Bunch evolution study in optimization of MeV ultrafast electron diffraction

Megaelectronvolt ultrafast electron diffraction (UED) is a promising detection tool for ultrafast processes. The quality of diffraction image is determined by the transverse evolution of the probe bunch. In this paper, we study the contributing terms of the emittance and space charge effects to the bunch evolution in the MeV UED scheme, employing a mean-field model with an ellipsoidal distribution as well as particle tracking simulation. The small transverse dimension of the drive laser is found to be critical to improve the reciprocal resolution, exploiting both smaller emittance and larger transverse bunch size before the solenoid. The degradation of the reciprocal spatial resolution caused by the space charge effects should be carefully controlled.     

Nanometer-scale resolution of strain and interdiffusion in self-assembled InAs/GaAs quantum dots

Tomographic nanometer-scale images of self-assembled InAs/GaAs quantum dots have been obtained from surface-sensitive x-ray diffraction. Based on the three-dimensional intensity mapping of selected regions in reciprocal space, the method yields the shape of the dots along with the lattice parameter distribution and the vertical interdiffusion profile on a subnanometer scale. The material composition is found to vary continuously from GaAs at the base of the dot to InAs at the top.     

X-ray resonant powder diffraction

X-ray resonant diffraction can be applied in structural chemistry studies on powder samples. It enables an important limitation of powder diffraction to be overcome. This limitation is related to the low ability of powder diffraction to differentiate elements with close atomic numbers when they occupy the same or close crystallographic sites (mixed occupancy case) and also to discriminate cations with different valence states in different sites. However the resonant effect usually has a second order influence on the measured intensity. As a consequence, the efficiency of this method directly implies the need for excellent quality data collection and has generally been better assessed on elements present in single phase powder samples. In recent years, instrumental developments have been made in synchrotron radiation facilities which allow easier use of resonant powder diffraction for site-specific contrast and valence i.e. oxidation state analyses. Moreover, resonant contrast diffraction tools also have been proposed for better visualization of the anomalous effect both in direct and reciprocal space by using differences between electron density maps or diffraction patterns. Finally the potentialities of this technique for de novo structure solution on macromolecular systems are mentioned.     

A method to predict the orientation relationship,interface planes and morphology between a crystalline precipitate and matrix. Part I. Approach

A model based on the near-coincidence of diffraction intensity weighted reciprocal-lattice spots is proposed to determine preferred orientation relationships between two crystalline phases. The preferred orientation is found by minimizing the three-dimensional lattice mismatch, i.e. by maximizing the total overlapping intensity, between the diffraction spots of two crystals. The procedure is biased towards matching reciprocal lattice sites with high structure-factor values, which is physically equivalent to matching planes of high atomic density. In contrast to previous reciprocal-lattice models, including the diffraction intensity in the present method makes it sensitive to the types of atoms in (chemistry of) crystals. The preferred orientation relationship is then used to identify the orientations of low-energy interfaces using a Δ g approach. A Voronoi (or Wigner–Seitz) construction based on the Δ g values is further used to qualitatively estimate the equilibrium shape of the precipitate in the matrix. The model was tested by performing calculations on hypothetical Au–Cu crystals to investigate the effects of chemistry and fcc truncated-octahedral precipitates in fcc matrices in Al–Ag, Al–Xe and Al–Pb alloys. The present model has the ability to sample the entire orientation space and rationalize and compare alternate orientation relationships in a reasonable timeframe, thereby providing insight into the formation of precipitate orientation relationships and shapes.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

Bragg diffraction of surface magnetostatic waves from magnetic lattices

We present a theoretical and experimental investigation of Bragg scattering of surface magnetostatic waves (SMSW) by a time-independent, spatially periodic magnetic field when the wave orientation is arbitrary with respect to the magnetization field. In the theoretical section the theory of single-mode Bragg diffraction is generalized to the case of waves with arbitrary dispersion propagating through an anisotropic medium. The calculated results are, on the whole, supported by experimental measurements on SMSW. We demonstrate that a geometry which in isotropic media leads to a sinusoidal distribution of diffraction order amplitudes as a function of penetration into the differing lattice, can lead to a nearly exponential distribution of such amplitudes in anisotropic media. The anisotropy of the interaction between SMSW and the magnetic diffracting lattice is manifested by anomalously high scattering efficiencies for certain cases of relative orientation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 76–85, November, 1988.     

Whole diffraction pattern-fitting of polycrystalline fcc materials based on microstructure

A method is proposed for modelling the complete diffraction pattern of fcc polycrystalline materials. The algorithm permits a simultaneous refinement of several parameters related to microstructure and lattice defects responsible for line broadening effects. Linear (dislocations) and planar (stacking faults) defects are considered in detail, together with the effect of size and shape of coherent scattering domains (crystallites). Experimentally observed profiles are modelled by Voigt functions, whose parameters are connected with those describing the dislocation field (dislocation density, outer cut-off radius, average contrast factor), twin and deformation fault probabilities, and domain size, also considering the effect of a symmetrical instrumental profile. Domain shape is assumed spherical, with a lognormal distribution of diameters; however, the approach can be generalised to different shapes and size distributions. The proposed algorithm can be extended to other crystalline structures, and can be used within the Rietveld method or as a Whole Powder Pattern Fitting (WPPF), as in the present work. Received 16 May 2000     

Surface-plasmon-polariton assisted diffraction in periodic subwavelength holes of metal films with reduced interplane coupling

Metal films grown on an Si wafer perforated with a periodic array of subwavelength holes have been fabricated and anomalous enhanced transmission in the midinfrared regime has been observed. High order transmission peaks up to Si(2,2) are clearly revealed due to the large dielectric constant contrast of the dielectrics at the opposite interfaces. The Si(1,1) peak splits at oblique incidence both in TE and TM polarization, which confirms that anomalous enhanced transmission is a surface-plasmon-polariton (SPP) assisted diffraction phenomenon. Theoretical transmission spectra agree excellently with the experimental results and confirm the role of SPP diffraction by the lattice.     

Studium von Einzelversetzungen in nahezu idealen Kristallen mit einer Röntgenmethode

The integrated intensities of X-ray diffraction for theLaue and theBragg case have been calculated for both an ideal and a mosaic crystal. The ratio of both intensities is thought to be a measure for the contrast of topographic X-ray work. Concerning to the Laue case, in thin crystals the distorted regions around dislocations have a higher diffraction intensity than the undistorted regions. In thick crystals the contrast is reverted. That is the case of anomalous transmission in ideal crystals. In the region of anomalous transparency some experiments have been made with slices of germanium crystals containing only few dislocations. Topographic pictures have been made by a simple method which is described. Secondary effects have been observed besides the normal contrast effects between distorted and undistorted regions. They can be explained assuming that the direction of propagation of the transmitting wave field is shifted in regions containing a long range lattice distorsion.     

Observation of the magnetic phase transition in PrCu2 below 58 mK by neutron diffraction

A neutron diffraction experiment on the coupled electron-nuclear compound PrCu₂ has been carried out at mili-Kelvin temperatures. Below 58 mK, several magnetic diffraction peaks have been observed at positions in the reciprocal space represented by G±τ, where G is the reciprocal lattice vector and $\text{τ}\text{= 0.24a}{}^1\text{±0.68c}{}^1$. The peak intensity of one of these diffraction peaks has also been measured as a function of temperature down to 10.5 mK.     

The reciprocal lattice construction from axial coordinates of diffraction spots on Weissenberg photographs

An alternative method for constructing of the reciprocal lattice planes from Weissenberg photograph is presented. The radial coordinates of the diffraction spots necessary for the reciprocal lattice plane construction in current method are not introduced into this procedure. The method takes advantage of the coupling of the rotational and translatory motion of the Weissenberg camera. Both the magnitudes and the mutual orientations of the reciprocal lattice vectors can be then determined solely from the measured axial coordinates of the diffraction spots on the Weissenberg photographs. The knowledge of the camera radius as well as the non-uniformity of the radial adhesion of the film to the camera are thus fairly eliminated. The method was successfully applied to the interpretation of Weissenberg photographs of small fragments of lunar olivines from the Sea of Fertility (Luna 16 sample).     

Diamond-anvil cell for radial x-ray diffraction

We have designed a new diamond-anvil cell capable of radial x-ray diffraction to pressures of a few hundred GPa. The diffraction geometry allows access to multiple angles of Ψ, which is the angle between each reciprocal lattice vector g(hkl) and the compression axis of the cell. At the 'magic angle', Ψ≈54.7°, the effects of deviatoric stresses on the interplanar spacings, d(hkl), are significantly reduced. Because the systematic errors, which are different for each d(hkl), are significantly reduced, the crystal structures and the derived equations of state can be determined reliably. At other values of Ψ, the effects of deviatoric stresses on the diffraction pattern could eventually be used to determine elastic constants.     

Simulations of X‐ray diffraction of shock‐compressed single‐crystal tantalum with synchrotron undulator sources

Polychromatic synchrotron undulator X‐ray sources are useful for ultrafast single‐crystal diffraction under shock compression. Here, simulations of X‐ray diffraction of shock‐compressed single‐crystal tantalum with realistic undulator sources are reported, based on large‐scale molecular dynamics simulations. Purely elastic deformation, elastic–plastic two‐wave structure, and severe plastic deformation under different impact velocities are explored, as well as an edge release case. Transmission‐mode diffraction simulations consider crystallographic orientation, loading direction, incident beam direction, X‐ray spectrum bandwidth and realistic detector size. Diffraction patterns and reciprocal space nodes are obtained from atomic configurations for different loading (elastic and plastic) and detection conditions, and interpretation of the diffraction patterns is discussed.     

约化胞与电子衍射谱的标定

对应于14种布喇菲点阵有44种约化胞,不但约化矢的选法是唯一的,而且可以根据约化矢标量积矩阵(a·a b·b c·c b·c c·a a·b)的不同形式,确定布喇菲点阵类型。在晶体点阵已知的情况下,从点阵参数计算出倒易点阵中的平面约化胞,并与试验得到的电子衍射谱对比以标定衍射斑点的指数。在晶体点阵未知的情况下,从已知转角的两个电子衍射谱中选三个接近中心的衍射斑点,相当于三个低指数倒易矢量。由它们构成倒易点阵的一个初基胞,变换成正点阵的初基胞后,经过约化得出约化胞和相应的布喇菲单胞的类型和参数,同时标定衍射斑点的指数。这些标定计算已编成电子计算机程序,可以用来直接确定晶体点阵类型和进行物相分析。     

GAPD: a GPU‐accelerated atom‐based polychromatic diffraction simulation code

GAPD, a graphics‐processing‐unit (GPU)‐accelerated atom‐based polychromatic diffraction simulation code for direct, kinematics‐based, simulations of X‐ray/electron diffraction of large‐scale atomic systems with mono‐/polychromatic beams and arbitrary plane detector geometries, is presented. This code implements GPU parallel computation via both real‐ and reciprocal‐space decompositions. With GAPD, direct simulations are performed of the reciprocal lattice node of ultralarge systems (～5 billion atoms) and diffraction patterns of single‐crystal and polycrystalline configurations with mono‐ and polychromatic X‐ray beams (including synchrotron undulator sources), and validation, benchmark and application cases are presented.     

Bragg diffraction of light in synthetic opals

Three-dimensional light diffraction from the crystal structure, formed by closely packed a-SiO₂ spheres of submicron size, of samples of synthetic opals was visualized. The diffraction pattern of a monochromatic light beam was established to consist of a series of strong maxima whose number and angular position depend on the wavelength and mutual orientation of the incident beam and the crystallographic planes of the sample. The diffraction patterns were studied under oblique incidence on the (111) growth surface of the sample and with light propagated in the (111) plane in various directions perpendicular to the sample growth axis. The spectral and angular relations of diffracted intensity were studied in considerable detail in both scattering geometries. The experimental data are interpreted in terms of a model according to which the major contribution to the observed patterns is due to Bragg diffraction of light from (111)-type closely packed layers of the face-centered cubic opal lattice. The model takes into account the disorder in the alternation of the (111) layers along the sample growth axis; this disorder gives rise, in particular, to twinning of the fcc opal lattice.     

Bunch evolution study in optimization of Me V ultrafast electron diffraction

Megaelectronvolt ultrafast electron diffraction（UED） is a promising detection tool for ultrafast processes.The quality of diffraction image is determined by the transverse evolution of the probe bunch. In this paper, we study the contributing terms of the emittance and space charge effects to the bunch evolution in the MeV UED scheme, employing a mean-field model with an ellipsoidal distribution as well as particle tracking simulation. The small transverse dimension of the drive laser is found to be critical to improve the reciprocal resolution, exploiting both smaller emittance and larger transverse bunch size before the solenoid. The degradation of the reciprocal spatial resolution caused by the space charge effects should be carefully controlled.     

Structure of metal nanowires in nanoporous alumina membranes studied by EXAFS and X-ray diffraction

The structure of nanowires of different metals grown within nanoporous alumina membranes has been studied by EXAFS, WAXS and high energy X-ray diffraction. Nanowires of gold, silver, copper and iron adopt the lattice structure and bond distances of the bulk metals. Cobalt nanowires on the other hand were composed of a mixture of hcp phase, stable at room temperature, and fcc phase, which in bulk cobalt is normally stable only at high temperatures, in a ratio depending on the pore size. The nanowires are non-continuous but are made of nanocrystallites whose shape and size was found to depend strongly on the metal. All the metals except gold showed the presence of a preferred orientation which was slight in the case of Ag and Cu but much stronger in the case of iron and cobalt nanowires. Received 30 November 2000     

弯曲Cu纳米线相干X射线衍射图的计算

本文提出了一种计算弯曲纳米线的相干X射线衍射图的方法, 即倒空间旋转法. 我们利用该方法计算了弯曲Cu纳米线的相干X射线衍射图, 并与常规方法的计算结果进行了比较. 发现利用倒空间旋转法计算所需的时间约为常规方法的1/(2N+1) (N为镜像盒子的个数). 另外, 倒空间旋转法可以拓展到其他纳米线的变形情况, 如拉伸(压缩)和扭转, 本文也对其作了相应的讨论.     

X-ray diffraction study of a sequence of phase transitions in Cs2HgCl4 crystals

The temperature behavior of lattice parameters and diffraction patterns of the reciprocal lattice in Cs₂HgCl₄ crystals is studied by x-ray diffraction in the temperature range from 4.2 to 300 K. A sequence of phase transitions is observed and attributed to the evolution of incommensurate and commensurate modulations along the crystallographic a and c axes of a unit cell in the initial Pnma structure.