Bragg Angle 2θ Research Articles

Impact of rare-earth ions on the physical properties of hexaferrites Ba0.5Sr0.5RE0.6Fe11.4O19, (RE = La, Yb, Sm, Gd, Er, Eu, and Dy)

Rare-earth ions RE3+ doped Sr/Ba-hexaferrite nanoparticles were prepared via the sol-gel auto-combustion method. The effect of replacing Fe3+ by RE3+ ions on the structural and morphological properties have been investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy dispersive X-ray spectroscopy (EDS). The functional groups were detected by Fourier Transform infrared spectroscopy (FTIR). Hysteresis loops were formed by applying a magnetic field of ± 20 kOe, using vibrating sample magnetometer (VSM). The electric and dielectric parameters; conductivity (σ), dielectric constant (ε′), dielectric loss (ε"), tangent loss (tan δ) were obtained using LCR Meter at frequencies up to 5 MHz and temperature up to 620 K. The XRD analysis showed a pure M-type hexagonal phase with a space group P63/mmc. The Bragg's angle 2θ has been shifted toward lower values by RE3+ addition. Sedimentation of RE3+ ions on the grain boundaries makes barriers for the grain growth, where the size of nanoparticles varies in the range (35.22−51.9 nm). The characteristic FTIR peaks of hexaferrites are obtained between 430 and 595 cm−1. The hexagonal shape shown in the (SEM) images reflects the quality of preparation and uniform distribution of RE3+ ions. (EDX) results showed that there is no significant difference between the theoretical and experimental data for the weight percent of each element. The hysteresis loops give rise to the ferromagnetic nature of the materials at 300 K. Substitution of RE3+ ions with different properties changes the hopping rate of electrons between cations of the same element, which affect the dielectric parameters.

Algorithms of Two-Dimensional X-Ray Diffraction

ABSTRACTX-ray diffraction pattern collected with two-dimensional detector contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be integrated to a conventional diffraction pattern and evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through the integration. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern can be expressed either in the laboratory coordinates or in the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation.

Algorithms for Two-dimensional XRD Data Evaluation

The diffracted x-rays from a polycrystalline (powder) sample form a series diffraction cones in space since large numbers of crystals oriented randomly in the space are covered by the incident x-ray beam. Each diffraction cone corresponds to the diffraction from the same family of crystalline planes in all the participating grains. When a two-dimensional (2D) detector is used for x-ray powder diffraction, the diffraction cones are intercepted by the 2D detector and the x-ray intensity distribution on the sensing area is converted to an image-like diffraction pattern. The 2D pattern contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be analyzed directly or by data reduction to the intensity distribution along γ or 2θ. The γ-integration can reduce the 2D pattern into a diffraction profile analogs to the conventional diffraction pattern which is the diffraction intensity distribution as a function of 2θ angles. This kind of diffraction pattern can be evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through γ-integration. The intensity distribution and 2θ variations along γ contain more information, such as the orientation distribution, strain states, crystallite size and shape distribution. In order to understand and analyze 2D diffraction data, new approaches and algorithms are necessary. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern measured in the laboratory coordinates can be transformed to the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation by γ-profile analysis. The unit diffraction vector is also used in polarization and absorption correction.

Low-stress superhard TiB films prepared by magnetron sputtering

The article reports on structure and mechanical properties of TiB alloy films sputter deposited from a sintered TiB 2 target using an unbalanced dc magnetron. We present results of a systematic investigation of the effect of negative substrate bias, U s, substrate ion current density i s, and substrate temperature, T s, on properties of TiB films. The X-ray diffraction (XRD) analysis shows that the TiB films consist of the hexagonal TiB 2 phase with the typical (0001) texture only. The TiB x films are over-stoichiometric with the ratio x=B/Ti≈2.4. All TiB films sputter ion plated in argon magnetron discharge are superhard films with hardness H>40 GPa and exhibit high values of (i) effective Young's modulus E*= E/(1− ν 2) up to approximately 600 GPa and (ii) elastic recovery, W e, up to approximately 82%; here E and ν are the Young's modulus and the Poisson's ratio, respectively. Besides, it was found that the value of the Bragg's angle 2θ of the (0001) reflection line can be easily controlled by the energy delivered to the film during its growth by (1) the substrate heating T s and (2) ion bombardment ( U s, i s). The angle 2θ of the (0001) reflection increases with increasing T s from 300 to 550 °C and decreasing U s from −150 to −50 V. In this range of process parameters, the energy E p delivered to the growing film per condensing atom by ion bombardment can be adjusted to a value, at which the (0001) reflection from sputtered films is close to that of the TiB 2(0001) powder standard. These films exhibit a low macrostress, which approaches to zero. It enables to sputter thick (up to 8 μm) superhard (H>40 GPa) TiB films. The optimum value of E p is achieved when the TiB film is sputtered at U s=−50 V, i s=1 mA/cm 2, T s=550 °C with a deposition rate a D=52 nm/min. The TiB film prepared under these conditions exhibits a maximum hardness of H≈77 GPa, measured using a computer controlled microhardness tester Fischerscope H100 at the Vickers diamond indenter load L=50 mN.

The sin2 ψ-method in pulsed neutron transmission

Abstract The transmission spectrum of thermal neutrons through polycrystalline samples as a function of wavelength displays sudden increases in intensity known as Bragg edges. These edges occur whenever the wavelength ceases to fulfil the Bragg condition for coherent scattering at Bragg angle 2Θ = 180°. The shape and position of these edges contain information about the stress state present in the sample. The transmission method has two key advantages over conventional neutron diffraction. For samples with essentially one or two-dimensional stress-fields the use of pixellated detector arrays enables simultaneous, therefore very fast, spatial imaging of strains. At the same time it allows for the determination of the unstrained lattice spacing as well as stresses in the sample by evaluating a set of strain images taken at different sample inclinations, similar to the sin2 ψ-technique of X-ray diffraction. We show how this technique has been successfully employed to determine accurately the unstrained latti...

The Distribution of Elastic Deformation in Textured Materials as Revealed by Peak Position Pole Figures

Pole figures of X-ray line peak position were used in the study of lattice elastic deformation as applied to textured metal materials. Diffractometric texture measurements were carried out by a position sensitive detector. Peak position pole figures were constructed either in units of the Bragg angle 2θ Φψ or in units of lattice relative elastic deformation Δd/d sv . Several modes of microstress equilibrium are revealed. In most studied cases the distribution of lattice elastic deformation shows the cross-wise pattern, consisting in alternation of quadrants with predominance of extension and compression. In addition, the mutual arrangement of regions with opposite signs of elastic deformation varies depending on the texture character: breaking of texture maxima into halves with opposite signs of elastic deformation, predominance of one-sign elastic deformation within different texture maxima, stretched zones of elastic extension and compression at opposite slopes of texture maxima. Besides, the identical microstress distribution in all quadrants of pole figure develops in some cases.

Ga substitution effect on magnetic and magnetostrictive properties of TbFe2 compounds

In the present paper magnetic and magnetostrictive properties of Tb(Fe1−xGax)2 (x=0–0.2) compounds were investigated. It was found that the iron moment of the compounds does not seem to vary much for x≤0.12. The Curie temperatures of the compounds decrease continuously by substituting Ga for Fe, which was attributed to the decrease of the R-T coupling strength due to Ga substitution. The intersublattice coupling constant JRFe was evaluated by molecular field model. The decrease of JRFe with increasing Ga content was found and related to the decrease of the number of the Tb-Fe interaction pairs when replacing Fe with Ga. By using an x-ray diffractometer the samples were step scanned with Cu radiation at a higher Bragg angle 2θ ranging from 71° to 74° to study the cubic (440) reflection. The splitting of (440) reflection for X≤1.2 was clearly seen and the easy direction magnetostriction λ111 of the compounds was calculated. It was found that λ111 decreases with increasing Ga content. This was attributed to the decrease of magnetic properties of the compounds. The polycrystal magnetostriction λs of the compounds has also been studied.

Proposed Methods for Depth Profiling of Residual Stresses using Beam-Limiting Masks

AbstractMethods are described which make use of x-ray absorbing masks to either limit beam penetration in the sample (Type I), or confine the diffracting volume within definite limits (Type II). The masks consist of a metal film of Au or U, containing many long, parallel apertures of effective width w and spacing c. The mask is either applied directly to the sample surface (Type I), or to a weakly absorbing film (Be or Kapton) on the sample surface (Type II). With the Type I mask, the diffracting volume can be limited to a surface layer whose maximum depth zm at ψ=0 varies linearly with w, irrespective of sample or wavelength. The masks can be used with ψ-tilts in an Ω-type goniometer, and strains and stresses can be determined by the Sin2ψ method. Depth profiles as a function of depth z (z-profiles) can be obtained with layer removal if gradients over the depth Zm can be neglected. With the Type n mask, the diffracting volume can be limited to a discrete subsurface layer whose average depth depends on (c+w) and the Bragg angle 2θ, and whose thickness depends on w and 2θ. z-Profiles can be obtained by varying the wavelength for a given reflection using a synchrotron source, without the need for layer removal. The methods have not yet been tested experimentally.

A new x-ray diffractometer design for thin-film texture, strain, and phase characterization

Powder diffraction techniques are potentially extremely useful for the characterization of a variety of metallic thin films which are used as interconnection materials in very large scale integrated (VLSI) devices. Phase identification, texture determination, elastic strain measurement, and grain size distribution can, in principle, be obtained nondestructively. Although x-ray techniques have long been applied to bulk materials for these purposes, conventional x-ray equipment, particularly the widely used Bragg–Brentano powder diffractometer, is often unsuitable for use on these thin films. High-angle reflections are extremely weak, strong texture renders many reflections inaccessible, and reflections from the silicon single crystal substrate can be a serious interference. The Seemann–Bohlin focusing geometry with a fixed low angle of incidence provides improved intensities and reduced substrate interference, but is unsuitable for texture determinations or strain measurements. We have designed a unique instrument, called a generalized focusing diffractometer (GFD), which combines the intensity advantages of a focusing geometry with the flexibility necessary for texture and strain measurements. The key capability is the arbitrary setting of the incidence beam angle α, independent of the Bragg angle 2θ, which allows accessing of practically any desired set of Bragg diffraction planes in the sample. The focusing condition is achieved in such a geometry by computer control of the sample to detector (receiving) slit distance. Four distinct modes of operation are possible with the GFD: Bragg–Brentano (BB), Seemann–Bohlin (SB), texture analysis (TA), and strain analysis (SA). The BB and SB modes are conventional, except that the incident beam angle α, can be varied arbitrarily in the SB mode, allowing small 2θ values to be explored. In the TA mode, the sample is rocked through a range of incidence angles while the detector is fixed in 2θ, but continuously positioned relative to the sample for optimal focus. In the SA mode, profile scans of particular Bragg reflections are obtained at varying beam incidence angles while the focusing conditions are continuously maintained by detector positioning. Several examples illustrate the application of the GFD. Untextured powdered Si provides a comparison of BB and SB modes. A film of 5 nm of Au on a glass substrate with well-developed (111) texture further illustrates the differences between these modes, and indicates the sensitivity of the GFD focusing geometry. A sample consisting of alternating layers of 50-nm sputtered amorphous TiSi2 and 500 nm of polycrystalline Al–Si on a Si substrate is examined in the BB and SB mode both as synthesized and after two thermal cycles at 450 °C. The scans indicate well-developed texture in the Al–Si film and the thermally induced growth of silicide crystallites. A sample of highly textured 1000-nm Al sputtered on Si is examined in TA mode to demonstrate this capability. Finally, SA scans on a sample of highly textured 750-nm Al-1% Sm sputtered on Si have been used to determine the strain in the thin film. The results are compared with those obtained by utilizing the wafer curvature method of strain analysis.

Relationship of the structure of the pseudobinary Laves phase compounds Sm-Er-Fe to their intrinsic magnetostriction

A series of pseudo-binary Laves phase compounds Sm1−xErxFe2 (x=0.1, 0.2...0.85) have been prepared and investigated. Using the method of x-ray diffractometry, the samples are step scanned with monochromatic Cu radiation at Bragg angle 2θ ranging from 50° to 110°. A detailed report is presented here on the broadening and splitting of the line profiles in some specimens at higher Bragg angles, like the cubic (533), (622), (642), and (731) reflections. The results are discussed in connection with the intrinsic magnetostriction of the material. The Curie temperatures and the room temperature saturation magnetization of the compounds have also been studied.

VARIATION OF DYNAMIC MECHANICAL PROPERTIES OF POLYACRYLONITRILE WITH HEAT TREATMENT

The effect of heat treatment on the dynamic mechanical properties of polyacrylonitrile (PAN) was investigated in connection with whether the change of the mechanical loss tangent (tan δ) peak at 160°C at the earlier stages of heat treatment can be attributed to thermal degradation proceeding preferentially in accordance with the ordering in polymer structure. The temperature dependence of the dynamic mechanical properties of the PAN films and fibers heat-treated at 220°C and 260°C for various periods, respectively, were measured at a constant frequency of 110Hz. The infrared absorbances at specified wave numbers and x-ray scatterings of those samples were also measured to characterize the chemical and physical changes of the polymer structure with heat treatment. The tan δ peak at 160°C decreased its peak height eminently by heat treatments for shorter periods, and simultaneously the x-ray scattering peaks at the Bragg angle 2θ=17.0° and 2θ=29.5° sharpened, whereas neither the infrared absorbance due to a carbon-carbon double bond nor the absorbance due to a carbon-nitrogen triple bond made a significant change. This indicates that the thermal degradation in PAN will not be a major cause of the decrease of the tan δ peak at 160°C. It is considered that the decrease of the tan δ peak at 160°C with heat treatment will be due to the change of the less ordered region to the ordered region, and that in thermo-degradative treatment under the proper conditions PAN will go through a step where the chain-to-chain lateral order augments, before the cyclization due to polymerization of the nitrile side groups proceeds substantially.

Absorption correction and normalization of X-ray small-angle scattering data for materials producing intense scattering at extremely low angles

Some materials of low absorption that contain particles in the several thousand Å range can produce an intensity of small-angle scattering that is a significant fraction of that of the transmitted beam. This is quite apparent in the range of a few s scattering angle when a Bonse–Hart small-angle scattering diffractometer is used. A method was developed that allows an accurate absorption correction to be calculated when the scattering by the sample can be approximated by an exponential function in the range of 0 to 5 s double Bragg angle 2θ. Variation of sample thickness allows the correction method to be checked.

X-Ray Measurement of Stress by the Double Exposure Method

There are two ways to measure stresses by means of X-rays, namely the counter method and the photographical method. There is tendency in recent years that the counter method has been gradually being employed in laboratories and factories because of its affording possibilities of easy handling and quick measuring. It is well known, however, that the photographical method has hither to been more frequently applied than the counter method to the measurement of residual stress on local and small positions. There are several difficult problems about the measuring technique of the conventional photographical method, for example, the difficulty in powdering the specimen surface with calibrating material and the difficulty in determination of peak positition on the broadened diffraction lines, since the distance between the diffraction lines from the specimen the calibrating material is close on the film.In the present study a new method of determining X-ray stress from this point of view by the photographical method without using calibrating material has been tested and those features are mentioned. The distance between the X-ray film and the surface of specimen can be precisely determined by the diameter of diffraction ring of the calibrating material which powders the specimen surface by the conventional method. Bragg's angle of specimen is obtained by using the value of the distance and the radius of the diffraction ring of the specimen. On the other hand, by a new method which is called the double exposure method, the first exposure is given on the X-ray film from which the distance to the specimen is l1, and when the distance between the specimen is set at l2, the second diffraction ring of the specimen is photographed. Bragg's angle 2θ is calculated from Δl, the difference between the distance l1 and the distance l2, and Δr, the difference between the radius r of the diffraction rings at the first and second exposures, as 2θ=tan-1[-Δr/Δl1].As was expected, it has been made clear from the theoretical and the experimental discussions that this double exposure method has many advantages as follows:(1) If the difference between the radius of both the diffraction rings, Δr, is larger than a quarter of diameter of the diffraction ring of the specimen on the conventional method, the accuracy of the measured value of stress by the double exposure method is better than that by the conventional method.(2) The two diffractions forming the similar patterns, the distance between the peaks of diffraction intensity curves, have been easily measured.(3) Irradiation of X-ray beams can be easily pointed at the measuring position on the specimen without using the metallic powder as calibrating materials.(4) There is a difficult problem in measuring by the conventional method, the stress on the specimen with broad diffraction lines, because these diffraction lines of the specimen interface with those of the calibrating material. In contrast with above mentioned case, the stress measurement of such a specimen is made possible by employing this double exposure method.