Study of the influence of higher—order Laue zones on the exit wavefunction

Based on an analytical expression of electron dynamical diffraction derived recently,the exit wavefunctions of nonperiodic samples have been calculated.The results have shown that the amplitude and phase obtained by the analytical expression were in good agreement with those obtained using the multi-slice method.Besides,the influence of the higher-order Laue zone on the wavefunction for different sample thickness was studied in detail and the results showed that the exit wavefunction is dominated by the zero-order Laue zone.When the sample is very thin,the influence of the higher-order Laue zone should be considered.     

Half analytical method with application to the high order Laue zone effects in monoclinic and triclinic crystals

The simulation of the high order Laue zone (HOLZ) diffractions of monoclinic and triclinic crystals is a very complicated problem. The conventional multislice (MS) method suffers from the problem of infinity of the phase grating size. To avoid the difficulty of the infinity, Chen et al. arranged the phase grating plane along the ab plane of the crystal lattice. In this paper we introduce a new method which allows the incident and exit wavefunction planes perpendicular to the zone axis without the difficulty of infinity. We name the method half analytical method. The results calculated by half analytical method are in good agreement with those calculated by the conventional MS method.     

用差矢法标定高级劳厄点

对于电子衍射谱的高级劳厄带斑点标定,提出一种新的方法。直接通过测定亮衍射斑的点间距和向量合成来标定高级劳厄带第一个衍射斑的指数,进一步导出最靠近入射斑和其它的斑点指数。 关键词：     

TEM image contrast from antiphase domains in GaAs: Ge(001) grown by MBE

Antiphase domains occur in thin GaAs epitaxial films grown on Ge(001) by molecular beam epitaxy. The domains have been imaged by transmission electron microscopy using 200-type reflections in dark field. The carefully chosen imaging conditions with convergent illumination ensure that doubly diffracted beams from a pair of first order Laue zone discs contribute to the singly diffracted 200-type beams. The three Bragg reflections may add in or out of phase to give domains in either light or dark contrast depending on their polarity.     

热处理引起3C-ZnS结构转变的X-射线衍射分析

为了论证层错是硫化锌晶体中交流电致发光的一个必要条件,我们把3C-ZnS单晶体在1100℃热处理后引入了层错.同时,我们对热处理前后的结构,用劳埃背反射法和文献[8、13]推导的公式进行了分析.结果表明,沿3C-结构<111>四个等价方向都可以产生无序、孪晶和2H-结构,而且当热处理时间足够长时,结构转变趋向于一个<111>方向.这些实验结果,在有关的文献中尚未见到.     

Nanometer linear focusing of hard x rays by a multilayer Laue lens

We report on a type of linear zone plate for nanometer-scale focusing of hard x rays, a multilayer Laue lens (MLL), produced by sectioning a multilayer and illuminating it in Laue diffraction geometry. Because of its large optical depth, a MLL spans the diffraction regimes applicable to a thin Fresnel zone plate and a crystal. Coupled wave theory calculations indicate that focusing to 5 nm or smaller with high efficiency should be possible. Partial MLL structures with outermost zone widths as small as 10 nm have been fabricated and tested with 19.5 keV synchrotron radiation. Focal sizes as small as 30 nm with efficiencies up to 44% are measured.     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

Emulation of the evolution of a Bose–Einstein condensate in a time-dependent harmonic trap

We emulate the ground state of a Bose–Einstein condensate in a time-dependent isotropic harmonic trap by constructing analytic simulacra of a transformed wavefunction in the regions around the origin and far from the origin. This transformed wavefunction is obtained through a pseudoconformal transformation and is a function of new spatial and temporal variables, while the simulacra are generalisations of asymptotic solutions of the nonlinear Schrödinger equation and they are matched by requiring continuity not only of the wavefunction and of its slope, but of its curvature as well. The resulting piecewise analytic simulacra coincide almost perfectly with the numerically obtained solutions of the time-dependent nonlinear Schrödinger equation and constitute an easy and accurate analytic method for describing fully the condensate ground state.     

Magnetic properties of Y2Fe15Cr2 single crystal

A Y₂Fe₁₅Cr₂ single crystal with the Th₂Ni₁₇-type structure has been prepared by the Czochralski method and investigated by means of Laue back-reflection, metallographic observation, X-ray diffraction, the singular point detection technique and magnetic measurements. A magnetohistory effect has been observed at a low temperature. Magnetization curves have been measured along the easy and hard directions in fields up to 6.5 T. The saturation magnetization and magnetocrystalline anisotropy field decrease with increasing temperature. The experimental magnetocrystalline anisotropy constant is in good agreement with the calculation results on first approximation.     

Fast and reliable evaluation of lattice distortions from convergent-beam electron diffraction patterns

A manual method for higher order Laue zone (HOLZ) line detection with an improved effective high-voltage correction for fast and reliable evaluation of local lattice distortions from convergent-beam electron diffraction (CBED) is presented. It is compared with a high-precision Hough transform method with a dynamic correction for each individual HOLZ line used by Krämer and Mayer. Both methods are applied to unfiltered and filtered experimental CBED patterns. As an example, the local lattice distortions in the γ ? γ′ raft-like structure of a creep-deformed single-crystal nickel-based superalloy (CMSX-6) were measured. The lattice distortions obtained from both methods were analysed and showed good agreement. As a by-product, it was noted that specimen cooling enhanced the contrast of CBED patterns to the extent that the quality of CBED patterns taken at low temperatures without energy filtering was found to be qualitatively similar to that of CBED patterns taken at room temperature with energy filtering.     

X-ray point- and line-projection microscopy and diffraction

A theoretical framework is presented to treat both imaging and diffraction experiments performed with point-focus and line-focus X-ray sources, with particular emphasis on two-dimensional and planar X-ray waveguides. In particular, point-projection and line-projection microscopy has been approached within the Huygens-Fresnel formalism; point-projection and line-projection diffraction, such as spatially-resolved Bragg/Laue diffraction of crystalline samples in a regime of dynamical scattering, has been treated both by means of the Huygens-Fresnel formalism and of the Takagi-Taupin dynamical theory. Both in point- and line- projection geometry, simply rotating the investigated crystalline samples, it is possible to switch from Fresnel self-imaging to Bragg/Laue diffraction conditions. This means to image, within the same experiment, either morphological features, with a sub-micrometric resolution, out of the exact diffraction condition, or the structure order on an atomic scale if placing the sample in diffraction.     

Positron-impact ionisation of atomic hydrogen in the presence of a bichromatic laser field

The positron impact-ionisation of atomic hydrogen in the presence of a linearly polarised bichromatic field is investigated in the first Born approximation.The field is composed of a fundamental frequency and its second harmonic.The state of positron in the field is described by the Volkov wavefunction,and the continuum state of the ejected electron is described by the Coulomb-Volkov wavefunction.The dressed ground state of target is a first order time-dependent perturbative wavefunction.The triple differential cross sections and their dependencies on laser field parameters are discussed and compared with the results modified by a monochromatic field.Numerical results show that the coherent phase control is significant and the laser-assisted ionisation cross sections caused by positron and electron are different.     

Analysis of large angle p-d elastic scattering: 100–400 MeV

An analysis is presented of large angle proton-deuteron elastic scattering experiments at deuteron energies of 291, 362 and 433 MeV and proton energies of 140 and 316 MeVon the basis of the Kerman-Kisslinger (KK) model (first order). Further analysis is made using the KK model with second order corrections included. The object of the analysis is to determine quantitatively the sensitivity of large angle scattering to the D-state probability (P_D) in the deuteron. It is found that the KK model (first order and also second order corrections included) is not very successful in fitting the data at those energies when used with existing wavefunctions obtained from phenomenological potentials. A value of 6.7% for P_D gives the best fit when the model is used with the modified Moravcsik analytic fit to the Gartenhaus S-state wavefunction (the third approximation). The incoherent contributions of first and second order non-exchange processes are roughly estimated and found to be negligible. An investigation of the ambiguities in the S-state part of the deuteron wavefunction is also presented.     

Accuracy of stress measurement by Laue microdiffraction (Laue‐DIC method): the influence of image noise,calibration errors and spot number

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so‐called Laue‐DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue‐DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.     

Brillouin zone unfolding of complex bands in a nearest neighbour tight binding scheme

Complex bands k(⊥)(E) in a semiconductor crystal, along a general direction n, can be computed by casting Schr?dinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary n. It is, however, possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. In this paper, we present a unified method to unfold real and complex bands. Our method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy E.     

The magnesium ramsey interferometer: Applications and prospects

In this paper it will be shown that an atom interferometer, based on the coherent splitting of the atomic wavefunction by four travelling waves (Ramsey interferometer), may be explained by a purely mechanical interpretation. As our first application of this Ramsey interferometer we have measured the phase shifts respectively optical length changes in a magnesium atomic beam caused by the acceleration of the partial atomic wave in one arm of the interferometer. This acceleration was achieved by the dipole force exerted by an off-resonant crossing laser beam which interacted with the ground state part of the wavefunction only. Further applications of this interferometer and improvements due to laser cooling will be discussed.     

多层膜劳厄透镜对8keV X射线的聚焦性能模拟研究

基于多层膜技术的劳厄(Laue)透镜能实现硬X射线纳米级聚焦,在X射线微纳分析领域具有重要的应用前景.基于衍射动力学理论,分析了X射线在多层膜劳厄透镜中的传播,计算了不同结构的多层膜劳厄透镜对8 keVX射线的聚焦性能.结果表明,最外层厚度为5 nm的倾斜多层膜劳厄透镜可获得5.7 nm的聚焦光斑和26%的平均衍射效率...     

Topological transition by dielectric control of exciton wavefunction in thin nanotube structure

Dielectric control of the topology of an exciton wavefunction is proposed and investigated theoretically. As we have shown in a previous paper, we can change the topology of an exciton wavefunction in a nanotube structure by controlling the length and radius of the nanotube. This nature yields a new device which utilizes the topology of an exciton wavefunction, however, its control via the structural parameters does not suit it to device applications. We found that the in-situ control can be achieved by changing the ambient dielectric constants of the nanotube structure and we calculated the transition condition of the topology of an exciton wavefunction.