Analysis Of X-ray Diffraction Lines Research Articles

Моделирование кривых дифракционного отражения рентгеновских лучей от протонообменных слоев монокристалла ниобата лития

In this work, within the framework of the dynamic theory of the X-ray scattering, a model is constructed that describes the diffraction reflection curves obtained from the proton-exchange layers of a lithium niobate monocrystal subjected to the post-exchange annealing. Planar proton-exchange waveguides based on the X-cut of the lithium niobate monocrystal are obtained experimentally. It was shown that the proton implantation leads to the formation of the new crystalline phases with a larger lattice parameter. The structure changes (by the method of the diffraction structural analysis) and the optical properties (by the method of the mode spectroscopy) of the obtained waveguides are investigated in the various temperature regimes. The microstrain of the crystal lattice caused by еру proton implantation was estimated by the analysis of X-ray diffraction line broadening. It is shown the thickness of the waveguide layer and the number of new crystalline phases depend not only on the temperature regime of the proton exchange, but also on the duration of post-exchange annealing. The simulation of the experimentally obtained curves of the diffraction reflection is carried out within the framework of the described model. As a result of the modeling, the depth of the waveguide layer was determined, which is consistent with the data obtained by the method of the mode spectroscopy. The models of the assumed profiles of the crystal lattice deformation caused by proton implantation are presented. The average values of the lattice microstrain and the phase composition of proton-exchange lithium niobate layers are determined.

Mechanism of thermal decomposition of the nonstoichiometric compound YBa2Cu3O6.8

Thermal decomposition of the nonstoichiometric high-temperature superconductor YBa2Cu3O6.8 at a temperature of 200°C in air has been investigated using the full-profile analysis of X-ray diffraction lines. Two mechanisms of decomposition are revealed. The first mechanism, i.e., separation into two phases with a different oxygen content, occurs continuously. The second mechanism, i.e., disordering of the heavy atoms Y, Ba, Ba, Y along the crystallographic axis c, begins to occur after a 20- to 35-h annealing and progresses with a further annealing.

Magnetic properties of nearly defect-free maghemite nanocrystals

Temperature variations of the magnetization $M$ and the electron magnetic resonance (EMR) parameters of maghemite $(\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3})$ nanocrystals are reported for the $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ range. Transmission electron microscopy of the nanocrystals shows them to be nearly spherical samples (aspect ratio $a∕b=1.15$) with diameter $D=7(1)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and analysis of x-ray diffraction lines yields $D=6.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with negligible strain. $M$ versus $T$ data show blocking temperatures ${T}_{B}\ensuremath{\simeq}101\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, $89\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and $68\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in measuring fields $H=50$, 100, and $200\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ respectively. $M$ versus $H$ data for $T>{T}_{B}$ fits the modified Langevin function $M={M}_{s}\mathcal{L}({\ensuremath{\mu}}_{p}H∕{k}_{B}T)+{\ensuremath{\chi}}_{a}H$ with ${\ensuremath{\mu}}_{p}=8000(500){\ensuremath{\mu}}_{B}∕\text{particle}$ and ${M}_{s}=80\phantom{\rule{0.3em}{0ex}}\mathrm{emu}∕\mathrm{g}$, identical to ${M}_{s}$ for bulk $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$. It is argued that this large value of ${M}_{s}$, the small value of coercivity ${H}_{c}\ensuremath{\simeq}20\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ at $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the lack of exchange bias in a field-cooled sample, and negligible strain point to nearly defect-free nanocrystals. In the EMR studies, two resonance lines are observed, one with the resonance field ${H}_{r}$ greater than that for the free-electron value and the other smaller. From the temperature variations of ${H}_{r}$ and the linewidths of the two lines, it is argued that the two lines are, respectively, due to nanocrystals with easy-axis aligned perpendicular and parallel to the applied field. The relatively narrow intrinsic linewidths $(\ensuremath{\simeq}400\phantom{\rule{0.3em}{0ex}}\mathrm{Oe})$ of the two lines in nearly defect-free nanocrystals facilitated their observation.

Alexander Rawson Stokes

Alexander Rawson Stokes

Shape and size determination for zinc–aluminium–chloride layered double hydroxide crystallites by analysis of X-ray diffraction line broadening

The Rietveld method, extended by a Fourier analysis of line profiles on the basis of the Warren–Averbach method, has been used for analysing the powder X-ray diffraction (PXRD) pattern of a [Zn–Al–Cl] layered double hydroxide, in order to separate size and strain effects. Assuming a given size distribution (Cauchy) and an adjustable strain variation in space, this method allows the simultaneous determination of structural parameters and the size and strain parameters of the sample. The shape, size, size distribution and orientation of the crystallites are determined. It is found that the shape is markedly anisotropic and compatible with plate-like crystallites with a hexagonal symmetry; the structure being described in the Rm space group. The strain parameter, i.e. the distribution of atomic positions around their equilibrium positions, varies by a factor of 2 while the mean particle size changes from 120 A to 2200 A in the [001] and [110] directions, respectively. Such shape and size are in good agreement with the transmission electron microscopy (TEM) observations.

Lattice Parameters of Fine Copper and Silver Particles

From an analysis of X-ray diffraction lines of fine Cu and Ag particles covered with thin oxide surface layers, the dependence of the lattice parameters on particle size in the core of the particles was determined. The lattice parameter particularly in fine Ag particles increases with decreasing particle size when the diameter is under 150 A. This experimental result can be interpreted in terms of the competition between the lattice softening and the surface tension in the ultrafine particles.

Role of X-Ray Diffraction Analysis in Surface Engineering: Investigation of Microstructure of Nitrided Iron and Steels

X-ray diffraction analysis can be very usefully applied in the field of surface engineering, since a depth of a few micrometres only is usually probed. This paper provides an overview of current X-ray diffraction methods for the analysis of surface layers. The treatment is illustrated by examples taken from recent work on nitrided iron and steels. Distinct ways to characterize the effective depth and layer thickness probed are presented. Composition-depth profiles can be measured accurately by tracing the lattice parameter (taking into account the possible presence of stresses) as a function of depth below the surface by successive sublayer removals. A correction for the penetration effect is required and methods for that are presented and demonstrated. The basis of the determination of (macro) stress (the sin2ψ method) is indicated. Attention is paid to the determination of the strain free lattice spacing and (diffraction) elastic constants, to the effect of a concentration-depth profile, and to the comparison of theoretically predicted and experimentally determined strain values. A stress (profile) in a surface layer often originates from the thermal history (cooling after treatment) and the presence of a concentration profile, as is illustrated by examples. Further, the analysis of X-ray diffraction line broadening is discussed. It is shown that nowadays an easily applicable method exists for line profile analysis (the single line Voigt method), allowing the determination of crystallite size and microstrain parameters. As demonstrated by the examples, knowledge of in particular microstrain in conjunction with macrostress is of importance in understanding and predicting material behaviour.

X-ray diffraction line broadening of cadmium oxide produced by cadmium hydroxide decomposition

A precise analysis of X-ray diffraction line broadening produced by cadmium oxide obtained by the thermal decomposition of Cd(OH)2 is described. The influence of experimental conditions is considered. It is shown, using different methods of analysis, that the broadening of the reflections is due to size and microstrains effects, with a mean apparent size of 6 nm in a direction perpendicular to (1 10) planes.

Use of the Voigt function in a single-line method for the analysis of X-ray diffraction line broadening

The use of the Voigt function for the analysis of the integral breadths of broadened X-ray diffraction line profiles forms the basis of a rapid and powerful single-line method of crystallite-size and strain determination which is easy to apply. To avoid graphical methods or interpolation from tables, empirical formulae of high accuracy are used and an estimation of errors is presented, including the influence of line-profile asymmetry. The method is applied to four practical cases of size-strain broadening: (i) cold-worked nickel, (ii) a nitrided steel, (iii) an electrodeposited nickel layer and (iv) a liquid-quenched AlSi alloy.

Profile Analysis of X-Ray Diffraction Lines and Its Application to Study on Deformation and Fracture of Metals (I)

Profile Analysis of X-Ray Diffraction Lines and Its Application to Study on Deformation and Fracture of Metals (I)

鉄-アルミニウムー窒素合金の再結晶挙動

Recovery, recrystallization, and texture-development in cold-rolled sheets of an Fe-Al-N alloy with 0.061% of acid soluble aluminum and 0.0047% of acid soluble nitrogen were studied. Two different initial conditions as for the AIN precipitation were given by quenching the hot-rolled strip into brine water either directly from the hot-finishing temperature or after keeping it at 800°C for 30 minutes so that AIN precipitated completely.Highly developed {111} recrystallization texture was found in the specimen with nitrogen and aluminum initially in solution, while in the course of heating a noticeable retardation of strain recovery occurred. An analysis of X-ray diffraction line broadening showed that the retardation of strain recovery was anisotropic, being most pronounced for grains with the {111} lattice plane parallel to the sheet plane. Such effect was not found in the specimen with AIN precipitated prior to cold-rolling. Comparing the above result with that of transmission electron microscopy, a discussion was made concerning the differences in the annealing behavior and the texture-development.

An Analysis of X-Ray Diffraction Lines of Iron Plates after Tensile Deformation

Measurements and analysis of X-ray diffraction lines of high diffraction angles were first carried out on iron specimens after tensile deformation. Changes in half value width of diffraction lines with changes in tensile strain or annealing condition were observed, and further, the profiles of the lines from (211) were analyzed by the method of Fourier analysis and the result obtained was as follows. The mean particle size, often 18% elongation was 3.5×10-5cm. and the strains in them were uniformal. The value 3.5×10-5cm corincided well with the value that had preciously been reported by the another, using X-ray micro beam technique. At the same time the recovering process were traced.

Method of moments in analysis of x-ray diffraction lines

A general relation between the moments of the functionsf,g, andh, in the integral equationh(x)=∫f(y)g(x−y) dy, is derived. This enables any moment of the unknown functionf to be calculated from the moments of the functionsg andh. In particular, if certain assumptions are fulfilled, the moments of the components of the doublet can be calculated with advantage from the moments of the total profile. The statistical significance of the moment characteristics is also emphasized.