Wave Vector K0 Research Articles

The {111}‐Modulated Domains in Tetragonal BaTiO3

Barium titanate (BaTiO3) base‐metal electrode multilayer ceramic capacitors of an X7R‐formulation, sintered at 1200°C under low oxygen partial pressures (of pO2≈10−9 and 10−11 atm, respectively), followed by annealing at 1000°C in an atmosphere containing a higher oxygen partial pressure (of pO2≈10−5–10−6 atm), have been analyzed for crystalline phases using X‐ray diffractometry, for microstructure using transmission electron microscopy, and for microchemistry using energy‐dispersive X‐ray spectroscopy and electron energy loss spectroscopy. The classical core–shell structure characterized by a core consisting of tetragonal ferroelectric {011) domains and featureless shell (designated type I) was observed only in sample A sintered in pO2≈10−9 atm. For sample B sintered in pO2≈10−11 atm, the core–shell structure is predominantly type II, consisting of a featureless shell similar to type I, but a core of modulated domains. The core of type II contained incommensurately modulated {111} superlattice domains along 〈111〉. The superlattice can be described by a displacive modulation with incommensurate wave vectors k1=0.58a*, k2=0.58b*, and k3=0.58c*. It is due to the ordering of defect associates , generated extrinsically from sintering in low pO2. Shell thickness was determined by the lattice diffusion of Ca2+ solute cations into BaTiO3 grains during sintering. The core–shell interface became less distinguishable in type II because defect associates , unlike those in type I, were not completely eliminated by re‐oxidizing in pO2≈10−5–10−6 atm, but became ordered along 〈111〉 and gave rise to structural modulation.

Spectrally resolved femtosecond 2-colour 3-pulse photon echoes: a new spectroscopic tool to study molecular dynamics

We present a new multidimensional femtosecond spectroscopy technique based on spectrally resolved 2-colour 3-pulse photon echoes for investigating molecular dynamics in a variety of systems including proteins. In this technique the sample is illuminated by two femtosecond 'pump' pulses with wave vectors k1, k2 and wavelength lambda(pump) and a femtosecond 'probe' pulse with wave vector k3 and wavelength lambda(probe). Nonlinear signals are generated in the phase-matching directions k4 = - k1 + k2 + k3 and k6 = - k3 + k1 + k2. These signals are analysed in spectrometers equipped with CCD detectors and the spectra of the signals are recorded for various values of (i) the delay t12 between pulses 1 and 2, (ii) the delay t23 between pulses 2 and 3, and (iii) the wavelengths lambda(pump), lambda(probe). The technique has been used for studying vibrational and electronic dynamics of dye molecules, such as cresyl violet in methanol, and ultra-fast transient processes that occur during the photo-dissociation of carbonmonoxy myoglobin (MbCO) into myoglobin (Mb) and CO.

Decay instability of a lower hybrid wave

A study is made of the decay instability of a lower hybrid wave with a finite wave vector (k0≠0) and a large amplitude such that the oscillatory velocity of the electrons with respect to the ions cannot be neglected. It is shown that, depending on the angle between the propagation direction of the lower hybrid wave and the external magnetic field and the angle through which the wave is scattered, the decay instability is primarily governed either by the oscillatory electron motion with respect to the ions or by the nonlinear response of the plasma to the lower hybrid wave propagating in it. The role of the nonlinear frequency shift in the saturation of the lower hybrid decay instability is clarified.

Instability of drift MHD waves in the upper ionosphere

We propose a mechanism for generation of low-frequency perturbations in a magnetoactive, almost ideal plasma. The perturbations comprising fluctuations of both plasma density and electromagnetic field can be presented in the form of rotating wave packets (MHD rotators) in k-space. It is shown that an instability leading to the formation of structures with wave numbers $$k_ \bot \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ \leqslant } k_{0 \bot } \sqrt {2\delta n_0^2 } $$ and the development of large-scale gyrotropic turbulence may occur if small-scale irregularities, which have the dispersion of the relative density fluctuations $$\sqrt {2\delta n_0^2 } $$ and the spectrum located near the wave vector k0,┴, exist in the plasma. These irregularities should be isotropic in the plane perpendicular to the regular magnetic field $$\bar B_0 $$ and stretched along $$\bar B_0 $$ .

Antiferromagnetism of RPtX (R = Ho, Er; X = Si, Ge) compounds

X-ray and neutron diffraction as well as magnetometric measurements performed for HoPtX and ErPtX (X = Si, Ge) compounds indicate that they are crystalline and that they have the orthorhombic TiNiSi-type crystal structure. They are antiferromagnetic at low temperatures. A collinear magnetic structure with the propagation vector k = |1/2,0,1/2|, stable between 1.5 K and the Néel point at 3.1 K is observed in HoPtSi. HoPtGe is paramagnetic at 1.8 K. A collinear magnetic order described by the wavevector k1 = |0,1/2,0| has been found in ErPtSi and ErPtGe. As the temperature rises this structure transforms in both compounds into a sine modulated one with the wavevector k2 = |0,ky,0|. The Néel points of ErPtSi and ErPtGe are 4.0 and 4.1 K respectively.

Stimulated Brillouin scattering of an electromagnetic wave in a strongly magnetized plasma

In a strongly magnetized nonisothermal plasma, a large amplitude electromagnetic wave propagating at an angle θ0 to a strong magnetic field undergoes stimulated Brillouin scattering off the ion mode. In an isothermal plasma the process goes over to stimulated Compton scattering with considerably lower growth rate. In both cases the growth rate is sensitive to the angle θ=(θ1−θ0), where θ0 is the angle of the pump wave vector k0 with the dc magnetic field, Bsẑ, and θ1 is the angle of the sideband wave vector k1 with Bsẑ.

Excitonic light-absorption and amplification bands in the presence of laser radiation

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k0. We assume that the detuning \(\tilde \Delta \) from resonance between the energy ħω ex (k0)+L0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at \(\tilde \Delta = 0\) the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when \(\tilde \Delta < 0\), instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at \(\tilde \Delta \approx 0\) and depend on the orientation of the vectors q and k0.

Magnetization of optically polarized gas atoms by an optical pulse train

The properties of the density matrix and the multipole moments arising in oriented and aligned atoms with zero nuclear spin through the interaction with strong resonant ultrashort pulses with wave vector k0 and circular or linear polarization have been found. Calculations have been made for the time-dependent light-induced magnetization μ(t′) of a gas of pre-oriented and prealigned atoms following the passage of a weak resonant elliptically polarized pulse with frequency ω and wave vector k collinear with k0. It is shown that for oriented atoms, μ(t′) is an even function of the detuning from resonance, ω-ωba, and can be split into two terms whose directions are a consequence of symmetry and are determined by the vectors k0 and k as well as by the direction of rotation of the electric fields corresponding to the pulses. For aligned atoms the vector μ(t′) is collinear with k, and the first term is an even function of ω-ωba. However, the second term is an odd function of ω-ωba and reverses direction when the sign of ω-ωba changes, as well as when the orientation of the axes of the polarization ellipse is changed. It is shown that if a series of weak linearly polarized pulses pass through the gas, the light-induced magnetization of the oriented and aligned gas atoms can be decomposed into three factors: the first determines the direction and is a consequence of the symmetry; the second (with the dimensions of magnetic moment) depends on the characteristics of the resonant transitions; and the third is a universal function of t′ and ω-ωba that does not depend on the underlying characteristics of the resonant transition. These vector factors and the universal functions are in principle different for oriented and aligned atoms.

Transmission of conduction electrons through a symmetric pair of delta-barriers or delta-wells embedded in a semiconductor or a metal

The transmission coefficient T(k0) is calculated for conduction electrons incident with a wave vector k0 upon a double barrier (double well) formed of two equal delta-barriers (of two equal delta-wells) embedded in a one-dimensional (1-D) semiconductor or in a 1-D metal. The stationary Schrödinger–Wannier equation E(−i∂/∂x)ψ+V(x)ψ=ℰψ is solved for V(x)=γ[δ(x+a/2)+δ(x−a/2)] (with real and time-independent parameters γ, a) and ℰ=E(k0)&amp;gt;0. (The interband transitions are neglected.) The operator E(−i∂/∂x) corresponds to a given (possibly nonquadratic) dispersion function E(k) of the conduction electrons [E(0)=0]. It is shown that T(k0) is an oscillating function reaching the maximum value [T(k0)→1] on an infinite set {K(j)} of values of k0. The shape of T(k0) depends on the shape of the dispersion function E(k) in a simple way: T(k0)=Tpar(mv(k0)/ℏ)) where Tpar(k0) means the transmission coefficient in the special case when the dispersion function is quadratic, Epar(k)=ℏ2k2/2m, and v(k)=(1/ℏ)∂E(k)/∂k is the group velocity due to E(k). [Here E(k) is taken as an increasing function.]

Double two-beam mixing in photorefractive materials

The mixing of two sets of mutually coherent beams, termed double two-beam mixing, is considered. At low modulation depth, combination gratings of the primaries are analyzed theoretically and show that the internal electric fields in photorefractive media also have cross components with wave vectors K1 ± K2 in addition to the primary components K1 and K2 and higher orders of 2K1 and 2K2, where K1 and K2 are wave vectors of two fringes. Each component is given in the form of an analytical solution, and the coupling behavior is studied for all relations between K1 and K2. The results show that the coupling behavior depends not only on the primary gratings but also on the combination grating K1 and K2 and the high-order grating 2K1 or 2K2. These features can be employed theoretically in phase-intensity transform and wavelength conversion.

Magnetic properties of DyAg2Si2 from magnetization, Mössbauer and neutron diffraction experiments

Magnetization, neutron diffraction and 161Dy Mössbauer measurements on DyAg2Si2 are reported. Below 11 K, DyAg2Si2 orders AF with a sine-modulated structure characterized by a wave vector k1 = (1, 0.328, 0). A second magnetic transition sets in at ∼ 5 K and the low-temperature magnetic structure is described by the coexistence of two wave vectors k1 (as above) and k2 = (1/2, 0, 1/2). The Dy moments are in the basal plane in both structures as expected from the positive sign of B20 (∼ 1K). Metamagnetic behaviour is inferred from the bulk magnetic data which showed that the full Dy moment (∼ 10μB) is reached in a two-step magnetization process.

Explicit results for the correlation length of the finite-sized spherical model of ferromagnetism

We report explicit results for the zero-field correlation length, xi (T;L), of a spherical-model ferromagnet confined to geometry Ld-d'* infinity d' (d>2, d'<or=2) and subjected to 'twisted' boundary conditions. In the region of first-order phase transition (T<Tc), xi under 'twisted' boundary conditions obeys the same scaling law as under periodic boundary conditions, though with a different amplitude. In the 'core' region (T approximately=Tc), the scaling behaviour changes radically as one moves from one set of boundary conditions to the other-affected greatly by the 'pinning' of the ground-state wavevector k0 of the system.

Characteristics of gyrotron scattering system for α particle diagnostics in TFTR (abstract)

In D-T plasmas, the understanding of the physics of confined α particles is extremely valuable for the future fusion plasma device. Among the various proposed α diagnostics, an X-mode collective Thomson scattering system employing a high-power gyrotron source (P≂200 kW, f=60 GHz, pulse length ≂0.5 s, and modulation frequency=10–25 kHz) is being designed for TFTR. The detailed description of the gyrotron source, transmission lines, optical designs, beam and viewing dump design, and receiver system will be presented in this paper. In particular, the test results of the beam and viewing dump indicate that the stray light can be reduced by 60 dB. The background emission level (∼20 eV) near 60-GHz range during high Q discharge may also be reduced with beam and viewing dump further. The optical system is designed to measure the radial profile of α particles and to orient the incident wavevector (k0) to test the electromagnetic effects of the scattered spectrum. Prior to the study of α physics in D-T plasmas, this scattering system will be used to measure not only a bulk ion temperature but also the scattered spectrum due to fast ions produced by NB and ICRF heating in TFTR. This work was supported by the U.S. Department of Energy Contract No. DE-AC02-76-CHO-3073.

Statistical mechanics of random bicontinuous phases

We consider a random wave description of bicontinuous microemulsions, where the structure is specified by a correlation length ξ and a preferred wave vector k0. The entropy of the system is calculated as the information content of a random field with an experimentally determined spectral distribution. Together with the elastic energy which has been previously derived by Teubner, we can minimise the free energy of the system and thus estimate the value of the elastic modulus κ of the film. For example, in water — toluene — SDS/butanol microemulsions the parameters ξ and k0 obtained from fits to the neutron scattering data lead to values for κ of about two units of kT.

TRANSFORMATION BETWEEN TAUPIN'S AND TAKAGI'S EQUATIONS AND THE PHYSICAL IMPLICATION

The transformation between Taupin's and Takagi's equations of X-ray dynamical theory in the case of distorted crystal is investigated. The physical implication of this transformation is presented. It is considered that the difference between these two quations is due to the different choice of the wave vector k0 but the function of these two equations is equivalent.

Nonlinear interaction of electrostatic waves in a magnetized Vlasov plasma

A new expression for the second-order dielectric function є(2) (K1,ω1, K2,ω2) is derived from the Vlasov–Poisson equations. The formula is also suitable for the calculation of this quantity in general situations when it is essential to use kinetic theory and when the wave vectors K1 and K2 have arbitrary directions with respect to each other as well as to the external magnetic field. We also consider two earlier formulae for this response function and discuss advantages and disadvantages of the different expressions.

Comments on absorption in Takagi–Taupin equations

The Takagi-Taupin theory of X-ray diffraction leaves an ambiguity in the choice of the wave vector inside the crystal. This holds also for its imaginary part which describes absorption. One consequence of this ambiguity is that the wave vector k0 inside the crystal need not always satisfy the continuity conditions for the tangential component of the wave vector at the entrance surface. But if the direction of the imaginary part is once fixed then it determines the particular manner of solution of the Takagi-Taupin equations. Thus a direction of the imaginary part of the wave vector in the crystal parallel to the reflecting net planes will in general ensure that the continuity condition is not satisfied; only a wave vector with an imaginary part perpendicular to the crystal surface can satisfy this condition.

Coherent and incoherent laser spectroscopy of spatial and temporal fluctuations

Abstract Information on spatial and temporal fluctuations of the transition frequency is theoretically shown to be obtained from transient four-wave mixing (FWM) at k =2 k 1 − k 2 or 2 k 2 − k 1 under coherent excitation by two laser pulses with wave vectors k1 and k2. The same information is available from the FWM by two CW incoherent laser beams k1 and k2 split off from a single source as a function of the relative delay time. In these cases, we can select a specified diagram for the FWM which depends on double sites. This makes it possible to observe the spatial fluctuations in addition to the temporal ones.

Three-wave mixing and light diffraction by transient light induced gratings for the study of fast relaxation processes

The action of two successive intense ultrashort coherent light pulses with different wave vectorsk1 andk2 on a nonlinear inhomogeneously broadened medium is considered. The resulting spatial and temporal polarization and saturation structure is calculated within a two level density matrix approach. Without use of perturbation theory, both the dynamic behaviour of the nonlinear medium under hole burning conditions and the temporal behaviour of the output pulse in the2k1-k2 direction generated by the polarization of the medium during and after the action of the second pulse are discussed. The diffraction of a third probe pulse by the saturation grating as well as by the polarization of the medium is calculated. Possibilities for measuring the longitudinal, transverse and inhomogeneous relaxation times are discussed.

Temperature shift of the maximum of neutron critical scattering in the second born approximation

AbstractTwo approximate forms of the cross‐section obtained in the second Born approximation are discussed with respect to the temperature shift of the main maximum of critically scattered neutrons in ferromagnets. The disscusion is given for the correlation of the Ornstein‐Zernike type and the correlation function reflecting the lattice symmetry of a simple cubic crystal. It is shown that the temperature shift depends on the momentum transfer vector q, the diffusion coefficient D, and the initial wave vector k0.