Anisotropic Displacement Parameters Research Articles

Synthesis and structure of analcime and analcime-zirconia composite derived from coal fly ash cenospheres

Cubic analcime and analcime-zirconia composite with the Si/Al ratio of 2.04 and 2.16, respectively, was synthesized by hydrothermal treatment of coal fly ash cenospheres (Si/Al = 2.7) at 150 °C. The scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS), powder X-ray diffraction (PXRD), X-ray photoelectron spectroscopy (XPS), synchronous thermal analysis (STA) methods were used to study the morphology, composition and structure of the products. Two main types of analcime bearing particles were obtained, such as hollow microspheres with attached analcime icositetrahedra of 5–50 μm in size and individual analcime crystals of a narrow particle size distribution (Dm = 41 μm) with incorporated zirconia (4.8 wt% Zr). The high quality of the crystalline fractions allowed an accurate full-profile PXRD analysis of complete analcime crystal structure and composition including anisotropic displacement parameters of all atoms and H-positions of water molecules.

Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene.

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.

Synthesis, Crystal Structure, and Transport Properties of the Hexagonal Mo9 Cluster Compound Ag3RbMo9Se11.

Mo-based cluster compounds are promising candidates for thermoelectric applications at high temperatures due to their very low lattice thermal conductivity values. Here, we report on a detailed investigation of the crystal structure and transport properties measured in a wide range of temperatures (2-800 K) of polycrystalline Ag3RbMo9Se11. Single-crystal X-ray diffraction shows that this compound crystallizes in the hexagonal space group P63/m. The crystal structure is formed by stacked Mo9Se11 units leaving channels that are randomly filled by Rb+ cations, while Ag+ cations are located between the Mo9Se11 units. The high disorder in the unit cell induced by these atoms and their large anisotropic thermal displacement parameters are two key characteristics that lead to very low lattice thermal conductivity as low as 0.6 W m-1 K-1 at 800 K. The combination of semiconducting-like electrical properties and low ability to transport heat leads to a maximum dimensionless thermoelectric figure of merit ZT of 0.4 at 800 K.

Ultra-high resolution X-ray structures of two forms of human recombinant insulin at 100 K

The crystal structure of a commercially available form of human recombinant (HR) insulin, Insugen (I), used in the treatment of diabetes has been determined to 0.92 Å resolution using low temperature, 100 K, synchrotron X-ray data collected at 16,000 keV (λ = 0.77 Å). Refinement carried out with anisotropic displacement parameters, removal of main-chain stereochemical restraints, inclusion of H atoms in calculated positions, and 220 water molecules, converged to a final value of R = 0.1112 and Rfree = 0.1466. The structure includes what is thought to be an ordered propanol molecule (POL) only in chain D(4) and a solvated acetate molecule (ACT) coordinated to the Zn atom only in chain B(2). Possible origins and consequences of the propanol and acetate molecules are discussed. Three types of amino acid representation in the electron density are examined in detail: (i) sharp with very clearly resolved features; (ii) well resolved but clearly divided into two conformations which are well behaved in the refinement, both having high quality geometry; (iii) poor density and difficult or impossible to model. An example of type (ii) is observed for the intra-chain disulphide bridge in chain C(3) between Sγ6–Sγ11 which has two clear conformations with relative refined occupancies of 0.8 and 0.2, respectively. In contrast the corresponding S–S bridge in chain A(1) shows one clearly defined conformation. A molecular dynamics study has provided a rational explanation of this difference between chains A and C. More generally, differences in the electron density features between corresponding residues in chains A and C and chains B and D is a common observation in the Insugen (I) structure and these effects are discussed in detail. The crystal structure, also at 0.92 Å and 100 K, of a second commercially available form of human recombinant insulin, Intergen (II), deposited in the Protein Data Bank as 3W7Y which remains otherwise unpublished is compared here with the Insugen (I) structure. In the Intergen (II) structure there is no solvated propanol or acetate molecule. The electron density of Intergen (II), however, does also exhibit the three types of amino acid representations as in Insugen (I). These effects do not necessarily correspond between chains A and C or chains B and D in Intergen (II), or between corresponding residues in Insugen (I). The results of this comparison are reported.Graphical abstractConformations of PheB25 and PheD25 in three insulin structures: implications for biological activity? Insulin residues PheB25 and PheD25 are considered to be important for insulin receptor binding and changes in biological activity occur when these residues are modified. In porcine insulin and Intergen (II) PheB25 adopts conformation B and PheD25 conformation D. However, unexpectedly PheB25 in Insugen (I) human recombinant insulin adopts two distinct conformations corresponding to B and D, Figure 1 and PheD25 adopts a single conformation corresponding to B not D, Figure 2. Conformations of this residue in the ultra-high resolution structure of Insugen (I) are therefore unique within this set. Figures were produced with Biovia, Discovery Studio 2016.

Modular structure of highly ordered eudialyte and its place among hydrated minerals of rastsvetaevite family

The crystal structure of a representative of eudialyte group, which was found by A.P. Khomyakov at the Rasvumchorr mountain of the Khibiny alkaline massif (Kola Peninsula), has been studied by X-ray diffraction. The trigonal unit-cell parameters are found to be a = 14.2328(5) A, c = 60.217(2) A, V = 10564.08(3) A3, sp. gr. R3m. The structure has been refined with the isotropic and anisotropic approximation displacement parameters to the total reliability factor R = 5.6%, based on 2989 reflections with |F| > 4σ(F). The idealized formula (Z = 3) is determined as [(H3O)11Na10K5]Cа12(Na3Fe2Mn)Si4Zr6(Si48O144)(OH,Cl)5(H2O)5. The unit cell of the mineral is doubled due to the presence of two modules of different composition and structure in it (alluaivite-and kentbrooksite-like ones) and the formation of a polyhedral cluster in the kentbrooksite module. A comparison with two hydrated minerals having a modular structure shows that these minerals, being similar in their chemical composition, differ in the cation ordering over the sites of the two modules. The sample under study contains potassium in only one module, while oxonium groups are distributed in both modules but over different sites.

Hydrogen bonding in goldichite, KFe(SO4)2⋅4H2O: structure refinement

The crystal structure of goldichite KFe(SO4)2⋅4H2O was determined on a single crystal from the Baiyinchang copper deposit, Gansu, China. [P121/c1, a = 10.395(2), b = 10.475(2), c = 9.0875(18) A, β = 101.65(3)°, V = 969.1(3) A3, Z = 4]. All non-H atoms were refined with anisotropic displacement parameters and positions of H-atoms were determined by difference Fourier methods and refined from X-ray diffraction data. The crystal structure of goldichite consists of corrugated sheets parallel to the (100) plane by sharing corners between FeO6 octahedra and SO4 tetrahedra. The interstitial potassium atom exhibits a [KO7(H2O)2] nine-fold coordination, which shares edges to form a column parallel to the c-axis and to build a slab with the corrugated sheet. These slabs are linked in the [100] direction through a network of hydrogen bonds. Three types of hydrogen bonds involve links of slabs: Ow(3)-H(3B)···O(1), Ow(6)-H(6B)···O(11) and Ow(9)-H(9B)···O(11). The FTIR spectrum of goldichite shows a strong absorption between ~3384 cm−1 and ~3592 cm−1, which is in accordance with the O-H···O distances derived from structure data.

A combined experimental and in silico characterization to highlight additional structural features and properties of a potentially new drug

LASSBio-1755 is a new cycloalkyl-N-acylhydrazone parent compound designed for the development of derivatives with antinociceptive and anti-inflammatory activities. Although single crystal X-ray diffraction has been considered as the golden standard in structure determination, we successfully used X-ray powder diffraction data in the structural determination of new synthesized compounds, in order to overcome the bottle-neck due to the difficulties experienced in harvesting good quality single crystals of the compounds. We therefore unequivocally assigned the relative configuration (E) to the imine double bond and a s-cis conformation of the amide function of the N-acylhydrazone compound. These features are confirmed by a computational analysis performed on the basis of molecular dynamics calculations, which are extended not only to the structural characteristics but also to the analysis of the anisotropic atomic displacement parameters, a further information – missed in a typical powder diffraction analysis. The so inferred data were used to perform additional cycles of refinement and eventually generate a new cif file with additional physical information. Furthermore, crystal morphology prediction was performed, which is in agreement with the experimental images acquired by scanning electron microscopy, thus providing useful information on possible alternative paths for better crystallization strategies.

Powder-X-ray diffraction analysis of the crystal structure of the η′-Al8Fe3 (η′-Al2.67Fe) phase

Al2+δFe intermetallic for 0.4 <δ < 0.7, frequently also referred to as η-Al5Fe2, has been investigated in detail by powder-X-ray diffraction. The lattice parameters of the disordered orthorhombic η-Al2+δFe phase quenched from 750 °C were precisely determined. The lattice parameter cη increases non-linearly with increasing Al content, whereas aη increases and bη decreases linearly to a respectively lesser extent. Moreover, the recently reported long-range ordered η′-Al2+δFe low-temperature phase (C2/c symmetry) was confirmed to exist around an ideal value of δ = 2/3 after annealing at 250 °C or 350 °C. The monoclinic long-range ordering of some Al atoms in channels of a framework structure is accompanied by a characteristic ordering strain, which is revealed by the refined lattice parameters aη’ = 11.35940(5) Å, bη’ = 6.42493(2) Å and cη’ = 8.68218(3) Å and βη’ = 104.2519(3)° determined by X-ray diffraction. These values imply a change of the β angle pertaining to the original orthorhombic cell to β’η’ = 90.51°. Experimentally determined atomic positions from Rietveld refinement of the η′ phase well agree with results from relaxed density functional energy calculations and can be related with earlier reported strongly anisotropic displacement parameters of certain atomic sites in the disordered η phase.

Plane-Wave Density Functional Theory Meets Molecular Crystals: Thermal Ellipsoids and Intermolecular Interactions.

Molecular compounds, organic and inorganic, crystallize in diverse and complex structures. They continue to inspire synthetic efforts and "crystal engineering", with implications ranging from fundamental questions to pharmaceutical research. The structural complexity of molecular solids is linked with diverse intermolecular interactions: hydrogen bonding with all its facets, halogen bonding, and other secondary bonding mechanisms of recent interest (and debate). Today, high-resolution diffraction experiments allow unprecedented insight into the structures of molecular crystals. Despite their usefulness, however, these experiments also face problems: hydrogen atoms are challenging to locate, and thermal effects may complicate matters. Moreover, even if the structure of a crystal is precisely known, this does not yet reveal the nature and strength of the intermolecular forces that hold it together. In this Account, we show that periodic plane-wave-based density functional theory (DFT) can be a useful, and sometimes unexpected, complement to molecular crystallography. Initially developed in the solid-state physics communities to treat inorganic solids, periodic DFT can be applied to molecular crystals just as well: theoretical structural optimizations "help out" by accurately localizing the elusive hydrogen atoms, reaching neutron-diffraction quality with much less expensive measurement equipment. In addition, phonon computations, again developed by physicists, can quantify the thermal motion of atoms and thus predict anisotropic displacement parameters and ORTEP ellipsoids "from scratch". But the synergy between experiment and theory goes much further than that. Once a structure has been accurately determined, computations give new and detailed insights into the aforementioned intermolecular interactions. For example, it has been debated whether short hydrogen bonds in solids have covalent character, and we have added a new twist to this discussion using an orbital-based theory that once more had been developed for inorganic solids. However, there is more to a crystal structure than a handful of short contacts between neighboring residues. We hence have used dimensionally resolved analyses to dissect crystalline networks in a systematic fashion, one spatial direction at a time. Initially applied to hydrogen bonding, these techniques can be seamlessly extended to halogen, chalcogen, and pnictogen bonding, quantifying bond strength and cooperativity in truly infinite networks. Finally, these methods promise to be useful for (bio)polymers, as we have recently exemplified for α-chitin. At the interface of increasingly accurate and popular DFT methods, ever-improving crystallographic expertise, and new challenging, chemical questions, we believe that combined experimental and theoretical studies of molecular crystals are just beginning to pick up speed.

Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks.

Amino acid structures are an ideal test set for method‐development studies in crystallography. High‐resolution X‐ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non‐standard amino acid. Structures were re‐investigated to study a widely applicable treatment that permits accurate X−H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen‐atom parameters with aspherical scattering factors with constrained “TLS+INV” estimated hydrogen anisotropic displacement parameters (H‐ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H‐ADPs, as free refinement frequently leads to over‐parameterization and non‐positive definite H‐ADPs irrespective of the aspherical scattering model used. Using estimated H‐ADPs, both methods yield accurate and precise X−H distances in best quantitative agreement with neutron diffraction data (available for five of the test‐set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.

K+···Cπ and K+···F Non-Covalent Interactions in π-Functionalized Potassium Fluoroalkoxides

Secondary interactions stabilize coordinatively demanding complexes of s-block metals [...]

Intrinsic Phase Diagram of Superconductivity in the BiCh2-Based System Without In-Plane Disorder

We have investigated the crystal structure and physical properties of LaO1-xFxBiSSe to reveal the intrinsic superconductivity phase diagram of the BiCh2-based layered compound family. From synchrotron X-ray diffraction and Rietveld refinements with anisotropic displacement parameters, we clearly found that the in-plane disorder in the BiSSe layer was fully suppressed for all x. In LaO1-xFxBiSSe, metallic conductivity and superconductivity are suddenly induced by electron doping even at x = 0.05 and 0.1 with a monoclinic structure. In addition, x (F concentration) dependence of the transition temperature (Tc) for x = 0.2-0.5 with a tetragonal structure shows an anomalously flat phase diagram. With these experimental facts, we have proposed the intrinsic phase diagram of the ideal BiCh2-based superconductors with less in-plane disorder.

Structure and Vibrational Dynamics of NASICON-Type LiTi2(PO4)3

Small single crystals of NASICON-type LiTi2(PO4)3 of high quality were grown by means of long-term annealing of polycrystalline specimens synthesized using conventional solid state reaction. A thorough study of their structural properties and vibrational dynamics was carried out by means of an integrated experimental and theoretical approach. A single-crystal X-ray diffraction analysis at room temperature allowed us to determine the precise crystal structure and the anisotropic displacement parameters of all atoms. In addition, all the 25 independent components of the polarizability tensor, expected on the basis of the group theory for the LiTi2(PO4)3 crystal, were observed using polarized Raman spectroscopy in backscattering geometry on a microcrystal, properly oriented by a micromanipulator. Thus, all the expected Raman modes have been unambiguously identified by determining both their wavenumber and symmetry throughout an accurate analysis of the spectral profiles observed in the different polarization...

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to L-alanine, naphthalene and xylitol.

In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206-214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of L-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of L-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol-1 K-1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.

Potassium Disorder in the Defect Pyrochlore KSbTeO6: A Neutron Diffraction Study

KSbTeO6 defect pyrochlore has been prepared from K2C2O4, Sb2O3, and 15% excess TeO2 by solid-state reaction at 850 °C. Direct methods implemented in the software EXPO2013 allowed establishing the basic structural framework. This was followed by a combined Rietveld refinement from X-ray powder diffraction (XRD) and neutron powder diffraction (NPD) data, which unveiled additional structural features. KSbTeO6 is cubic, a = 10.1226(7) Å, space group F d 3 ¯ m , Z = 8 and it is made of a mainly covalent framework of corner-sharing (Sb,Te)O6 octahedra, with weakly bonded K+ ions located within large cages. The large K-O distances, 3.05(3)–3.07(3) Å, and quite large anisotropic atomic displacement parameters account for the easiness of K+ exchange for other cations of technological importance.

Lattice thermal expansion and anisotropic displacements in 𝜶-sulfur from diffraction experiments and first-principles theory.

Thermal properties of solid-state materials are a fundamental topic of study with important practical implications. For example, anisotropic displacement parameters (ADPs) are routinely used in physics, chemistry, and crystallography to quantify the thermal motion of atoms in crystals. ADPs are commonly derived from diffraction experiments, but recent developments have also enabled their first-principles prediction using periodic density-functional theory (DFT). Here, we combine experiments and dispersion-corrected DFT to quantify lattice thermal expansion and ADPs in crystalline α-sulfur (S8), a prototypical elemental solid that is controlled by the interplay of covalent and van der Waals interactions. We begin by reporting on single-crystal and powder X-ray diffraction measurements that provide new and improved reference data from 10 K up to room temperature. We then use several popular dispersion-corrected DFT methods to predict vibrational and thermal properties of α-sulfur, including the anisotropic lattice thermal expansion. Hereafter, ADPs are derived in the commonly used harmonic approximation (in the computed zero-Kelvin structure) and also in the quasi-harmonic approximation (QHA) which takes the predicted lattice thermal expansion into account. At the PPBE+D3(BJ) level, the QHA leads to excellent agreement with experiments. Finally, more general implications of this study for theory and experiment are discussed.

Monoclinic superstructure of Pr3Rh4Ge4

Abstract Pr3Rh4Ge4 was synthesized by melting of the elements in an arc-melting furnace followed by annealing in a sealed tantalum ampoule in a muffle furnace. Structure refinement was based on temperature dependent single-crystal X-ray diffractometer data. At ambient temperature Pr3Rh4Ge4 adopts the U3Ni4Si4 type structure with strongly enhanced anisotropic displacement parameters for Rh1. Below 230 K additional reflections start to appear and at 110 K the structure could be described with the (3+1)D superspace group I2/m(α0γ)00; α=1/2, γ=1/2; (Z=2). This commensurately modulated structure could be refined with 1448 F 2 values, 39 variables and residuals of wR=0.0417 for the main reflections and wR=0.1520 for the satellites of 1st order, [a=408.36(2), b=421.12(3) and c=2504.4(2) pm]. The commensurate description could be transformed to a 3D supercell with space group A2/m and Z=4: a=816.72(2), b=421.12(3), c=2537.5(1) pm, β=99.26(1)°, 1448 F 2 values, 69 variables and wR=0.0499. The relation of the U3Ni4Si4 type structure, the (3+1)D modulated and the 3D supercell is discussed on the basis of a group–subgroup scheme. Temperature dependent magnetic susceptibility data reveal Curie–Weiss paramagnetism with an experimental moment of 3.72(2) μB/Pr atom and a Weiss constant of –12.6(5) K. No magnetic ordering is evident down to 3 K.

Accurate unrestrained DDM refinement of crystal structures from highly distorted and low-resolution powder diffraction data.

The structure of benzene:ethane co-crystal at 90 K is refined with anisotropic displacement parameters without geometric restraints from high-resolution synchrotron X-ray powder diffraction (XRPD) data using the derivative difference method (DDM) with properly chosen weighting schemes. The average C-C bond precision achieved is 0.005 Å and the H-atom positions in ethane are refined independently. A new DDM weighting scheme is introduced that compensates for big distortions of experimental data. The results are compared with density functional theory (DFT) calculations reported by Maynard-Casely et al. [(2016). IUCrJ, 3, 192-199] where a rigid-body Rietveld refinement was also applied to the same dataset due to severe distortions of the powder pattern attributable to experimental peculiarities. For the crystal structure of 2-aminopyridinium fumarate-fumaric acid formerly refined applying 77 geometric restraints by Dong et al. [(2013). Acta Cryst. C69, 896-900], an unrestrained DDM refinement using the same XRPD pattern surprisingly gave two times narrower dispersion of interatomic distances.

The Sampling of Conformational Dynamics in Ambient-Temperature Crystal Structures of Arginine Kinase

Arginine kinase provides a model for functional dynamics, studied through crystallography, enzymology, and nuclear magnetic resonance. Structures are now solved, at ambient temperature, for the transition state analog (TSA) complex. Analysis of quasi-rigid sub-domain displacements show that differences between the two TSA structures average about 5% of changes between substrate-free and TSA forms, and they are nearly co-linear. Small backbone hinge rotations map to sites that also flex on substrate binding. Anisotropic atomic displacement parameters (ADPs) are refined using rigid-body TLS constraints. Consistency between crystal forms shows that they reflect intrinsic molecular properties more than crystal lattice effects. In many regions, the favored directions of thermal/static displacement areappreciably correlated with movements on substrate binding. Correlation between ADPs and larger substrate-associated movements implies that the latter approximately follow paths of low-energy intrinsic motions.

Crystal structure of Re-substituted lanthanum tungstate La5.4W1−yReyO12–δ(0 ≤y≤ 0.2) studied by neutron diffraction

A precise determination of sample composition and water uptake of La6−xWO12−δ(0.4 ≤x≤ 0.8) and Re-substituted La5.4W1−yReyO12−δ(0 ≤y ≤ 0.2) lanthanum tungstate is carried out. Sample compositions and water uptake were determined by electron probe micro-analysis and thermogravimetry, respectively. A single-phase region of Re-substituted lanthanum tungstates is reported. The crystal structure of two selected specimens produced by the citrate-complexation route based on the Pechini method, namely La5.4WO12−δand La5.4W0.8Re0.2O12−δ, was investigated by neutron diffraction in the temperature range 1.5 ≤T≤ 1200 K. The structural model for lanthanum tungstates is validated, according to which the Wyckoff site shared by La and W (Fm{\overline 3}m space group, 24dsite) is split with half-site occupancies (Fm{\overline 3}m space group, 48hsite). Replacement of W by up to 20 mol% Re does not change the lattice structure, and Re atoms substitute for W statistically in both 4aand 48hWyckoff sites of the Fm{\overline 3}m space group, as shown by combining the average neutron scattering length procedure, thermogravimetry and electron probe micro-analysis. Using the Willis and Pryor approach to anisotropic displacement parameters it is shown that the remaining static disorder in the unit cell found in La5.4WO12−δand La5.4W0.8Re0.2O12−δstructures is comparable, when the Fm{\overline 3}m space group with split 48hsite is employed. Through the estimation of the Debye temperature for both compounds, extracted from the analysis of thermal expansion coefficients and from the Willis and Pryor approach, anion anharmonic vibrations like those in yttria-stabilized zirconia are proven to exist in LaWO for the first time.