Diffraction Intensity Profiles Research Articles

X-ray diffraction analysis of interdiffusion in Al[sub x]In[sub 1−x]As[sub y]Sb[sub 1−y]∕GaSb multilayers

We report the results of a detailed x-ray diffraction analysis of two AlxIn1−xAsySb1−y∕GaSb multilayer samples grown by molecular beam epitaxy on GaSb (100). The kinematical scattering theory was used to fit the x-ray diffraction intensity profiles to determine the lattice spacing, composition, and strain of the multilayers, allowing for interdiffusion between the layers and variation in the multilayer wavelength. It has been determined that the quaternary alloy composition varies throughout the layer and that there is an interfacial quaternary layer that differs in composition from that of the bulk AlxIn1−xAsySb1−y layer. A rationale for this graded composition and interfacial layer will be discussed based on the growth dynamics for this system.

Diffraction characteristics of 10 fs laser pulses passing through an aperture

Results are presented on experimental and theoretical work performed to compare diffraction phenomena for ultrashort 10 fs pulses and continuous-wave propagation modes illuminating different-sized pinholes and slits. Results demonstrate that 10 fs pulses do not produce high-frequency diffraction like that produced with continuous-wave illumination. The diffraction through a 1 mm pinhole of temporally stretched pulses obtained by using fused silica plates whose frequency spectrum remains the same is compared with those of 10 fs pulses. The overall diffraction intensity profiles are, however, nearly identical in this case. The simulations of diffraction patterns for 100 fs, 10 fs, and 1 fs incident pulse were compared theoretically for different aperture sizes and frequencies. Calculations indicate that the lack of high-frequency diffraction for the mode-locked case is due to the broadband nature of the ultrashort laser pulses; i.e., the distribution of the frequency contained in the pulse ends up washing out when objects are illuminated with pulses of broad frequency content. The results of this work have important application in biomedical imaging and remote imaging applications, to name only a few.

Liquid Ammonia Treatment of Regenerated Cellulosic Fabrics

Liquid ammonia is effective at improving the strength, shrink resistance, and hand of cotton fabric. In this study, we apply a liquid ammonia (NH3) treatment to three regenerated cellulosic fabrics—rayon taffeta, cupro taffeta, and polynosic broadcloth— and subsequently process these with hot water and dry heat. We investigate the effect of the processes on crystal form, crystallinity, moisture regain, water absorption, and dyeing properties. Also, the mechanical properties of the NH3-treated fabrics are measured in relation to fabric hand. The diffraction intensity profiles of the rayon taffeta are unchanged by the NH3 treatment and subsequent heat processing. The profile of cupro taffeta is not changed by the NH3 treatment, but it is transformed to cellulose IIIII by subsequent hot water and dry heat processes. On the other hand, although the profile of polynosic broadcloth is transformed to cellulose IIIII by the NH3 treatment, the profile is not changed by hot water and dry heat. Furthermore, fabric crystallinity decreases with the NH3 treatment and increases somewhat after the hot water and dry heat processes. Water absorption and equilibrium dye uptake decrease with the NH3 treatment. Excellent washing shrinkage resistance is obtained with the NH3 treatment. The shearing and bending parameters of the rayon and cupro fabrics decrease somewhat with the NH3 treatment, so this treatment of regenerated cellulosic fabrics is effective at improving hand as well as washing shrinkage.

Fast nondestructive technique to determine the content of components in a strain-compensated crystalline ternary alloy

The x-ray Bragg diffraction intensity profile for a model strain-compensated structure consisting of a thin SiGe alloy layer grown on a thick Si substrate is derived using a Laplace transform interpretation of the kinematical approximation of x-ray diffraction theory. It is shown that in the case of fully strain-compensated crystals a simplified x-ray phase-retrieval technique can be applied to determine the alloy composition from this x-ray diffraction data. An experimental intensity profile from an almost perfectly unstrained SiGe:C/Si structure is analyzed using this method.

X-ray Bragg diffraction profiles from unstrained layered single-crystal structures: theoretical considerations, simulation and reconstruction using phase-retrieval X-ray diffractometry

The X-ray Bragg diffraction intensity profile for a model strain-compensated single-crystal structure consisting of a thin alloy layer grown on a thick substrate is derived using a Laplace transform interpretation of the kinematical approximation of X-ray diffraction theory, assuming a step-like attenuation depth-profile. The effects of the model physical parameters on the measurable Bragg diffraction intensity profile are discussed. The intensity profiles for model SiGe:C/Si perfectly unstrained layer thicknesses of 50 and 100 nm are simulated for three characteristic X-ray radiation wavelengths (0.05–0.15 nm). The simulations are performed near the absorption edge of Ge to maximise the observable diffraction contrast. The complex structure factor profiles are then reconstructed from the simulated intensity distributions using phase-retrieval X-ray diffractometry (PRXRD) method.

Ammonia-Gas Treatment of Cellulosic Fabrics

Native and regenerated cellulosic fabrics such as cotton, cupro, polynosic, viscose rayon taffeta and viscose rayon muslin were treated with ammonia-gas under various conditions. The dyeing and KES (Kawabata Evaluation System) mechanical properties were obtained. Although X-ray diffraction intensity profiles of the cotton showed almost no change by the treatment for 10 min, the peaks assigned to cellulose I decreased in intensity by the treatment for 60 min, and new peak intensity maxima assigned to cellulose IIII appeared at scattering angles of 2θ = 11.6° and 21.0°. On the other hand, the profiles of the regenerated cellulosic fabrics were not changed at all by the ammonia-gas treatment. Apparent dyeing rate of the cotton decreased regardless of the treating conditions, whereas the dyeing rate of the regenerated fabrics was unchanged by the treatment. KES shearing and bending properties (the moduli G and B; the hysteresis widths 2HG, 2HG5 and 2HB) in relation to the fabric hand decreased. Therefore, it is clear that the ammonia-gas treatment is effective to improve the soft hand of the cellulosic fabrics, especially for the regenerated cellulosic fabrics.

Optical Properties of a Switchable Diffraction Grating

We have performed detailed measurements of the far field diffraction pattern of an electrically switchable liquid crystal grating. The grating, with a period of 25 microns, was formed using interdigitated aluminum electrodes with a 15 micron gap between adjacent electrodes. The homeotropically aligned liquid crystal (ZLI-4792) had a thickness of 5 microns. We measured the diffracted intensity profile of HeNe laser light (633nm) for different applied between adjacent electrodes. The amount of light diffracted into the first order relative to zeroth order is strongly dependent on the applied voltage. The locations of successive maxima and minima also shift with the applied voltage. We studied the diffraction theoretically using geometrical optics coupled with Kirchoff diffraction theory. This theoretical model is in substantial agreement with the empirical results.

Experimental Studies of 90° Bragg Reflection from a Sub-Micron InxGa1-xAs Single-Crystal Film Deposited on a GaAs Substrate

Experimental studies of a 90° Bragg reflection from a thin surface InxGa1-xAs layer grown on a GaAs substrate are reported and discussed. The experiment was performed on the undulator beamline BL29XU at the SPring-8. Two-dimensional (angular deviation from 90° position versus incident synchrotron radiation energy) diffraction intensity profiles were collected from six samples with different In contents (x=0.2–1.5%) and different layer thicknesses (0.5–1.5 µm). Observation of the layer performing as a thin-film optical interferometer (filter) and a discrepancy between layer-substrate lattice mismatch values obtained from standard (400) and extreme 90° reflection measurements (using the same radiation energy) are discussed.

Influence of the transverse and longitudinal coherence in the dynamicaltheory of x-ray diffraction

We investigate dynamical diffraction phenomena of a quasi-monochromatic x-ray beam emitted by a small source at a large distance from the sample. Under certain conditions of coherence the diffraction intensity profile in a recording plane reproduces the angular profile of the rocking curve of the crystal. The coherence requirements are stronger for thicker crystals. This has been verified in experiments at the ESRF. In these experiments the effective crystal thickness was varied by rotating the crystal around an axis perpendicular to the reflecting planes.

The characterization of SiGe/Si multilayers via an unambiguous solution of the inverse problem in x-ray Bragg diffraction

New experimental results concerning the model-independent unique characterization of SiGe/Si alloy multilayer structures are presented. The experimental technique uses x-ray diffracted intensity profiles collected for two different radiation wavelengths. The analytical method exploits the retrieval of the x-ray wave phase from its experimental intensity profile via a logarithmic Hilbert transform. High-resolution x-ray Bragg diffraction data have been collected at the European Synchrotron Radiation Facility. The physical dimensions and chemical composition of the SiGe alloy layers were determined with a record 15 Å spatial resolution.

Theory of X-ray measurement of microfibril angle in wood

A diffraction intensity function for material bodies composed of arrays of crystalline fibres such as occurs with the cellulose of wood has been derived. It is implied in the analysis that the crystalline fibres making up the body have fibre symmetry- that there is a tendency for groups of fibres to have one set of crystal axes parallel while in the orthogonal direction the axes assume a low degree of order. It is further assumed that the patterns of the angular arrangement of the fibre groups relative to one axis of the body is independent of the direction about that axis. These conditions are believed to be compatible with the cellulosic structure found in wood. Thus it becomes possible to calculate the expected diffraction intensity profiles of realistic (and therefore complex) models of wood. This has aided the interpretation of the reflections from the (040) crystal planes of cellulose which are contaminated by low level reflections from other crystal planes, and it has been found that it might be possible by conjoint analysis of the paratropic (002) reflections and the diatropic (040) reflections to measure the complete cell wall planar microfibril angle distribution and the shape of the cell wall cross-section.

Unambiguous determination of crystal-lattice strains in epitaxially grown SiGe/Si multilayers

A new method for unambiguous reconstruction of crystal-lattice strains in epitaxially grown layers from high-resolution x-ray diffraction data is proposed. The technique uses x-ray diffracted intensity profiles collected for two different radiation wavelengths. We enhance the theory for the previously developed algorithm for model-independent determination of crystal-lattice strain profiles in single crystals with epitaxially grown top-surface layers. The method relies on the retrieval of the scattered x-ray wave phase from its intensity profile via a logarithmic Hilbert transform. This phase-retrieval technique is always associated with the problem of complex polynomial root finding. A practical procedure for the mapping of complex polynomial roots is proposed to distinguish true and virtual zeros. This allows the phase of the diffracted x-ray wave to be retrieved unambiguously. The method was applied to determine physical dimensions and concentration composition of a Si/Si1−xGex/Si alloy multilayer structure typical for SiGe heterobipolar transistor device.

Subpixel detection in video RHEED image analysis

A CCD camera and computer data acquisition system is used for surface investigation by means of the reflection high energy electron diffraction (RHEED) method. Accuracy of these measurements, especially of lattice parameter determination, is limited by camera spatial distortion, high noise, and diffraction-spot broadening. In order to resolve this problem a detection method of a virtual camera subpixel detector is proposed. The conversion function between a real camera and a perfect virtual pinhole model camera is established using a method of reference calibrate grid. The RHEED intensity diffraction patterns are approximated by analytical functions which fit the simple diffraction intensity profiles well. Then the centres of the diffraction lines and points are calculated with high (subpixel) precision.The accuracy of the method is demonstrated by analysis of RHEED diffraction patterns obtained from a Pd(111) surface. It is shown that the error of determination of the diffraction spot position is lower than 0.4%. The use of the method is shown for the example of Pd epitaxial film growth on a NaCl substrate where increased vertical lattice parameters are found.

Submicroscopic twinning and chemical inhomogeneity of ilvaite, a mixed-valence iron sorosilicate HCaFe2 2 + Fe3 + Si2O9

Abstract Series of structural studies of systematically selected local portions of the same crystal of ilvaite CaFe2 2 + Fe3 + OOHSi2O7 with moderate size have revealed a trend that the monoclinic and apparently orthorhombic structures co-exist in the crystal regardless of their mode of occurrence. The diffraction-intensity profiles of high angle reflections such as 24,0,0 and 008 were then studied by means of step-scanning on a four-circle diffractometer, using graphite monochromatized MoKα radiation: the former was scanned along c* and the latter along a*. The result has brought out that either reflection from the crystals of high monoclinicity (β ≈ 90.2° ∼ 90.3°) splits into a double peak, suggesting that those crystals are most likely made up of two kinds of domains, each having a monoclinic structure with β = 90.45°, one twinned on (001) and the other twinned on (100). In the case of crystals of low monoclinicity (β ≈ 90.0°), those reflections tend to exhibit single broad profiles with fine structure. A profile-fitting procedure has shown that they are in general composite of three peaks, suggesting that they consist of complex composites of fine monoclinic components twinned on (001) and those twinned on (100). The distribution of Mn in the crystals studied tends to increase towards their marginal portions. Crystal portions containing more than roughly 0.25 Mn per formula unit assume orthorhombic symmetry without exception. The coexistence of the different symmetries in the same crystal of ilvaite is thus originated in the variation in scale or mode of twinnings incorporated mainly with inhomogeneous distribution of Mn in the crystal. The occurrence of orthorhombic ilvaite is unlikely.

Beam propagation factor of diffracted laser beams

The recent emergence of the characterization of general optical beams by means of the variance of their transverse intensity distribution has given rise to the concept of the beam propagation factor (usually referred to as the beam quality factor), which appears as a meaningful way for comparing the divergences of optical beams having the same minimum spot size. Unfortunately, a direct calculation of this factor for a beam having sharp discontinuities in its transverse intensity profile leads to an infinite result. This difficulty is addressed by deriving a general expression for the axial dependence of the variance of the beam's transverse intensity profile in free space. A new definition for the beam propagation factor can be introduced, provided that the evanescent waves of the plane-wave spectrum of the beam are ignored. This modified beam propagation factor is then calculated for some specific diffracted intensity profiles. Finally, it is shown how the proposed definition for the variance of the plane-wave spectrum of an optical beam is connected to its far-field angular spread.

The diffraction patterns of crystals with layer defects

A method for the calculation of X-ray and neutron diffraction profiles of crystals with layer defects is described. Averages over a computer model of a configurational ensemble of crystallites with defects are used to define the scattering cross section. The method easily accommodates the modeling of complex defect geometries or correlations. Diffracted intensity profiles for the NixAl1−x (5, \overline 2) monoclinic martensite, trigonal polytypes and body-centered-cubic crystals are presented as examples.

Irreversible island formation during deposition: separation distributions and diffraction profiles

Abstract We consider irreversible island formation during deposition on single crystal faces, at coverages θ ⪡ 1. We focus on the effective scaling of the island-island and island-adatom pair separation distributions, at fixed coverage and varying ratio of diffusion to deposition rates. We quantify the depletion of islands and adatoms in the immediate vicinity of an island, in terms of a single characteristic length. Simulation results are supplemented by a rate-equation analysis. The diffracted intensity profile is calculated neglecting correlations between island size and separations. We find a ring structure whose diameter correlates with the average island separation.

Irreversible island formation during deposition: separation distributions and diffraction profiles

We consider irreversible island formation during deposition on single crystal faces, at coverages θ ⪡ 1. We focus on the effective scaling of the island-island and island-adatom pair separation distributions, at fixed coverage and varying ratio of diffusion to deposition rates. We quantify the depletion of islands and adatoms in the immediate vicinity of an island, in terms of a single characteristic length. Simulation results are supplemented by a rate-equation analysis. The diffracted intensity profile is calculated neglecting correlations between island size and separations. We find a ring structure whose diameter correlates with the average island separation.

Nucleation and Growth Model for Metal-On-Fcc(100) Metal Deposition

AbstractWe present results of Monte Carlo simulations of irreversible diffusion-mediated nucleation and growth of square islands during deposition. This model mimics metal-on-fcc(100) metal epitaxy at lower temperatures. Our analysis focuses on the scaling of the island size and separation distributions, and their evolution with coverage. The depletion in the density of nearby island pairs is shown to produce a “Henzler ring” structure in the diffraction intensity profile.

Lattice Expansion of Ultrafine Cr Particles

The temperature dependence of the lattice constant and the diffraction intensity profiles of ultrafine bcc Cr particles with 750 A in the average diameter were investigated by X-ray diffraction and least-squares pattern fitting methods in a wide temperature range from 88 K to 375 K. Coefficient of a thermal expansion differed by about 30% at T > T N and 10% at 170 K < T < T N respectively from the bulk data. New extra peak was observed below about 210 K at the low angle side of the observed 110, 211 and 310 reflection positions for the bcc Cr structure. The feature in the experimental results was discussed on the basis of a lattice expansion which was closely related to an enhancement of the magnitude of the magnetic moments relative to the maximum value of the spin density wave in bulk Cr.