Single-crystal Electron Diffraction Data Research Articles

Refining short-range order parameters from the three-dimensional diffuse scattering in single-crystal electron diffraction data.

Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Å for the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Å for the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

Synthesis and Structure of COE-11, a New Borosilicate Zeolite with a Two-Dimensional Pore System of 12-Ring Channels

The new zeolite, COE-11, was synthesized at 155 °C to 168 °C by hydrothermal synthesis from a reaction mixture of SiO2/tetraethylammonium hydroxide/H3BO3/NaOH/H2O. Because tetraethylammonium is an unspecific structure directing agent, COE-11 crystallizes in all cases together with at least one impurity phase from a selection of phases: zeolite types *BEA, CHA, FER, MFI, MOR, MTW; the layered silicates magadiite and kenyaite; and searlsite and silica polymorph quartz. The crystal structure was solved from 3D electron diffraction (3D ED) data. Subsequent structure refinements of X-ray powder diffraction (PXRD) data and single crystal electron diffraction data converged to residual values of RF = 0.039, chi2 = 3.6 (PXRD) and RF = 21.81% (3D ED) confirming the structure model. COE-11 crystallizes in space group C2 with unit cell dimensions of a0 = 17.3494(11) Å, b0 = 17.3409(11) Å, c0 = 14.2789(4) Å and β = 113.762(2) °. The structure of COE-11 is characterized by a microporous borosilicate framework with intersecting, highly elliptical 12-ring channels running parallel (110) and (1–10) and forming a two-dimensional pore system. The Rietveld refinement provided a hint that boron partly substitutes silicon on three specific T sites of the framework. The idealized chemical composition of as-made COE-11 is [(CH3CH2)4N]4[B4Si62O132] per unit cell. Physico-chemical characterization using solid-state NMR spectroscopy, SEM, TG-DTA, and ATR-FTIR spectroscopy confirmed that COE-11 is a microporous borosilicate zeolite. COE-11 is structurally closely related to zeolite beta polymorph B but differs concerning the dimensionality of the pore system, which is 2D instead of 3D.

Quantitative analysis of diffuse electron scattering in the lithium-ion battery cathode material Li1.2Ni0.13Mn0.54Co0.13O2

In contrast to perfectly periodic crystals, materials with short-range order produce diffraction patterns that contain both Bragg reflections and diffuse scattering. To understand the influence of short-range order on material properties, current research focuses increasingly on the analysis of diffuse scattering. This article verifies the possibility to refine the short-range order parameters in submicrometre-sized crystals from diffuse scattering in single-crystal electron diffraction data. The approach was demonstrated on Li1.2Ni0.13Mn0.54Co0.13O2, which is a state-of-the-art cathode material for lithium-ion batteries. The intensity distribution of the 1D diffuse scattering in the electron diffraction patterns of Li1.2Ni0.13Mn0.54Co0.13O2 depends on the number of stacking faults and twins in the crystal. A model of the disorder in Li1.2Ni0.13Mn0.54Co0.13O2 was developed and both the stacking fault probability and the percentage of the different twins in the crystal were refined using an evolutionary algorithm in DISCUS. The approach was applied on reciprocal space sections reconstructed from 3D electron diffraction data since they exhibit less dynamical effects compared with in-zone electron diffraction patterns. A good agreement was achieved between the calculated and the experimental intensity distribution of the diffuse scattering. The short-range order parameters in submicrometre-sized crystals can thus successfully be refined from the diffuse scattering in single-crystal electron diffraction data using an evolutionary algorithm in DISCUS.

Crystal structure analysis of a star-shaped triazine compound: a combination of single-crystal three-dimensional electron diffraction and powder X-ray diffraction

The solid-state structure of star-shaped 2,4,6-tris{(E)-2-[4-(dimethylamino)-phenyl]ethenyl}-1,3,5-triazine is determined from a powder sample by exploiting the respective strengths of single-crystal three-dimensional electron diffraction and powder X-ray diffraction data. The unit-cell parameters were determined from single crystal electron diffraction data. Using this information, the powder X-ray diffraction data were indexed, and the crystal structure was determined from the powder diffraction profile. The compound crystallizes in a noncentrosymmetric space group, P212121. The molecular conformation in the crystal structure was used to calculate the molecular dipole moment of 3.22 Debye, which enables the material to show nonlinear optical effects.

Why powder diffractionists need help from electron crystallography

Although X-ray powder diffraction (XPD) is used as a routine tool for solving crystal structures of polycrystalline materials, its weakness is obvious: not only is the phase information lost during the diffraction experiment, but reflections with similar d-spacings, which are well-separated in a single-crystal measurement, overlap in a powder pattern. These effects increase the difficulty of structure solution especially when dealing with complex structures. Compared to XPD, the advantages from electron microscopy are: (1) single-crystal electron diffraction data, either in 2-dimensional or 3-dimensional form, can be obtained from a very tiny crystallite in a powder sample; and (2) high-resolution images can be collected and used to extract phase information in reciprocal space or to provide a direct view of structural features (ordered and disordered) [1]. With the extra information supplied by electron microscopy, the limits of structure determination for polycrystalline materials can be extended [2]. Here we will present a few examples to demonstrate why powder diffractionists need help from electron microscopy and how to integrate these two techniques into the structure determination process.

Ab initio structure determination of interlayer expanded zeolites by single crystal rotation electron diffraction.

Layered solids often form thin plate-like crystals that are too small to be studied by single-crystal X-ray diffraction. Although powder X-ray diffraction (PXRD) is the conventional method for studying such solids, it has limitations because of peak broadening and peak overlapping. We have recently developed a software-based rotation electron diffraction (RED) method for automated collection and processing of 3D electron diffraction data. Here we demonstrate the ab initio structure determination of two interlayer expanded zeolites, the microporous silicates COE-3 and COE-4 (COE-n stands for International Network of Centers of Excellence-n), from submicron-sized crystals by the RED method. COE-3 and COE-4 are built of ferrierite-type layers pillared by (-O-Si(CH3)2-O-) and (-O-Si(OH)2-O-) linker groups, respectively. The structures contain 2D intersecting 10-ring channels running parallel to the ferrierite layers. Because both COE-3 and COE-4 are electron-beam sensitive, a combination of RED datasets from 2 to 3 different crystals was needed for the structure solution and subsequent structure refinement. The structures were further refined by Rietveld refinement against the PXRD data. The structure models obtained from RED and PXRD were compared.

The Crystal Structure of Bi2PbMnO4(PO4)2, a Member of a New Solid Solution Series in the Bi–Pb–Mn–P Oxide System

Single crystals of a new oxyphosphate were found while exploring the Bi–Pb–Mn–P oxide phase diagram. The reaction product from a mixture of Bi2O3, PbO, MnO2, and (NH4)2HPO4 in the ratio 1:1:2:2 displayed several phases including a Bi-rich phase with the approximate composition (Bi3−xPbx)MnP2Oy and a Pb-rich phase with the approximate composition (BixPb4−x)MnP3Oy. A single crystal of the Bi-rich phase was selected. The title compound is tetragonal, P421c, a=13.275(3) Å, c=5.500(2) Å, Z=4. The structure refinement converged to R1=0.0442. On the basis of the X-ray diffraction refinement, the formula is Bi2PbMnP2O12. The crystal is an inverse twin. Electron diffraction revealed that the X-ray diffraction lattice parameters are from a subcell and the unit cell is 2asub, 2bsub, 3csub. The detailed study of reciprocal space, reconstructed from observations made using single-crystal electron diffraction data, leads us to an apparent wave vector q*=12a*+12b*+13c*, compatible with the Bravais lattice 4/mmmP (1212γ). However, this choice leads to forbidden reflections, e.g. h00, h=2n+1, due to the presence of a 21 axis. An assumption that the crystal consists of a modulated, twinned orthorhombic structure with space group Ccc2 based on the cell√2a,√2a, c leads to a modulation vector q*=a*+γc*. The (3+1)-dimensional Bravais lattice becomes mmmC(10γ) and the super space group is Ccc2(10γ). The refinement of the single crystal X-ray diffraction data based on Ccc2 consisting of two 90° twin domains led, as expected, to the identical result as the refinement in P421c.The crystal structure was determined from the X-ray diffraction intensities based on the subcell and hence represents an averaged structure. The PO4 radical can be present in two orientations. Pb occupies only 12 of the crystallographic 8e positions. The Pb atoms bond through oxygen atoms from PO4 to form a ring, creating channels parallel to c. Manganese and oxygen are present within the channels but the average structure prevents the determination of their location with certainty. Valence bond sums show that lead is tetravalent. The oxygen content requires tetravalent manganese.

Electron crystallography of the polymethylene chain. 4. Defect distribution in lamellar interfaces of paraffin solid solutions

As is also found for paraffin lamellar crystals heated near the rotator or melt transition, the major change in electron diffraction patterns imposed by lamellar disorder in binary or multicomponent solid solutions is the attenuation and intensity modification of low-angle (00l) reflections. Using a Gaussian model for atomic occupancies near the interface, a systematic basis is found for the interfacial disorder thickness, describing the phenomenological ‘void’ distribution at the lamellar interface. (Vibrational spectroscopy has shown that this is actually a distribution of non-planar chain conformations.) Single crystal electron diffraction data from various co-soluble paraffin chain assemblies, used previously to determine their crystal structures (but also including a new determination for n-C36H74/ n-C38H78/ n-C40H82 1: 1: 1), are re-analyzed so that further distinctions can be made among simple binary and ternary solid solutions, multicomponent waxes, and low molecular weight polyethylene. Expressions of the latter polyethylene structure, involving ‘bridging molecules’ can be found in certain natural insect and plant waxes.

Fiber diffraction as a useful supplement to single-crystal electron diffraction data in the direct three-dimensional structure analysis of polymers

When zonal electron diffraction data from chain-folded lamellae are combined with the three-dimensional (3-D) information from a microfiber, it is possible to determine a polymer crystal structure by direct methods to visualize the atomic arrangement in the unit cell. An analysis of the polyethylene sulfide) structure (space group Pbcn, a = 8.51, b = 4.94, c = 6.69 Å) is presented as an example of such a determination. The crystallographic phases—including 17 of 20 unique zonal hkO data collected earlier from chain-folded lamellae, as well as two other phases permitted for origin definition in three dimensions—served as a basis set for extension into three dimensions by the Sayre equation. The phase extension into the 3-D indices of the fiber diffraction set (39 unique amplitudes including 32 estimated from 14 overlapped maxima) was quite accurate, especially for the most intense reflections. Combination of these phases with amplitude values to generate the three-dimensional potential map allowed direct visualization of the atomic distribution in the unit cell. The structure could then be refined by a match of a chain model to the observed potential distribution, after optimizing the bonding geometry. These results demonstrate that, with the use of fiber data as a supplement, alternative experimental approaches to true three-dimensional structure determinations exist in polymer electron crystallography, even if epitaxial crystallization methods cannot provide the necessary orthogonal orientation of the chain packing. By this approach, the “missing cone” problem for goniometry in the electron microscope can be largely overcome.

The structure of γ-polypivalolactone: a combined analysis of single-crystal electron diffraction data and powder X-ray diffraction profiles with the Rietveld method

The crystal structure of the γ-phase of polypivalolactone (γ-PPVL) has been determined from electron diffraction data and tested with the Rietveld method against X-ray powder diffraction profiles. The electron diffraction study is based on single-crystal patterns obtained from melt-crystallized solution-cast thin films, while the Rietveld analysis was performed on data from melt-crystallized samples containing comparable amounts of α- and γ-phase PPVL. The crystal class is orthorhombic (space group P2 12 12 1), and two molecules with the same chirality and opposite directions pass through the unit cell having lattice dimensions a = 8.23, b = 11.28, c( chain repeat) = 6.02 A ̊ . Both h k 0 and tilted-specimen electron diffraction data were used in the refinement, carried out in the kinematic approximation. The analysis based on these data and on powder profiles coherently indicates that the refined structural model has a main-chain conformation intermediate between the one found in the α-phase and the minimum-energy conformation, while differing significantly from both.

Crystal Packing of Odd-Chain Saturated Triglycerides

Single crystal electron diffraction data from an odd-chain triglyceride, glycerol triheptadecanoate, are compared with the known structure of the even-chain homo-acid triglycerides. Both class­es of triglycerides are found to resemble one another in chain packing: they both have the same chain tilt (61 °) for the β-polymorph and, further, the orientation of the T∥ subcell in the crystal structure is identical. The existence of the T∥ subcell is quantitatively verified for the first time with the diffraction intensities from suitably tilted crystals. Given these similarities in β-poly­morph structure, the major difference between triglycerides with even or odd chains (indicated by published long spacing and melting point alternation) must be due to the methyl end group pack­ing - i.e., the end group packing volume for the odd-chain glycerides must be larger than found for the even-chain materials.

Poly(ethylene sulfide): Reevaluation of the electron diffraction structure analysis

Abstract The single-crystal electron diffraction data of poly(ethylene sulfide) reported by Hasegawa, Claffey, and Geil have been reinvestigated. Taking into account possible crystal bending effects and dynamical scattering leads to an improved structural model. The final agreement factor of R = 0.21 is considerably better than that determined in the original analysis, R = 0.33, attesting to the quality of the zonal electron diffraction data obtained by these investigators.

Stereo analysis of single crystal electron diffraction data

In the analysis of single crystal electron diffraction data, full advantage of information on sample geometry can be taken if one first determines sample coordinates for a crystallographic basis triplet. Using this strategy, a unified approach is possible for (i) computer indexing of diffraction spots, (ii) testing of diffraction data for consistency with known structures, (iii) measuring the lattice parameters of an unknown crystal, (iv) determining the crystallographic orientation of micrograph features, and (v) calculating goniometer coordinates to access a desired crystallographic orientation. The approach, which can be implemented with only modest microprocessor support, increases the usefulness of diffraction “patterns” with only one diffraction spot. It therefore extends the versality of a single-tilt goniometer stage, and allows the above tasks to be performed on smaller crystals and more beam-sensitive samples than could otherwise be considered.

Stereo analysis of single crystal electron diffraction data

In the analysis of single crystal electron diffraction data, full advantage of information on sample geometry can be taken if one first determines sample coordinates for a crystallographic basis triplet. Using this strategy, a unified approach is possible for (i) computer indexing of diffraction spots, (ii) testing of diffraction data for consistency with known structures, (iii) measuring the lattice parameters of an unknown crystal, (iv) determining the crystallographic orientation of micrograph features, and (v) calculating goniometer coordinates to access a desired crystallographic orientation. The approach, which can be implemented with only modest microprocessor support, increases the usefulness of diffraction “patterns” with only one diffraction spot. It therefore extends the versality of a single-tilt goniometer stage, and allows the above tasks to be performed on smaller crystals and more beam-sensitive samples than could otherwise be considered.

A fine-particle transmission electron microscope investigation of CrO2and CrO(OH)

Abstract A transmission electron microscope imaging and diffraction investigation has been performed on small CrO2 crystallites. The acieular crystal morphology has been observed and electron-diffraction evidence is presented which indicates the presence of a very thin CrO(OH) layer of 6-13 A. CrO2 has been partly converted topotactically to orthorhombic CrO(OH) in hot water and single-crystal electron-diffraction evidence is used to establish this topotactic relationship. Under sufficiently high temperatures or electron-beam irradiation, CrO2 and CrO(OH) convert topotactically to Cr2O3, as seen from single-crystal electron-diffraction data. This last conversion is further characterized using high-resolution dark-field microscopy which reveals the presence of interference patterns from the formation of microcrystalline domains.

Fluorite-related phases Ln3MO 7, Ln = rare earth, Y or Sc, M = Nb, Sb, or Ta : II. Structure determination

The crystal structures of the orthorhombic fluorite-related compounds La 3NbO 7 ( Cmcm), Y 3TaO 7, and Y 2GdSbO 7, ( C222 1) have been determined from X-ray powder diffraction intensities and single-crystal electron diffraction data. The structures are basically similar. One third of the Ln cations are 8-coordinated, and lie in [001] rows which alternate with parallel rows of corner-linked MO 6 coordination octahedra within slabs parallel to (100). The remaining Ln cations lie in between these slabs in seven-fold coordination. This interslab cation arrangement distinguishes the structure from the closely related pyrochlore ( A 2 B 2O 7) and weberite (Na 2MgAlF 7) structures. The compounds YGdScSbO 7 and Nd 2ScNbO 7, also examined, have the pyrochlore structure, with Sc and Sb, or Sc and Nb distributed on the octahedral B sites.

Temperature-Pressure Phase Relationships in Niobium Pentoxide.

A pressure-temperature (P-T) section of the phase equilibrium diagram for Nb2O5 has been determined. Four single phase regions, H-Nb2O5, B-Nb2O5, and two L-Nb2O5 areas, were characterized by x-ray powder diffraction data. The superstructure of L-Nb2O5 was indexed on the basis of similarities to the known superstructures of L-Ta2O5 and confirmed with single crystal electron diffraction data. The correct unit cell is orthorhombic with a = 6.168, b = 29.312, c = 3.938 Å, with the b axis 8 times the subcell (8 × 3.664 Å).

Kaolinite Layer Structure: Relaxation by Dehydroxylation

Single-crystal electron-diffraction data reveal features of metakaolin. The basal plane parameters increase 2.2 percent in formation of metakaolin produced by heating kaolinite in air at 700 degrees C for 12 hours. This increase results from removal of the distortion of sheet structure (relaxation).