(2) (PO4) (Zn-KDP)

The structure of K0.92₍₂₎ Zn_0.08(2) H_1.92(2) (PO₄) was determined using single-crystal X-ray diffraction. The crystal structure of the Zn-KDP belonged to the tetragonal space group $ \mathrm{I}\overline{4}2\mathrm{d} $ , with cell parameters of a?=?b?=?7.4487(5)?Å and c?=?6.9703(5)?Å, 386.73(5) Å3, Z?=?4, and R?=?0.023. Zn²⁺ ions were used as substitutes for K⁺ ions with hydrogen vacancy. The Zn-KDP single crystals were submitted to further Raman, infrared, and ¹H NMR studies to investigate chemical group functionalisation, possible bonding between the organic and inorganic materials, and partial substitution of K⁺ by Zn²⁺. The latter partial substitution was confirmed by the deviation of IR frequencies for O–H stretching, the variation of IR and Raman frequencies for stretching and bending vibrations ν(PO₄) of H₂PO₄, and the appearance of additional Raman (147, 386 and 481 cm^?1) vibrational bands. Electrical conductivity measurements were performed on polycrystalline pellets of Zn-KDP and pure KDP at room temperatures (RT) of up to 473K. In both cases, a conductivity jump close to 453K was observed, and a stronger increase of conductivity was measured.