High-pressure effect on the ferroelectric-paraelectric transition in PbTiO<Subscript>3</Subscript>

The crystal structure of lead titanate PbTiO₃ was investigated by energy dispersive X-ray diffraction at high pressures up to 4 GPa in a temperature range of 300–950 K. At the ambient conditions, the PbTiO₃ structure is tetragonal with the space group P4mm (ferroelectric phase). A structural phase transition into the cubic phase with a space group Pm[`3]mPm\bar 3m is observed at T = 747 K. It was found that the phase transition temperature decreases upon applying the high pressure with the coefficient dT _C /dP = -65 K/GPa. Dependences of parameters and volume of the unit cell on the pressure and temperature was found, and the bulk modulus and thermal expansion coefficients for the tetragonal and cubic phases of lead titanate have been calculated.     

Raman and X‐ray investigations of the incorporation of Ca2+ and Cd2+ in the ZrO2 structure

The formation of solid solution and ZrO₂ phase stabilization were investigated by Raman spectroscopy and X‐ray diffraction (XRD) in calcium‐containing and cadmium‐containing zirconium oxide samples heated at 1073 K in air. The adopted preparation procedure led to the incorporation of calcium and cadmium in solid solution into the zirconia structure. The solid solution favored the tetragonal and cubic zirconia phases at the expense of the thermodynamically stable monoclinic modification. Combined macro‐ and micro‐Raman spectroscopy disclosed that instead of forming a homogeneous phase t″, intermediate between the tetragonal t′ and the cubic phase, the tetragonal and cubic phases coexisted in the range 9.49–13.89 mol% for Ca and 11.88–17.23 mol% for Cd. At higher dopant contents the cubic form stabilized. The impurity content necessary to stabilize the high‐symmetry phases was defined. Copyright © 2007 John Wiley & Sons, Ltd.     

LaAg x In1−x

The phonon dispersion of LaAg _x In_1–x (x=1, 0.89, 0.8) has been studied by inelastic neutron scattering in the cubic high temperature phase. A soft mode behaviour was observed at theM-point. The doubling and the cubic to tetragonal deformation of the elementary cell was observed through the phase transition. The measurements of the elastic constants were extended to 450 K and their magnetic field dependence was investigated.This work was supported by the BMFT and the Sonderforschungsbereich 65 Darmstadt/Frankfurt     

Ferromagnetism in the high-pressure phases of (GaSb)1−x Mnx

The electrophysical and magnetic properties of recently discovered high-pressure phases in the GaSb-Mn system with simple cubic and tetragonal structures have been examined. It has been shown that samples with the primitive cubic structure for low temperatures are in the ferromagnetic state and the Curic temperature depends on the initial manganese content and reaches T _c = 280 K for x = 0.6. It has been shown that these samples for a manganese content x ≤ 0.5 are in the semiconducting state with large impurity conduction and pass to the metallic state as x increases. The GaSbMn phase with the tetragonal structure has ferromagnetic properties up to temperatures of T ～450 K (at which the phase begins to decay) and exhibits metallic properties. The magnetization at T = 77.3 K is equal to M = 0.58 μ_B and 0.28 μ_B per manganese ion for the simple cubic and tetragonal phases, respectively.     

Thermal expansion and spontaneous strain of KMnF3 near the 186 K-structural phase transition

Abstract

By means of high-angle double-crystal X-ray diffractometry (HADOX), the thermal expansivity of KMnF₃ has been determined. The linear thermal expansion coefficient along each crystallographic axis exhibits a divergent anomaly at the structural phase transition at 186 K. The critical exponents of these coefficients are determined: in the cubic phase α = 0.21 ± 3, and in the tetragonal phase α′ = 0.19 ± 3 for the a axis and α″ = 0.35 ± 3 for the c axis.

In addition, the critical exponent of the spontaneous strain, c/a ? 1, is determined to be 0.4248 ± 8, which is smaller than that of the order parameter 2β = 0.5714 ± 12. These values are reasonable if the transition occurs in the vicinity of a tricritical point.     

First-principles study of electronic structure and optical properties of Sr(Ti,Zr)O3

Electronic and optical properties of Sr(Ti,Zr)O₃ crystals in the cubic (Pm-3m) and tetragonal (I4/mcm) phase were calculated by the first-principles calculations using the density functional theory and the local density approximation. The band structure of cubic and tetragonal phases show an indirect band gap at (R-Γ) point and at (M-Γ) point in the Brillouin zone, respectively. The linear photon-energy dependent dielectric functions and some optical properties such as the absorption coefficient, energy-loss function and reflectivity are calculated for both phases. The optical properties of tetragonal phase of Sr(Ti,Zr)O₃ were investigated by theoretical methods for the first time. We have also made some comparisons with the available related experimental and theoretical data.     

Synchrotron X-ray diffraction studies on the phase transitions in the spinel LixMn3−xO4 intercalation compounds

Detailed investigations have been undertaken of the lithium for manganese substitution effect on the LiMn₂O₄, in the system Li_xMn_3−xO₄, for 0.95≤x≤1.05, that is for the nearly stoichiometric lithium content. Synchrotron X-ray measurements have been performed in the temperature range 10–300 K. The diffraction experiments were carried out at the DESY-HASYLAB high-resolution powder diffractometer (beamline B2), equipped with a closed-cycle He-cryostat. Very small changes in the lithium content influence clearly the low-temperature crystal structure of Li_xMn_3−xO₄, spinels and the nature of phase transitions. It was found that for x=0.95 the sample remains tetragonal in the whole 10–300 K temperature range. The stoichiometric LiMn₂O₄ transforms from cubic to orthorhombic at about 280 K. For x=1.0125 the temperature of phase transition from cubic to orthorhombic decreases down to about 260 K, whereas for x=1.025 the transformation goes from cubic to tetragonal phase, at the temperature 220 K. No phase transition has been observed for the cubic sample with x=1.0375. These results partly explain the divergences in recent reports on the low-temperature structure and phase transformations of lithium manganese oxides.     

Phase transition in (NH4)3FeF6

By use of Mössbauer spectroscopy we have found that the transition from tetragonal to cubic structure in (NH₄)₃FeF₆ takes place at 263 K. The phase transition exhibits a hysteresis of 0.5 K. The experimental data indicate that the tetragonal deformation found at low temperatures diminishes gradually as the transition temperature is approached. The spectra are influenced by electronic relaxation.     

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.     

Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T −T _c)². The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature.     

Superconductivity of A15-and σ-phase of Nb-Ir

The superconducting properties of A15-, σ-, and tetragonal phases of the system Nb−Ir were investigated. The alloys were prepared by sintering and arc melting. They were subjected to optical and scanning electron microscopy. The lattice parameters were determined by x-ray diffraction technique. Superconducting transition temperatures,T _c , as well as upper critical fields,H _c2, were measured inductively and resistively. TheT _c -values of the σ-phase vary between 2.15 and 2.40 K whereas for the A15-phase they vary between 1.83 and 2.73 K. TheT _c -value of the tetragonal phase is 3.81 K. The upper critical fields of the tetragonal and the A 15-phase are nearly the same (≈13 kG) and lower compared with that of the σ-phase (≈18 kG). Several theoretically predicted values ofH _c2(0) are evaluated and compared with the experimental ones.     

Phase diagrams of the CoMnO system in air

A retrospective critical analysis of phase diagrams of the CoMnO system in air has been made. A high-temperature phase equilibrium of the CoMnO system in air and phase diagrams of this system under different cooling conditions (quenching in water, quenching in air, cooling at rate of 25°K h^?1) have been constructed. A comparative analysis of these diagrams shows that whatever the cooling rate, cooling does not preserve the high-temperature state of the system and is accompanied (depending on cooling conditions, temperature and Co/Mn ratio) by one or more of the following phenomena: (1) oxidation of the Co_NMn_1?NO solution to spinel-type solid solutions (2) merging of a cubic and tetragonal spinel phase and formation of a homogeneous tetragonally distorted spinel (3) tetragonal distortion of the spinel lattice (4) decomposition of the cubic spinel into a cubic and tetragonal spinel. (5) decomposition of the cubic spinel into a cubic, tetragonal and slightly distorted tetragonal spinel. Therefore, the form of the phase diagram of the CoMnO system in air is entirely determined by the method of cooling.     

Phase transitions in AgTaO3 single crystals

AgTaO₃ single crystals have been obtained by the molten salt method; two different solvents, AgCl and V₂O₅, were used. X-ray investigations have been carried out in the temperature region from 300 K to 800 K. At room temperature AgTaO₃ possesses a pseudocubic perovskite-type unit cell with rhombohedral distortion. Two structural phase transitions, to tetragonal at 650 K and to cubic symmetry at 770 K, have been observed. In the tetragonal phase a jump of the lattice constants has been observed at approximately 680 K. DTA and domain structure investigations confirm the presence of these phase transitions.     

Investigation of ferroelectric phase transition for modified barium titanate in multilayer ceramic capacitors by in situ Raman scattering and dielectric measurement

The ferroelectric phase behaviors of modified BaTiO₃ in X7R multilayer ceramic capacitors (MLCCs) were investigated by dielectric measurements and in situ Raman scattering. The in situ thermo-Raman scattering shows that because of a residual stress existing in the MLCCs, the tetragonal to cubic phase transition for modified BaTiO₃ in MLCCs takes place over a wide temperature range of 373 K to 473 K, suggesting a diffuse-like characteristic which can be well explained by a modified phenomenological thermodynamic model, while the dielectric measurement indicates that the tetragonal to cubic transition occurs at 393 K. A disagreement exists between the two experimental results. Furthermore, a dc field-induced paraelectric to ferroelectric transition was identified by the two measurement techniques, but their phase-transition mechanisms are different. The dielectric measurement reveals the polar-micro-region to macro-domain transformation in the shell part of the core–shell structure while the in situ Raman scattering shows the cubic to tetragonal transition under a dc bias field. PACS 74.20.De; 77.22.Ch; 77.84.Dy; 77.80.Bh; 78.30.-j     

Heusler合金Mn2 NiAl的电子结构和磁性对四方畸变的响应及其压力响应

运用基于密度泛函理论的第一性原理的投影缀加波方法,对Hg₂CuTi型Mn₂NiAl在由立方结构至四方结构的畸变过程中电子结构和磁性的变化规律及其对压力响应的规律进行了研究.研究发现:在由奥氏体相到马氏体相的相变中,由于Ni-Mn(A)原子间距的减小而使得杂化程度增强,导致占据态的态密度向低能区域移动,体系的能量降低,致使在马氏体相中的稳定性增大;在从奥氏体相到马氏体相的相变中,能带变宽,成键作用加强,从而在马氏体相中的稳定性增大;在四方畸变过程中,总磁矩的变化主要来源于Ni原子磁矩的变化;计算得到Mn₂NiAl的零压体积弹性模量为125.69 GPa,其抗压缩性比其他常见的Heusler型合金弱. 关键词： 第一性原理 电子结构 磁性 四方畸变     

First-principles study of martensitic phase transformation of TiRh alloy

Geometric structures and atomic positions were studied with plane wave pseudo-potential method based on density functional theory for cubic, tetragonal, and monoclinic phases of TiRh alloy. Their phonon dispersion curves were obtained with frozen phonon method at harmonic approximation using density-functional perturbation theory. Our calculations revealed that both B2 and L1₀ phases are thermodynamically unstable. Jahn-Teller effect triggers the occurrence of Bain transformation from cubic to tetragonal phase, and then soft-mode phonon further leads to the transition from tetragonal to monoclinic phase on cooling. The monoclinic phase was predicted to be P2/m space group through atomic vibrational movement along [001] direction of virtual frequency modes of L1₀ phase. The temperature from B2 to L1₀ and then to P2/m were predicted to be about T=1100.53 K and T=324.48 K through free energy calculations with the electronic plus vibrational energy of formation, respectively, which is in good agreement with experimental observations.     

Order-disorder phase transition in ZrV2D3.6

The deuterated C15-type Laves phase ZrV₂D_3.6 undergoes a structural phase transition near room temperature (T ≈ 325 K). In the cubic high-temperature phase the deuterium atoms are disordered over two types of tetrahedral interstices, the centres of which are 1.3 Å apart. In the tetragonal low-temperature phase the D atoms are ordered and occupy only the energetically more favourable interstices. The tetragonal structure is isotypic with the low-temperature phase of HfV₂D₄. The shortest D—D distance is 2.1 Å.     

Formation of a cubic Sr2MnWO6 phase at elevated temperature; a neutron powder diffraction study

In a temperature dependent neutron powder diffraction (NPD) study we observed the high temperature cubic phase at 973 K in the polycrystalline double perovskite Sr₂MnWO₆. Rietveld analysis of the NPD data shows that the room temperature tetragonal phase exists up to 573 K (space group P4₂/n, a=8.0119 (4) Å, c=8.0141(8) Å). At 773 K, the primitive tetragonal symmetry change to body-centred tetragonal (space group I4/m, a=5.6935(5) Å, c=8.077(1) Å) and finally at 973 K it becomes face-centred cubic (space group Fm-3m, a=8.0864(8) Å). The changes in the structural symmetry are connected to the small distortion of the B-site octahedra, which are insensitive to the Differential Thermal Analysis (DTA) signal.     

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)     

Magnetic and quadrupolar properties of PrPb3

The cubic rare earth intermetallic compound PrPb₃ (AuCu₃-type structure) undergoes a transition at 0.35 K: as it is a Van Vleck paramagnet, the low temperature phase was assumed to be quadrupolarly ordered. In order to specify this possibility, we first discuss the cubic level scheme using specific heat and first-order magnetic susceptibility results; afterwards we present an extensive study of the two (tetragonal and trigonal) symmetry lowering modes, investigated in the cubic paramagnetic phase by means of parastriction and third-order magnetic susceptibility. For the tetragonal symmetry, the quadrupolar pair interactions appear as negative, dominating the magnetoelastic coupling; as a result, the low temperature ordering may be antiferroquadrupolar, a new situation among rare earth intermetallics, the TmZn and TmCd ordering being ferroquadrupolar.