Orthorhombic-tetragonal Transition Research Articles

Anisotropy in thermal expansion of La 2−xSr xCuO 4

We report on the anisotropy of thermal expansion α of La 2− x Sr x CuO 4 ( x=0.14) detwinned single crystals. Using observed discontinuities in α at the tetragonal-orthorhombic transition temperature, T d , the uniaxial stress dependence along the a-, b- and c-axis are estimated as d T dd P i= a, b, c, ∼+130, −310 and +60 K/GPa, respectively. We also discuss the structural fluctuation near T d .

Crystal growth of YBa2Cu3O7 by the SRL-CP method under low oxygen partial pressure atmosphere

Single crystals of YBa2Cu3O7−x (Y123) were grown by a modified top-seeded crystal pulling method using a BaO-CuO solution with the solid Y2BaCuO5 (Y211) as a solute in an yttria crucible [the so-called solute-rich liquid crystal pulling (SRL-CP) method] under 2% oxygen partial pressure atmosphere [P(O2) = 0.02 atm]. According to the pseudo-binary phase diagrams of Lee and Lee,1 the temperature of Y123 crystal growth was expected to be lower for 0.02 atm oxygen pressure than for 0.21 atm oxygen pressure. The single crystals grown under P(O2) = 0.02 atm and cooled under the same atmosphere after the separation of crystal from a solution had twins near the microcracks on the crystal surface. On the other hand, the single crystals grown under P(O2) = 0.02 atm and cooled under pure nitrogen atmosphere (6N) showed no twin structure. These results indicate that twins did not form during crystal growth but formed due to tetragonal-orthorhombic transition as a consequence of oxygenation at cooling under low oxygen partial pressure.

Formation and decomposition of LaBa2Cu3O7 –δ

The formation and decomposition of LaBa2Cu3O7 –δ has been studied by X-ray diffraction and thermogravimetric analysis. The attempted preparation of LaBa2Cu3O7 –δ in air or oxygen gives a mixture of a solid solution of composition La1 +xBa2 –xCu3O7 –δ(x≈ 0.2), and BaCuO2(J. M. S. Skakle and A. R. West, Physica C, 1994, 220, 187). However, heating this mixture in a less oxidising atmosphere such as flowing argon at temperatures above 850 °C for a short time, ca. 16 h, yields a single-phase tetragonal product, which, when annealed in oxygen at lower temperature, gives an orthorhombic superconductor with Tc(onset)≈94 K. The orthorhombic and tetragonal structures have been confirmed by Rietveld refinement of X-ray powder diffraction data; an orthorhombic–tetragonal transition occurs at δ= 0.2. The stability of the single-phase material under air and oxygen has been studied by thermogravimetry. It is stable up to 800 °C in air; at higher temperatures, decomposition to La1 +xBa2 –xCu3O7 –δ(x≈ 0.2), and BaCuO2 occurs. On prolonged heating of single-phase tetragonal LaBa2Cu3O7 –δ at high temperatures, e.g. 875 °C for 64 h under argon, decomposition to give La4 – 2xBa2 + 2xCu2 –xO10 – 2x(x≈ 0.2), BaCuO2 and BaCu2O2 occurs. This is similar to the behaviour of YBCO under low oxygen pressure. Thus, under all conditions studied so far, LaBa2Cu3O7 –δ may be considered to be a non-equilibrium phase. In orthorhombic samples of LaBa2Cu3O7 –δ prepared by quenching, Tcvaries linearly with δ samples cooled slowly show evidence of a plateau at ca. 94 K for δ≈–0.05 to –0.15.

Successive phase transition of a cubic system

Abstract Devonshire's potential for description of the successive phase transition in BaTiO3 has been considered in the light of the catastrophe theory. The general perturbation to triple butterfly x 6 + y 6 + z 6 is expressed by 124 unfolding terms. The unfolding coefficients are diffeomorphically mapped to field variables of the same number. Cubic symmetry reduces this to 9. Devonshire's potential is a result of a physical simplification retaining only one field variable: temperature. Addition of symmetry-breaking terms for external fields in three directions enables us to calculate many physical properties of BaTiO3. Phase diagram in temperature-external field space has been given. In connection to this, triple hysteresis loops near tetragonal-orthorhombic and orthorhombic-rhombohedral transitions are expected from calculations, besides the well-known double hysteresis loop just above cubic-tetragonal transition.

Structural and transport properties of YBa 2Cu 3−yCo yO 7−x solid solutions

The X-ray study of YBa 2 Cu 3- y Co y O 7 solid solutions showed that in addition to the orthorhombic-tetragonal transition existing in the compositional range of 0.0< y<0.1, reported elsewhere, a reverse change to the orthorhombic structure appears for compositions of y>0.4. A model based on an arrangement of microwatwins, formed owing to a tendency of cobalt ions to be six-fold coordinated, was proposed to explain the observed structural changes. A comparison of the oxygen stoichiometry and Hall charge carriers density data showed that this tendency is decisive for the charge distribution in the (Me(1)O) sublattice. Besides the geometrical arrangement, the quality of the bonds and consequent character of the transport properties is influenced by a more ionic character of cobalt ions in comparison with copper ones.

Magnetic ordering and chain transport of PrBa2Cu3O7-y.

The effects of Fe, Co, and Ni substitution on the structural, magnetic, and electrical properties of ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$ have been investigated by means of powder x-ray diffraction, magnetization, and electrical-resistivity measurements. All three systems ${\mathrm{PrBa}}_{2}$(${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{M}}_{\mathit{x}}$${)}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$ (M=Fe, Co, and Ni) exhibit an orthorhombic-tetragonal transition at about x=0.025 for Fe and Co, and x=0.05 for Ni. The magnetic ordering temperature ${\mathit{T}}_{\mathit{N}}$ of ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$ is reduced by the doping of Fe, Co, and Ni with the depression rate ${\mathit{dT}}_{\mathit{N}}$/dx\ensuremath{\sim}0.65, 0.75, and 0.45 K/at. %, respectively. The doping of Fe or Co has a larger effect than Ni on the increase of room-temperature resistivity. Combining these results with those observed previously in Zn- and Ga-doped ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$, it is interpreted that the Cu-O chain is considered to play a crucial role in the magnetic-coupling mechanism of ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$.

High-temperature superconductivity: The roles of soft-phonon driven structural phase transitions and biphonon-electron coupling

For the first time, fully self-consistent soft phonon data, associated with the tetragonal-orthorhombic structural transition in the high-temperature superconductor La2−xSr x CuO4, are used to solve Eliashberg equations. It is found that the electron-phonon coupling constant is stronglyx- and temperature-dependent. The superconducting transition temperatureT c follows the experimentalx-dependence but does not exceed 28 K. The higherT c values observed are attributed to nonlinear electronphonon interactions, due to high oxygen ion polarizability, which producebiphonon resonances and bound states and significantly increaseT c .

Shell model description of the phonon dispersion in La2CuO4

The phonon dispersion in La2CuO4, a base compound for high-Tc superconductors, is analysed in terms of a shell model. Shell charges and core-shell interactions are considered as anisotropic tensors. Short-range potentials of Born-Mayer type are taken to act between shells of different ions. An anisotropic screening of the Coulomb interaction is incorporated in order to describe the observed degeneracy of LO and TO modes polarized parallel to the CuO2 planes. The phonon energies measured for wavevectors along the three principal symmetry directions are adjusted for the first time with a shell model and a good simulation is achieved with a relatively low number of parameters. Copper-oxygen and lanthanum-oxygen interactions turn out to be of comparable magnitude and much stronger than the oxygen-oxygen interaction. The soft mode that leads to the tetragonal-orthorhombic transition is found to be most sensitive to the La-O interaction. This suggests that anharmonicity in this interaction may be responsible for the lattice instability.

HIGH-TEMPERATURE SUPERCONDUCTIVITY FROM ELECTRON-LATTICE COUPLING

Within the polaron theory of superconductivity for La 2−x Sr x CuO 4 and La 2−x Ba x CuO 4 the coupling is considered between the charge carriers and both the stretching mode of the apical oxygens and the sheet-bending mode of the basal-plane oxygens, the latter via the tilting angle of the Cu-oxygen octahedra. The same tilting angle enters the coupling strengths of these lattice vibrations, leading to renormalized frequencies and their oxygen-isotope shifts. It is suggested that the anomalies occurring in the superconducting critical temperature, its isotope shift and the isotope shifts of the lattice frequencies around x=0.12 are related to the orthorhombic-tetragonal transition of these compounds.

Specific-heat anomalies in La 2−xM xCuO 4( M= Ba, Sr; x=0.09, 0.12, 0.15) near 70 and 100K

Specific heat measurements show, for LMCO [ M= B( Ba), S(Sr); x=0.09, 0.12, 0.15], hysteresis and anomalous behavior in the 85–125K region and, for LBCO(0.12) and LSCO(0.09), similar magnetic field-dependent anomalies near 70K. Neutron and x-ray studies by others have shown the existence of an orthorhombic-tetragonal transition for LBCO near 70K but gave no indication of structural transitions in the other cases. The occurrence of transitions, and their x-dependence, in these materials is of interest for the possibility of its connection with the x-dependence of superconducting properties including the isotope effect.

Magnetic and structural properties of Fe in single crystals of YBa2Cu3-xFexO7- delta.

Magnetization and lattice-constant measurements were done on four single crystals of YBa{sub 2}Cu{sub 3{minus}{ital x}}Fe{sub {ital x}}O{sub 7{minus}{delta}} with Fe concentrations of {ital x}=0.06, 0.09, 0.15, and 0.24 to determine the structural and normal-state properties. Measurements of magnetization as a function of temperature were done in a temperature range between 90 and 300 K and analyzed using a Curie-Weiss law with a temperature-independent background. The effective magnetic moment obtained corresponds to a low spin state of Fe{sup 3+} with a magnitude of 2.18{mu}{sub {ital B}}. Magnetic anisotropy between the {ital ab} plane and the {ital c} direction is only present for the concentration of {ital x}=0.06 and is attributed to the various oxygen environments surrounding the iron. For concentrations larger than {ital x}=0.06, the moment on Fe is isotropic and Curie-Weiss fits predict uniform antiferromagnetic ordering. Structural measurements exhibit an orthorhombic-tetragonal transition at an Fe concentration of {ital x}=0.15, similar to that observed in the polycrystalline material.

Low temperature pyroelectric behaviour of barium titanate

Abstract The pyroelectric and dielectric properties of barium titanate crystals have been investigated in the temperature range from 300K to 150K. The pyroelectric coefficient has peaks at the tetragonal-orthorhombic transition and at the orthorhombic-rhombohedral transition. A thermal hysteresis of about 10K is recorded for the T-O transition and one of about 15K for the O-R transition. In the temperature range near the phase transitions, an unusual pyroelectric response was observed. Following a temperature variation, the pyroelectric charge changed its polarity with time. This behaviour can be attributed to the coexistence of two ferroelectric phases.

Magnetic and elastic properties of La2NiO4+x.

We present experimental data on elastic constants, magnetic susceptibility, and magnetization for single-crystal ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$. Strong acoustic anomalies especially for the ${\mathit{c}}_{66}$ mode are observed for the structural tetragonal-orthorhombic transition at 360 K, whereas for the lower structural transition at 80 K the acoustic effects are rather smeared out. With the help of our magnetic measurements, we can construct a spin model describing the essential features of the magnetic structure in ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$.

Relation between electronic and atomic structure ofYBa2Cu3O6+x

Using a model with strong interatomic correlations previously proposed to explain the electronic structure and pairing in ${\mathrm{CuO}}_{2}$ superconductors, we obtain a staircase behavior of the Fermi level, and a tendency of O(1) ions to order in Cu-O chains. We study the competition between this tendency and long-range Coulomb repulsion, using an Ising model and group-theoretical techniques. Using the cluster variation method, we also study the orthorhombic-tetragonal transition and correlations of the tetragonal phase. All results agree qualitatively with experiments.

Gapless Peierls transition.

For one-dimensional chains, transverse displacements of atoms produce zigzag structures, which are encountered in such diverse areas as polymers and metallic overlayers on semiconductor surfaces. Such displacements lead to an apparent reduction of translational symmetry but do not open a gap at the zone edge [gapless Peierls transition (GPT)]. The total energy remains analytic and hence the formation of zigzag chains on semiconductors is governed by material-specific interactions. The applications of the GPT ideas are illustrated by examining the stability issues and electronic structure of trans-(CH${)}_{\mathit{x}}$, Al chains on Si(001), and consequences of the tetragonal-orthorhombic transition in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.

Thermoanalytical characterization (DTA and TG) of RBa 1.5Sr 0.5Cu 3O 7−x and RBaSrCu 3O 7−x (R = Y, Gd, Sm OR Nd) superconductors

Differential thermal analysis and thermogravimetric analysis were used to characterize RBa 1.5Sr 0.5Cu 3O 7− x and RBaSrCu 3O 7− x superconductors (R=Y, Gd, Sm or Nd). It was found that the replacement of Ba by Sr increases the onset melting temperature of the perovskites. The effect is larger for compounds which contain an R atom with a small ionic radius. TG curves show that the temperature of the orthorhombic-tetragonal transition is modified by the presence of Sr.

Structural defects in YBa 2Cu 3O x superconductors

Structural features mainly associated with the ordering of oxygen in YBa 2Cu 3O x are studied by electron microscopy. The geometry and the mechanism of twin formation has been studied in detail. Models are proposed for twinning dislocations and it is shown that the ordering stresses resulting from the tetragonal-orthorhombic transition induce a synchroshear glide motion of these dislocations along the twin interfaces. The model also leads to an atomic mechanism for the detwinning of crystals under a uniaxial compressive stress. In oxygen deficient samples evidence is found for vacancy ordered long period superstructures of the nao type with n = 2,3,4,… The presence of these phases is related to T c. The 2√2 × 2√2 structure, previously considered as being a vacancy ordered structure, is suggested to be a deformation modulated structure. The distortions are of the Jahn-Teller type and are located in the CuO 2 layers.

Review and theory of oxygen ordering in the high-temperature superconductor YBa2Cu3O7-δ

Abstract The basal-plane ordering of oxygen vacancies into “chains,” which characterizes the tetragonal-orthorhombic structural transition in the high-temperature superconductor YBa2Cu3O7-δ, has heretofore been regarded as an example of a simple Ising lattice gas model with nearest- and next-nearest-neighbor interactions. This model is reviewed within a general framework that unifies and compares previous treatments. The observed transition temperature T 1 ≃ 1000K is, however, one to two orders of magnitude smaller than predicted by this Ising model when realistic physical values are assigned to its repulsive coupling constants. Attempts to resolve this dilemma by inclusion of farther-neighbor couplings or screening effects are shown to be unsuccessful. Rather, it appears that the crucial missing ingredients are the energy associated with Cu-O bonds, and an oxygen valence charge which depends on the atom's bonding configuration, the average valence being O- in the tetragonal phase but O2- in the orthorhom...

Percolation of linear clusters in YBa2Cu3Ox: A tool for explaining the ortho-tetragonal phase transition

The recent experimental results on the dependence of the oxygen content versus the temperature and the oxygen partial pressure show that orthorhombic-tetragonal transition occurs for x>6.6 with T>814 K. We deduce from molecular arguments that linear chains are favoured even in the tetragonal phase. Then, by applying the percolation theory we re-find the transition at 6.67. The consequence of such a computation is the knowledge of the cluster population, a quantity useful for interpreting the electron-transport properties.

Several Important Problems in YBaCuO and Its Doped Systems

ABSTRACTThe orthorhombic-tetragonal transition, relationship between oxygen content and TC, electronic state of Cu and TC, lattice energy and TC in YBCO and its doped systems (Cu doped by Sn, Al, Fe, Zn, Ni; Ba by Sr, Ca; Y by Pr,Gd,Dy, respectively.) have been studied systematically. The experiments show that the O-T transition may not be the predominant factor governing superconductivity; there is no regular relationship between superconductivity and the oxygen content. In order to fully understand superconductivity, other defects must be considered; the valence of Cu has a strong correlation with oxygen content, but has no direct relationship with the TC value. The correlation among the electronic states of Ba, Cu and O are discovered, which is helpful to know the electfonic behavior of this material. Finally, we show that the lattice energy has a close relationship with the magnitude of TC. As the lattice energy is decreased, the TC is always depressed without any exception. The authors suggest that the lattice energy may be a probable predominant factor to superconductivity.