Two-dimensional light diffraction from thin opal films

This paper reports on experimental and theoretical investigations of light diffraction from thin films of synthetic opal. The diffraction patterns have been studied visually and recorded in different scattering geometries with the films illuminated with white unpolarized light. The diffraction pattern obtained with the film illuminated with a light beam along the [111] axis, which is normal to the film surface, has C ₆ symmetry and consists of six strong reflections arranged symmetrically with respect to the incident beam. This pattern becomes substantially more complicated when the film is illuminated by white light at an arbitrary angle to the [111] axis. An experimental study of the spectral response and angular relations of the diffraction patterns has established a fairly full pattern of transformation of diffraction reflections obtained under variation of the angle of light incidence on an opal film. The remarkably good matching of experimental and calculated data provides compelling evidence for light diffraction from thin opal films being two-dimensional.     

A New Method for the Measurement of Thickness in Single Crystals

A new method for thickness determination of single-crystal thin samples at exact zone axis orientation, based on pattern recognition in convergent beam electron diffraction (CBED), is presented. The method is especially well suited to materials with a large unit cell in zone axis directions where the reciprocal lattice is uniformly dense with diffraction points. The new method is based on comparison of a measured CBED zone axis pattern with a set of calculated ones. Its accuracy was estimated to be around 10% in the 5–100 nm thickness range as checked for garnets at the [111] zone orientation.     

Evolution of Optical Diffraction Patterns on Disordered Woodpile Photonic Structures

Using three-dimensional direct laser writing, ordered and disordered photonic woodpile structures have been produced. An ideal woodpile is formed by layers of parallel “logs” turned through 90° with respect to logs of the previous layer. The disorder was specified by a random deviation in the angle with respect to their parallel arrangement in each layer of the woodpile. The quality of samples was tested by scanning electron microscopy. The optical diffraction patterns were studied experimentally on microsamples with different degrees of disorder and structure periods. With an increase in the degree of the disorder, the diffraction patterns changed qualitatively with the preservation of the zero diffraction order and formation of a speckle field pattern by higher diffraction orders.

     

Anisotropy of elastic strains and specific features of the defect structure of <Emphasis Type="Italic">a</Emphasis>-plane GaN epitaxial films grown on <Emphasis Type="Italic">r</Emphasis>-plane sapphire

The structural state of GaN epitaxial layers grown on r-plane sapphire through metal-organic vapor phase epitaxy has been investigated using X-ray diffraction. The interplanar spacings in two directions in the (11$ \bar 2 $ \bar 2 0) plane of the interface and in the direction perpendicular to it, as well as the diffraction peaks in the ϑ and ϑ-2ϑ scan modes in the Bragg and Laue geometries, are measured on double- and triple-crystal diffractometers. The intensity distribution maps for asymmetric Bragg reflections are constructed for two azimuthal positions of the sample. An analysis of the data obtained has demonstrated that the elastic strain is anisotropic and that the X-ray diffraction pattern parallel to the interface plane is broadened. The layers are contracted in the [1$ \bar 1 $ \bar 1 00] direction and unstrained in the [0001] direction. The broadening of the Bragg reflections in the [1$ \bar 1 $ \bar 1 00] direction is considerably larger than that in the [0001] direction. It is shown using the Williamson-Hall plots for the Bragg and Laue reflections that these broadenings are not related to different degrees of mosaicity but are determined by the local dilatations and misorientations around defects. The data obtained are analyzed, and the conclusions regarding the dislocation structure of the samples are drawn.     

The diffraction of light at ultrasonic waves in acoustic resonators

A theoretical treatment is given of the diffraction of light by hypersonic waves excited in solid prismatic samples. For a fixed frequency, a set of modes exists in such a resonator. The modes differ in the spatial distribution of the field, which corresponds to a set of partial waves propagating over an entire solid angle. The diffraction occurs only at the partial waves which satisfy the Bragg condition and the diffraction pattern has the form of a circle consisting of a large number of points. An expression is found for the angular separation of adjacent points which correspond to different modes. It is shown experimentally that for the scattered light field in the far zone the diffraction patterns are similar to Shaefer-Bergmann patterns. Explanations are given for the shape and fine structure of these patterns. The structure of the diffracted light beams in the near zone is also studied and the frequency intervals between the excitation of the various resonator modes are measured. The experimental results are in qualitative agreement with the theory.     

面心立方晶体中生成孪晶或六角密堆相的电子衍射分析

用指数变换矩阵将面心立方晶体的晶带轴[uvw]变换成孪晶的[u^tv^tw^t]及六角密堆结构的[u′v′w′],在略去这些指数的公共系数后,如u^(t2)+v^(t2)+w^(t2)>u²+v²+w²或u′,v′≠3n而u′+v′=3n,则孪晶或六角密堆结构与面心立方晶体有完全相重的电子衍射谱。这种标定的不唯一性是广泛存在的。 关键词：     

A method for thin foil thickness determination by transmission electron microscopy

With the intention of determining the local thickness within a crystalline thin foil specimen, by means of transmission electron microscopy (TEM), a method previously proposed by Zuo and Shi [J.M. Zuo, Y.F. Shi, Microsc. Microanal. 7 (Suppl. 2) (2001) 224-225] was applied. Using the convergent beam technique, with the incident beam parallel to a zone axis with low indices, diffraction patterns were obtained for some aluminum alloys with low solute content. These patterns were contrasted with those obtained from simulations based on the dynamic theory with Bloch's waves formalism. The local thickness of the thin foil was then obtained by visually comparing the simulated patterns with the experimental one.Comparison of the proposed method with that based on the analysis of two-beam convergent beam patterns [P.M. Kelly, A. Jostsons, R.G. Blake, J.G. Napier, Phys. Stat. Solidi (a) 31 (1975) 771-780] and with that based on the ratio of intensity of the zero loss peak to the total intensity in an electron energy loss spectrum [R.F. Egerton, Electron Energy Loss Spectroscopy in the Electron Microscope, second ed., Plenum Press, New York, 1996] was carried out. A very good agreement between thicknesses determined using the different methods was found. The sensitivity of the method of Zuo et al. was found to be about 1 or 2 nm. The advantages and limitations of the different methods are discussed. The method of Zuo et al. can provide fast and reliable results and can be applied in all modern instruments.     

Models for an adsorbed layer and their evaluation by comparison of LEED and optical diffraction patterns: The system W(112)O2

The LEED patterns produced by the system W(112)-(2 × 1)-O at θ < 0.5 are known to consist of sharp integral and streaked half order features and have been previously interpreted in terms of separate islands of adsorbed oxygen out of phase with each other in the [111&#x0304;] direction. The diffraction properties of various structures of this type are examined theoretically and by optical diffraction methods using laser light. The results show that if the island model was correct integral order spots would be streaked, in addition to those of half order. An alternative model is therefore developed which correctly simulates the LEED patterns. On the basis of a number of assumptions regarding the formation of a mobile precursor layer, diffusion mechanism and diffusion distances within this layer, and attractive forces between adsorbed and diffusing species, a simple statistical method is used to follow the progress of individual molecules between gas phase and final adsorption site. The resulting adsorbate layer consists of out of phase regions, many of which are in contact even at low coverage; vacant sites are permitted at random positions within each region. Changes which have been observed in details of the LEED patterns at high (2 × 1) coverage are shown to be consistent with an adsorbate rearrangement leading to elimination of the antiphase boundaries.     

Multiple small-angle neutron scattering for an arbitrary value of the born parameter

Computer calculations are made of the intensity of multiple small-angle neutron scattering using the general Moliére formula [8] over a wide range of variation of the Born parameter, embracing the diffraction and refraction regimes, and a transition region between diffraction and reflection. A comparison is made with approximate formulas obtained earlier by Maleev et al. [9, 10] in the limiting cases of the Born parameter α ? 1 and α ? 1 for the diffraction and refraction regimes, respectively. It is shown that over a wide range of values of α the results of the calculations using the approximate and general formulas are the same. The theoretical conclusions were checked experimentally using data from measurements of small-angle neutron scattering for the domain structure of ferromagnets. Measurements were made of the neutron beam broadening for samples of different thickness and these were used to determine the effective domain sizes in pure iron and nickel exposed to thermal treatment and plastic deformation, and also in the Invar alloys Fe⁶⁵Ni³⁵and Fe³Pt. An analysis is made of the angular dependence of magnetic small-angle neutron scattering at the asymptote.     

基于原位X射线衍射技术的动态晶格响应测量方法研究

获取动态压缩条件下结构演化过程是冲击相变及其动力学机理研究最为关注的基础问题之一.对此,基于激光驱动瞬态X射线衍射技术,通过系列实验的物理状态关联和抽运-探测时序控制,实现了静态与动态晶格衍射信号的同时获取,消除了不同实验的装置结构和样品差异带来的测量误差,建立了一种基于原位X射线衍射技术的动态晶格响应测量方法.利用上述实验方法,成功实现了激光冲击加载下[111]单晶铁晶格压缩过程的原位测量,获取弹性及塑性响应的晶格压缩度与宏观雨贡纽测量结果完全符合,从晶格层面证实了超快激光加载下的高屈服强度(雨贡纽弹性极限值大于6 GPa),以及可能与晶向效应或加载率效应相关的相变迟滞现象(至终态压力23.9 GPa仍为体心立方结构),相关物理机制仍有待进一步研究.上述测量方法的建立为后续开展相变动力学机理研究提供了可行的技术途径和重要的参考价值.     

LEED studies of adsorption on vicinal copper surfaces

As a means for studying the role of atomic steps in adsorption phenomena LEED has been used to investigate the properties of vicinal copper surfaces. Single crystalline surfaces were cut at angles up to 20° from the (100) pole along [001] and [011&#x0304;] zones. The diffraction patterns obtained for the clean surfaces and after adsorption of oxygen, nitrogen ions, carbon and sulphur are described. The emphasis of the paper is on the method of interpretation of the geometry of the patterns, which may be done by straightforward kinematic analyses. In the case of nitrogen it is found that if the steps are widely separated the structure of the layer adsorbed on the terrace is the same as that on the low index surface. When the step spacing is small, and comparable with the crystalline parameter of the adsorbed layer, modifications occur which give rise to different superlattices which extend over several terraces. Adsorption of sulphur on 〈11〉 steps can produce a change in the periodicity of the adsorbed layer parallel to the step direction. The study of diffraction patterns for vicinal surfaces with different step spacings may provide an interesting technique for verifying the interpretation of patterns for low index surfaces.     

Powder diffraction from a continuous microjet of submicrometer protein crystals

Atomic‐resolution structures from small proteins have recently been determined from high‐quality powder diffraction patterns using a combination of stereochemical restraints and Rietveld refinement [Von Dreele (2007), J. Appl. Cryst. 40 , 133–143; Margiolaki et al. (2007), J. Am. Chem. Soc. 129 , 11865–11871]. While powder diffraction data have been obtained from batch samples of small crystal‐suspensions, which are exposed to X‐rays for long periods of time and undergo significant radiation damage, the proof‐of‐concept that protein powder diffraction data from nanocrystals of a membrane protein can be obtained using a continuous microjet is shown. This flow‐focusing aerojet has been developed to deliver a solution of hydrated protein nanocrystals to an X‐ray beam for diffraction analysis. This method requires neither the crushing of larger polycrystalline samples nor any techniques to avoid radiation damage such as cryocooling. Apparatus to record protein powder diffraction in this manner has been commissioned, and in this paper the first powder diffraction patterns from a membrane protein, photosystem I, with crystallite sizes of less than 500 nm are presented. These preliminary patterns show the lowest‐order reflections, which agree quantitatively with theoretical calculations of the powder profile. The results also serve to test our aerojet injector system, with future application to femtosecond diffraction in free‐electron X‐ray laser schemes, and for serial crystallography using a single‐file beam of aligned hydrated molecules.     

Modulated structure of the superconducting phases in Pb-modified Bi[sbnd]Sr[sbnd]Ca[sbnd]Cu[sbnd]O

Abstract

High resolution electron microscopy has shown that a modulated structure occurs in the Bi[sbnd]Sr[sbnd]Ca[sbnd]Cu[sbnd]O system. Electron diffraction and x-ray diffraction observations show that this modulation produces extra reflections. Diffraction patterns of the Pb-free material have superstructure reflections with wave vectors [0, 1/4.7, 1] and [0, ?1/4.7, 1]. These two waves vectors can generate all of the superstructure relections associated with each fundamental reflection. When PbO is added to the BSCCO system a new wave vector [0. 1/8.5, 0] is introduced. Observations show that within a single grain the two wave vectors coexist for a Pb and Bi ratio of about 0.25. This produces a non-uniform modulated structure which may be due to a superposition of the two wave vectors. The intensity of the [0, 1/4.7, 1] wave vector is substantially reduced in the Pb-modified material. The b' component of both wave vectors in incommensurate with the lattice period. The same superstructures occurs in both the low-T_c phase and the high-T_c phase.     

Formation of preferred orientations in aluminum, copper, and nickel irradiated with intense ion beams

The formation of preferred orientations in metal targets under exposure to intense ion beams was studied using x-ray diffraction. The formation of axial textures with [111] and [100] axes, observed in aluminum, copper, and nickel samples, depends on both the ion current density and thermal characteristics of the target material. In the case of rapid propagation of the thermal front to the material depth, the texture is apparently formed by the dislocation mechanism, which occurs in copper samples having the highest thermal conductivity. For aluminum and nickel, the most probable are recrystallization and regrowth mechanisms, respectively. An analysis of inverse pole figures showed that the main direction of heat sink in textured samples corresponds to the normal to the (111) atomic plane.     

Structural analysis of the SiO2/Si100 interface by means of photoelectron diffraction

The local environment of Si atoms at the interface between a thermally grown SiO2 film and Si(100) was studied by angle-scanned photoelectron diffraction. Experimental photoelectron diffraction patterns for each Si oxidation state were obtained from the results of least squares fitting on Si 2p core-level spectra. A comparison of the diffraction patterns with multiple-scattering calculations including an R-factor analysis was performed. An excellent agreement between experimental and simulated data was achieved within the proposed bridge-bonded interface model [Phys. Rev. Lett. 84, 4393 (2000)]].     

Structural analysis of oxygen segregated Nb(110) surface by photoelectron diffraction

The atomic structure of the Nb(110) surface with oxygen segregated from bulk by annealing at 1500K in UHV has been analyzed by electron and photoelectron diffraction techniques. The observed LEED patterns indicate the modulation of topmost Nb layer in [11ˉ0] direction. Relation of unit cells of substrate and overlayer was determined. The surface component in the Nb 3d photoelectron spectra has a chemical shift of 1.6eV corresponding to that of NbO. The thickness of Nb oxide overlayer is estimated to be about one or two atomic layers. The Nb 3d spectra collected at 4945 different directions are fitted with bulk and surface components. Photoelectron diffraction patterns from Nb atoms within overlayer as well as bulk are successfully extracted. Topmost oxygen atoms are found to be located at about 1.2 Å above the Nb plane. Presented at the X-th Symposium on Suface Physics, Prague, Czech Republic, July 11–15, 2005.     

Polarization-Independent Ultrasonic Modulation of Light in Gyrotropic Cubic Bismuth Germanate Crystals

An intermediate regime of light diffraction by ultrasound propagating along the [001] and [110] axes of a gyrotropic cubic bismuth germanate crystal is investigated. The possibility of polarization-independent light modulation in the intermediate regime of diffraction close to the Bragg regime is shown. The dependences of the diffraction efficiency on the incident light polarization azimuth at different ultrasonic wave intensities are given.     

Thermoelastic behaviour of hexagonal graphite-like boron nitride

Abstract

A synchrotron X-ray diffraction study on hexagonal graphite-like boron nitride (h-BN) was performed under high pressures and temperatures. From the measured P-V-Trelation for h-BN (with a three-dimensional ordering parameter P₃ = 0.9) in the temperature range from 298 to 1273 K and up to 6.7 GPa, the thermoelastic parameters are derived by fitting a modified high temperature Birch-Murnaghan equation of state. The results are: bulk modulus B₀[GPa] = 27.6-0.0081(T[K]-298) and its pressure derivative B¹ = 10.5 + 0.0016(T [K] - 298). These values are for samples with P₃ = 0.9 and are quite different for samples with different values of the order parameter. This parameter is shown to have a leading role in the determination of the thermoelastic properties of h-BN, which explains and reconciles the differences between previous results.     

POLYMERIZATION,MORPHOLOGY, AND CRYSTAL STRUCTURE OF POLY(p-BENZAMIDE)*

Isothermal polymerization of acetaminobenzoic acid at various temperatures in bulk and solution was monitored by acetic acid evolution. The polymerization took place initially in a homogeneous phase, but it soon changed to heterogeneous as the polymer precipitated from the melt or solution. The reaction course consisted of a short induction period, followed by a fast second-order reaction and a third slow, also second-order, reaction. The different polymerization rates in the second and third stage were due to polymer precipitation. The degree of polymerization of the resulting polymer was generally low, usually less than 5. The polymer was highly crystalline and prone to decarboxylation at temperatures above 300°C. Sample structure and morphology were characterized by various lamellar formations similar to those seen previously in many aromatic polyesters. Epitaxial solution polymerization/crystallization on mica resulted in three different morphologies, the most unique being shish kebab–type structures. Polybenzamide [poly(p-aminobenzoate)] is polymorphic; the most frequently seen hk0 electron diffraction patterns were similar to those from phase I of aromatic polyesters. Phase II of polybenzamide was seen only rarely. Simulation, using Cerius², suggested equal agreement with [001], [100], and fiber electron diffraction (ED) patterns and X-ray powder patterns for two different orthorhombic unit cells (a = 7.71, b = 5.35, c = 12.94 Å, ρ = 1.55 g/cm³); both have a parallel packing of adjacent molecules, but in one, successive phenyl rings along a given chain are parallel, while in the other they are twisted at ±30°. For both unit cells, neighboring molecules were displaced by ±0.14 Å along c to obtain better agreement with the observed patterns. The [010] patterns could distinguish between the two cells, but were not obtainable.

     

Photoelectron diffraction effects in XPS angular distributions from GaAs(110) and Ge(110) single crystals

Angular distribution measurements of XPS intensities have been made for various spectral lines from GaAs(110) and Ge(110) single-crystal surfaces. Observed angular distribution curves (ADC's) showed steep intensity variations and sharp peaks due to X-ray photoelectron diffraction (XPED) phenomena. The effects of the type of transition process (photoelectron or Auger), electron kinetic energy and crystal structure on the XPED patterns were examined. Considerably different ADC patterns were observed for high-energy photoelectrons and Auger electrons and for low-energy photoelectrons. ADC's for Ga 3d, As 3d and Ge 3d showed almost the same patterns for scans of the type [110] → [100] → [1$\text{1}$0], but they showed substantially different patterns for [110] → [11$\text{1}$] → [00$\text{1}$] scans. These features correspond well with the structural characteristics of GaAs and Ge crystals. A discussion of the applicability of XPS angular distribution measurements to the geometric analysis of crystal surfaces is presented.