Orthorhombic Transition Research Articles

Structure de SnPb 2O 4 à quatre températures: relation entre dilatation et agitation thermiques

The structural study of SnPb 2O 4 oxide, an isomorphic compound belonging to the general family “ MeX 2O 4” like Pb 3O 4, is made from accurate X-ray and neutron diffraction techniques on powdered samples. The structural evolution of SnPb 2O 4 is analyzed from 300 to 5 K: no phase transition is observed, contrary to Pb 3O 4, which exhibits a tetragonal → orthorhombic transition at 170 K. The thermal expansion tensor is practically isotropic in this temperature range: the α a , α c and α V coefficients are neighboring those observed in the Pb 3O 4 tetragonal phase at the same temperature. On the other hand, the thermal vibrations are strongly anisotropic, with large amplitudes in the ( a, b) plane. In this study the thermal vibrations are connected to the thermal expansion. Bab and Bc temperature factors are considered as functions of the a and c cell parameters. The relation established by Grüneisen between the mean-square amplitudes of vibrations and the thermal volume expansion is discussed. The interatomic distances found show that the bindings are similar to that of Pb 3O 4: only the [ Sn 4+O 6] octahedrons are smaller than [Pb 4+O 6] octahedrons.

Ionic conductivity, activation volumes, and high-pressure phase transitions in PbF2and SrCl2

The effect of hydrostatic pressure on the ionic conductivities and phase transitions in Pb${\mathrm{F}}_{2}$ and Sr${\mathrm{Cl}}_{2}$ has been investigated. The cubic to orthorhombic transition in Pb${\mathrm{F}}_{2}$ was studied in the temperature range of 300 to 850 K for pressures up to 0.55 GPa; the similar transition in Sr${\mathrm{Cl}}_{2}$ was investigated in the range 500 to 1050 K for pressures to 0.45 GPa. The transition temperature was seen to increase linearly with increasing pressure at higher temperatures in both materials. There is considerable hysteresis in the transition at lower temperatures. The activation volumes were extracted from the effect of pressure on the conductivity. The volumes are small at all times, and are consistent with the dominance of Frenkel defects in these materials.

Neutron and X-ray precession studies of the incommensurate reflections near the 300°C transition in barium sodium niobate.

Abstract Reflections at positions incommensurable with respect to the basic tetragonal lattice are disclosed for the first time in Ba2NaNb5O15 in the region of the tetragonal to orthorhombic transition, near 300°C, through neutron scattering and X-ray precession experiments. The satellite reflections are observed at ± (1 + δ) (a* + b*)/4+ c*/2 with δ ⋍ 0.1 and a strong temperature dependence. In the orthorhombic phase these reflections “lock-in” at (± (a*+b*)/4 + c*/2). In the transition region we observed diffused scattering of neutrons and X-ray as well as a soft phonon. The probable occurence of an incommensurate phase is discussed. The observations are consistent with a 4 dimensional order parameter at (a*/4, b*/4, c*/2).

The effects of pressure and crystallinity on the hexagonal to orthorhombic transition temperature in dysprosium

Although the dependence on pressure of Tc, the temperature at which the hexagonal-orthorhombic transition occurs, in dysprosium has been determined previously, data obtained for single-crystal and for polycrystalline specimens have not always agreed (Bartholin and Bloch 1968). In an effort to explain the discrepancies, measurements of Tc as a function of pressure have been made on two samples of the same material that differed in their crystallinity. The results for Tc of (88.1+or-0.1)K and (88.3+or-0.4)K and for dTc/dP of (-1.05+or-0.05)K kbar-1 and (-1.34+or-0.2)K kbar-1 indicate that factors other than the crystallinity of the specimen may be the source of the discrepancies.

A study of the early stages of tempering in an Fe-1.2 Pct alloy

Mossbauer effect spectroscopy has been used to study changes in the microstructure of an Fe-1.22. wt pct C alloy due to tempering between 373 and 523 K. The orthorhombic transition carbide, η-Fe2C, was identified by transmission electron microscopy and the similarity of ∈-carbide electron diffraction patterns to η-carbide diffraction patterns is noted. Systematic changes in the Mosbauer parameters of martensite and austenite are presented for the various stages of tempering. The same amount of C remains randomly dissolved in the retained austenite throughout tempering and some C is retained in the martensite throughout the range of transition carbide formation. Two sets of Mossbauer parameters corresponding to magnetic phases other than martensite and cementite have been found. These parameters may come from η-carbide, but alternative interpretations are presented.

Linear Electro-Optic Effect in Ferroelectric KTN

The low-frequency linear electro-optic coefficients have been measured in ferroelectric KTN (KTax Nb1−xO3) as a function of temperature. A measurement of the field-induced retardation shows that the half-wave voltage is about one 100th of that for KDP and about one half that for BaTiO3. The half-wave voltage increases from about 20 V at 3°C below the Curie point to approximately 115 V at 40°C below the Curie point. The possibility of tailoring the Curie point by varying the Ta-to-Nb ratio therefore makes KTN attractive for light modulation and deflection.An ac technique was developed to determine the electro-optic coefficient r42. This coefficient is extremely large, showing the expected increase towards the orthorhombic transition temperature but it is not useful for modulation or deflection.

Secondary Piezoresistivity in Oxygen Deficient BaTiO3 Single Crystals

The anomalous resistive and piezoresistive characteristics of BaTiO3−x ceramics and single crystals are related to domain orientations. It is proposed that an anisotropy in resistivity exists in the different crystallographic directions in the tetragonal phase, reaching a maximum at the tetragonal to orthorhombic transition. A small stress is sufficient to change domain orientations resulting in a large piezoresistive effect (secondary piezoresistivity) because of the anisotropy of resistivity. The change in resistivity was found to be proportional to strain.

Activation Field and Coercivity of Ferroelectric Barium Titanate

The activation field of BaTiO3 c-domain crystals may be calculated from an experimental determination of the frequency dependence of the coercivity. The ratio of activation fields above and below the orthorhombic transition is equal to the respective ratio of coercivities. The decrease in coercivity in passing through this transition is related to the change in thickness of the space charge layer within the ferroelectric.

Triple Hysteresis Loops and the Free-Energy Function in the Vicinity of the 5°C Transition in BaTiO3

The effect of an electric field on the transition between the orthorhombic and tetragonal states in single crystals of BaTi${\mathrm{O}}_{3}$ has been investigated. With zero bias the tetragonal to orthorhombic transition occurs near 5\ifmmode^\circ\else\textdegree\fi{}C and the inverse transition at 11\ifmmode^\circ\else\textdegree\fi{}C, exhibiting a temperature hysteresis of about 6\ifmmode^\circ\else\textdegree\fi{}C. As expected, an external field in the direction of the polarization in the tetragonal state lowers both transition temperatures. Measurements show that the temperature depression varies linearly with the field. A strong field (>20 kv/cm) can lower both transition temperatures below the 5\ifmmode^\circ\else\textdegree\fi{}C transition at zero field. Thus at a constant temperature, in a small temperature range below 5\ifmmode^\circ\else\textdegree\fi{}C, the crystal can be switched reversibly between the two states by means of an electric field. Since the spontaneous polarization is smaller in the orthorhombic state, this phenomenon can be displayed as a "triple loop" in the familiar polarization vs electric field hysteresis plot. The dielectric constant has been measured as a function of temperature, and as a function of field at fixed temperatures. Transitions between states are sharp whether the transition is produced by varying the temperature or the electric field, provided the faces are completely electroded.Numerical coefficients for various terms in the free-energy expansion for BaTi${\mathrm{O}}_{3}$, have been determined from certain of the experimental measurements. Calculations for various physical properties based upon the free-energy expansion agree reasonably well with these properties determined experimentally.