Group-theoretical analysis of possible structural phase transitions in the high-temperature superconductors

A group-theoretical analysis is performed for the complete condensation of order parameters at structural phase transitions (SPT's) in the high-temperature superconductors belonging to the D ¹⁷ _4h -14/mmm space group in the high-symmetry phase. As a rule, such transformations are due to a successive softening of phonons with wave vectors k ₁ = 1/2 b ₃ and k ₂ = 1/2 (b ₁ - b ₃) belonging to the K13(X) star of the Brillouin zone of a tetragonal body-centered Bravais cell. SPT's in system La_2-x Ba _x CuO₄ are considered in detail.     

The crystal structure of Rb2CdCl4 in para- and ferroelastic phases

Abstract

The crystal structure of Rb₂CdCl₄ has been studied by X-ray diffraction at 295 and 160 K in the initial phase D ¹⁷ _4h as well as at 105 K in the ferroelastic phase. It was found that the phase transition D ¹⁷ _4h ? D ¹⁰ _2h takes place instead of D ¹⁷ _4h ? D ¹⁸ _2h as proposed earlier. The first of the transitions corresponds to unequal and the second to equal Φ-tilts of CdCl₆-octahedra around the a and b axes of the tetragonal unit cell.     

Crystal structure,characterisation and vibrational study of a mixed compound Cs0.4Rb0.6H2Po4

Abstract

The crystal structure of Cs_1-x Rb _x H₂PO₄, x = 0.6 (CRDP) which crystallises in space group P2₁/m and is isostructural with the monoclinic phase of CsH₂PO₄ (CDP), has been refined at room temperature using single-crystal X-ray diffractometer data. The cell parameters are a = 4.8183(9)å, b = 6.2671(6) å, c = 7.7620(10)å, β= 108.260(10)°, V = 222.58(5)å³, Z = 2, D_x = 3.009g cm^?3. F(000)=187, T = 298(2)K (room-temperature phase), R = 0.0355 and wR = 0.0949 for 654 observed reflections. CRDP contains two crystallography inequivalent hydrogen bonds in the unit cell. The shorter bond (Ko – o = 2.453(7) A) links the phosphate groups into chains running along the b-axis and the longer bond (Ko – o = 2.488(6) A) which is always ordered, crosslinks the chains to form (001) layers. The phase transitions in the mixed Cs_0.4Rb_0.6H₂PO₄ (CRDP) were characterised by differential scanning calorimetry which shows two anomalies at about 293 and 525 K. The Raman and infrared spectra at room temperature were investigated in the frequency ranges 10–3500 and 200–4000 cm^?1 respectively. An assignment of all the bands is given. The bands are in agreement with the monoclinic room-temperature phase implying high dynamical disorder of the acidic proton O-H s–O hydrogen bond.     

Bromine metallization studied by X-ray absorption spectroscopy

The experimental data carried out by M?ssbauer and magnetic resonances investigations of the structural phase transitions in K₂ZnCl₄ crystals are discussed by a simple electrostatic model, calculating, the lattice contributions to the local electric potential V(r), electric field intensity E(r) and electric field gradient tensor, (r) and taking into account both the fractional electric point charges and rigid lattice approximations. The validity of the model is proved by a good fit of the computing results and experimental data of quadrupole splitting parameters at K sites obtained by ³⁹K-NMR methods in high temperature incommensurate phase ( Pnam symmetry). The experimental results obtained by M?ssbauer and EPR methods in commensurate phase (Pna2₁ symmetry) of iron and copper doped K₂ZnCl₄ crystals are explained by relaxing the rigid lattice approximation. The insertion of probe ions appear to be done on not-exactly-Zn²⁺ site. Received 3 February 1999 and Received in final form 4 May 1999     

Crystal Structures of Tetrakis‐(4‐chlorophenylthio)‐butatriene and Tetrakis‐(tert‐butylthio)‐butatriene

Tetrakis‐(4‐chlorophenylthio)‐butatriene (3a) and tetrakis‐(tert‐butylthio)‐butatriene (3b) were synthesized, and their crystal structures were determined. The compound 3a is monoclinic, space group P2₁/c, a=6.9785(8), b=8.6803(9), c=22.884(2) Å, β=93.887(6)^o, V=1383.0(3) ų, Z=2. The compound 3b is monoclinic, space group P2₁/n, a=11.0615(6), b=10.8507(4), c=11.2717(6) Å, β =116.427(2)^o, V=1211.5(1) ų, Z=4. The title compounds 3a and 3b reside on an inversion center so that only half of the molecule is crystallographically unique. Both compounds are not planar. The crystal structures of 3a and 3b have cumulated double bonds. The C7–C8–C8ⁱ and C5–C6–C6ⁱ angles that show the linearity in both structures, respectively, are 176.4(3)° in 3a and 175.6(2)° in 3b.     

The magnetic structure of neodymium crystal below the néel temperature

The phase transition in neodymium crystal from the paramagnetic to the magnetically ordered phase at the temperature T _N = 19.9 K is discussed in the terms of Landau's theory. It is shown that the calculated six-dimensional active representations at the point q = vb ₁, with—0.5 < v < 0.5, v ≠ 0, induce transitions to “single-q”, “double-q” and “triple-q” spin structures. A general formula for the spin vector S(r) for T < T _N is derived, from which a variety of spin structures can be obtained depending on the choice of the free parameters. The spin structure calculated by Bak and Lebech (1978) is obtained from that formula as a particular solution which is compatible with Landau's theory. An antiferromagnetic spin structure which represents a modification of that given by Bak and Lebech (1978) is calculated. The corresponding cross-section for neutron elastic magnetic scattering fulfils the experimental conditions listed by Lebech (1981). It is shown that the magnetic satellites of the type (h ± v, 0, 0) cannot appear for any type of structure following from our general formula for S(r). These satellites therefore can be connected only with representations at the point q = μ₁ b ₁ + μ₂ b ₂,—0.5 < μ₁, μ₂ < 0.5, μ₁, μ₂ ≠ 0, μ₁ ≠ μ₂.     

Evolution of the structure of Rb2ZnCl4 over the temperature range 4.2–310 K

X-ray diffraction is used to study the temperature dependence of the lattice parameters and the sequence of structural realignments in crystalline Rb₂ZnCl₄ over temperatures of 4.2–310 K. The appearance of and changes in the system of satellite reflexes indicative of structural ordering are studied. Below 74 K, on going into the monoclinic phase (space group A11a), anomalies are observed in the behavior of the lattice parameters, and superstructural reflexes develop with wave vectors q=a ^*/3+b ^*/2+c ^*/2 corresponding to an increase by a large factor in initial parameters a, b, and c of the Pnma-phase. Fiz. Tverd. Tela (St. Petersburg) 41, 1084–1090 (June 1999)     

Transmission Electron Microscopy Study of Polymorphism in Barium Gallate BaGa2O4

Polymorphism in barium gallate BaGa₂O₄ was studied using electron diffraction and high resolution electron microscopy. Three modifications of BaGa₂O₄ with structures closely related to the high-temperature α-form were observed. The phase transitions from γ-BaGa₂O₄ (a _γ = 18.6143(2) Å = 2<formula><radical><radicand>3</radicand></radical></formula>a _α, c _γ = 8.6544(1) Å = c _α, S.G. P6₃) to β-BaGa₂O₄ (a _β = 2a _α, c _β = c _α S.G. P6₃) and to the new δ-polymorph having a monoclinic structure (a _δ = c _α, b _δ = 2a _α + b _α, c _δ = 2b _α and β ≈ 92°, S.G. P2₁/c) were induced by electron beam irradiation. High resolution electron microscopy (HREM) observations allow to establish the close similarity between the structures of δ-BaGa₂O₄ and β-SrGa₂O₄. The γ→β and β→δ transitions involve a rearrangement of oxygen atoms in the BaO layers together with a tilting distortion of the tetrahedral framework. The microstructure of the δ-phase is characterised by the presence of numerous translation and orientation domains.     

Infrared spectra and lattice vibrations of the spin-chain compound LiCuVO 4

The infrared spectra of the one-dimensional antiferromagnet LiCuVO₄ are measured in the frequency range from 10 cm^-1 to 10 000 cm^-1 and at temperatures from 2 K to 300 K, for the electric field vector E of the radiation polarized either along the a- or along the b-crystallographic directions. For each polarization six infrared active phonon modes are observed in accordance with factor group analysis of the crystal structure of LiCuVO₄. The theoretical group analysis of the possible spinel low-symmetry phases is performed within the framework of Landau's theory of phase transitions. The parameters of several phonon lines show noticeable anomalies around 150 K where the magnetic correlations appear in the copper chains, which may indicate a finite interaction between the phonon and the magnon subsystems in LiCuVO₄. Received 19 February 2001 and Received in final form 26 June 2001     

Configuration interaction calculations for the ground and excited states of ozone and its positive ion: Energy locations and transition probabilities

Large-scale configuration interaction calculations (including energy extrapolation) are reported for the various states of ozone and its positive ion. The first four dipole-forbidden electronic transitions in the O₃ spectrum are calculated to occur at 1.20, 1.44, 1.59, and 1.72 eV, respectively, while the corresponding low-energy-allowed species known as the Chappuis, Huggins, and Hartley bands are predicted to possess vertical excitation energies of 1.95, 3.60, and 4.97 eV, respectively. These results all appear to fit in quite well with the observed location of the pertinent spectral features, with respect to both energy and intensity. The 5- to 8-eV region of the ozone spectrum is found to be characterized by a series of double-excitation transitions out of the highest three occupied orbitals to the lowest unoccupied 2b₁(π^*) species. The strong features observed at 9.3 and 10.2 eV are thereupon calculated to result primarily from transitions into the 7a₁ (σ^*) MO (calculated 9.29 and 10.05 eV) and in the former case also from the 3s members of the various O₃ Rydberg series (calculated 9.21 and 9.38 eV). Finally the order of the first three ip's is found to be 6a₁, 4b₂, and 1a₂, while the feature in the neighborhood of 16 eV is attributed to a shake-up state of ²B₁ symmetry.     

Magnetic and structural transitions in La1−x Sr x MnO3: T-x phase diagram

The electrical conductivity, magnetic susceptibility, magnetization, and submillimeter (v=5∓20 cm⁻¹) permittivity and dynamic conductivity of La_1−x Sr _x MnO₃ (0≤x≤ 0.45) single crystals are investigated. The anomalies in the temperature dependences of these quantities are identified with diverse magnetic and structural phase transformations, including antiferromagnetic and ferromagnetic ordering, structural transitions between strongly distorted (Jahn-Teller) and weakly distorted (pseudocubic) orthorhombic phases, structural transitions to a rhombohedral phase and unusual transitions to a polaron-ordering state. As a result, the complete T-x phase diagram of the system La_1−2x Sr _x MnO₃ is constructed in a wide interval of temperatures T=4.2∓1050 K and concentrations x=0−0.45. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 331–336 (25 August 1998)     

Incommensurate cooperative tilting modes of MnF6 octahedra relatedto the structural phasetransitions in BaMnF4

The structural phase transitions of the layer compound BaMnF₄ were studied by high-resolution X-ray diffraction using synchrotron radiation. The intensities and profiles of two kinds of superlattice reflections having incommensurate reduced wave vectors q ₁= (～ ± 1/5,0,0) _p and q ₂ =(～ ± 2/5,1/2,1/2)_p, respectively, were measured as a function of temperature from 25 K to 280 K. These temperature dependencies show that incommensurate structural phase transitions of second order occur at 234 K and 244 K. These structural phase transitions are interpreted as successive condensations of a folding-screen-like incommensurate plane-distortion mode and a commensurate anti-ferro-distortive tilting mode of the MnF₆ octahedra around the primitive a₀ - and b₀ -axes, when cooled down. It is also found that there is another structural phase transition at about 45 K related to a precursor structural distortion for the antiferromagnetic transition occurring at about 26 K.     

A CCD based detector for quick detection of pressure induced phase transitions

Abstract

A high sensitivity CCD based two dimensional angle dispersive X-ray are a detector has been developed for quick detection of pressure induced phase transitions for a laboratory X-ray source such as a rotating anode generator. The performance of this detector was tested by successfully carrying out powder X-ray diffraction measurements on element Pd, intermetallics AuIn², AuGa² and low Z scatterer adamantane (C₁₀H_l6) at ambient conditions. Its utility for quick detection of phase transitions at high pressures with diamond anvil cell (DAC) is demonstrated by reproducing the known pressure induced structural phase transitions in RbI and KI. The importance of this detector system in search of unknown phase transitions has been established by observing new structural phase transitions in In_0.25Sn_0.75 and AuGa₂. Various softwares have also been developed such as interactive location of centre of diffraction rings, radial integration and image enhancement to analyze data from this detector.     

X-ray diffraction analysis of the modulated structure of Bi2Sr2CaFe2O y

The modulated structure of the Bi₂Sr₂CaFe₂O _y compound isomorphous with the Bi₂Sr₂CaCu₂O _y phase was refined by the method of the full profile analysis on the basis of the powder X-ray diffraction data. The analysis was carried out in the superspace group ofN:Abmm: 1 – 11 using the parameters of the unit cell of the basic structurea = 5.466(3),b = 5.446(5) andc = 31.25(9) Å and the modulation vectorq = 0.220(5)b* +c*. The model of excess oxygen interstitials into the BiO plane was used by applying a saw-tooth-type function of the form:U = 2U ₀ [(X ₄ -X ₄ ⁰ /)] [1]. The results point to a strong displacement of the atoms from their positions in the basic structure. An essential improvement of theR factors was obtained by taking into account the modulation waves of the higher harmonics.     

The structure of the glass phase of Rb1−x(ND4)xD2PO4

X-ray scattering techniques have been used to study the diffuse scattering from a single crystal of Rb_1–x(ND₄)_xD₂PO₄ withx=0.65. This system has a structural glass phase at low temperatures resulting from the competing ferroelectric interactions of RbD₂PO₄ and antiferroelectric interactions of (ND₄)D₂PO₄. The diffuse scattering shows a broad peak with a maximum occurring at a wavevector of about 0.3a ^*, and the intensity of these peaks is surprisingly different for wavevectorsq on opposite sides of the Bragg reflections. A model of the D bonding is developed which suggests that the diffuse scattering arises from the interaction between ferroelectric displacements alongc, ferroelectric displacements alongb, and transverse acoustic modes polarized alongb andc. The model accounts for the incommensurate wavevector and, qualitatively, for the intensity of the diffuse scattering around different Bragg reflections. The temperature dependence of the scattering is also measured.     

Charge ordering-disordering in the Th-doped CaMnO3

The structural transitions that appear in the manganites Ca_1-xTh_xMnO₃ versus temperature are studied in connection with their magnetic and transport properties, and compared to those of the Ca_1-xLn_xMnO₃ manganites. An orthorhombic to monoclinic transition is observed for low x values (;this structural distortion, also observed for Ln-doped oxides, is related to the magnetoresistance properties. For higher x values (), modulated commensurate and incommensurate phases are obtained at low temperature, with , b =2 a p and , which are related to Mn³⁺/Mn⁴⁺ charge ordering (CO) phenomena. T values, determined from electron diffraction, are in agreement with those determined from the M ( T ) curves. The low temperature electron microscopy shows that the CO in those oxides is more complex than in Ln-doped manganites. In particular, the destabilisation of CO and consequently of the antiferromagnetic interactions is evidenced as the thorium content increases which may explain the appearance of a spin-glass like behavior for higher x values not seen for Ca_1-xSm_xMnO₃ phases . Received 2 November 1998     

Mechanisms of EPR line broadening in Pb5Ge3O11 near a structural transition

The polar angular dependence of the anomalous linewidth of three EPR transitions in the Gd³⁺ trigonal center has been used to determine the broadening mechanism. It is shown that the dominant mechanism of Gd³⁺ EPR signal broadening in the vicinity of the ferroelectric transition is the critically growing spread of the b ₂₁ and c ₂₁ parameters accounting for the odd-order fields of remote charge-compensating defects. Fiz. Tverd. Tela (St. Petersburg) 40, 321–326 (February 1998)     

High resolution FTIR spectroscopy of CH2DF: analysis of the v 3 and v 4 interacting bands

The high resolution (0.004cm^?1) Fourier transform infrared spectrum of the monodeuterated form of methyl fluoride, CH₂DF, has been recorded and analysed in the v ₃ and v ₄ band region around 1420cm^?1. Both bands, coming from A′ symmetry vibrations, have a/b hybrid character, although in v ₃ the b-type component prevails over the a-type. The rotational structure has been analysed using a dyad model including c-type Coriolis coupling and high order vibrational resonance between these states. Accurate upper state molecular parameters and interaction terms have been obtained by fitting about 3270 assigned transitions to Watson's A-reduced Hamiltonian in the I^r representation. In addition, from a simultaneous fit of ground state combination differences coming from this analysis and 42 literature microwave transitions, an improved and more complete set of ground state constants, including three new sextic centrifugal distortion terms (Φ_JK, Φ_KJ and Φ_K), has been derived.     

Theory and computer simulation of tweed texture

Abstract

An analytical theory of the ordering interaction J(R _ij ) in structural phase transitions mediated by elastic relaxation in the material is outlined. The ordering process in cell i sets up a local stress field due to the sizes, shapes or displacements of atoms or atomic groups, which is propagated elastically to a distant cell j. The atomistic theory for ferro- and antiferro-elastic transitions takes into account two types of singularity, one due to elastic anisotropy and the other to the Zener interaction J _z of infinite range in ferroelastic transitions. The form of J _k in Fourier space is highly anisotropic with a few “soft” directions coinciding with the orientation of twin boundaries. The asymptoptic J(R) at large R is shown to be very anisotropic as well and decays as R ^?3 in ferroelastic and R ^?5 in antiferroelastic systems.

Computer simulations for a three-dimensional model of about 29,000 particles show a strong tendency to form tweed texture, as observed experimentally. Well above the structural phase transition temperature, the strain fluctuations show well-developed embryos of the tweed texture. On quenching to below the transition temperature, a pronounced micro-twinning appears which follows almost exactly the shape of the embryos and then develops towards a stripe texture. After a certain time needle-shaped domains are formed and a peculiar step-wise process of generating new stripes is observed.