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Determination of cellulose crystallinity from powder diffraction diagrams: Powder Diffraction Diagrams

Commonly one-dimensional (1D) (spherically averaged) powder diffraction diagrams are used to determine the degree of cellulose crystallinity in biomass samples. Here, it is shown using molecular modeling how disorder in cellulose fibrils can lead to considerable uncertainty in conclusions drawn concerning crystallinity based on 1D powder diffraction data alone. For example, cellulose microfibrils that contain both crystalline and noncrystalline segments can lead to powder diffraction diagrams lacking identifiable peaks, while microfibrils without any crystalline segments can lead to such peaks. Moreover, this leads to false positives, that is, assigning disordered cellulose as crystalline, and false negatives, that is, categorizing fibrils with crystalline segments as amorphous. Finally, the reliable determination of the fraction of crystallinity in any given biomass sample will require a more sophisticated approach combining detailed experiment and simulation.

36 MATERIALS SCIENCE↗

Powder diffraction

Powder diffraction is a non-destructive technique, which is experimentally simple in principle. Because the physics behind diffraction is well understood, an exceptionally large amount of information can be obtained from a single measurement. The positions and relative intensities of the peaks yield a fingerprint that can be used for qualitative phase analysis. Quantitative phase analysis can be obtained by detailed analysis of the intensities. Unit cells can be derived from the peak positions. Crystal structures can be solved using powder diffraction data and refined by the Rietveld method. The peak profiles contain information about crystallite size, strain and nanostructure. Non-idealities in the intensities give information on texture. Abandoning the crystallographic model provides information about local structure, by pair distribution function analysis. For powder diffraction, everything is a sample; the technique is commonly applied to characterize minerals, ceramics, metals and alloys, catalysts, polymers, pharmaceuticals, organic compounds, environmental and forensic samples, among others. The major features of contemporary laboratory powder diffractometers are described. Methods for obtaining suitable powder specimens are summarized. Major applications of qualitative and quantitative phase analysis, structure solution, size/strain/nanostructure analysis using peak profiles, texture analysis and pair distribution function analysis are introduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Rietveld Refinement for Macromolecular Powder Diffraction

Powder X-ray diffraction (PXRD) has been employed extensively for the structural characterization of materials, quantitative analysis of multicomponent mixtures, phase identification, texture, and microstructural analysis. At the heart of all those lies the Rietveld method, which has revolutionized the use of powder diffraction for materials studies. Initially applied to minerals and inorganics, the Rietveld method has progressively been used for more complex materials, for instance, zeolites and pharmaceuticals. A major advance of the method came some 20 years ago, when the first protein structure was successfully refined. Because of the sheer complexity of macromolecules, several new approaches and algorithms had to be pioneered or adapted from macromolecular single-crystal diffraction experiments, thus constituting macromolecular PXRD a quite unique field of study. This review aims to provide necessary elements of theory and application of structure solution and refinement via the Rietveld method for macromolecular PXRD data. Here, practical explanations and highlighted case studies are also presented.

36 MATERIALS SCIENCE↗

In situ X-ray powder diffraction study of Ho{sub 5}Ge{sub 4}

In Ho{sub 5}Ge{sub 4} the magnetostructural transition (MST) from high temperature paramagnetic Sm{sub 5}Ge{sub 4}-type (O-II type) orthorhombic structure to a new low temperature antiferromagnetic (AFM) monoclinic structure (Mβ-structure; the distortion occurs in the ac-plane) results in discontinuities of 400, 400, and 300 ppm along a, b, and c axes, respectively. During MST the unit cell volume exhibits discontinuity of 1000 ppm, and changes in both inter and intra slab bonds are less than 2%. In the AFM state the application of 35 kOe magnetic field leads to a partial reconstruction of the high temperature O-II structure, which is accompanied with a large magnetostriction. The strain energy associated with magnetostriction effects leads to an incomplete field driven MST in the magnetically ordered state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structural characterization of Bi{sub 2}Te{sub 3} and Sb{sub 2}Te{sub 3} as a function of temperature using neutron powder diffraction and extended X-ray absorption fine structure techniques

The structure of Bi{sub 2}Te{sub 3} (Seebeck coefficient Standard Reference Material (SRM™ 3451)) and the related phase Sb{sub 2}Te{sub 3} have been characterized as a function of temperature using the neutron powder diffraction (NPD) and the extended X-ray absorption fine structure (EXAFS) techniques. The neutron structural studies were carried out from 20 K to 300 K for Bi{sub 2}Te{sub 3} and from 10 K to 298 K for Sb{sub 2}Te{sub 3}. The EXAFS technique for studying the local structure of the two compounds was conducted from 19 K to 298 K. Bi{sub 2}Te{sub 3} and Sb{sub 2}Te{sub 3} are isostructural, with a space group of R3{sup ¯}m. The structure consists of repeated quintuple layers of atoms, Te2-M-Te1-M-Te2 (where M = Bi or Sb) stacking along the c-axis of the unit cell. EXAFS was used to examine the bond distances and static and thermal disorders for the first three shells of Bi{sub 2}Te{sub 3} and Sb{sub 2}Te{sub 3} as a function of temperature. The temperature dependencies of thermal disorders were analyzed using the Debye and Einstein models for lattice vibrations. The Debye and Einstein temperatures for the first two shells of Bi{sub 2}Te{sub 3} are similar to those of Sb{sub 2}Te{sub 3} within the uncertainty in the data. However, the Debye and Einstein temperatures for the third shell of Bi-Bi are significantly lower than those of the third shell of Sb-Sb. The Einstein temperature for the third shell is consistent with a soft phonon mode in both Bi{sub 2}Te{sub 3} and Sb{sub 2}Te{sub 3}. The lower Einstein temperature of Bi-Bi relative to Sb-Sb is consistent with the lower value of thermal conductivity of Bi{sub 2}Te{sub 3} relative to Sb{sub 2}Te{sub 3}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic pair distribution function and half polarized neutron powder diffraction at the HB-2A powder diffractometer

Local magnetic order and anisotropy are often central for understanding fundamental behavior and emergent functional properties in quantum materials and beyond. Advances in neutron powder diffraction experiments and analysis tools now allow for quantitative determination. Here, we demonstrate this here with complementary total neutron scattering and polarized neutron measurements on the HB-2A neutron powder diffractometer at the High Flux Isotope Reactor (HFIR). In recent years, magnetic pair distribution function (mPDF) analysis has emerged as a powerful technique for probing local magnetic spin ordering of magnetic materials. This method can be broadly applied to any magnetic material but is particularly effective for studying systems with short-range magnetic order, such as materials with reduced dimensionality, geometrically frustrated magnets, thermoelectrics, multiferroics, and correlated paramagnets. Magnetic anisotropy often underpins the short-range order adopted. Half-polarized neutron powder diffraction (pNPD) can be used to determine the local susceptibility tensor on the magnetic sites to quantify the magnetic anisotropy. Combining the techniques of mPDF and pNPD can therefore provide valuable insights into local magnetic behavior. A series of measurements optimized for these techniques are presented as exemplar cases focused on frustrated materials where short-range order dominates, these include measurements to ultra-low temperature (<100 mK) not typically accessible for such experiments.

Half polarized neutron scattering↗

On the estimation of statistical uncertainties on powder diffraction and small-angle scattering data from two-dimensional X-ray detectors

Optimal methods are explored for obtaining one-dimensional powder pattern intensities from two-dimensional planar detectors with good estimates of their standard deviations. Methods are described to estimate uncertainties when the same image is measured in multiple frames as well as from a single frame. The importance of considering the correlation of diffraction points during the integration and the resampling process of data analysis is shown. It is found that correlations between adjacent pixels in the image can lead to seriously overestimated uncertainties if such correlations are neglected in the integration process. Off-diagonal entries in the variance–covariance (VC) matrix are problematic as virtually all data processing and modeling programs cannot handle the full VC matrix. It is shown that the off-diagonal terms come mainly from the pixel-splitting algorithm used as the default integration algorithm in many popular two-dimensional integration programs, as well as from rebinning and resampling steps later in the processing. When the full VC matrix can be propagated during the data reduction, it is possible to get accurate refined parameters and their uncertainties at the cost of increasing computational complexity. However, as this is not normally possible, the best approximate methods for data processing in order to estimate uncertainties on refined parameters with the greatest accuracy from just the diagonal variance terms in the VC matrix is explored.

Yang, X.↗

An Easy‐to‐Use Custom‐Built Cell for Neutron Powder Diffraction Studies of Rechargeable Batteries

Abstract In operando powder diffraction remains one of the most powerful tools for non‐destructive investigation of battery electrode materials. While in operando X‐ray, especially synchrotron radiation, powder diffraction is by now a routine experimental technique, in operando neutron powder diffraction is still less established. We present a new electrochemical cell for in operando neutron powder diffraction, which is, first and foremost, easy to use, but can also cycle electrode materials under electrochemical conditions close to those achieved using standard laboratory cells. The cell has been designed in multiple sizes, and high‐quality electrochemical and neutron powder diffraction data is presented for sample sizes as low as 48 mg total active material. The cell handles lithium‐ion and sodium‐ion materials equally well, with no difference in how the cell is prepared and assembled. The cell is intended to be used as sample environment at powder diffractometers at the neutron facilities MLZ, ORNL and ACNS.

25 ENERGY STORAGE↗

Hydrogenation properties of Li{sub x}Sr{sub 1−x}AlSi studied by quantum-chemical methods (0≤x≤1) and in-situ neutron powder diffraction (x=1)

In-situ neutron powder diffraction studies of the Half-Heusler phase LiAlSi under high deuterium pressures and first principle calculations of solid solutions of Li{sub x}Sr{sub 1−x}AlSi and their hydrides Li{sub x}Sr{sub 1−x}AlSiH were carried out. In contrast to an earlier study, there is no experimental evidence for hydrogen (deuterium) uptake up to gas pressures of 15 MPa and temperatures of 550 °C. Instead a slow decomposition reaction according to LiAlSi+1/2H{sub 2}=LiH+Al+Si was found by in-situ neutron powder diffraction. Theoretical calculations by DFT methods on hypothetical solid solutions of Li{sub x}Sr{sub 1−x}AlSi show the LiAlSi type to be the energetically most stable structure for 0.7<x and the SrAlSi type structure for lower values of x. Hydrides Li{sub x}Sr{sub 1−x}AlSiH favor the SrAlSiH type for all values of x instead of the structure proposed earlier with hydrogen occupying tetrahedral voids in a LiAlSi structure. As an alternative for a cubic structure for LiAlSiH, we suggest the existence of LiAlSiH in the trigonal SrAlSiH type structure and it might be a candidate worthwhile to be considered for preparative work. - Graphical abstract: In-situ neutron powder diffraction of LiAlSi under high D{sub 2} pressure. - Highlights: • In-situ neutron powder diffraction of LiAlSi under high D{sub 2} pressure was carried out. • LiAlSi decomposes according to LiAlSi + ½ H{sub 2} = LiH + Al + Si. • Mixed crystals Li{sub x}Sr{sub 1-x}AlSi and LixSr{sub 1-x}AlSiH were studied theoretically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

White Laue and powder diffraction studies to reveal mechanisms of HCP-to-BCC phase transformation in single crystals of Mg under high pressure

Mechanisms of hexagonal close-packed (HCP) to body-centered cubic (BCC) phase transformation in Mg single crystals are observed using a combination of polychromatic beam Laue diffraction and monochromatic beam powder diffraction techniques under quasi-hydrostatic pressures of up to 58 ± 2 GPa at ambient temperature. Although experiments were performed with both He and Ne pressure media, crystals inevitably undergo plastic deformation upon loading to 40–44 GPa. The plasticity is accommodated by dislocation glide causing local misorientations of up to 1°–2°. The selected crystals are tracked by mapping Laue diffraction spots up to the onset of the HCP to BCC transformation, which is determined to be at a pressure of 56.6 ± 2 GPa. Intensity of the Laue reflections from HCP crystals rapidly decrease but no reflections from crystalline BCC phase are observed with a further increase of pressure. Nevertheless, the powder diffraction shows the formation of 110 BCC peak at 56.6 GPa. The peak intensity increases at 59.7 GPa. Upon the full transformation, a powder-like BCC aggregate is formed revealing the destructive nature of the HCP to BCC transformation in single crystals of Mg.

36 MATERIALS SCIENCE↗

Considerations for quantitative in situ X-ray powder diffraction studies of solid-state reactions

The importance of sample preparation in collecting high-fidelity powder diffraction data suitable for quantitative structure and phase analysis is well established. Such powder diffraction experiments are increasingly being appliedin situ, during reactions, to explore solid-state reactivity. When appliedin situ, X-ray diffraction is widely used to gain insight into the mechanism and kinetics, and to identify dynamic intermediate states. Here, using a model ion-exchange reaction (NaFeO 2 + LiCl → LiFeO 2 + NaCl), we show that sample preparation not only influences the fidelity of powder diffraction analysis but also impacts the observed reaction progress. Specifically, we found that the observed reaction progress can differ by ∼50% depending on the capillary sample preparation. Thus, forin situdiffraction studies of solid-state reactions, packing fraction is an important and previously unrecognized consideration that impacts reproducibility and fidelity of the reaction study.

Chemistry↗