A method for reconstructing the three‐dimensional grain structure from data collected with a recently introduced laboratory‐based X‐ray diffraction contrast tomography system is presented. ...Diffraction contrast patterns are recorded in Laue‐focusing geometry. The diffraction geometry exposes shape information within recorded diffraction spots. In order to yield the three‐dimensional crystallographic microstructure, diffraction spots are extracted and fed into a reconstruction scheme. The scheme successively traverses and refines solution space until a reasonable reconstruction is reached. This unique reconstruction approach produces results efficiently and fast for well suited samples.
A novel reconstruction method to retrieve grain structure from laboratory diffraction contrast tomography is presented and evaluated.
Despite the abundance of shales in the Earth's crust and their industrial and environmental importance, their microscale physical properties are poorly understood, owing to the presence of many ...structurally related mineral phases and a porous network structure spanning several length scales. Here, the use of coherent X‐ray diffraction imaging (CXDI) to study the internal structure of microscopic shale fragments is demonstrated. Simultaneous wide‐angle X‐ray diffraction (WAXD) measurement facilitated the study of the mineralogy of the shale microparticles. It was possible to identify pyrite nanocrystals as inclusions in the quartz–clay matrix and the volume of closed unconnected pores was estimated. The combined CXDI–WAXD analysis enabled the establishment of a correlation between sample morphology and crystallite shape and size. The results highlight the potential of the combined CXDI–WAXD approach as an upcoming imaging modality for 3D nanoscale studies of shales and other geological formations via serial measurements of microscopic fragments.
Combined coherent X‐ray diffraction imaging and wide‐angle X‐ray diffraction is demonstrated to study the morphology, internal structure and mineralogy of shale fragments. Estimates of the unconnected nanoscale pore structure of shale microparticles are obtained.
A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three‐dimensional X‐ray diffraction (scanning 3DXRD) data is presented and evaluated. Given ...an a priori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimized with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning 3DXRD reconstruction methods and, thus, offer a more robust strain field estimation. The method is twofold validated: firstly by reconstruction from synthetic diffraction data, and secondly by reconstruction of a previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root‐mean‐square errors, mean absolute errors and maximum absolute errors across all six components of strain.
A novel regression method for estimating intragranular strain in polycrystalline materials from three‐dimensional X‐ray diffraction data is presented and evaluated. The method incorporates an equilibrium constraint to the reconstructed strain field by using a Gaussian process.
Hybrid potassium‐ion capacitors (KICs) show great promise for large‐scale storage on the power grid because of cost advantages, the weaker Lewis acidity of K+ and low redox potential of K+/K. ...However, a huge challenge remains for designing high‐performance K+ storage materials since K+ ions are heavier and larger than Li+ and Na+. Herein, the synthesis of hierarchical Ca0.5Ti2(PO4)3@C microspheres by use of the electrospraying method is reported. Benefiting from the rich vacancies in the crystal structure and rational nanostructural design, the hybrid Ca0.5Ti2(PO4)3@C electrode delivers a high reversible capacity (239 mA h g−1) and superior rate performance (63 mA h g−1 at 5 A g−1). Moreover, the KIC employing a Ca0.5Ti2(PO4)3@C anode and activated carbon cathode, affords a high energy/power density (80 W h kg−1 and 5144 W kg−1) in a potential window of 1.0–4.0 V, as well as a long lifespan of over 4000 cycles. In addition, in situ X‐ray diffraction is used to unravel the structural transition in Ca0.5Ti2(PO4)3, suggesting a two‐phase transition above 0.5 V during the initial discharge and solid solution processes during the subsequent K+ insertion/extraction. The present study demonstrates a low‐cost potassium‐based energy storage device with high energy/power densities and a long lifespan.
A hybrid potassium‐ion capacitor using hierarchical Ca0.5Ti2(PO4)3@C microspheres as anode and activated carbon as cathode is shown. The potassium‐ion storage device delivers a high power density of 5144 W kg−1 at an energy density of 34 W h Kg−1 with a long lifespan of 4000 cycles in the potential range of 1.0–4.0 V.
Dolomite CaMg(CO3)2 forms in numerous geological settings, usually as a diagenetic replacement of limestone, and is an important component of petroleum reservoir rocks, rocks hosting base metal ...deposits and fresh water aquifers. Dolomite is a rhombohedral carbonate with a structure consisting of an ordered arrangement of alternating layers of Ca2+ and Mg2+ cations interspersed with CO32− anion layers normal to the c‐axis. Dolomite has R3¯ symmetry, lower than the (CaCO3) R3¯c symmetry of calcite primarily due to Ca–Mg ordering. High‐magnesium calcite also has R3¯c symmetry and differs from dolomite in that Ca2+ and Mg2+ ions are not ordered. High‐magnesium calcite with near‐dolomite stoichiometry (≈50 mol% MgCO3) has been observed both in nature and in laboratory products and is referred to in the literature as protodolomite or very high‐magnesium calcite. Many dolomites display some degree of cation disorder (Ca2+ on Mg2+ sites and vice versa), which is detectable using transmission electron microscopy and X‐ray diffractometry. Laboratory syntheses at high temperature and pressure, as well as studies of natural dolomites show that factors affecting dolomite ordering, stoichiometry, nucleation and growth include temperature, alkalinity, pH, concentration of Mg and Ca, Mg to Ca ratio, fluid to rock ratio, mineralogy of the carbonate being replaced, and surface area available for nucleation. In spite of numerous attempts, dolomite has not been synthesized in the laboratory under near‐surface conditions. Examination of published X‐ray diffraction data demonstrates that assertions of dolomite synthesis in the laboratory under near‐ambient conditions by microbial mediation are unsubstantiated. These laboratory products show no evidence of cation ordering and appear to be very high‐magnesium calcite. Elevated‐temperature and elevated‐pressure experiments demonstrate that dolomite nucleation and growth always are preceded by very high‐magnesium calcite formation. It remains to be demonstrated whether microbial‐mediated growth of very high‐magnesium calcite in nature provides a precursor to dolomite nucleation and growth analogous to reaction paths in high‐temperature experiments.
The crystal grain size can be quantitatively calculated by Scherrer equation according to the diffraction peak broadening in the XRD curves. Actually, the results calculated by the Scherrer equation ...are the thickness that perpendicular to the crystal planes. However, in the actual XRD measurements, the broadening of the diffraction peaks is not only because of the Micro‐level changes of crystal such as grain size and lattice distortion, but also due to the instrumental broadening. Thus, the Scherrer equation is less reliable if the full width at half maximum caused by the physical broadening is smaller than that caused by the instrumental broadening. In this paper, it is concluded that the applicable range of the Scherrer equation will increases with the increasing diffraction angle. As an example of Scherrer equation's application, the calculation result for the maximum applicable scope of Si(100) films is 137 nm.
In this paper, the relationship between the applicable scope of Scherrer equation and the variation of X‐ray diffraction angle are calculated. Meantime, Si(100) is taken as an example to calculate the maximum grain size of Si(100) that can be obtained in the actual measurement processing based on the Scherrer equation.
This paper presents the Domain Auto Finder (DAFi) program and its application to the analysis of single‐crystal X‐ray diffraction (SC‐XRD) data from multiphase mixtures of microcrystalline solids and ...powders. Superposition of numerous reflections originating from a large number of single‐crystal domains of the same and/or different (especially unknown) phases usually precludes the sorting of reflections coming from individual domains, making their automatic indexing impossible. The DAFi algorithm is designed to quickly find subsets of reflections from individual domains in a whole set of SC‐XRD data. Further indexing of all found subsets can be easily performed using widely accessible crystallographic packages. As the algorithm neither requires a priori crystallographic information nor is limited by the number of phases or individual domains, DAFi is powerful software to be used for studies of multiphase polycrystalline and microcrystalline (powder) materials. The algorithm is validated by testing on X‐ray diffraction data sets obtained from real samples: a multi‐mineral basalt rock at ambient conditions and products of the chemical reaction of yttrium and nitrogen in a laser‐heated diamond anvil cell at 50 GPa. The high performance of the DAFi algorithm means it can be used for processing SC‐XRD data online during experiments at synchrotron facilities.
This paper presents the Domain Auto Finder (DAFi) program and its application to the analysis of single‐crystal X‐ray diffraction (SC‐XRD) data from multiphase mixtures of microcrystalline solids and powders. The DAFi algorithm is designed to quickly find subsets of reflections from individual domains in a whole set of SC‐XRD data and neither requires a priori crystallographic information nor is limited by the number of phases or individual domains.
Transformation-induced plasticity (TRIP) assisted duplex stainless steels, with three different stabilities of the austenite phase, were investigated by synchrotron x-ray diffraction characterization ...during in situ uniaxial tensile loading. The micromechanics and the deformation-induced martensitic transformation (DIMT) in the bulk of the steels were investigated in situ. Furthermore, scanning electron microscopy supplemented the in situ analysis by providing information about the microstructure of annealed and deformed specimens. The dependence of deformation structure on austenite stability is similar to that of single-phase austenitic steels with shear bands and bcc-martensite (α′) generally observed, and blocky α′ is only frequent when the austenite stability is low. These microstructural features, i.e. defect structure and deformation-induced martensite, are correlated with the micro- and macro-mechanics of the steels with elastoplastic load transfer from the weaker phases to the stronger α′, in particular this occurs close to the point of maximum rate of α′ formation. A clear strain-hardening effect from α′ is seen in the most unstable austenite leading to a pronounced TRIP effect.
X-Ray Diffraction: Instrumentation and Applications Bunaciu, Andrei A.; Udriştioiu, Elena gabriela; Aboul-Enein, Hassan Y.
Critical reviews in analytical chemistry,
10/2015, Letnik:
45, Številka:
4
Journal Article
Recenzirano
X-ray diffraction (XRD) is a powerful nondestructive technique for characterizing crystalline materials. It provides information on structures, phases, preferred crystal orientations (texture), and ...other structural parameters, such as average grain size, crystallinity, strain, and crystal defects. X-ray diffraction peaks are produced by constructive interference of a monochromatic beam of X-rays scattered at specific angles from each set of lattice planes in a sample. The peak intensities are determined by the distribution of atoms within the lattice. Consequently, the X-ray diffraction pattern is the fingerprint of periodic atomic arrangements in a given material. This review summarizes the scientific trends associated with the rapid development of the technique of X-ray diffraction over the past five years pertaining to the fields of pharmaceuticals, forensic science, geological applications, microelectronics, and glass manufacturing, as well as in corrosion analysis.
The Scherrer equation and the dynamical theory of X-ray diffraction Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla dos Santos, Cássio ...
Acta crystallographica. Section A, Foundations and advances,
05/2016, Letnik:
72, Številka:
3
Journal Article
Recenzirano
The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its ...derivation is based on the kinematical theory of X‐ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X‐ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X‐ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half‐maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm−1 the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.
The maximum crystal size is determined for application of the Scherrer equation.
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