Experimental X-ray Diffraction Patterns Research Articles

Quantifying the Likelihood of Structural Models through a Dynamically Enhanced Powder X-Ray Diffraction Protocol.

Structurally characterizing new materials is tremendously challenging, especially when single crystal structures are hardly available which is often the case for covalent organic frameworks. Yet, knowledge of the atomic structure is key to establish structure‐function relations and enable functional material design. Herein, a new protocol is proposed to unambiguously predict the structure of poorly crystalline materials through a likelihood ordering based on the X‐ray diffraction (XRD) pattern. Key of the procedure is the broad set of structures generated from a limited number of building blocks and topologies, which is submitted to operando structural characterization. The dynamic averaging in the latter accounts for the operando conditions and inherent temporal character of experimental measurements, yielding unparalleled agreement with experimental powder XRD patterns. The proposed concept can hence unquestionably identify the structure of experimentally synthesized materials, a crucial step to design next generation functional materials.

Quantifying the Likelihood of Structural Models through a Dynamically Enhanced Powder X‐Ray Diffraction Protocol

AbstractStructurally characterizing new materials is tremendously challenging, especially when single crystal structures are hardly available which is often the case for covalent organic frameworks. Yet, knowledge of the atomic structure is key to establish structure‐function relations and enable functional material design. Herein, a new protocol is proposed to unambiguously predict the structure of poorly crystalline materials through a likelihood ordering based on the X‐ray diffraction (XRD) pattern. Key of the procedure is the broad set of structures generated from a limited number of building blocks and topologies, which is submitted to operando structural characterization. The dynamic averaging in the latter accounts for the operando conditions and inherent temporal character of experimental measurements, yielding unparalleled agreement with experimental powder XRD patterns. The proposed concept can hence unquestionably identify the structure of experimentally synthesized materials, a crucial step to design next generation functional materials.

A Comprehensive Study of Ca9Tb(PO4)7 and Ca9Ho(PO4)7 Doped β-Tricalcium Phosphates: Ab initio Crystal Structure Solution, Rietveld Analysis, and Dielectric Properties

The scientific interest toward the structural, luminescence, and dielectric properties of tricalcium phosphate (TCP) materials, in particular, the doped TCP-based compounds, is mainly due to their biocompatibility and bioactivity behavior and the increasing number of their applications. In the literature, structural investigations of a doped β-TCP compound are usually carried out by powder diffraction data under the assumption that it has a centrosymmetric whitlockite structure. Recent studies have shown that this assumption is not always fulfilled. For this reason, it is necessary to use methods of nonlinear and dielectric spectroscopy to prove the true symmetry of whitlockite-like phases. This work provides a detailed and comprehensive study on the structural, dielectric, and nonlinear properties of the polycrystalline Tb- and Ho-doped tricalcium phosphates, chemically Ca9Tb(PO4)7 and Ca9Ho(PO4)7. Their crystal structure was explored using powder X-ray diffraction, adopting an ab initio approach for the structure solution followed by the Rietveld refinement. For Ca9Tb(PO4)7, the qualitative analysis of the experimental powder X-ray diffraction pattern revealed that the sample was not a single phase. Nevertheless, its crystal structure has been determined by Direct Methods. The presence of the dopant cation was omitted in the solution process by Direct Methods and considered in the successive Rietveld refinement step. The analysis of the occupancies has clarified the Tb3+ cation distribution in its preferential sites. The same pathway has been followed for the Ca9Ho(PO4)7 sample, which corresponded to a single-phase structure. The dielectric properties of the two doped compounds (Tb3+ and Ho3+) were also examined, and reversible ferroelectric-paraelectric phase transitions were found at 862 and 872 K, respectively.

On the structural complexity of tetragonal tungsten bronze type niobium tungsten oxides

AbstractIn this comparative study, two samples with a slightly different oxygen : metal ratio have been characterized by various electron microscopy methods and by single‐crystal and powder X‐ray diffraction (XRD). A reasonably good fit to the experimental powder XRD patterns could be achieved by Rietveld refinement for both samples Nb8W9O47 and Nb7W10O47.5 using the structural models of Nb6.7W10.3O47 and Nb8W9O47 both obtained from X‐ray crystal structure analysis. HRTEM investigations confirm that Nb8W9O47 crystallizes as a pure phase in the well‐known threefold superstructure of the tetragonal tungsten bronze type (TTB). In contrast, a more complex real structure was found for the sample Nb7W10O47.5 with small domains of Nb4W7O31 appearing besides large ones of Nb8W9O47 and in addition extended TTB‐based areas with short‐range order only. The diffuse scattering caused by this disorder is easily detected in the electron diffraction pattern but does not affect the Rietveld refinement of the powder XRD patterns. However, on the basis of powder diffraction experiments, it is clearly possible to distinguish between the above compounds and the hypothetical, but non‐existing compound “Nb18W16O93”, a composition recently postulated for battery materials.

A Nonlinear Optical Switchable Sulfate of Ultrawide Bandgap

Nonlinear optical (NLO) switchable materials have attracted intense attention because of their promising applications in optoelectronic devices. However, previous studies are mainly limited to mole...

Intrinsic defects and non-stoichiometry in undoped cadmium silicate hosts

Cadmium silicates, mainly the CdSiO3 phase, are interesting materials due to their persistent and intrinsic luminescence, making them possible candidates for a number of applications. Although many of the luminescence properties of these materials are known from the experimental point of view, the current problem that still remains is to understand the origin of the intrinsic luminescence. Different types of point defects were considered in the literature and, most of them are contradictory and/or controversial and lack direct evidence for the assumptions. The aim of the present work is to investigate in depth the possible origin of the luminescence properties of cadmium silicates, focusing on the CdSiO3 phase, considering not only the possibilities reported in the literature but all other mechanisms involving intrinsic defects in these materials. Our results predicted that CdSiO3 tends to show stoichiometric deviation due to CdO pseudo-Schottky defects and the simulated structure for the deficient matrix is much closer to the experimental X-ray diffraction pattern than the stoichiometric one. This feature indicates that most of the available CdSiO3 phases are truly CdO deficient. Additionally, it was found that this defect induces the formation Si–Si bonds that are responsible for the intrinsic luminescence in this matrix. The CdO deficiency also accounts for the presence of additional cadmium silicate phases, like Cd2SiO4 or Cd3SiO5, during the synthesis of CdSiO3, a common feature found in many works in the literature. These results strongly indicate that CdO pseudo-Schottky defects, that trigger the CdO deficiency naturally present in cadmium silicate structures, should be considered not only in all luminescent models proposed, including intrinsic and extrinsic matrix, but also for the structural properties of these materials.

A Genetic Algorithmic Approach to Determine the Structure of Li-Al Layered Double Hydroxides.

Layered double hydroxides (LDH) demonstrate significant potential across a range of applications, including as catalysts, delivery vehicles for pharmaceuticals, environmental remediation, and supercapacitors. Explaining the mechanism of LDH action at the atomic scale in these and other applications is challenging, however, due to the difficulty in precisely defining the bulk and surface structure and chemical compositions. Here, we focus on the determination of the structure of lithium-aluminum (Li-Al) LDH, which has shown promise in the catalytic depolymerization of lignin, both directly as the catalyst and as a support for gold nanoparticles. While the relative positions of the Li and Al metals are generally well resolved by X-ray crystallography, it is the structures of the anionic layers, consisting of water and carbonate, that are less well established. Combinatorial analyses of all possible positions and rotations of the water and carbonate in the three-layered Li-AL LDH polytope reveals that the phase space is much too large to examine in any reasonable time frame in a one-by-one structure exploration. To overcome this limitation, we develop and deploy a genetic algorithm (GA) wherein fitness is determined by matching a calculated X-ray diffraction (XRD) pattern for a given structure to the known experimental XRD pattern. The GA approach results in structures of high fitness that portend the bulk Li-Al LDH structure. Importantly, the GA approach offers the potential to determine the structures of other LDH, and more generally layered materials, which are generally difficult to describe given the large chemical and structural space to be explored.

FCC-to-HCP Phase Transformation in CoCrNix Medium-Entropy Alloys

A hybrid first-principles/Monte Carlo simulation is combined with experiments to study the structure and elastic properties of CoCrNix (x = 1–0.5) alloys. The experimental X-ray diffraction patterns show that the structures have changed from the single-phase face-centered cubic (FCC) structure at x = 1–0.8 to the coexistence of FCC and the hexagonal close-packed structures at x = 0.7–0.5, which is further confirmed by calculations on mixing energies. The elastic moduli by calculation are basically in agreement with experiments. Room-temperature tension shows that the six alloys have a certain plasticity, the strength and plasticity of the alloys have a linear decrease with the decrease in Ni contents, and the plasticity of the alloys drops from 84 to 23%. Furthermore, first-principles density function theory calculations were employed to reveal the electronic and magnetic structures of alloys. The electron density of states for all alloys is asymmetrical, which illustrates that the alloys are ferromagnetism. It is found that Cr atoms can suppress the ferromagnetism of alloys, since Cr atoms have both positive and negative magnetic moments in all alloys.

Modeling of gyroidal mesoporous CMK-8 and CMK-9 carbon nanostructures and their X-Ray diffraction patterns

1. Abstract Powder X-ray diffraction (XRD) patterns of ordered mesoporous CMK-8 and CMK-9 carbon materials are simulated by geometric modeling. The materials are amorphous at the atomic length scale but exhibit highly symmetric gyroidal structures at the nanometer scale, corresponding to regular, continuous nanopore systems with cubic symmetry. Their structures lead to characteristic low-angle XRD signatures. We introduce a model based on geometrical considerations to simulate CMK-8 and CMK-9 structures with variable volume fraction of carbon (vs. pore volume, i.e., variable 'pore wall thickness'). In addition, we also simulate carbon materials with variable amounts of guest species (e.g., sulfur) residing in their pores. The corresponding XRD patterns are calculated. The carbon volume fraction turns out to have a significant impact on the relative diffraction peak intensities, especially in case of CMK-9 carbon that features a bimodal porosity. Likewise, the presence of guest species in the pores may also strongly affect the relative peak intensities. Our study suggests that careful evaluation of experimental low-angle XRD patterns of (real) CMK-8 or CMK-9 materials offers an opportunity to obtain detailed information about the nanostructural properties in addition to the mere identification of the pore systems geometry.

Charge mobility calculation of organic semiconductors without use of experimental single-crystal data

Prediction of material properties of newly designed molecules is a long-term goal in organic electronics. In general, it is a difficult problem, because the material properties are dominated by the unknown packing structure. We present a practical method to obtain charge transport properties of organic single crystals, without use of experimental single-crystal data. As a demonstration, we employ the promising molecule C10–DNBDT. We succeeded in quantitative evaluation of charge mobility of the single crystal using our quantum wave-packet dynamical simulation method. Here, the single-crystal data is computationally obtained by searching possible packing structures from structural formula of the molecule. We increase accuracy in identifying the actual crystal structure from suggested ones by using not only crystal energy but also similarity between calculated and experimental powder X-ray diffraction patterns. The proposed methodology can be a theoretical design technique for efficiently developing new high-performance organic semiconductors, since it can estimate the charge transport properties at early stage in the process of material development.

Determination of the phase composition of partially dehydroxylated kaolinites by modelling their X-ray diffraction patterns

AbstractModelling of experimental X-ray diffraction (XRD) patterns is used to determine the phase composition of partially dehydroxylated kaolinite samples. To identify unambiguously the presence of two or three phases in the heated kaolinite samples, the full range of their XRD patterns has to be analysed. Two different kaolinites, from Imerys (UK) and from Georgia (USA; KGa-21), were studied. The heating temperatures were selected to cover the entire range of dehydroxylation for both kaolinites (400–550°C for Imerys and 400–495°C for KGa-21). Two different dehydroxylation pathways were observed. At each stage of partial dehydroxylation, the kaolinite from Imerys consisted of the original, non-dehydroxylated kaolinite and of a fully dehydroxylated phase, metakaolinite. During partial dehydroxylation of kaolinite KGa-21, each product formed at a given heating temperature consisted of three phases: the original kaolinite; a dehydroxylated phase, metakaolinite; and a phase with diffraction features corresponding to a defective kaolinite-like structure. To determine the content of metakaolinite in a partially dehydroxylated specimen, its experimental XRD pattern was reproduced by the optimal summation of the diffraction patterns of the initial kaolinite and metakaolinite. A procedure that reveals the basic diffraction features of the third phase is suggested. The XRD patterns and thus the structures of the metakaolinites formed after dehydroxylation of the Imerys and KGa-21 samples differ substantially. The conventional determination of the initial kaolinite and metakaolinite contents in partially dehydroxylated kaolinite based on the analysis of basal reflections and weight losses may lead to overlooking the formation of the intermediate phases.

Cluster-based CaII, MgII and CdII coordination polymers based on amino-functionalized tri-phenyl tetra-carboxylate: Bi-functional photo-luminescent sensing for Fe3+ and antibiotics

Excess and deficiency of iron(III) and antibiotics from normal permissible limits will induce serious disorders, so their detection is important but challenging. In this work, the asymmetric amino-functionalized tetra-carboxylate H4L (2′-amino-1,1’:4′,1″-terphenyl-3,3″,5,5″-tetracarboxylic acid) containing large conjugated ter-phenyl aromatic backbones have been synthesized and employed. Through a one-pot powerful solvo-thermal synthetic strategy, a series of unique tri-nuclear cluster-based CaII, MgII and CdII coordination polymers, namely [Ca1.5(μ8-HL)(DMF)]n (1), {[Mg1.5(μ7-HL)·(H2O)2]·3H2O}n (2) and {[Cd1.5(μ10-L)0.75]n·H2O·DMF}n (3) have been successfully prepared. 1–3 exhibit excellent photo-luminescent properties and good fluorescence stability. Structural analyses reveal that tri-nuclear CaII secondary building blocks (SBUS) are linked via HL3−, forming the 2D clustered-based micro-porous coordination polymer 1. As for 2, three carboxylate groups of partly de-pronated HL3− also link these neighboring tri-nuclear MgII SBUS, which constructs the 2D MgII coordination framework 2. As for 3, fully de-pronated L4− also links these neighboring tri-nuclear CdII SBUS, which ultimately constructs the 3D micro-porous coordination framework 3. Experimental powder x-ray diffraction (PXRD) patterns coincide well with the theoretical patterns, which indicate that we have successfully synthesized the pure phase material 1–3. Photo-luminescent experiments demonstrate that coordination polymers 1–3 can be successfully applied towards bi-functional sensing for sensitive detection of Fe3+ and the antibiotics NZF (Nitrofurazone). To the best of our knowledge, this is the first example of the application of amino-functionalized tri-phenyl tetra-carboxylate based MOFs towards bi-functional discrimination of Fe3+ and NZF antibiotics with high efficiency Ksv values (For Fe3+: 7.28 × 104 M−1 for 1; 3.38 × 104 M−1 for 2 and 3.29 × 104 M−1 for 3 and for NZF antibiotics: 4.47 × 103 M−1 for 1; 4 × 103 M−1 for 2 and 5.6 × 103 M−1 for 3).

Revealing Transition States during the Hydration of Clay Minerals.

A molecular-scale understanding of the transition between hydration states in clay minerals remains a challenging problem because of the very fast stepwise swelling process observed from X-ray diffraction (XRD) experiments. XRD profile modeling assumes the coexistence of multiple hydration states in a clay sample to fit the experimental XRD pattern obtained under humid conditions. While XRD profile modeling provides a macroscopic understanding of the heterogeneous hydration structure of clay minerals, a microscopic model of the transition between hydration states is still missing. Here, for the first time, we use molecular dynamics simulation to investigate the transition states between a dry interlayer, one-layer hydrate, and two-layer hydrate. We find that the hydrogen bonds that form across the interlayer at the clay particle edge make an important contribution to the energy barrier to interlayer hydration, especially for initial hydration.

Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions

Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing ${\mathrm{In}}_{0.6}{\mathrm{Ga}}_{0.4}\mathrm{As}$ quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.

Search for common minima in joint optimization of multiple cost functions

We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all the cost functions. Given a set of multiple cost functions that have qualitatively different distributions of local minima with each other, the proposed method finds the common minima with a high success rate without the help of any metaheuristics. As a demonstration, we apply the COM to the crystal structure prediction in materials science. By introducing the concept of data assimilation, i.e., adopting the theoretical potential energy of the crystal and the crystallinity, which characterizes the agreement with the theoretical and experimental X-ray diffraction patterns, as cost functions, we show that the correct crystal structures of Si diamond, low quartz, and low cristobalite can be predicted with significantly higher success rates than the previous methods.

Analysis of theoretical and experimental X-ray diffraction patterns for distinct mordenite frameworks

Experimental and theoretical XRD patterns of mordenite frameworks were correlated in this work. The experimental XRD analysis showed that the incorporation of Ag and Fe ions in mordenite modified the intensity of peaks in the diffraction patterns. For theoretical studies, two framework models of mordenite (MOR6 and MOR7) were used. Theoretical results conducted through DFT computational simulations were able to predict correctly the angular positions of the experimental peaks observed in XRD patterns. These theoretical results showed that the ion exchange of $${\hbox {Na}^{+}}$$ by $${\hbox {Ag}^{+}}$$ cations in the zeolitic framework leads to a decrease in intensity of XRD peaks {2 0 0}, {0 2 0} and {1 5 0}, similar to observed experimentally. This is caused by local structural rearrangements produced by the ion exchange. For $${\hbox {Fe}}$$ incorporation in zeolite, two options were considered theoretically: ion exchange and isomorphous substitution of $${\hbox {Al}^{3+}}$$ in tetrahedral positions.

Understanding the Nanoscale Structure of Inverted Hexagonal Phase Lyotropic Liquid Crystal Polymer Membranes.

Periodic, nanostructured porous polymer membranes made from the cross-linked inverted hexagonal phase of self-assembled lyotropic liquid crystals (LLCs) are a promising class of materials for selective separations. In this work, we investigate an experimentally characterized LLC polymer membrane using atomistic molecular modeling. In particular, we compare simulated X-ray diffraction (XRD) patterns with experimental XRD data to quantify and understand the differences between simulation and experiment. We find that the nanopores are likely composed of five columns of stacked LLC monomers which surround each hydrophilic core. Evidence suggests that these columns likely move independently of each other over longer time scales than accessible via atomistic simulation. We also find that wide-angle X-ray scattering structural features previously attributed to monomer tail tilt are likely instead due to ordered tail packing. Although this system has been reported as dry, we show that small amounts of water are necessary to reproduce all features from the experimental XRD pattern because of asymmetries introduced by hydrogen bonds between the monomer head groups and water molecules. Finally, we explore the composition and structure of the nanopores and reveal that there exists a composition gradient rather than an abrupt partition between the hydrophilic and hydrophobic regions. A caveat is that the time scales of the dynamics are extremely long for this system, resulting in simulated structures that appear too ordered, thus requiring careful examination of the metastable states observed in order to draw any conclusions. The clear picture of the nanoscopic structure of these membranes provided in this study will enable a better understanding of the mechanisms of small-molecule transport within these nanopores.

Roles of Hydration and Magnetism on the Structure of Ferrihydrite from First Principles

We report density functional theory calculations aimed at predicting thermodynamically stable structures for ferrihydrite across a range of possible compositions determined by the amount of structural water. Based on an assumed formula unit of Fe5O8H + nH2O, we performed ab initio calculations with evolutionary searching to find the lowest enthalpy structures as a function of the water content up to n = 2. This is the most exhaustive search for the ferrihydrite structure conducted so far; more than 5000 unique configurations were generated and evaluated over five states of hydration. Among them, the Michel akdaliate model was generated, along with several energetically comparable new structures at higher states of hydration. However, a direct comparison between calculated and experimental pair distribution function and X-ray diffraction patterns for the 50 lowest energy structures shows that none beyond the Michel model could be associated with ferrihydrite. Nevertheless, this energetically comparable str...

Synthesis and Magnetic Properties of Solid Solutions of Ferromagnetic Layered Coordination Polymers Prepared from Solution and the Solid State

Reaction of mixtures of Co(NCS)2 and Ni(NCS)2 with ethylisonicotinate in EtOH in a ratio of 1:2 leads to the formation of solid solutions (mixed crystals) of the layered compound [CoxNi1–x(NCS)2(ethylisonicotinate)2]n that are always contaminated with an additional crystalline phase. Pure samples of the desired layer compound are accessible by using an excess of the metal salts, but in this case the Co content in the solid solutions, as determined by atomic absorption spectroscopy and energy dispersive X-ray spectroscopy, is always lower than that used in the synthesis. Therefore, solid solutions of CoxNi1–x(NCS)2(ethylisonicotinate)4 were synthesized that upon heating transform into solid solutions of the desired layered compound, and in this case the Co/Ni ratio exactly corresponds to that used in the synthesis. The formation of solid solutions of all compounds is already indicated by comparison of the experimental powder X-ray diffraction pattern of the solid solutions with that of physical mixtures wi...

Quantitative Phase Analysis of Plasma-Treated High-Silica Materials

The paper presents the X-ray diffraction (XRD) analysis of the crystal structure of SiO2 in two modifications, namely quartzite and quartz sand before and after plasma treatment. Plasma treatment enables the raw material to melt and evaporate after which the material quenches and condenses to form nanoparticles. The Rietveld refinement method is used to identify the lattice parameters of SiO2 phases. It is found that after plasma treatment SiO2 oxides are in the amorphous state, which are modeled within the microcanonical ensemble. Experiments show that amorphous phases are stable, and model X-ray reflection intensities approximate the experimental XRD patterns with fine precision. Within the modeling, full information is obtained for SiO2 crystalline and amorphous phases, which includes atom arrangement, structural parameters, atomic population of silicon and oxygen atoms in lattice sites.