Bragg Lines Research Articles

Surface phases analysis by grazing incidence of X-rays in a Bragg-Brentano diffractometer

A technique which utilizes an unmodified commercial Bragg-Brentano X-ray diffractometer, for the study of thin surface layers is presented. The considered diffractometer setup permits data acquisition with Θ fixed at 1° and 2Θ scanning the Bragg line. The results obtained with this technique are shown for some examples regarding the study of surface or near surface interfaces.

Small-angle scattering of X-rays in a conventional Bragg–Brentano diffractometer for quantitative analysis

A technique is presented utilizing an unmodified commercial X-ray diffractometer, equipped with a Bragg–Brentano geometry, for reducing preferred orientation effects in measured intensities during quantitative diffraction analysis. The diffractometer setup examined makes possible data acquisition with Θ fixed at 1° and 2Θ scanning the Bragg line. The results obtained with this technique are shown in the quantitative X-ray diffraction analysis of three international standards of carbonate rocks (401,402,403).

Interlayer correlation of Fe spins and charges in the 2-D triangular ferrimagnet ErFe 2O 4

Neutron polarization analysis was applied to Bragg lines at (⅓, ⅓, l) and (⅔, ⅔, l) of an ErFe 2O 4 single crystal at 15 K. The magnetic scattering intensity is composed of three sinusoidal curves, corresponding to the spin correlations between next-nearest-neighbor Fe Fe or Fe Er layers. The correlation length along the c-axis is only about 8 Å, in contrast to 50 Å in the c-plane. The nuclear part of the scattering indicates correlation of atomic displacements up to about 50 Å along the c-axis, independent of the spin ordering.

Cladding-mode coupling characteristics ofBragg gratings in depressed-cladding fibre

Experimental transmission spectra of UV-written Bragg gratings in depressed-cladding fibre are characterised. The fine-structure features on the short-wavelength side of the fundamental Bragg line are shown to be due to coupling between the LP01 and higher-order LP0n and LP1n modes.

Optical and X-ray evidence of structural phase transitions in mixed (Rb1−xKx)CaF3crystals

Abstract Structural phase transitions have been found in the mixed fluoroperovskites crystals (Rb1−xKx)CaF3 (x=0.05, 0.2, 0.35, 0.5, 0.88, 1.0) by optical birefringence and X-ray diffraction. Profile analysis of powder diffraction lines was performed to determine the change of lattice parameters versus temperature in order to establish the crystal symmetry of each structural phase and to measure the temperatures of the transitions. From the splitting of the 400 cubic Bragg line and consideration of Glazer's classification of tilted octahedra in perovskites, the various types of distortions were found. Sequences of CaF6 tilting octahedra occurring during the phase transitions are suggested and discussed for each concentration.

Interlayer spin correlation in a 2-D triangular ferrimagnet ErFe2O4

Neutron polarization analysis was carried out for Bragg lines at (13, 13, ℓ) and (23, 23, ℓ) of an ErFe2O4 single crystal at 15 K. Magnetic part of the intensity was analyzed as a sum of three sinusoidal curves. Correlation length of spins along the c axis is only up to about 8 Å or 13 of the unit cell.

Magnetic and structural properties of KCoxMg1− xF3 compounds

The mixed crystals KCo x Mg 1− x F 3 with 0.25 < x < 1 were studied by static susceptibility and X-ray diffraction meth in the temperature range 4.2–350 K. From these measurements, the variations of several quantities, viz. T N, t= T N ( x)/ T N (1), θ (Curie-Weiss temperature), μ eff (effective moment), and a, c (lattice parameters) with concentration or temperature were determined. The exchange constant was evaluated using theoretical results obtained for random, dilute magnetic systeṁs with magnetic ions having nonvanishing orbital momenta. From the temperature evolution of the cubic (400) Bragg line, the values of temperature for the structural phase transition and tetragonal deformation lattice with c a < 1 were estimated. A strong correlation was found between the magnetic and structural phase transition, with the lattice deformation resulting from the magnetic properties of the crystals studied.

Structure and Magnetism in Mo/Co Multilayers

ABSTRACTThe magnetic and structural properties of Co in Mo/Co multilayers are an unresolved issue. Two independent studies report different structures for thicker Co layers in multilayers of comparable dimensions as well as significant differences in both the form and the layer thickness for a loss of ferromagnetism. Both studies base their structural claims on a limited number of Bragg lines. We have used x-ray diffraction, transmission electron diffraction, and EXAFS to probe the structure of Mo/Co multilayers having Co layer thicknesses from 4 to 63Å. Our structural and magnetic results for these samples are compared to those of the above studies and are contrasted with results for Mo/Fe multilayers having comparable dimensions.

Surface relaxation of strained heterostructures revealed by Bragg line splitting in LACBED patterns

Bragg line splitting near the shadow image of a thin strained InGaAs layer, buried in GaAs and without strain relief by misfit dislocations, was found in large angle convergent beam electron diffraction (LACBED) patterns of cross-section specimens. The surface relaxation of the built-in strain and the Bragg line intensities were calculated. A qualitative agreement between the experimental Bragg line splitting and the theoretical calculations is demonstrated Closer matching was achieved using a “line-force” model of the surface relaxation, whereas a Fourier transform solution showed significant underestimation of the Bragg line splitting. The possibility of characterising the built-in strain in thin strained layers, by measuring this Bragg line splitting in LACBED patterns, has been explored.

An empirical relation between ocean‐surface wind direction and the Bragg line ratio of HF radar sea echo spectra

Twelve days of tests with six U.S. Air Force OTH‐B over‐the‐horizon radars produced a large surface wind direction data set covering much of the North Atlantic and Pacific oceans. We compare wind directions derived from the sea echo Bragg line ratio with concurrent in situ measurements made by ships and buoys and with the National Meteorological Center (NMC) Global Data Assimilation System model. Using 1900 such comparisons, we derive an empirical model for the dependence of surface wind direction on the Bragg line ratio of HF radar sea echoes. The rms difference between the empirical model and the combined NMC and in situ data is about 33°. When only very high quality radar data are used, the rms difference between the radar and buoy measurements alone is 24°. The pattern of surface streamlines derived from 1 day's radar measurements over the northeastern Pacific Ocean closely matches that derived from the NMC model.

Reasonably good images of dislocations in LACBED patterns and effects of dislocation strain fields on the Bragg lines

An improved large-angle convergent beam electron diffraction (LACBED) experiment method using a Philips CM12 electron microscope is discussed. Dislocations in silicon parallel to the Bragg lines have been studied by this improved LACBED technique. Images of dislocations of reasonably good spatial resolution superimposed on LACBED patterns have been obtained. It has been found that only when the image of the dislocation is parallel and close to the low-order contour with g · b ≠ 0 can it be formed with reasonably good contrast in the LACBED patterns. Both the image of the dislocation and the changes of the contours can be visible in a single LACBED pattern, making it a convenient technique for studying the strain field of a dislocation.

Effects of dislocation strain fields on Bragg lines in an Al70Co15Ni15 decagonal quasicrystal studied by an improved LACBED technique

Effects of dislocation strain fields on Bragg lines in an Al70Co15Ni15 decagonal quasicrystal have been studied by using an improved large-angle convergent-beam electron diffraction technique. It is found that the effects are the same as that in conventional crystals.

Characterization of dislocations in anisotropic materials by large angle convergent beam electron diffraction

It is shown that the characterization of the Burgers vector of dislocations, by large angle convergent beam electron diffractions using the Cherns and Preston rules, is possible in elastically anisotropic materials, provided some care is taken in the choice of the Bragg lines used for the analysis

Structural phase transitions in (K1-xNax)MnF3 and (K1-xLix)MnF3 mixed perovskite crystals

Profile analysis of powder diffraction lines was used to determine the variations in lattice parameters as a function of temperature. Using this procedure, phase diagrams of (K1-xNax)MnF3 and (K1-xLix)MnF3 were obtained in the concentration range x<or=0.02. From the splitting of cubic (220) and (400) Bragg's lines the temperatures of the structural phase transitions and the types of distortion were determined. The following sequence of distortions was observed: cubic to tetragonal to orthorhombic to monoclinic.

Structure determination using convergent-beam electron diffraction

There are many different approaches in quantitative electron diffraction which are being vigorously pursued at present. The approach we adopt is based on the insights provided by the Bloch-wave formulation of dynamical electron diffraction theory into the physics of dynamical scattering. This insight is used to select diffraction situations where a pseudo-kinematical approximation may be made. A forwards route is then possible directly from the experimental observations to the structural implications. This contrasts with the model-building, multi-parameter fitting procedures used in many other approaches where a problem of uniqueness inevitably arises.Because the pseudo-kinematical approach ignores many of the detailed dynamical interactions which occur locally over small angular ranges we do not attempt to make accurate measurements, and wherever possible average (visually at least) along Bragg lines to eliminate local perturbations. In a sense the work resembles early X-ray crystallography where reflections were put in one of six or so classes from very weak to very strong.

Saw-tooth peaks in elastic neutron scattering by rhombohedral Heisenberg antiferromagnets

The phenomenology of the Heisenberg rhombohedral antiferromagnet (RAF) in classical approximation is characterized by the frustration of the minimum energy configuration consisting of infinite inequivalent helices. In absence of anisotropy long range order (LRO) is lost but a weak single ion anisotropy is sufficient to restore LRO and to produce unusual elastic neutron scattering profiles as Bragg lines for monocrystalline samples and saw-tooth peaks for policrystalline samples. The effect of quantum and thermal fluctuations as well as of a magnetic field is also considered.

Effects of heavy boron doping upon oxygen precipitation in Czochralski silicon

In this investigation, diffuse x-ray scattering, Bragg line profile, and transmission electron microscopy have been employed for the study of point defects and their interaction with oxygen impurities in heavily boron-doped Czochralski Si wafers during various thermal treatments between 450 and 1050 °C for time intervals from 2 to 128 h. Bragg line profile data show that (1) materials tend to become more perfect during the initial stages of thermal annealing regardless of anneal temperatures and (2) the integral width and full width at half-maximum both exhibit minima after a thermal treatment at 450 °C for 32 h while the opposite behavior is observed for a thermal treatment at 1050 °C. The diffuse x-ray scattering data have shown that (1) the nature of the predominant defects depends upon annealing temperature, time and ramping cycles; and (2) the mean cluster size ranges between 1.4 and 2.0×103 nm regardless of annealing temperature and time. Transmission electron microscopy results show (1) slower precipitation kinetics occur than in lightly doped materials, (2) virtually no precipitates have been observed, even after 128 h for annealing temperatures up to 650 °C, (3) amorphous precipitates with a {100} platelet morphology are observed after prolonged anneals at 800 °C, and (4) the appearance of complex precipitate structures have been observed at 1050 °C. These results indicate significantly different behavior from that of lightly doped silicon. Finally, using a thermodynamic and kinetic model, we attempt to explain these heavy boron doping effects on SiO2 precipitation in Czochralski Si.

Structural properties of heteroepitaxial Ge films on a Si(100)-2×1 surface

Structural and electrical properties of epitaxial Ge films grown on a Si(100)-2×1 surface have been studied by means of low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), x-ray diffraction, and Raman scattering. The attempt has been made to find the growth conditions, such as the substrate temperature TSi and Ge thickness dGe, for the single-crystalline Ge (100) on the Si surface. The sharp (2×1) LEED pattern of Ge (100) accompanied by the absence of any AES signals from the Si substrate is unambiguous evidence for the growth of single-crystalline Ge films. The structural quality of the Ge films was examined by the peak position and width of the Ge(400) Bragg line in x-ray diffraction. From these results, we found that more than 1000-Å Ge thickness is required to grow the high-quality epitaxial Ge films on the Si substrate at elevated temperatures. This is due to island formation at the initial stage of Ge deposition. Therefore, we also studied the role of thin Ge buffer layers fabricated at low temperatures below TSi=200 °C to grow thinner epitaxial Ge films without island formation. It was found that the amorphous buffer layers are poorly crystallized during the rapid increase in TSi up to 400–500 °C, prior to subsequent Ge deposition on the buffer layer. Consequently, single-crystalline Ge films are grown at relatively thin dGe in such a way that the underlying buffer layers accommodate the strains or misfit dislocations near the Si-Ge interface. The single-crystalline Ge films with and without the buffer layers thus grown on the Si substrates were also characterized by the line shape of the phonon Raman scattering spectra. Depending on the details of sample preparation, the spectra exhibited a characteristic change in shape including peak position and width. Having estimated the probing depth of the Raman scattering, we were able to gain deep insight into not only the Ge–Ge bond strength, but also the inhomogeneity of the Ge films and the extent of the strains into the Ge films, which were not accessible by LEED or x-ray diffraction.

Effects of boron concentration upon oxygen precipitation in CZ silicon

Effects of boron concentration upon oxygen precipitation were studied in Czochralski (CZ) silicon annealed from 2 to 128 h between 450 and 1050°C. In this ivestigation Bragg line profile (BLP), high resolution diffuse X-ray scattering (DXS) and transmission electron microscopy (TEM) were employed. The BLP and DXS data have shown that the nature of the predominant deffects depend upon annealing time and temperature, as well as, on dopant concentration. The long range displacement field of these defects, however, does not seem to be affected by these parameters. The TEM results have shown a dependence of precipitate growth kinetics, as well as, structure upon dopant concentration, and annealing temperature and time. Differences in oxide precipitate growth kinetics between lightly and heavily doped materials and a correlation between DXS parameters and TEM images are discussed.

Use of maximum entropy spectral analysis to improve ship detection by over‐the‐horizon radar

The over‐the‐horizon radar is able to detect ships over very large oceanic areas. Detection performance is sometimes reduced because of smearing of the sea echo due to variations of the Doppler shift imposed by the ionosphere. In this paper we propose a decontamination procedure, based upon maximum entropy spectral analysis of sea scatter Bragg lines, to correct the phase of the signal before performing classical fast Fourier transform processing. The improvement in quality of the signal after phase correction results in a sharpening of spectral peaks. In the example presented the signal was chosen to contain spectral lines of a transponder installed on board a ship, to be used as reference lines. The decrease in the spectral width is significant for the sea scatter Bragg lines and for the transponder lines. As the Bragg lines sharpen, the ship echo is more easily detected in the spectrum. The proposed decontamination procedure involves more computation load than the simpler frequency shift method used for sea state monitoring, but, on the other hand, it can handle Doppler shift variations during coherent integration time.