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The structure of opal has long fascinated scientists. It occurs in a number of structural states, ranging from amorphous to exhibiting features of stacking disorder. Opal‐CT, where C and T signify cristobalite‐ and tridymite‐like interstratification, represents an important link in the length scales between amorphous and crystalline states. However, details about local atomic (dis)order and arrangements extending to long‐range stacking faults in opal polymorphs remain incompletely understood. Here, a multilevel modeling approach is reported that considers stacking states in correlation with the abundance of C and T segments as a high‐level structural parameter (i.e. not each atom). Optimization accounting for inter‐tetrahedral bond lengths and angles and the regularity of the silicate tetrahedra is included as lower levels of structural parameters. Together, a set of parameters with both coarse‐grained and atomistic features for different levels of structural details is refined. Structural disorder at the ∼10–100 Å distance scale is evaluated using experimental pair distribution function and diffraction datasets, comparing peak intensities, widths and asymmetry. This work presents a complete multilevel structural description of natural opal‐CT and explains many of the unusual features observed in X‐ray powder diffraction patterns. This modeling approach can be adopted generally for analyzing layered materials and their assembly into 3D structures. [ABSTRACT FROM AUTHOR]

Diffraction data acquired from cryocooled protein crystals often include diffraction from ice. Analysis of ice diffraction from crystals of three proteins shows that the ice formed within solvent cavities during rapid cooling is comprised of a stacking-disordered mixture of hexagonal and cubic planes, with the cubic plane fraction increasing with increasing cryoprotectant concentration and increasing cooling rate. Building on the work of Thorn and coworkers [Thorn et al. (2017), Acta Cryst. D73, 729-727], a revised metric is defined for detecting ice from deposited protein structure-factor data, and this metric is validated using full-frame diffraction data from the Integrated Resource for Reproducibility in Macromolecular Crystallography. Using this revised metric and improved algorithms, an analysis of structure-factor data from a random sample of 89 827 PDB entries collected at cryogenic temperatures indicates that roughly 16% show evidence of ice contamination, and that this fraction increases with increasing solvent content and maximum solvent-cavity size. By examining the ice diffraction-peak positions at which structure-factor perturbations are observed, it is found that roughly 25% of crystals exhibit ice with primarily hexagonal character, indicating that inadequate cooling rates and/or cryoprotectant concentrations were used, while the remaining 75% show ice with a stacking-disordered or cubic character.

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single‐crystal X‐ray analysis of a tiny needle. The α phase was investigated using three‐dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit‐cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice‐energy minimization with dispersion‐corrected DFT. A four‐layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X‐ray powder data. Additionally, five further phases of P.O.13 are described. [ABSTRACT FROM AUTHOR]

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single‐crystal X‐ray analysis of a tiny needle. The α phase was investigated using three‐dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit‐cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice‐energy minimization with dispersion‐corrected DFT. A four‐layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X‐ray powder data. Additionally, five further phases of P.O.13 are described. [ABSTRACT FROM AUTHOR]

Ice formation within protein crystals is a major obstacle to the cryocrystallographic study of protein structure, and has limited studies of how the structural ensemble of a protein evolves with temperature in the biophysically interesting range from ∼260 K to the protein-solvent glass transition near 200 K. Using protein crystals with solvent cavities as large as ∼70 Å, time-resolved X-ray diffraction was used to study the response of protein and internal solvent during rapid cooling. Solvent nanoconfinement suppresses freezing temperatures and ice-nucleation rates so that ice-free, low-mosaicity diffraction data can be reliably collected down to 200 K without the use of cryoprotectants. Hexagonal ice (Ih) forms in external solvent, but internal crystal solvent forms stacking-disordered ice (Isd) with a near-random stacking of cubic and hexagonal planes. Analysis of powder diffraction from internal ice and single-crystal diffraction from the host protein structure shows that the maximum crystallizable solvent fraction decreases with decreasing crystal solvent-cavity size, and that an ∼6 Å thick layer of solvent adjacent to the protein surface cannot crystallize. These results establish protein crystals as excellent model systems for the study of nanoconfined solvent. By combining fast cooling, intense X-ray beams and fast X-ray detectors, complete structural data sets for high-value targets, including membrane proteins and large complexes, may be collected at ∼220-240 K that have much lower mosaicities and comparable B factors, and that may allow more confident identification of ligand binding than in current cryocrystallographic practice.

Our systematic explorations of the complex rare earth tellurite halide family have added several new [Ln12(TeO3)12][M6X24] (M = Cd, Mn, Co) representatives containing strongly deficient and disordered metal-halide layers based on transition metal cations. The degree of disorder increases sharply with decrease of M2+ radius and the size disagreements between the cationic [Ln12(TeO3)12]+12 and anionic [M6Cl24]−12 layers. From the crystal chemical viewpoint, this indicates that the families of both rare-earth selenites and tellurites can be further extended; one can expect formation of some more complex structure types, particularly among selenites. Analysis of the polytypism of compounds have been performed using the approach of OD ("order–disorder") theory. [ABSTRACT FROM AUTHOR]

PtSe2 is one of the most promising materials for the next generation of piezoresistive sensors. However, the large‐scale synthesis of homogeneous thin films with reproducible electromechanical properties is challenging due to polycrystallinity. It is shown that stacking phases other than the 1T phase become thermodynamically available at elevated temperatures that are common during synthesis. It is shown that these phases can make up a significant fraction in a polycrystalline thin film and discuss methods to characterize them, including their Seebeck coefficients. Lastly, their gauge factors, which vary strongly and heavily impact the performance of a nanoelectromechanical device are estimated. [ABSTRACT FROM AUTHOR]

Ice, one of the most enigmatic materials on Earth, exhibits diverse polymorphism, with research mainly focusing on the most commonly observed phases: hexagonal ice (I h ), cubic ice (I c ), and stacking-disordered ice (I sd ). While their formation or structural changes are crucial for advancements in cloud science, climate modeling, and cryogenic technology, the molecular mechanisms driving these phenomena remain unexplored. Herein, utilizing cryogenic transmission electron microscopy, we investigate the formation of ice at two different temperatures, demonstrating a size-dependent phase shift from I c to I sd . Furthermore, a relatively metastable cubic phase in I sd transitions to a hexagonal phase under electron beam radiation. This transition, facilitated by crystal defects, contrasts with perfect crystalline I c , which maintains its original phase, emphasizing the importance of defects in polymorphic phase transitions. Our findings provide novel insights on phase control during the ice growth processes and polymorphic phase transitions from the cubic-to-hexagonal phases.

The present study deals with accurate identification of polytypes, twins, and allotwins – oriented crystal associations of more than one polytype. The trioctahedral 1:1 layered silicate cronstedtite was studied using single-crystal X-ray diffraction data collected with a four-circle diffractometer equipped with a CCD detector. The sample from the skarn occurrence, Ouedi Beht, El Hammam, Morocco, was explored. It contains cronstedtite in fibrous massive aggregates in the central part, and euhedral crystals in surrounding veinlets and druses. The reciprocal space (RS) sections created by the diffractometer software and presented here were used to determine the OD (ordered-disordered) subfamilies (Bailey's group A, B, C, D) and to identify polytypes. The chemical compositions of some crystals were determined thereafter by electron probe microanalysis (EPMA-WDS). Some crystals studied are more or less complicated allotwins. Polytypes were thus separated by cleaving crystals into smaller parts in many cases. All polytypes found belong to subfamilies A or D. The following polytypes of the subfamily A were identified: 2M1 (a = 5.49, b = 9.51, c = 14.40 Å, β = 97.30°, space group Cc), 1M (a = 5.51, b = 9.54, c = 7.33 Å, β = 104.5°, Cm), 3T (a = 5.51, c = 21.32 Å, P31), 6T2 (a = 5.50, c = 42.60 Å, P31). 2M1 and 3T were present as isolated crystals or separated by cleaving, otherwise all these polytypes are parts of allotwins. The 2M1 polytype is sometimes twinned by reticular pseudo merohedry with twin index n = 3 and 120° rotation about the chex axis as the twin operation. Allotwins of 1M + twinned 2M1 polytypes are also present. Another kind of twinning, with rotation by (2n+1)×60° about chex is rare. The subfamily D is represented mostly by 2H1 and 2H2 polytypes, a = 5.50, c = 14.25 Å, space groups P63cm (2H1), P63 (2H2). In addition, several six-layer (a = 5.49, c = 42.80 Å), mostly non-MDO polytypes were separated from allotwins by cleaving. In order to identify them, 24 possible stacking sequences were modeled, diffraction patterns calculated, graphical identification diagrams constructed, and comparisons made with actual RS sections. This simulation revealed that five pairs of sequences provided identical diffraction patterns. Polytypes actually found correspond to the following sequences: 1 (6T1), 5 (proposed Ramsdell's symbol 6T3), 8+10 (6T5), 11+12 (6T4), 24 (6T6, trigonal polytypes, space group type P3), 22 (6R1), and 23 (6R2, rhombohedral polytypes, space group type R3c and R3, respectively). The RS section corresponding to the hexagonal polytype 6H2 (sequence 14) was also found. However, diffraction patterns geometrically indistinguishable can be produced by the twin with rotation by 180° about chex as a twin operation of the rhombohedral polytype 6R2 (sequence 23). Several aggregates with fiber texture of polytype 2H2 were separated from the central part. Use of EPMA-WDS revealed Fe and Si along with significant amounts of Mn and Mg. Crystals from veins were more Mn- and Mg-rich than these from the central part. Traces of Cl, S, and Al are present also. [ABSTRACT FROM AUTHOR]

The layered iron silicate cronstedtite was encountered in ore veins in the exploration shaft mined in the Neoproterozoic black shale-hosted pyrite-manganese deposit near Litošice (Eastern Bohemia, Czech Republic) around 1955. It forms up to 2 mm thick black double or single bands in symmetrically zoned hydrothermal veins cutting shales. The specimens selected from available material were studied by single-crystal X-ray diffraction using the four-circle diffractometer with an area detector. The chemical composition of some of the specimens was determined by the electron probe microanalysis (EPMA) in the WDS mode. Furthermore, a polished section of the ore material with cronstedtite bands was prepared, and the mineral association was analyzed with the aid of back-scattered electron (BSE) images. The interpretation of reciprocal space (RS) sections produced by the diffractometer software allowed the determination of OD subfamilies (Bailey's groups) A, B, C, D, and polytypes. The 1T polytype (subfamily C), a = 5.52, c = 7.12 Å, space group P31m, is the most abundant in the occurrence. In rare cases, it forms oriented crystal associations (allotwins) with the 1M polytype (subfamily A), a = 5.52 Å, b = 9.55, c = 7.136 Å, ß = 104.4°, space group Cm. Fully disordered allotwinned crystals of the A + C subfamilies were found, too. In addition, few allotwins of the polytype 2H1 (subfamily D) with a small amount of 2H2, were identified. Unit cell parameters are a = 5.49, c = 14.21 Å, space groups are P63cm (2H1), and P63 (2H2). EPMA-WDS of selected crystals of prevailing 1T polytype revealed elevated contents of Mn (0.19-0.62 apfu) and low contents of Mg (up to 0.13 apfu) and Cl (up to 0.05 apfu), respectively. More rare 2H1 (+ 2H2) polytypes show elevated contents of Mg in the range of 0.19-0.62 apfu and distinctly lower Mn (up to 0.07 apfu) and Cl contents (up to 0.01 apfu). The BSE images reveal that cronstedtite bands are associated with multiple generations of carbonates (rhodochrosite, siderite, rarely magnesite and calcite), quartz, opal, pyrite and carbonate-fluorapatite. Intense metasomatic replacement of cronstedtite by opal and siderite appeared especially around the center of the studied vein. [ABSTRACT FROM AUTHOR]

Our systematic explorations of the complex rare earth tellurite halide family have added several new [Ln12(TeO3)12][M6X24] (M = Cd, Mn, Co) representatives containing strongly deficient and disordered metal-halide layers based on transition metal cations. The degree of disorder increases sharply with decrease of M2+ radius and the size disagreements between the cationic [Ln12(TeO3)12]+12 and anionic [M6Cl24]−12 layers. From the crystal chemical viewpoint, this indicates that the families of both rare-earth selenites and tellurites can be further extended; one can expect formation of some more complex structure types, particularly among selenites. Analysis of the polytypism of compounds have been performed using the approach of OD (“order–disorder”) theory.

Ice formation within protein crystals is a major obstacle to the cryocrystallographic study of protein structure, and has limited studies of how the structural ensemble of a protein evolves with temperature in the biophysically interesting range from ∼260 K to the protein–solvent glass transition near 200 K. Using protein crystals with solvent cavities as large as ∼70 Å, time-resolved X-ray diffraction was used to study the response of protein and internal solvent during rapid cooling. Solvent nanoconfinement suppresses freezing temperatures and ice-nucleation rates so that ice-free, low-mosaicity diffraction data can be reliably collected down to 200 K without the use of cryoprotectants. Hexagonal ice (Ih) forms in external solvent, but internal crystal solvent forms stacking-disordered ice (Isd) with a near-random stacking of cubic and hexagonal planes. Analysis of powder diffraction from internal ice and single-crystal diffraction from the host protein structure shows that the maximum crystallizable solvent fraction decreases with decreasing crystal solvent-cavity size, and that an ∼6 Å thick layer of solvent adjacent to the protein surface cannot crystallize. These results establish protein crystals as excellent model systems for the study of nanoconfined solvent. By combining fast cooling, intense X-ray beams and fast X-ray detectors, complete structural data sets for high-value targets, including membrane proteins and large complexes, may be collected at ∼220–240 K that have much lower mosaicities and comparable B factors, and that may allow more confident identification of ligand binding than in current cryocrystallographic practice.

The present study provides an example of the accurate identification of polytypes of trioctahedral 1:1 layered silicates from single-crystal X-ray diffraction data collected with the aid of a four-circle diffractometer equipped with an area detector. Single crystals of the mineral cronstedtite from the Nagybörzsöny gold ore deposit, northern Hungary, were studied. The chemical composition of some crystals was determined by electron probe microanalysis (EPMA). The precession-like images of the reciprocal space (RS) sections created by the diffractometer software and presented in the study were used to determine the OD (ordered-disordered) subfamilies (Bailey's groups A, B, C, D) and particular polytypes. With one exception, all crystals studied belong to subfamily A. The rare polytype 1M, a = 5.51, b = 9.54, c = 7.33 Å, β = 104.5°, space group Cm is relatively abundant in this occurrence. Another polytype 3T, a = 5.51, c = 21.32 Å, space group P31 was also found. Both polytypes occur separately or in mixed, mostly 1M dominant crystals. Some 1M polytype crystals are twinned by order 3 reticular merohedry with a 120° rotation along the chex axis as the twin operation. A rare 1M+3T mixed crystal with 1M part twinned also contains a small amount of subfamily C. A possible presence of the most common 1T polytype of this subfamily cannot be confirmed because of overlap of the characteristic reflections with those of 3T. Several completely disordered crystals produced diffuse streaks instead of discrete characteristic reflections on the RS sections. The EPMA revealed Fe, Si, traces of Mg, Al, S, and Cl. One black crystal originally considered to be cronstedtite was identified as (111) twinned sphalerite. Some crystals of cronstedtite are covered partially by a honey-brown crust or small crystals of siderite. [ABSTRACT FROM AUTHOR]

The primary aim of this study was the accurate determination of unit-cell parameters and description of disorder in chlorites with semi-random stacking using common X-ray diffraction (XRD) data for bulk powder samples. In the case of ordered chlorite structures, comprehensive crystallographic information can be obtained based on powder XRD data. Problems arise for samples with semi-random stacking, where due to strong broadening of hkl peaks with k ≠ 3n, the determination of unit-cell parameters is demanding. In this study a complete set of information about the stacking sequences in chlorite structures was determined based on XRD pattern simulation, which included determining a fraction of layers shifted by ±1/3b, interstratification with different polytypes and 2:1 layer rotations. A carefully selected series of pure Mg-Fe tri-trioctahedral chlorites with iron content in the range from 0.1 to 3.9 atoms per half formula unit cell was used in the study. In addition, powder XRD patterns were carefully investigated for the broadening of the odd-number basal reflections to determine interstratification of 14 and 7 Å layers. These type of interstratifications were finally not found in any of the samples. This result was also confirmed by the XRD pattern simulations, assuming interstratification with R0 ordering. Based on h0l XRD reflections, all the studied chlorites were found to be the IIbb polytype with a monoclinic-shaped unit cell (β ≈ 97°). For three samples, the hkl reflections with k ≠ 3n were partially resolvable; therefore, a conventional indexing procedure was applied. Two of the chlorites were found to have a monoclinic cell (with α, γ = 90°). Nevertheless, among all the samples, the more general triclinic (pseudomonoclinic) crystal system with symmetry C1 was assumed, to calculate unit-cell parameters using Le Bail fitting. A detailed study of semi-random stacking sequences shows that simple consideration of the proportion of IIb-2 and IIb-4/6 polytypes, assuming equal content of IIb-4 and IIb-6, is not sufficient to fully model the stacking structure in chlorites. Several, more general, possible models were therefore considered. In the first approach, a parameter describing a shift into one of the ±1/3b directions (thus, the proportion of IIb-4 and IIb-6 polytypes) was refined. In the second approach, for samples with slightly distinguishable hkl reflections with k ≠ 3n, some kind of segregation of individual polytypes (IIb-2/4/6) was considered. In the third approach, a model with rotations of 2:1 layers about 0°, 120°, 240° was shown to have the lowest number of parameters to be optimized and therefore give the most reliable fits. In all of the studied samples, interstratification of different polytypes was revealed with the fraction of polytypes being different than IIbb ranging from 5 to 19%, as confirmed by fitting of h0l XRD reflections. [ABSTRACT FROM AUTHOR]

Recently, ice with stacking disorder structure, consisting of random sequences of cubic ice (Ic) and hexagonal ice (Ih) layers, was reported to be more stable than pure Ih/Ic. Due to a much lower free energy barrier of heterogeneous nucleation, in practice, the freezing process of water is controlled by heterogeneous nucleation triggered by an external medium. Therefore, we carry out molecular dynamic simulations to explore how ice polymorphism depends on the lattice structure of the crystalline substrates on which the ice is grown, focusing on the primary source of atmospheric aerosols, carbon materials. It turns out that, during the nucleation stage, the polymorph of ice nuclei is strongly affected by graphene substrates. For ice nucleation on graphene, we find Ih is the dominant polymorph. This can be attributed to structural similarities between graphene and basal face of Ih. Our results also suggest that the substrate only affects the polymorph of ice close to the graphene surface, with the preference for Ih diminishing as the ice layer grows.

Assemblies of nanosheets are often characterized by extensive layer‐position disorder. Coupled with the often minute coherent scattering domain size and relaxation of the nanosheet structure itself, unambiguous interpretation of X‐ray and neutron scattering data from such materials is non‐trivial. This work demonstrates a general approach towards refinement of layer‐disorder information from atomic pair distribution function (PDF) data for materials that span the gap between turbostratism and ordered stacking arrangements. X‐ray total scattering data typical of a modern rapid‐acquisition PDF instrument are simulated for a hypothetical graphene‐like structure using the program DIFFaX, from which atomic PDFs are extracted. Small 1 × 1 × 20 supercell models representing the stacking of discrete layer types are combined to model a continuous distribution of layer‐position disorder. Models optimized using the differential evolution algorithm demonstrate improved fit quality over 75 Å when a single mean layer‐type model is replaced with a constrained 31‐layer‐type model. Posterior distribution analyses using the Markov chain Monte Carlo algorithm demonstrate that the influence of layer disorder and finite particle size are correlated. However, the refined mean stacking vectors match well with the generative parameter set. [ABSTRACT FROM AUTHOR]

The structural transformations occurring during the intercalation of lithium into disordered graphite in a working battery were studied in detail by operando X‐ray powder diffraction (XRPD). By using a capillary‐based micro‐battery cell, it was possible to study the stacking disorder in the initial graphite as well as in lithiated graphites. The micro‐battery cell was assembled in its charged state with graphite as positive electrode and metallic lithium as counter electrode. The battery was discharged until a stage II compound (LiC12) was formed. The operando XRPD data reveal that the graphitic electrode material retains a disordered nature during the intercalation process. A DIFFaX+ refinement based on the initial operando XRPD pattern shows that the initial graphite generally has an intergrown structure with domains of graphite 2H and graphite 3R. However, the average stacking sequence of the initial graphite also contains a significant concentration of AA‐type stacking of the graphene sheets. DIFFaX+ was further used to refine structure models of a stage III type compound and the final stage II compound. The refinement of the stage II compound showed that it is dominated by AαAAαA‐type stacking, but that it also contains a significant concentration of AαABβB‐type slabs in the average stacking sequence. [ABSTRACT FROM AUTHOR]

Stacking‐disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close‐packed metals, ice I and diamond to open‐framework materials and small‐molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking‐disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking‐disordered samples with complicated and high‐order memory effects. In the context of this work, the limitations of current structure‐reconstruction approaches are also discussed. [ABSTRACT FROM AUTHOR]

The possible presence of the high-density carbon polymorph with hexagonal symmetry known as “lonsdaleite” provides an important marker for shock impact events. It is typically considered to form as a metastable phase produced from graphite or other carbonaceous precursors. However, its existence has recently been called into question. Here we collected high-resolution synchrotron X-ray diffraction data for laboratory-shocked and natural impact diamonds that both show evidence for deviations from cubic symmetry, that would be consistent with the appearance of hexagonal stacking sequences. These results show that hexagonality can be achieved by shocking diamond as well as from graphite precursors. The diffraction results are analyzed in terms of a general model that describes intermediate stacking sequences between pure diamond (fully cubic) and “lonsdaleite” (fully hexagonal) phases, with provision made for ordered vs disordered stacking arrangements. This approach provides a “hexagonality index” that can be used to characterize and distinguish among samples that have experienced different degrees of shock or static high pressure-high temperature treatments. We have also examined the relative energetics of diamond and “lonsdaleite” structures using density functional theoretical (DFT) methods. The results set limits on the conditions under which a transformation between diamond and “lonsdaleite” structures can be achieved. Calculated Raman spectra provide an indicator for the presence of extended hexagonal stacking sequences within natural and laboratory-prepared samples. Our results show that comparable crystallographic structures may be developed by impact-generated shockwaves starting from ambient conditions using either of the two different allotropes of carbon (diamond, graphite). This broadens the scope for its occurrence in terrestrial and planetary systems. [ABSTRACT FROM AUTHOR]

The atomic structure of NiSn 4 intermetallic forming at ambient temperature in different types of Sn/Ni diffusion couples was investigated by powder X-ray diffraction. The recorded diffraction patterns show narrow Bragg reflections as well as characteristic broad diffraction bands indicative of stacking disorder in the crystal structure of NiSn 4 . The crystal structure consists of NiSn 4 layers with square-antiprismatic coordination of Ni by Sn. The stacking of these layers is irregular (faulted) by being an intermediate between the pseudotetragonal PtSn 4 - (space group Aeaa ) and the tetragonal β-IrSn 4 -type (space group I 4 1 / acd ) ideal structures. Thereby, the shape of the diffraction bands reveals that the stacking more closely corresponds to β-IrSn 4 - than to the PtSn 4 -type. The obtained lattice parameters are: a (β-IrSn 4 ) = a (PtSn 4 ) = b (PtSn 4 ) = (6.248 ± 0.001) Å and 2 c (PtSn 4 ) = c (β-IrSn 4 ) = (23.001 ± 0.004) Å. Pronounced stacking corresponding to a PtPb 4 -type structure discussed in the literature is not present in NiSn 4 on the basis of the diffraction data. The latter finding is compatible with density functional theory (DFT) based first-principles calculations, indicating a higher energy for PtPb 4 -type NiSn 4 as compared to PtSn 4 - and β-IrSn 4 -type NiSn 4 . [ABSTRACT FROM AUTHOR]

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the β phase was determined using single-crystal X-ray analysis of a tiny needle. The α phase was investigated using three-dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit-cell parameters with the β phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice-energy minimization with dispersion-corrected DFT. A four-layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X-ray powder data. Additionally, five further phases of P.O.13 are described., (open access.)

Ion-exchanged Aurivillius materials form perovskite nanosheet booklets wherein well-defined bi-periodic sheets, with ~11.5 Å thickness, exhibit extensive stacking disorder. The perovskite layer contents were defined initially using combined synchrotron X-ray and neutron Rietveld refinement of the parent Aurivillius structure. The structure of the subsequently ion-exchanged material, which is disordered in its stacking sequence, is analyzed using both pair distribution function (PDF) analysis and recursive method simulations of the scattered intensity. Combined X-ray and neutron PDF refinement of supercell stacking models demonstrates sensitivity of the PDF to both perpendicular and transverse stacking vector components. Further, hierarchical ensembles of stacking models weighted by a standard normal distribution are demonstrated to improve PDF fit over 1-25 Å. Recursive method simulations of the X-ray scattering profile demonstrate agreement between the real space stacking analysis and more conventional reciprocal space methods. The local structure of the perovskite sheet is demonstrated to relax only slightly from the Aurivillius structure after ion exchange. [ABSTRACT FROM AUTHOR]

A transmission electron microscopy (TEM) investigation was undertaken in order to elucidate the nature of the structural disorder in a tobelite specimen from the sedimentary rocks of the Armorican sandstones (western France). This structural disorder may be the origin of residual electron-density maxima in difference-Fourier maps reported previously in single-crystal XRD studies of tobelite. The TEM investigation of tobelite confirmed that it is the 2M2 polytype in subfamily-B, but the ordered sequence is interrupted by numerous stacking faults parallel to (001), for which the stacking vectors belong to both subfamilies-A and -B of mica polytypes, with a prevalence of the latter. Chemical heterogeneity depending on the Si/Al ratio and Na and Mg concentration was observed at the nanoscale among different mica lamellae in a single crystal. The observed variations are consistent with a change in mica chemistry leading to interlayer vacancies which may cause shortening of the interlayer separation, as revealed by the singlecrystal structure refinements. [ABSTRACT FROM AUTHOR]

Hexagonal diamond has been predicted computationally to display extraordinary physical properties including a hardness that exceeds cubic diamond. However, a recent electron microscopy study has shown that so-called hexagonal diamond samples are in fact not discrete materials but faulted and twinned cubic diamond. We now provide a quantitative analysis of cubic and hexagonal stacking in diamond samples by analysing X-ray diffraction data with the DIFFaX software package. The highest fractions of hexagonal stacking in materials previously referred to as hexagonal diamond are below 60%. The remainder of the stacking sequences is cubic. We show that the cubic and hexagonal sequences are interlaced in a complex way and that naturally occurring Lonsdaleite is not a simple physical mixture of cubic and hexagonal diamond. Instead, it is structurally best described as stacking disordered diamond. The future experimental challenge will be to prepare diamond samples beyond 60% hexagonality and towards the so far elusive ‘perfect’ hexagonal diamond. [ABSTRACT FROM AUTHOR]

X-ray diffraction is one of the most effective tools for the characterization of the stacking defects which occur frequently in clay minerals. Modelling of the diffraction patterns of oriented mounts is often used for obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and the results are user dependent and especially troublesome if a consistent model of the same mineral measured under different conditions needs to be obtained. It was shown recently that the Rietveld method could be applied successfully for the evaluation of the X-ray patterns of oriented mounts. Nevertheless, this automatic refinement procedure can also lead to inconsistent results if independent refinements are performed that describe the same sample measured under different conditions. One way to solve this problem is the application of parametric Rietveld refinement. For this approach a set of different measurements of the same sample was collected and fitted in one combined refinement by the connection of the structural models via external parameters. These conditions may involve different pre-treatments (e.g. different intercalations), different temperatures or relative humidities and/or different experimental setup (powder or oriented samples). All patterns were fitted in one overall refinement process by the BGMN software. This approach was demonstrated on a mixture of two disordered reference materials and on a set of geological samples. Two different states for each sample were refined independently and parametrically and it was shown that this approach leads to consistent results, saves computation time and may even resolve small structural differences. [ABSTRACT FROM AUTHOR]

The crystalline structure assembled out of charge-stabilized asymmetric dumbbell-like colloidal particles in ethyl alcohol by sedimentation has been probed using small-angle X-ray scattering with microradian resolution. The existence of plastic face-centered cubic crystals was inferred from the observed Bragg peaks. The presence of stacking faults and the mosaic structure of the sample lead to the appearance of diffuse scattering, forming Bragg scattering cylinders in the three-dimensional reciprocal space. The quality of the crystalline structure, as ascertained from a detailed analysis of the diffuse scattering intensity distribution, indicates the presence of only 1.5% of stacking faults between the hexagonal close-packed layers. [ABSTRACT FROM AUTHOR]

Different descriptions of the stacking disorder of the so-called 'cubic' phase 'ice Ic' and stacking-faulted hexagonal ice Ih exist. We present an overview of the effect of different stacking disorder interaction ranges s from s = 2 to s = 4 after Jagodzinski on the (neutron) powder diffraction patterns of stacking-disordered ice I, which we propose to name ice Ich. We fit in a systematic approach simulated diffraction data of ice Ich for s up to 4 with a multi-peak approach. In this way we allow for estimating the relative proportion of cubic sequences in the stacking sequences by using readily accessible observables of a diffraction pattern. [ABSTRACT FROM AUTHOR]

O'3-Na 3 Ni 2 SbO 6 with a honeycomb cation order, as a potential cathode, presents simplified phase-transition steps and a high average voltage. To mitigate the intrinsic phase irreversibility, Mg, Zn, and Co have been introduced to displace part of the Ni, which inevitably reduces the theoretical capacity related to the Ni 2+ /Ni 3+ redox reaction. In this work, an unusual dual-site substitution is carried out to increase the P'3-O'3 structure reversibility without sacrificing the practical capacity. In addition, it is found that special stacking faults along the c -axis direction can be induced by doping to result in incomplete Sb/Ni disorder, though the honeycomb order remains in every TM (transition-metal) layer. The codoped Na 2.85 Cs 0.15 Ni 1.9 Mg 0.1 SbO 6 has a high degree of disorder, which breaks the ideal monoclinic symmetry ( C 2/ m ) and partly upgrades its structure to higher-symmetry models. Profiting from the influence of stacking disorder and doping ions on the coordination environment around Na, more gradual and smaller variations of the lattice parameters appear upon Na-ion extraction/insertion. Consequently, this cathode displays a high initial discharge capacity (120 mAh g -1 ), long-term cycling stability, and excellent rate performance (66 mAh g -1 under 10 C). These findings reveal that not only a full TM-disordered arrangement but also this incomplete stacking disorder can effectively improve the performance of a layered cathode.

A novel capillary-based micro-battery cell for in situ X-ray powder diffraction (XRPD) has been developed and used to study the initial intercalation and deintercalation of lithium into graphite in a working battery. The electrochemical cell works in transmission mode and makes it possible to obtain diffraction from a single electrode at a time, which facilitates detailed structural and microstructural studies of the electrode materials. The micro-battery cell is potentially also applicable for in situ X-ray absorption spectroscopy and small-angle X-ray scattering experiments. The in situ XRPD study of the initial intercalation and deintercalation process revealed marked changes in the diffraction pattern of the graphitic electrode material. After the formation of the solid electrolyte interphase layer, the d spacing of the diffraction peak corresponding to the 002 diffraction peak of graphite 2H changes nearly linearly in two regions with slightly different slopes, while the apparent half-width of the diffraction peak displays a few minima and maxima during charging/discharging. DIFFaX+ refinements based on the initial XRPD pattern and the one after the initial discharging-charging cycle show that the structure of the graphite changes from an intergrown structure of graphite 2H and graphite 3R to a nearly ideal graphite 2H structure. DIFFaX+ was also used to refine a model of the stacking disorder in an apparent stage III compound with Aα AB- and Aα AC-type slabs. [ABSTRACT FROM AUTHOR]

PtSe 2 is one of the most promising materials for the next generation of piezoresistive sensors. However, the large-scale synthesis of homogeneous thin films with reproducible electromechanical properties is challenging due to polycrystallinity. It is shown that stacking phases other than the 1T phase become thermodynamically available at elevated temperatures that are common during synthesis. It is shown that these phases can make up a significant fraction in a polycrystalline thin film and discuss methods to characterize them, including their Seebeck coefficients. Lastly, their gauge factors, which vary strongly and heavily impact the performance of a nanoelectromechanical device are estimated., (© 2022 The Authors. Advanced Science published by Wiley-VCH GmbH.)

Abstract: Low temperature (333K) crystallization of hyperalkaline carbonate containing aluminosilicate gels has been studied. Nanocrystalline carbonate enclathrated zeolite-type with intermediate structure between sodalite and cancrinite was observed already after 3h. Its crystal size was found to be around 40nm over synthesis periods from 3h to 96h. A further experimental series was performed under addition of triethanolamine to study its effect on crystallization kinetics, crystal size and morphology. Nucleation deceleration of aluminosilicates but recrystallization of large crystals of sodium carbonate could be revealed in the early stage of these reactions. As a result big elongated rectangular hollow plates of the intermediate phase composed of small spherical crystal aggregates consisting of numerous nanocrystallites were observed. Heterogeneous nucleation and growth of the intermediate phase on the surfaces of the previously formed big plate-like Na2CO3 crystals was responsible for this unusual particle aggregation. All products were characterized by X-ray powder diffraction, scanning electron microscopy, Fourier transform infrared spectroscopy and simultaneous thermal analysis. The intermediate phase were compared with microcrystalline carbonate–cancrinite and hydro-sodalite of common synthesis at 473K. The thermal and hydrothermal behavior of the nanocrystalline intermediate phase was further characterized and discussed in terms of its specific structural features. Compared with microcrystalline cancrinite remarkable thermal stability could be stated. In contrast a much higher decomposition rate of the intermediate phase under hydrothermal stress was observed. [Copyright &y& Elsevier]

Abstract: A sodium brittle mica with the ideal composition [Na4]inter[Mg6]oct[Si4Al4]tetO20F4 was synthesized via melt synthesis in a gas tight crucible. This mica is unusual inasmuch as the known mica structure holds only room for two interlayer cations per unit cell and inasmuch as it readily hydrates despite the high layer charge while ordinary micas and brittle micas are non-swelling. The crystal structure of one-layer hydrate sodium brittle mica was determined and refined from single crystal X-ray data. Interlayer cations reside at the center of the distorted hexagonal cavities and are coordinated by the three inner basal oxygen atoms. The coordination of the interlayer cation is completed by three interlayer water molecules residing at the center of the interlayer region. The relative position of adjacent 2:1-layers thus is fixed by these octahedrally coordinated interlayer cations. Pseudo-symmetry leads to extensive twinning. In total five twin operations generate the same environment for the interlayer species and are energetically degenerate. [Copyright &y& Elsevier]

Two (1-adamantyl)methyl esters, (1-adamantyl)methyl-1-adamantanecarboxylate (1) and bis[(1adamantyl)methyl]-1,3-adamantanedicarboxylate (2) were prepared in good yields and characterized by spectroscopic methods. The structure of 1 was determined by single-crystal X-ray diffraction structural analysis. The structure shows two kinds of whole-molecule disorder: the ester molecule statistically occupies two different sites in the crystal asymmetric unit with occupancies of 95 and 5 % (positional disorder), and at each of the sites there is additional disorder over a crystallographic 2-fold rotation axis (orientational disorder). Analysis of diffuse scattering patterns in the diffraction images revealed the positional disorder as stacking disorder of molecular layers with two-dimensional translational symmetry. In the absence of other, more directional interactions, the molecules in the crystal structure of 1 are held together only by van der Waals interactions which provide the rationale for the observed whole-molecule disorder. [ABSTRACT FROM AUTHOR]

The broadening effect of stacking disorder in hexagonal graphite is found experimentally by XRD to be identical to that of stacking faults in hexagonal-closed-packing (HCP) structure, which has obvious selective broadening effect. The Langford’s method for dealing with the twofold broadening effects of the crystallite-faults in hexagonal ZnO has been extended in this paper, and then applied to the determination of stacking disorder in 2H-graphite, which indicates that our extension method is convenient to both the experiments and data process, and may be generalized further. Two stacking disorder model in 2H-graphite and data processing method have been proposed in this study. The two disorder degrees of P AB and P ABC can be computed when the two reliable FWHMs of 101 and 102 diffraction peaks were obtained. [ABSTRACT FROM AUTHOR]

Abstract: We have performed Monte Carlo simulations of hard spheres under gravity. Vertical boundaries are hard walls, which are well separated with each other. On the other hand, the periodic boundary condition is imposed in the horizontal direction. While we previously reported enhancement of crystallinity as well as crystallization due to gravity, we present here the results that demonstrate the succession of a defect. In case that the crystal formed at the bottom of the system includes kinds of stacking disorders for the (001) growth, twin band structure develops as mediated by a stacking disorder succeeded in the crystal formed in the fluid region which lies on the bottom crystal. In case that the stacking structure along horizontal direction changes from the (111) stacking to the (001) stacking, twin band structure in the (001) stacking region develops as succeeded in the crystal transformed. The twin band structure also becomes large with its upward growth. [Copyright &y& Elsevier]

Columnar-shaped colloidal crystals (width and length of the columns -0.1-1.0 mm and 10 mm, respectively) have been grown by centrifugation of the dispersion of polystyrene particles. The crystals were re-dispersed reversibly. Close-packed colloidal crystals were obtained by drying the columnar crystals gently. The dried crystals contained no macroscopic cracks over several mm³. Some stacking disorders were observed on the cross sections of the dried crystals. The average grain size of the columnar crystals increased with decreasing centrifugal acceleration. Too fast centrifugation caused the sedimentation of randomly oriented small grains in front of the growth interfaces. [ABSTRACT FROM AUTHOR]

Abstract: The title phase and its homogeneity range () have been established via several controlled solid state reactions at 630 °C. X-ray diffraction and TEM investigations indicate that the diffraction patterns are dominated by diffuse scattering due to heavily faulted layer stacking. After several attempts crystals of better quality were obtained and studied. The structural refinements carried out on one selected crystal from a batch treated at 700 °C and annealed at 600 °C during 4 days presents a formula slightly richer in Mo6+ and V4+, corresponding to , i.e., Mo1.5V1.5O8. The main structural features are reported and analysed. The structure of these crystals is still affected by stacking defects, but in lower concentrations, leading to twinning phenomena. A detailed investigation by TEM and HREM of crystals corresponding to confirms the drastic stacking disorder of these materials. Magnetic and electric measurements allow to ascribe the mixed valence formula, Mo6+ 1+x V5+ 2−2x V4+ x O8 for these various compositions which shows a semi-conducting behaviour with an activation energy for phase being . [Copyright &y& Elsevier]

The crystallization of tris(bicyclo[2.1.1]hexeno)benzene at the interface between a benzene solution and acetonitrile leads to two distinct crystal morphologies, one hexagonal and one monoclinic. There are also examples of monoclinic growth twins and intergrown samples consisting of both hexagonal and monoclinic macroscopic domains. X-ray diffractograms of the hexagonal form are dominated by diffuse scattering due to heavily faulted layer stacking. Faint diffuse lines for the monoclinic form probably result from the presence of hexagonal domains. We also present diffractograms of a growth twin of the monoclinic form and show how the twinning leads to an apparent hexagonal metric. We describe the crystal structures of both the hexagonal and monoclinic form. The hexagonal structure is identical to that determined previously [Angew. Chem. Int. Ed. Engl., 34 (1995) 1454] whereas the monoclinic one is new. The structures consist of layers interconnected by C–H⋯π interactions. These layers are flat in the hexagonal structure but very slightly buckled in the monoclinic one. The monoclinic crystals are ordered as is reflected in the buckling of the layers. The tris(bicyclo[2.1.1]hexeno)benzene molecules display significant bond alternation, 0.089(4) A˚, in the central benzene ring. [Copyright &y& Elsevier]