A note on the Berry phase for systems having one degree of freedom

A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.

Unconventional mechanism of stabilization of a tetragonal phase in the perovskite ferroelectric (PbTiO3)(1-x)(BiFeO3)(x)

Temperature-dependent x-ray powder-diffraction study of the tetragonal compositions of PbTiO3-BiFeO3 series has revealed that, unlike for all the known ferroelectric perovskites, the compositions exhibiting giant tetragonality is stabilized from the cubic phase via a complex transition pathway which involve (i) formation of minor monoclinic phase with a large pseudotetragonality along with an intermediate tetragonal phase (major) with a small tetragonality, (ii) gradual vanishing of the intermediate tetragonal phase and concomitant increase in the monoclinic regions, and finally (iii) gradual transformation of the monoclinic phase to the tetragonal phase with giant tetragonality.The system seems to adopt such a complex transition pathway to create amicrostructure with very large number of domains and interfaces for stress relief, which would not have been possible in case of a direct cubic-tetragonal transition.

Electron-Paramagnetic-Res study of LiKSO4 in phase IV below -138 degrees C

A detailed single-crystal EPR study of phase IV of lithium potassium sulphate below -138 degrees C has been carried out using NH3+, which substitutes for K+, as the paramagnetic probe. The spin-Hamiltonian parameters have been evaluated at -140 degrees C and yield an isotropic g=2.0034; (AH)XX=(AH)YY=25.3 G and (AH)ZZ=23.8 G; (AN)XX=8.1 G, (AN)YY=21.2 G and (AN)ZZ=25.9 G. In this phase there are 12 magnetically inequivalent K+ sites and their occurrence is ascribed to the loss of a c glide.

Ferroelastic phase transition in CslO4

An optical investigation of the high-temperature structural phase transition in gel-grown single crystals of CslO4 is reported. This crystal undergoes a phase transition from the room-temperature orthorhombic phase of symmetry Pnma to a tetragonal phase at 150°C. The birefringence Δn = |na-nb| falls abruptly at Tc, indicating the first-order nature of the phase transition. Microscopic examination has revealed the existence of ferroelastic domains in the crystal. The domain structure and its dependence on temperature was studied in detail. The experimental results suggest that this crystal can be assigned to the ferroelastic Aizu species 4/mmmFmmm (p).

Freezing of a colloidal liquid subject to shear flow

A nonequilibrium generalization of the density-functional theory of freezing is proposed to investigate the shear-induced first-order phase transition in colloidal suspensions. It is assumed that the main effect of a steady shear is to break the symmetry of the structure factor of the liquid and that for small shear rate, the phenomenon of a shear-induced order-disorder transition may be viewed as an equilibrium phase transition. The theory predicts that the effective density at which freezing takes place increases with shear rate. The solid (which is assumed to be a bcc lattice) formed upon freezing is distorted and specifically there is less order in one plane compared with the order in the other two perpendicular planes. It is shown that there exists a critical shear rate above which the colloidal liquid does not undergo a transition to an ordered (or partially ordered) state no matter how large the density is. Conversely, above the critical shear rate an initially formed bcc solid always melts into an amorphous or liquidlike state. Several of these predictions are in qualitative agreement with the light-scattering experiments of Ackerson and Clark. The limitations as well as possible extensions of the theory are also discussed.

Theoretical Estimation of Length Dependent In-Plane Stiffness of Single Walled Carbon Nanotubes Using the Nonlocal Elasticity Theory

In the present paper, Eringen's nonlocal elasticity theory is employed to evaluate the length dependent in-plane stiffness of single-walled carbon nanotubes (SWCNTs). The SWCNT is modeled as an Euler-Bernoulli beam and is analyzed for various boundary conditions to evaluate the length dependent in-plane stiffness. It has been found that the nonlocal scaling parameter has a significant effect on the length dependent in-plane stiffness of SWCNTs. It has been observed that as the nonlocal scale parameter increases the stiffness ratio of SWCNT decreases. In nonlocality, the cantilever SWCNT has high in-plane stiffness as compared to the simply-supported and the clamped cases.

Identification of corona discharge-induced SF6 oxidation mechanisms using SF6/18O2/H216O and SF6/16O2/H218O gas mixtures

The absolute yields of gaseous oxyfluorides SOF2, SO2F2, and SOF4 from negative, point-plane corona discharges in pressurized gas mixtures of SF6 with O2 and H2O enriched with18O2 and H2 18O have been measured using a gas chromatograph-mass spectrometer. The predominant SF6 oxidation mechanisms have been revealed from a determination of the relative18O and16O isotope content of the observed oxyfluoride by-product. The results are consistent with previously proposed production mechanisms and indicate that SOF2 and SO2F2 derive oxygen predominantly from H2O and O2, respectively, in slow, gas-phase reactions involving SF4, SF3, and SF2 that occur outside of the discharge region. The species SOF4 derives oxygen from both H2O and O2 through fast reactions in the active discharge region involving free radicals or ions such as OH and O, with SF5 and SF4.

Thermal expansion and phase transition in NaVO3

The present x-ray study has been undertook in order to correlate the phase transition in sodium metavanadate NaVO3 crystal with its structural aspects. The thermal expansion behaviour of NaVO3 was studied from room temperature up to 500 C, well beyond the transition temperature.

Phase space methods and the Hamilton-Jacobi form of dynamics

A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.

Computer estimation of the Cd---Hg---Te phase diagram

The compounds CdHgTe and its constituent binaries CdTe, HgTe, and CdHg are semiconductors which are used in thermal, infrared, nuclear, thermoelectric and other photo sensitive devices. The compound CdHgTe has a Sphaleritic structure of possible type A1IIB1IIC6VI. The TERCP program of Kaufman is used to estimate the stable regions of the ternary phase diagram using available thermodynamic data. It was found that there was little variation in stochiometry with temperature. The compositions were calculated for temperatures ranging from 325K to 100K and the compositional limits were Cd13−20Hg12−01Te75−79, Hg varying most. By comparison with a similar compound, Cd In2Te4 of forbidden band width. 88 to .90 e.V., similar properties are postulated for Cd1Hg1Te6 with applications in the infra red region of the spectrum at 300K where this composition is given by TERCP at the limit of stability.

Studies on the phase transitions in thiourea

Thiourea (CS(NH2)2) is one of the few examples of molecular crystals exhibiting ferroelectric properties. The dielectric constant along the ferroelectric axis [100] shows maxima at 169, 177 and 202 K. An inflection point occurs at 170.5 KZ Following Goldsmith and White the phases are named as I (F.E. below 169 K), II (A.F.E. 169 Kphases 11, 111 and IV.4,5 The effect of structural modulation is to destroy the local n glide symmetry, though the overall structure is Pnma. Thiourea also exhibits thermoluminescence after being irradiated with x-rays which is accounted for by defects like NH3+ and NH- formed by the breaking of hydrogen bonds.

Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pn) for a disordered conductor of length L in the quasi-metallic regime L<phases. A direct proof of the validity of the random-phase assumption for studying scaling of resistance in one dimension is thus obtained.

Vapor phase oxidation of p-xylene

The kinetics of the vapor phase oxidation of p-xylene over ferric molybdate catalyst were studied in an isothermal, differential, tubular flow reactor in the temperature range of 360 to 420° C. The major product obtained was p-tolualdehyde with small amounts of maleic anhydride and p-toluic acid. No terephthalic acid or CO2 were observed. The reaction rate data collected fit the redox model given by Equation 1. The values of activation energies Ex, Eo and frequency factors Ax, Ao obtained are 72, 63 kJ/mol and 0.64, 2.89 m3/kg catalyst s respectively. The reaction mechanism was established by studying the oxidation of p-tolualdehyde, toluic and terephthalic acids. It is concluded that the reaction follows a parallel-consecutive scheme. On a étudié la cinétique de l'oxydation, en phase gazeuse, du para-xylène sur un catalyseur consistant en molybdate ferrique; cette oxydation s'est faite dans un réacteur à écoulement tubulaire, isothermique et différentiel, dans une échelle de températures comprises entre 360°C et 420°C. Le produit principal obtenu a été le para-tolualdéhyde; on a aussi trouvé de faibles quantités d'anhydride maléique et d'acide para-toluique, mais on n'a pas noté la présence d'acide téréphtalique ni d'anhydride carbonique (CO2). Les résultats obtenus en ce qui a trait à la vitesse de réaction concordent bien avec les données du modèle redox indiquées par l'équation 1. Les valeurs des énergies d'activation Ex et Eo ainsi que des facteurs de fréquence Ax et Ao obtenus sont respectivement 72 et 63 kilojoules/mol. et 0.64 × 103 et 2.89 m3/kg de catalyseur. On a établi le mécanisme de la réaction en étudiant l'oxydation du para-tolualdéhyde et des acides toluique et téréphtalique. On conclut que la réaction se fait d'une manière parallèle et consécutive.

Formant extraction from linear-prediction phase spectra

Extraction of formant information from linear-prediction phase spectra is proposed. It is shown that the derivative of phase spectrum gives reliable formant information. Since the phase spectra for several resonators in cascade are additive, the resonance peaks are additive in the derivative of the phase spectrum unlike in the magnitude spectrum and hence the problem of identifying merged peaks is very easily solved by this method. Application of the method is illustrated through examples of linear-prediction spectra obtained for simulated models and for actural speech segments.

Resistance fluctuations, phase randomness and noise in one-dimensional conductors with a long-range correlated potential

When the size (L) of a one-dimensional metallic conductor is less than the correlation length λ-1 of the Gaussian random potential, one expects transport properties to show ballistic behaviour. Using an invariant imbedding method, we study the exact distribution of the resistance, of the phase θ of the reflection amplitude of an incident electron of wave number k0, and of dθ/dk0, for λL ll 1. The resistance is non-self-averaging and the n-th resistance moment varies periodically as (1 - cos 2k0L)n. The charge fluctuation noise, determined by the distribution of dθ/dk0, is constant at low frequencies.