Overlapping Diffraction Peaks Research Articles

Multi-phase transition behavior over a wide temperature range in magnetocaloric (Mn, Fe, Ni)2(P, Si) alloys

This study investigates the magnetocaloric property of MnFe0.95-xNixP0.6Si0.4 (x = 0.02, 0.03, 0.04) alloys over a wide temperature range and their related phase transitions. These P-rich composition alloys, with a P/Si ratio of 1.5, exhibit multi-phase transition behavior across a broad temperature range. In-situ 2D X-ray diffraction reveals overlapping diffraction peaks of the Fe2P-type hexagonal structure throughout the ferromagnetic-paramagnetic transition, rather than a single, drastic transition. This observation suggests the formation of a multi-phase structure within the alloys. Consequently, these alloys exhibit high refrigeration capacity (RC) values ranging from 168.6 to 218.1 J kg−1 under an applied magnetic field of 2 T. Notably, these RC values are superior to those observed in other P/Si ratio compositions without multi-phase transitions or even Gd, a representative magnetocaloric material. This improved performance demonstrates the promising potential of these multi-phase transition alloys as candidates for magnetocaloric refrigeration systems.

Sphalerite and Pyrite on Kuroko-Type Ore Deposit: A Case Study of Phase Ambiguity and Its Prediction Technique by Means of X-Ray Diffraction Analysis

Kuroko-type VMS (volcanogenic massive sulfide) ore deposit is a deposit that has some abundant sulfide minerals such as pyrite, chalcopyrite, galena and sphalerite. Besides them, other common sulfide minerals also occur, such as bornite, acanthite (argentite) and some of tennantite-tetrahedrite series. In some cases, we can find sphalerite and pyrite on these deposits. These cases often make the difficulty of XRD analysis. It is caused by some overlapping diffraction peaks between pyrite and sphalerite, which are difficult to be distinguished. This problem can cause miscalculation of weight fraction between them. Therefore, this study was done in order to make sure the true phase between pyrite and sphalerite of the overlapping diffraction peaks. Cubic structure analysis and precise lattice parameter calculation were used as the method in this study in order to determine the true phase of sphalerite-pyrite overlapping peaks. An XRD analysis on the case study sample shows that there are five cubic planes, i.e. (111), (200), (220), (113), and (222) on some overlap diffraction peaks. By utilizing this method, these cubic planes can be distinguished where (111) and (113) are pyrite phases while (200), (220) and (222) are sphalerite phases.Keywords: Kuroko, sphalerite, pyrite, XRD, precise lattice parameter.

Input4MAUD: an efficient program for automatic two-dimensional diffraction image series input and/or batch refinement withMAUD

In materials science or applied crystallography, X-ray diffraction represents a versatile and useful method with which one can obtain the orientation of single crystals or even the texture of a polycrystalline material. When the investigated sample consists of many phases, or phases of low symmetry, it becomes difficult to measure pole figures from single diffraction peaks. A combined Rietveld–texture analysis with the programMAUDis perfectly suitable to deal with conditions of overlapping diffraction peaks, including those arising from different phases. Even though nearly no alternative toMAUDexists, it is not always easy to use. The input of a file series of two-dimensional diffraction images, for example from a texture measurement, can be time consuming since each individual image must be loaded manually, and only the newest beta version ofMAUDallows semi-automated file input. The new programinput4MAUD, which is presented in this paper, offers a much more efficient way to automate both single and batch file series input intoMAUDas well as the preparation of basic batch refinements withMAUD. input4MAUDis written in Visual C++ and is currently available as a 32-bit statically compiled binary executable file for Windows.

A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup

A data-analysis methodology is presented for the characterization of three-dimensional microstructures of polycrystalline materials from data acquired using three-dimensional X-ray diffraction (3DXRD). The method is developed for 3DXRD microscopy using a far-field detector and yields information about the centre-of-mass position, crystallographic orientation, volume and strain state for thousands of grains. This first part deals with pre-processing of the diffraction data for input into the algorithms presented in the second part [Sharma, Huizenga & Offerman (2012).J. Appl. Cryst.45, 705–718] for determination of the grain characteristics. An algorithm is presented for accurate identification of overlapping diffraction peaks from X-ray diffraction images, which has been an issue limiting the accuracy of experiments of this type. The algorithm works in two stages, namely the identification of overlapping peaks using a seeded watershed algorithm, and then the fitting of the peaks with a pseudo-Voigt shape function to yield an accurate centre-of-mass position and integrated intensity for the peaks. Regions consisting of up to six overlapping peaks can be successfully fitted. Two simulations and an experiment are used to verify the results of the algorithms. An example of the processing of diffraction images acquired in a 3DXRD experiment with a sample consisting of more than 1600 grains is shown. Furthermore, a procedure for the determination of the parameters of the experimental setup (global parameters) without the need for a calibration sample is presented and validated using simulations. This is immensely beneficial for simplifying experiments and the subsequent data analysis.

Calculation of anisotropic properties of dental enamel from synchrotron data

Obtaining information about the intrinsic structure of polycrystalline materials is of prime importance owing to the anisotropic behaviour of individual crystallites. Grain orientation and its statistical distribution, i.e. the texture, have an important influence on the material properties. Crystallographic orientations play an important role in all kinds of polycrystalline materials such as metallic, geological and biological. Using synchrotron diffraction techniques the texture can be measured with high local and angular resolving power. Here methods are presented which allow the spatial orientation of the crystallites to be determined and information about the anisotropy of mechanical properties, such as elastic modulus or thermal expansion, to obtained. The methods are adapted to all crystal and several sample symmetries as well as to different phases, for example with overlapping diffraction peaks. To demonstrate the abilities of the methods, human dental enamel has been chosen, showing even overlapping diffraction peaks. Likewise it is of special interest to learn more about the orientation and anisotropic properties of dental enamel, since only basic information is available up to now. The texture of enamel has been found to be a tilted fibre texture of high strength (up to 12.5×). The calculated elastic modulus is up to 155 GPa and the thermal expansion up to 22.3 × 10(-6)°C(-1).

有機粉末構造解析をはじめよう！（１）粉末未知結晶構造解析の紹介

Structure Determination from Powder Diffraction data (SDPD) technique for organic and organo-metallic molecular crystals has been developed since 1990s, and is now widely used. The X-ray powder diffraction data has a difficulty in extraction of correct intensity data from overlapping diffraction peaks, however, the development of direct space method overcomes the difficulty, leading to the progress of this area. The SDPD technique was composed of the indexing, intensity extraction, initial structure solution, structure refinement steps and each of them requires very careful treatments. This technique is usually used for crystal structure determination of powdery crystals, and also phase transition and crystalline-state reaction are examined by SDPD technique because single crystallinity is lost in such phenomena.

Solving crystal structures from two-wavelength X-ray powder diffraction data - breaking the phase ambiguity in the noncentrosymmetric case

Direct methods of breaking phase ambiguities in protein crystallography have been introduced in powder diffraction analysis. This is aiming at ab initio solution of noncentrosymmetric structures using two-wavelength anomalous powder diffraction data. The known structure of the hydrogen bromide salt of leotidine (C(14)H(20)O(2)N(2).HBr) in space group P2(1)2(1)2(1) was used for simulating two-wavelength anomalous powder diffraction with the Br atom as anomalous scatterer. X-ray wavelengths are selected at lambda(1) = 0.920 and lambda(2) = 1.500 A. Unique reflections from the diffraction pattern of lambda(2) were able to locate the Br atom accurately. All overlapping diffraction peaks were uniformly partitioned to decompose into single reflections. Structure-factor amplitudes were then extracted. With these and the substructure of Br atoms, unique phases for centric reflections (hk0, h0l and 0kl) and phase doublets for noncentric reflections were obtained. The direct method was used to break the phase ambiguity leading to an interpretable electron-density map, from which five cycles of Fourier iteration yielded the complete structure.

Determination of orientation distribution functions in a TiNi alloy austenite and a TiNiCu alloy martensite

In this study, the incomplete pole figures for a TiNi alloy austenite and a TiNiCu alloy martensite were obtained using the texture goniometer. For the TiNiCu martensite pole figures, a position sensitive detector was used to simultaneously record the X-ray diffraction spectra in a 7{degree} angular range. The overlapping diffraction peaks were then separated by the fitting of Gauss profile function. Subsequently, the program system established in terms of Bunge's series expansion method was used to calculate the orientation distribution functions for the austenite and martensite. Finally, the austenitic and martensite textures were shown to be related to each other using the 12 lattice correspondence variants proposed by Miyazaki et al.

Temperature change of the lamellar structure of DPPC/disaccharide/water systems with low water content

Temperature change in l- α-dipalmitoyl phosphatidylcholine (DPPC)/disaccharide systems with low water content (less than 8 wt.%) was investigated using X-ray diffraction within a range of two transition temperatures. X-ray diffraction above the higher transition temperature showed a broad symmetric peak, indicating the L α phase. Below the higher transition temperature, two overlapping diffraction peaks were observed. After peak separation, temperature change in these systems was analyzed using peak parameters of the two peaks. Peak parameters of the lower angle peak changed continuously up to and above the higher transition temperature, suggesting the systems to be in a liquid crystal phase below the higher transition temperature. Fourier-transform infrared (FT-IR) spectra of the DPPC/trehalose system with 5.5 wt.% water showed the wave number of asymmetric stretching of phosphate groups to change at the lower transition temperature and that of symmetric stretching of CH 2 groups, to change between the lower and higher transition temperatures. Thus, below the lower transition temperature, the system is shown to be in a gel phase. Conformational change in phosphate groups occurred at the lower transition temperature. Within the lower and higher transition temperatures, two phases were found to coexist and transition from the gel phase to L α phase to occur continuously. Above the higher transition temperature, the system is in the L α phase.

The Modified Maximum Entropy Method (MMEM) in QTA for Lower Symmetry Polycrystalline Aggregates

A new algorithm of quantitative texture analysis (QTA), which is called the modified maximum entropy method (MMEM), has been proposed and applied to determination of textures in polycrystalline samples of lower crystal symmetry with overlapping diffraction peaks (Wang and Xu, 1995a). By introducing directly the maximum entropy principle into the least square procedure of pole figure inversion (Bunge, 1969), then both minimizing the differences between experimental and postulated pole figure data, and maximizing entropy may be satisfied simultaneously. Thus, the maximum entropy principle is applied to the entire process of QTA in frame of the harmonic method (HM). The detailed comparisons among the three pole figure inversion methods, i.e. the traditional HM, the primary maximum entropy method (MEM) and the MMEM, are given through a model example of simulated fiber texture. It is shown that the precise and stable solution of inverse pole figure for the polycrystalline samples with smooth or sharp textures will be obtained by the MMEM even using a less number of pole figures. The minimum range of polar angle and the least number of pole figures, which are needed in the QTA for pretended tetragonal materials by the MMEM, are discussed in detail.

Determination of low levels of quartz in calcium carbonates by x-ray diffractometry

Naturally occurring calcium carbonates often have a complex accessory mineralogy. Quartz is a common associate, typically present at concentrations < 1 wt.%. A method is described whereby x-ray powder diffractometry may be used to quantify quartz in such samples to better than ±0.01 wt.% (1σ error) at the 0.1 wt.% level. The quartz in the samples is pre-concentrated by partial acid dissolution of the calcium carbonate, and careful attention is given to reproducible sample preparation of the resultant partial residues. Calibration is by an external standard with mass absorption corrections being applied to compensate for variations in sample chemistry. The presence of additional accessory minerals such as mica and feldspar can lead to problems due to overlapping diffraction peaks. These problems are discussed and the use and limitations of the short range profile fitting techniques employed in this method are described. The significance of particle statistics, counting statistics, and the variability associated with sample preparation in limiting the accuracy of quantification at low levels is also examined.

Residual stress analysis using overlapping diffraction peaks. Case of textured cubic materials

Residual stresses in polycrystalline materials can be determined from the 2θ shift of a reflection peak's line profile. Recently, multiple reflections have been used for residual stress analysis in single-phase textured cubic materials. Analogously, residual stresses in two-phase materials could be determined from overlapping peaks of both phases. Equations are derived for residual stress analysis using partially or completely overlapping diffraction peaks. Mainly textured cubic materials are considered. It is shown that the so-called quasi-isotropic diffraction elastic constants become connected to texture-dependent quantities. In the examples treated the calculated diffraction strains of three multiple reflections exhibit only small nonlinearities although the intensities oscillate strongly.

Profile separation in complex powder patterns

Diffraction patterns from multi-element alloys, composite materials, enriched ores and other materials involving a mix of several phases often contain regions of overlapping diffraction peaks. In many cases, the peaks can be separated by a combination of numerical differentiation of the data and non-linear least-squares curve-fitting techniques. The derivative provides a powerful but simple technique for distinguishing the number of peaks and their locations within a scramble. These results are required as input to a least-squares curve-fitting routine. The end result of this two-step procedure is a set of parameters that define the positions, shape, width and areas of the separate peaks. A statistical analysis of the data requirements indicates that a good second derivative can be obtained with a peak count in the ~ 105 range using raw data, and the ~ 104 range with digital smoothing. The use of less accurate analog scans is also discussed. Examples are given with overlapping peaks in a 2θ range of less than 1° . The theoretical results describing the data requirements, resolution, distortion effects, and peak enhancement are based upon a Pearson VII function which is capable of describing all shapes continuously between the Cauchy, modified Lorentzian and the Gaussian.

The separation of overlapping peaks in X-ray powder patterns with the use of an experiment profile

A method for least-squares estimation of the intensities of overlapping diffraction peaks has been successfully applied in structure refinement with powder data. The diffraction peaks are taken to have arbitrary but similar shape, a single set of experimentally determined Fourier coefficients representing this `universal profile' is used, and the abscissa is transformed to take account of angular dependence of the actual profiles. The method has been implemented with a Fortran IV program which also separates α1 and α2 contributions and yields the correlation matrix for the parameters representing the overlapping peaks.