Characteristics of phonon scattering in electron diffraction by a vibrating crystal lattice

In a departure from the generally accepted approach using rigid-body potentials, the diffraction of electrons by a deformation (compliant) potential is investigated, where the charge distribution in the crystal is treated as a continuous medium and its elastic deformability is taken into account. The deformability property in the presence of thermal “broadening” of the lattice planes in a metal leads to discontinuities at the boundaries of the Brillouin zone in the electron-phonon scattering spectrum and to the partial suppression of such scattering in the higher zones (or enhancement in the first Brillouin zone). Fiz. Tverd. Tela (St. Petersburg) 39, 18–22 (January 1997)     

X-ray diffraction in a crystal with a linear lattice parameter variation

The dynamical X-ray diffraction in a crystal with a linear lattice parameter variation (LLPV) and its applications to the X-ray diffractional investigations of thin solid state films are studied. For the interpretation of the reflection coefficients angular dependence is the Fresnel layers construction developed. Some particular cases of the general diffractional problem solutions for the crystals with LLPV are treated.     

利用高分辨X射线衍射研究磷酸二氢钾晶体晶格应变应力

采用高分辨X射线衍射技术对大尺寸磷酸二氢钾(KDP)晶体的晶格应变进行了测量,并定量分析了其晶格应力.探讨出KDP晶体容易沿着[001]方向发生开裂,与实际工作中的开裂现象相符合;进一步归纳总结了晶体生长过程中引入内应力而导致晶体开裂的主要因素.研究结果为提出相应的晶体防裂措施提供了重要的理论基础.     

Offline estimation of 2D crystal lattice parameters by processing the electron diffraction image

Electron diffraction provides useful information about the internal composition of materials and has been in the use of material scientists for more than fifty years. In order to extract useful information from offline diffraction images, they are manually analyzed by using some photometric technique. Manual analysis is however a cumbersome, laborious and difficult task. To reduce the labors of material scientists one can employ image processing techniques to perform automated analysis, due to the well established popularity and clear evidence of widely used image processing techniques. In this work an image processing technique is being proposed for the extraction of 2D unit cell information from diffraction images on one hand and finding the 2D point group contained by the lattices on the other. The technique employs a morphological shrinking operation to find the center of each spot in the underlying preprocessed diffraction image. This is followed by the extraction of eight points with reference to the spot produced by the transmitted electron beam. The resultant nine points, i.e. the extracted eight plus the reference spot generated by the transmitted electron beam, are then subjected to symmetry operations, rotation symmetry and mirror symmetry, in polar coordinate system, to classify the point group of the lattice produced by the electron diffraction. One of the difficult task, even in manual analysis, is to ascertain the exact spot where the transmitted electron beam hit the sample at the time of realization of the image. This has been accurately and intuitively done by employing the notion that the transmitted spot must have greater number of pixels, with the highest gray value, among the diffracted spots. The proposed strategy has been applied to a sample set of various images and the results shows that the technique is efficient in determining the unit cell in 2D and classify the point group with good accuracy.     

Feature of kinematic diffraction of nonmonochromatic divergent X-ray beams in a crystal with a periodically strained lattice

Coherent scattering of a nonmonochromatic divergent beam of X-ray quanta in a crystal excited by an acoustic wave is described using a kinematic approach. The possibility of manifestation of a peculiar effect of amplification of the diffracted X-ray beam by the acoustic wave is predicted using this approach.     

中子衍射法研究单晶镍基高温合金热机械疲劳引起的应力和晶格错配

采用中子衍射法对热机械疲劳后的单晶镍基高温合金样品内部中心点进行了实验测量,数据处理采用了双相叠加峰和单峰分析两种方法,计算得到了样品材料的宏观等效应力、应力偏量、γ相和γ′相的等效应力和晶格错配度等.实验结果表明,两种分析方法得到的宏观等效应力基本一致.在热机械疲劳循环100周出现最大宏观等效应力和应力偏量,此时位错等微缺陷达到饱和,偏离中心点处γ′相应力减小显著;在热机械疲劳开始阶段负错配度明显减小,随循环周次增多基体塑性应变累积又使负错配度以每次81×10^-6的速度逐渐线形增大. 关键词： 中子衍射 单晶高温合金 等效应力 应力偏量     

Discrete diffraction in a cascade-induced anisotropic lattice

The features of anisotropic discrete diffraction in a cascade-induced lattice formed by two crossed pump waves in a quadratically nonlinear medium have been studied. The transition from the diffraction of a signal beam in free space to discrete diffraction with the further capture in a waveguide in a defocusing lattice by the increasing of the pump wave intensity has been traced.     

Discrete diffraction on a cascade-induced periodic lattice

A method for cascade generation of a periodic lattice in a medium with quadratic nonlinearity is proposed. Such a lattice is induced as a result of interference of two or four crossed fundamental-frequency waves. Numerical simulation of the discrete diffraction of a signal beam coupled to one of the lattice waveguides is performed. With an increase in the modulation depth of the refractive index, the signal wave is trapped in the waveguide.     

Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice

We investigate the dynamics of a particle on a periodic lattice, coupled to phonons with ohmic dissipation. At T = 0 a symmetry breaking appears, which corresponds to a transition between a localized and a delocalized regime. For T > 0 we recover a diffusive motion for which the diffusion coefficient is computed.     

Neutron forward diffraction by single crystal prisms

We have derived analytic expressions for the deflection as well as transmitted fraction of monochromatic neutrons forward diffracted by a single crystal prism. In the vicinity of a Bragg reflection, the neutron deflection deviates sharply from that for an amorphous prism, exhibiting three orders of magnitude greater sensitivity to the incidence angle. We have measured the variation of neutron deflection and transmission across a Bragg reflection, for several single crystal prisms. The results agree well with theory.      

Depolarization of a neutron beam in Laue diffraction by a noncentrosymmetric crystal

The depolarization of a neutron beam executing Laue diffraction in a thick (～3.5 cm) noncentrosymmetric α-quartz crystal is observed. This effect was predicted by us earlier and suggested for measuring the electric dipole moment (EDM) of a neutron. The effect is due to an interaction of the magnetic moment of a moving neutron with a strong crystal electric field, as a result of which the neutron spin rotates in opposite directions for waves of two types excited in the crystal. The effect is studied for neutron diffraction by a system of crystallographic (110) planes at Bragg angles close to π/2, up to 87°. It is shown that, for a crystal of thickness L=3.5 cm, a direct beam initially polarized along the reciprocal lattice vector becomes depolarized upon diffraction, irrespective of the value of Bragg angle, whereas the beam polarized perpendicular to the diffraction plane retains its polarization. The Eτ value determining the sensitivity of the method to EDM is experimentally estimated.     

Morphological instabilities of a thin film on a Penrose lattice: A Monte Carlo study

We computed by a Monte Carlo method derived from the solid on solid model, the thermal relaxation of a polycrystalline thin film deposited on a Penrose lattice. The thin film was modeled by a 2-dimensional array of elementary domains, which have each a given height. During the Monte Carlo process, the height of each of these elementary domains is allowed to change as well as their crystallographic orientation. After equilibrium is reached at a given numerical temperature, all elementary domains have changed their orientation into the same one and small islands appear, preferentially on the domains of the Penrose lattice located in the center of heptagons. This method is a numerical approach to study the influence of the substrate and its defects on the islanding process of polycrystalline films.     

Babinet's principle in the Fraunhofer diffraction by a finite thin wire

The scattered waves by a thin finite wire are evaluated by using the Rayleigh-Sommerfeld integral in the Fraunhofer approximation. The scattered fields by the complementary thin wire are also obtained with the aid of the Babinet's principle. The scattering integrals are evaluated directly. It is shown that Babinet's principle holds excellently for this problem. The scattered fields are examined numerically.     

Waves trapped by a thin curved screen in a waveguide with rigid walls

The conditions are derived for the existence of waves trapped by a symmetrical thin rigid screen in a two-dimensional waveguide with rigid walls. Asymptomatic formulas are found for the corresponding eigenvalues, while the asymptomatic structures differ from those pertaining to the eigenvalues of problems in bounded domains. Various generalizations of the results are discussed, and open questions are formulated.     

Generalization of a nonstandard approach in dynamic diffraction theory to the case of deformed crystal

A nonstandard X-ray diffraction theory for crystals taking lattice deformation into account is generalized in this paper. The vector of atomic-plane displacement is introduced in a model of crystal polarizability in analogy with the Takagi generalized dynamic theory. The solution of the wave equation is sought using the technique of expanding the field amplitude and vector operators in terms of the Fourier polarizability component χ _H in accordance with the multiscale method. It is shown that, in the general case, taking lattice distortions into account requires consideration of various characteristic spatial regions for the diffraction equation. This corresponds wholly to the basic idea of the multiscale method. The particular case of the displacement field depending on a single scale is considered. If a relative change in deformation occurs at a length on the order of the extinction length in this case, then equations generalizing the Takagi equations to the case of arbitrary diffraction geometry are obtained as a result.