Crystallographic Unit Cell Research Articles

Kinematics Meets Crystallography: The Concept of a Motion Space1

In this paper, it is shown how rigid-body kinematics can be used to assist in determining the atomic structure of proteins and nucleic acids when using x-ray crystallography, which is a powerful method for structure determination. The importance of determining molecular structures for understanding biological processes and for the design of new drugs is well known. Phasing is a necessary step in determining the three-dimensional structure of molecules from x-ray diffraction patterns. A computational approach called molecular replacement (MR) is a well-established method for phasing of x-ray diffraction patterns for crystals composed of biological macromolecules. In MR, a search is performed over positions and orientations of a known biomolecular structure within a model of the crystallographic asymmetric unit, or, equivalently, multiple symmetry-related molecules in the crystallographic unit cell. Unlike the discrete space groups known to crystallographers and the continuous rigid-body motions known to kinematicians, the set of motions over which MR searches are performed does not form a group. Rather, it is a coset space of the group of continuous rigid-body motions, SE(3), with respect to the crystallographic space group of the crystal, which is a discrete subgroup of SE(3). Properties of these “motion spaces” (which are compact manifolds) are investigated here.

Solid‐State NMR Study of Mn2+ for Ca2+ Substitution in Thermally Processed Hydroxyapatites

In the present study calcium hydroxyapatites enriched at 0.08 wt% in Mn2+ ions (Mn–HA) and their unsubstituted forms (HA) were synthesized using the same standard wet chemical route. Mn‐HA and HA were both calcined at 800°C to give Mn‐HAc and HAc, respectively or sintered at 1250°C, to give Mn‐HAs and HAs, respectively. The influence of the heat treatment on physicochemical properties of Mn‐HA was investigated using powder X‐ray diffraction (PXRD), scanning, and transmission electron microscopy (SEM and TEM), and solid‐state nuclear magnetic resonance (ssNMR). Mn‐HAc and Mn‐HAs were compared to each other and to HAc and HAs, respectively. Assignment of the proton ssNMR peaks from high‐temperature‐treated apatites has been revised. It was found that Mn–HAc and HAc were nanocrystalline, while Mn‐HAs and HAs comprised micrometer sized, partially fused particles (SEM and TEM). PXRD and ssNMR demonstrated that the incorporation of Mn2+ into the crystal lattice of hydroxyapatite significantly facilitates its dehydroxylation and decomposition to oxyhydroxyapatite during calcination at 800°C, and induces its transformation to tetracalcium phosphate (TTCP) and alpha‐tricalcium phosphate (α‐TCP) at 1250°C. Contamination by CaO has also been detected. The 1H→31P NMR cross‐polarization experiments have indicated that the Mn2+ ions preferentially occupied the Ca(I) position in the crystallographic unit cell of Mn‐HAc. In Mn‐HAs, the Mn2+ ions were evenly distributed between the Ca(I) and Ca(II) positions.

Termination and hydration of forsteritic olivine (0 1 0) surface

Termination and hydration of the forsteritic (Fo90Fa10) olivine (010) surface have been investigated with high-resolution specular X-ray reflectivity and Atomic Force Microscopy. The surface was prepared by polishing a naturally grown {010} face, from which we found the polished surface in acidic (pH 3.5) alumina suspension exhibits regular steps while the basic (pH 9.5) silica polished surface is irregularly roughened, indicating there are two distinguishable mechanochemical processes for the surface dissolution. The quantitative interpretation of the regular steps from the alumina-polished surface suggests that the observed step heights correspond to multiples of crystallographic unit cell. Only this atomically terraced surface is investigated with the high-resolution X-ray reflectivity (HRXR) to determine the surface termination and hydration. The basic silica paste polished surface turned out too rough to measure with X-ray reflectivity. HRXR reveals that the alumina polished olivine (010) surface in pure water is terminated at a plane including half-occupied metal ion sites (M1), an oxygen vacancy site, and a silicate tetrahedral unit with one of its apices pointing outward with respect to the surface. An ideal termination with the oxygen vacancy would fulfill the stoichiometry of the formula unit; however, in the observation, the vacancy site is filled by an adsorbed water species and about a quarter of the remaining metal ions are further depleted. The terminating plane generates two distinct atomic layers in the laterally averaged electron density profile, on which two highly ordered adsorbed water layers are formed. The first layer formation is likely through the direct interaction with the M1 plane and the second layer is likely through the hydrogen bonding interaction with the first water layer. With this multilayered adsorbed water structure, the surface metal ion is partially hydrated by the vacancy-filling water species and adsorbed water molecules. The bulk water links to these distinct adsorbed water layers, with weak density oscillations that almost completely damp out after the first bulk water layer. The total thickness of the layered water structure including the two distinct adsorbed layers and the first layer of bulk water is slightly less than 1nm, which corresponds to roughly three molecular layers of water. These results describe the steric constraints of the surface metal ion hydration and the iron redox environment during water–olivine interactions in this particular crystallographic orientation.

Neutron Diffraction Studies: Structure and Physical Properties of La2 O 3−x F x Fe2Se2

We report on substantial changes in the crystal structure as well as in the magnetic and transport properties of the La2O3−xFxFe2Se2 system with x from 0.0 to 0.5 measured by neutron diffraction and magnetic bulk measurements. With increasing x, the size of the crystallographic unit cell decreases as well as the amplitude of the ordered magnetic moments, while the configuration of the magnetic order and the development of the resistivity on cooling remains unchanged.

Sheding light on the multiferroicity in Mn1-xCoxWO4using superspace formalism

The use of the superspace symmetry formalism allows to rationalize the physical properties induced by an incommensurate magnetic ordering [1]. The incommensurate magnetic structures (ICMS) in Mn1-xCoxWO4 have been studied in the light of this formalism. MnWO4 is a multiferroic material in which the magnetic order of one of its magnetic phases induces ferroelectricity. Like most multiferroic materials MnWO4 is extremely sensitive to small perturbations such as chemical substitution. It turned out that doping with Co2+ is particularly interesting since it strongly stabilizes the multiferroic phase at low temperatures, and moreover, by increasing the cobalt amount in the crystals the orientation of the electric polarization flops from the b axis to the ac plane [2]. This change of orientation is linked to a symmetry change. The ICMS of the x = 0 and x = 0.10 compounds, which exhibit completely different behavior, have been studied thoroughly using superspace formalism. We have found, not only the symmetry of the magnetic structures and their intrinsic restrictions, but also information about the tensor properties of each incommensurate phase, such as ferroelectric and magnetostructural properties [3]: in the paramagnetic state, there is a unique independent magnetic atom in the crystallographic unit cell in both cases, but when the system enters into the multiferroic phase, this is no-longer true. In the multiferroic phase of MnWO4, the two Mn atoms in the unit cell become symmetry independent, whereas in the x = 0.10 substituted compound, they are still symmetry-related. This difference is related to the change of the electric polarization.

Periodic cation segregation in Cs0.44[Nb2.54W2.46O14] quantified by high-resolution scanning transmission electron microscopy.

The atomic structure of Cs0.44[Nb2.54W2.46O14] closely resembles the structure of the most active catalyst for the synthesis of acrylic acid, the M1 phase of Mo10V2(4+)Nb2TeO42-x. Consistently with observations made for the latter compound, the high-angle electron scattering signal recorded by scanning transmission electron microscopy shows a significant intensity variation, which repeats periodically with the projected crystallographic unit cell. The occupation factors for the individual mixed Nb/W atomic columns are extracted from the observed intensity variations. For this purpose, experimental images and simulated images are compared on an identical intensity scale, which enables a quantification of the cation distribution. According to our analysis specific sites possess low tungsten concentrations of 25%, whereas other sites have tungsten concentrations above 70%. These findings allow us to refine the existing structure model of the target compound, which has until now described a uniform distribution of the niobium and tungsten atoms in the unit cell, showing that the similarity between Cs0.44[Nb2.54W2.46O14] and the related catalytic compounds also extends to the level of the cation segregation.

Crystallographic phasing with NMR models: an envelope approach.

X-ray crystallography and NMR are complementary tools in structural biology. However, it is often difficult to use NMR structures as search models in molecular replacement (MR) to phase crystallographic data. In this study, a new approach is reported utilizing a molecular envelope of NMR structures for MR phasing with the program FSEARCH at low resolution (about 6 Å). Several targets with both crystallographic and NMR structures available have been tested. FSEARCH was able to find the correct translation and orientation of the search model in the crystallographic unit cell, while conventional MR procedures were unsuccessful.

Raman and Photoluminescence Properties of Red and Yellow Rubrene Crystals

In this article, we use a combination of micro-Raman and microphotoluminescence measurements to demonstrate that rubrene single crystals, which appear as yellow platelets and red needles, are two distinct orientations of the same crystallographic unit cell. As confirmed by X-ray diffraction and polarization microscopy, we show that red and yellow crystals represent the crystallographic orientations (020) and (002), respectively, with the crystallographic c-axis being the optically activated orientation in red crystals and the b-axis in yellow crystals. Raman measurements of red crystals are characterized by a pronounced Raman shift at 217 cm–1, which to the best of our knowledge is the first report of this peak at its predicted spectral position. The Raman and photoluminescence spectra obtained from yellow crystals change abruptly at their borders into the spectra of red crystals, confirming the distinct spectroscopic properties of each crystal orientation. The combination of Raman and photoluminescence measurements applied at different focal planes within red crystals reveals that the 217 cm–1 peak can be classified as a surface active mode.

Combining Crystallographic and Structure-Modeling Approaches in Macromolecular Crystallography

Molecular replacement is a powerful method for determining macromolecular crystal structures. The method remains limited by the requirement for a template structure that is similar to the structure to be determined. Here we describe two approaches for carrying out molecular replacement with distant homology models, each approach bringing in new information about the structure to be determined.The first approach combines the power of Rosetta structure modeling with macromolecular structure determination. Rosetta and other tools from the structure-modeling field have optimized force fields that are focused on obtaining a physically plausible model. In contrast, crystallographic model-building tools focus on interpretation of patterns of density in an electron density map. As these sources of information are nearly orthogonal, putting them together can increase the range of cases where crystal structures of macromolecules can be determined. An easy-to-use tool has been developed in the Phenix crystallographic software system for carrying out extensive molecular replacement searches followed by model-building using both Rosetta and crystallographic tools. This mr_rosetta software is able to find solutions to challenging molecular replacement problems.The second approach takes advantage of the observation that many pairs of proteins have local structures that can be superimposed much more closely than can their complete structures. For example, a β-sheet in one protein may be locally similar to a sheet in another, but when the two structures are superimposed using all atoms, the sheets may be translated relative to each other. We have developed a method for applying local distortions to a structure (morphing it) using an electron density map to guide the distortions. This procedure allows local similarity to be maintained while global structure is changed. We show that morphing molecular replacement templates after placing them in their approximate locations in the crystallographic unit cell can greatly improve subsequent model-building.

Investigating the Gas Sorption Mechanism in an rht-Metal–Organic Framework through Computational Studies

Grand canonical Monte Carlo (GCMC) simulations were performed to investigate CO2 and H2 sorption in an rht-metal–organic framework (MOF) that was synthesized with a ligand having a nitrogen-rich trigonal core through trisubstituted triazine groups and amine functional groups. This MOF was synthesized by two different groups, each reporting their own distinct gas sorption measurements and crystal structure. Electronic structure calculations demonstrated that the small differences in the atomic positions between each group’s crystal structure resulted in different electrostatic parameters about the Cu2+ ions for the respective unit cells. Simulations of CO2 sorption were performed with and without many-body polarization effects and using our recently developed CO2 potentials, in addition to a well-known bulk CO2 model, in both crystallographic unit cells. Simulated CO2 sorption isotherms and calculated isosteric heats of adsorption, Qst, values were in excellent agreement with the results reported previousl...

Calculating NMR parameters in aluminophosphates: evaluation of dispersion correction schemes

Periodic density functional theory (DFT) calculations have recently emerged as a popular tool for assigning solid-state nuclear magnetic resonance (NMR) spectra. However, in order for the calculations to yield accurate results, accurate structural models are also required. In many cases the structural model (often derived from crystallographic diffraction) must be optimised (i.e., to an energy minimum) using DFT prior to the calculation of NMR parameters. However, DFT does not reproduce weak long-range "dispersion" interactions well, and optimisation using some functionals can expand the crystallographic unit cell, particularly when dispersion interactions are important in defining the structure. Recently, dispersion-corrected DFT (DFT-D) has been extended to periodic calculations, to compensate for these missing interactions. Here, we investigate whether dispersion corrections are important for aluminophosphate zeolites (AlPOs) by comparing the structures optimised by DFT and DFT-D (using the PBE functional). For as-made AlPOs (containing cationic structure-directing agents (SDAs) and framework-bound anions) dispersion interactions appear to be important, with significant changes between the DFT and DFT-D unit cells. However, for calcined AlPOs, where the SDA-anion pairs are removed, dispersion interactions appear much less important, and the DFT and DFT-D unit cells are similar. We show that, while the different optimisation strategies yield similar calculated NMR parameters (providing that the atomic positions are optimised), the DFT-D optimisations provide structures in better agreement with the experimental diffraction measurements. Therefore, it appears that DFT-D calculations can, and should, be used for the optimisation of calcined and as-made AlPOs, in order to provide the closest agreement with all experimental measurements.

Hingeless negative linear compression in the mechanochromic gold complex [(C6F5Au)2(μ-1,4-diisocyanobenzene)

The compression of a crystalline material under hydrostatic pressure always results in a reduction in volume of the solid, with the observed reduction typically occurring in all crystallographic cell parameters.1 However, there are a number of exceptional materials that have been shown to expand in a specific direction upon hydrostatic compression while maintaining a positive volume compression. The phenomenon of uni-or biaxial expansion under compression is known as negative linear compressibility (NLC).1 Rare examples of NLC have attracted attention recently owing to the potential applications in a range of materials, including body armor, artificial muscle actuators, and pressure sensors.2

Reinvestigation of Np2Se5: A Clear Divergence from Th2S5 and Th2Se5 in Chalcogen–Chalcogen and Metal–Chalcogen Interactions

Single crystals of Np2Se5 have been prepared through the reactions of Np and Se at 1223 K in an Sb2Se3 flux. The structure of Np2Se5, which has been characterized by single-crystal X-ray diffraction methods, crystallizes in the tetragonal space group P42/nmc. The crystallographic unit cell includes one unique Np and two Se positions. Se(1) atoms form one-dimensional infinite chains along the a and b axes with alternating intermediate Se-Se distances of 2.6489 (8) and 2.7999 (8) Å, whereas Se(2) is a discrete Se(2-) anion. Each Np is coordinated to 10 Se atoms and every NpSe10 polyhedron shares faces, edges, or vertices with 14 other identical metal polyhedra to form a complex three-dimensional structure. Np LIII-edge X-ray Absorption Near Edge Structure (XANES) measurements show a clear shift in edge position to higher energies for Np2Se5 compared to Np3Se5 (Np(3+)2Np(4+)Se(2-)5). Magnetic susceptibility measurements indicate that Np2Se5 undergoes a ferromagnetic-type ordering below 18(1) K. Above the transition temperature, Np2Se5 behaves as a paramagnet with an effective moment of 1.98(5) μB/Np, given by a best fit of susceptibilities to a modified Curie-Weiss law over the temperature range 50-320 K.

Incommensurate spin spiral of the geometrically-frustrated antiferromagnet CdCr2O4

CdCr2O4 is a cubic spinel with geometrically-frustrated antiferromagnetic interactions between Cr3+ ions. We investigated the structural and magnetic phase transitions in powder samples by using magnetization and neutron diffraction measurements. An antiferromagnetic phase transition was observed at TN = 8.1 K, below which the crystallographic unit cell was tetragonal (c < a = b). Its incommensurate antiferromagnetic ordering below TN resembles dimerized spin chains in the ab planes with the propagation vector k = (0, 0.088, 1). We argue that the Dzyaloshinskii-Moriya interaction and the magnetic frustration play important roles in establishing the observed magnetic ordering.

Neutron diffraction study on the magnetic structure of Fe2P-based Mn0.66Fe1.29P1−xSix melt-spun ribbons

We report on the magnetic and structural properties of Mn0.66Fe1.29P1−xSix melt-spun ribbons with 0.34≤x≤0.42 that are promising candidates for high-temperature magnetocaloric applications. A magnetic moment of up to 4.57μB/f.u. for x=0.34 indicates high magnetic density in the system, which is certainly advantageous for the magnetocaloric effects. Introducing site disorder at the 3g site by replacing 1/3 of Fe with Mn appears to enhance the magnetic interaction, while the strong magnetoelastic coupling is maintained. This site disorder also shows a stabilizing effect on the hexagonal crystal structure, which is maintained to a high Si content. The moment alignment within the crystallographic unit cell is also affected when the Si content is increased from x=0.34 to 0.42 in the Mn0.66Fe1.29P1−xSix compounds as the canting angle with respect to the c-direction increases.

X-ray diffraction analysis of secondary phases in zirconium alloys before and after neutron irradiation at the MARS synchrotron radiation beamline

To further advance understanding of microstructural evolution in zirconium alloys for high burnup applications in PWR, it is important to obtain precise characterizations of second-phase particles present in the bulk alloys as a function of the neutron-irradiation fluence.X-ray diffraction from a synchrotron radiation source (SOLEIL) was used to identify and follow the evolution of second-phase particles that are in very small volume fractions in two zirconium alloys: Zy-4 in stress-relieved metallurgical state before irradiation and Zr–1%Nb (M5®) in recrystallized metallurgical state before and after neutron irradiation. Despite the fact the neutron irradiated sample is not in the as-irradiated state due to a thermal treatment and creep test performed after irradiation, interesting results have been obtained on secondary phases using XRD techniques.Analyses have been performed at the MARS beamline, fully dedicated to advanced structural and chemical characterizations of radioactive matter.A first proof of the improvement brought by these new analyses performed at the MARS beamline is given with Zr(Fe, Cr)2 precipitates found in unirradiated Zy-4 alloy in stress relieved metallurgical state, highly textured and displaying significant residual stresses and numerous dislocations: lattice parameters, crystallite size and microstrains (line profile analysis using the Williamson–Hall method after correction for instrumental broadening) have been estimated with very good accuracy.Then, second phase particles of the Zr–1%Nb alloy (M5®) have been analyzed before and after irradiation. For the Zr(Fe, Nb)2 Laves phase, the diffraction line disappeared after neutron irradiation. For β-Nb phases, the evolution of diffraction peaks clearly show the convolution of two phenomena: in one hand slight decreases in Nb content for native β-Nb particles and on the other hand irradiation-enhanced precipitation of nano-sized needle-like β-Nb particles. To our knowledge, this is the first time that the crystallographic unit cell, lattice parameter and Nb content of the β-Nb irradiation-enhanced precipitates have been determined using synchrotron radiation on irradiated Zr–1%Nb (M5®) alloy.

Hydrophobic Interaction Drives Surface-Assisted Epitaxial Assembly of Amyloid-like Peptides

The molecular mechanism of epitaxial fibril formation has been investigated for GAV-9 (NH(3)(+)-VGGAVVAGV-CONH(2)), an amyloid-like peptide extracted from a consensus sequence of amyloidogenic proteins, which assembles with very different morphologies, "upright" on mica and "flat" on the highly oriented pyrolytic graphite (HOPG). Our all-atom molecular dynamics simulations reveal that the strong electrostatic interaction induces the "upright" conformation on mica, whereas the hydrophobic interaction favors the "flat" conformation on HOPG. We also show that the epitaxial pattern on mica is ensured by the lattice matching between the anisotropic binding sites of the basal substrate and the molecular dimension of GAV-9, accompanied with a long-range order of well-defined β-strands. Furthermore, the binding free energy surfaces indicate that the longitudinal assembly growth is predominantly driven by the hydrophobic interaction along the longer crystallographic unit cell direction of mica. These findings provide a molecular basis for the surface-assisted molecular assembly, which might also be useful for the design of de novo nanodevices.

On the Hydrogen Bonding Structure at the Aqueous Interface of Ammonium-Substituted Mica: A Molecular Dynamics Simulation

Molecular dynamics (MD) computer simulations were performed for an aqueous film of 3 nm thickness adsorbed at the (001) surface of ammonium-substituted muscovite mica. The results provide a detailed picture of the near-surface structure and topological characteristics of the interfacial hydrogen bonding network. The effects of deuterium=hydrogen isotopic substitution in N(H=D)4+ on the dynamics and consequently on the convergence of the structural properties have also been explored. Unlike many earlier simulations, a much larger surface area representing 72 crystallographic unit cells was used, which allowed for a more realistic representation of the substrate surface with a more disordered distribution of aluminium=silicon isomorphic substitutions in muscovite. The results clearly demonstrate that under ambient conditions both interfacial ammonium ions and the very first layer of water molecules are H-bonded only to the basal surface of muscovite, but do not form H-bonds with each other. As the distance from the surface increases, the H-bonds donated to the surface by both N(H=D)4+ and H2O are gradually replaced by the H-bonds to the neighbouring water molecules, with the ammonia ions experiencing one reorientational transition region, while the H2O molecules experiencing three such distinct consecutive transitions. The hydrated N(H=D)4+ ions adsorb almost exclusively as inner-sphere surface complexes with the preferential coordination to the basal bridging oxygen atoms surrounding the aluminium=silicon substitutions.

Atomic-layer synthesis and imaging uncover broken inversion symmetry in La2−xSrxCuO4films

Materials with broken inversion symmetry are of great interest for their exotic electronic properties but are relatively rare. We show here that even if a material is inversion-symmetric in the bulk form, in epitaxial thin films of the same compound the crystallographic unit cell can be quite asymmetric. To demonstrate this, we have used atomic layer-by-layer molecular beam epitaxy to synthesize La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$ films with Sr-dopant atoms deposited above, below, or on both sides of each CuO${}_{2}$ layer. Surface x-ray diffraction experiments analyzed by the Coherent Bragg Rod Analysis (COBRA) method have been carried out in combination with energy-differential diffraction measurements to determine whether the actual Sr distribution coincided with the nominal one (that would be expected in absence of La-Sr interdiffusion). The differential approach minimizes the systematic errors, and the combination with COBRA is potentially capable to determine the concentration of atomic species on a monoatomic layer-by-layer basis. The results show that the concentration of Sr in La/Sr layers just above the CuO${}_{2}$ layers is much larger than in layers just below them, irrespective of the deposition sequence, and drastically breaking the inversion symmetry.

Hydrazine-Processed Ge-Substituted CZTSe Solar Cells

The p-type Cu2ZnSn(SxSe1–x)4 (with x ≈ 0; CZTSe) thin-film solar cell absorber, made from earth-abundant elements, was substituted with Ge using a hydrazine-based mixed particle-solution approach for the film deposition. The crystallographic unit cell parameters of the absorber layer decrease with gradual incorporation of Ge. A solar cell fabricated from a 40% Ge-substituted absorber showed a 9.1% power conversion efficiency, a higher open-circuit voltage, and a wider band gap compared with the device based on the unsubstituted absorber layer. This result shows the possibility of substituting, using the hydrazine-processing approach, the metal site of CZTSe with Ge for further device optimization. One area for further improvement in the substituted absorber layer devices includes reduction of a ZnSe secondary phase, which was apparent in the higher-Ge-content films.