Polarization factor for the X-ray powder diffraction method with a single-crystal monochromator

Polarization effects of X-ray monochromators modeled using dynamical scattering theory

The difference in the diffracted intensity of the σ- and π-polarized components of an X-ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X-ray scattering. Although this treatment is correct for powders and post-sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident-beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the π component relative to the σ component then becomes approximately proportional to |cos  2θ_m| rather than to cos²2θ_m, where θ_m is the Bragg diffraction angle of the monochromator crystal. This changes the predicted intensities of X-ray powder diffraction patterns produced on instruments with incident-beam monochromators, especially in the regions far from 2θ = 90° in the powder pattern. Experimental data, based on well known standard reference materials, are presented, confirming that the dynamical polarization correction is required when a Ge 111 incident-beam monochromator is used. The dynamical correction is absent as an option in the Rietveld analysis codes with which the authors are familiar.

The Optics and Alignment of the Divergent Beam Laboratory X-ray Powder Diffractometer and its Calibration Using NIST Standard Reference Materials

The laboratory X-ray powder diffractometer is one of the primary analytical tools in materials science. It is applicable to nearly any crystalline material, and with advanced data analysis methods, it can provide a wealth of information concerning sample character. Data from these machines, however, are beset by a complex aberration function that can be addressed through calibration with the use of NIST Standard Reference Materials (SRMs). Laboratory diffractometers can be set up in a range of optical geometries; considered herein are those of Bragg-Brentano divergent beam configuration using both incident and diffracted beam monochromators. We review the origin of the various aberrations affecting instruments of this geometry and the methods developed at NIST to align these machines in a first principles context. Data analysis methods are considered as being in two distinct categories: those that use empirical methods to parameterize the nature of the data for subsequent analysis, and those that use model functions to link the observation directly to a specific aspect of the experiment. We consider a multifaceted approach to instrument calibration using both the empirical and model based data analysis methods. The particular benefits of the fundamental parameters approach are reviewed.

Structure of sphingomyelin bilayers and complexes with cholesterol forming membrane rafts

Sphingomyelin and cholesterol are of interest to biologists because they interact to form condensed structures said to be responsible for a variety of functions that membranes perform. Synchrotron X-ray diffraction methods have been used to investigate the structure of bilayers of D-erythro palmitoyl-sphingomyelin and complexes formed by palmitoyl- and egg-sphingomyelin with cholesterol in aqueous multibilayer dispersions. D-erythro palmitoyl sphingomyelin bilayers exist in two conformers that are distinguished by their lamellar repeat spacing, bilayer thickness, and polar group hydration. The distinction is attributed to hydrogen bonding to water or to intermolecular hydrogen bonds that are disrupted by the formation of ripple structure. The coexisting bilayer structures of pure palmitoyl sphingomyelin are observed in the presence of cholesterol-rich bilayers that are characterized by different bilayer parameters. The presence of cholesterol preferentially affects the conformer of D-erythro sphingomyelin with thicker, more hydrated bilayers. Coexisting bilayers of sphingomyelin and complexes with cholesterol are in register and remain coupled at temperatures at least up to 50 °C. Cholesterol forms a complex of 1.8 mols of sphingomyelin per cholesterol at 37 °C that coexists with bilayers of pure sphingomyelin up to 50 °C. Redistribution of the two lipids takes place on cooling below the fluid- to gel-phase transition temperature, resulting in the withdrawal of sphingomyelin into gel phase and the formation of coexisting bilayers of equimolar proportions of the two lipids. Cholesterol-rich bilayers fit a stripe model at temperatures less than 37 °C characterized by alternating rows of sphingomyelin and cholesterol molecules. A quasicrystalline array models the arrangement at higher temperatures in which each cholesterol molecule is surrounded by seven hydrocarbon chains, each of which is in contact with two cholesterol molecules. The thickness of bilayer complexes of sphingomyelin and cholesterol is less than that of coexisting bilayers of pure sphingomyelin. The implications for protein sorting theories based on bilayer thickness are discussed.

The effect of tocopherol on the structure and permeability of phosphatidylcholine liposomes

There are numerous phospholipid formulations that incorporate α-tocopherol as a stabilizing agent but there are few studies of the effect of α-tocopherol on phospholipid structure and bilayer permeability. This study uses synchrotron X-ray powder diffraction methods to investigate how α-tocopherol changes the structure of distearoylphosphatidylcholines bilayers. Increasing proportions of α-tocopherol up to 20 mol% induces ripple structures in the bilayers. Two types of ripple structure are produced which are seen in electron micrographs of freeze-fracture replicas with periodicities of 16 and 12 nm, respectively. The stoichiometry of phospholipid: α-tocopherol in the ripple structures at 37 °C is 8:1. The presence of α-tocopherol tends to reduce the angle of tilt of the hydrocarbon chains of the phospholipid in the gel phase from about 34° to the bilayer normal at 20 °C into a more vertical orientation. Increasing proportions of α-tocopherol progressively decrease the temperature of the gel to liquid-crystal phase transition of the phospholipid. The presence of up to 20 mol% α-tocopherol in 1-palmitoyl-2-oleoyl-phosphocholine inhibits leakage of phenol red dye from liposomes. The effect of 7 mol% α-tocopherol on leakage was compared with phospholipid liposomes containing 50 mol% cholesterol. The cholesterol-containing liposomes inhibited leakage to a greater extent than the vesicles incorporating α-tocopherol but the effect of α-tocopherol at equivalent molar proportions was comparable to cholesterol.

Quantitative analysis of crystalline pharmaceuticals in powders and tablets by a pattern-fitting procedure using X-ray powder diffraction data

A pattern-fitting procedure for quantitative analysis of crystalline pharmaceuticals in solid dosage forms using X-ray powder diffraction data is described. This method is based on a procedure for pattern-fitting in crystal structure refinement, and observed X-ray scattering intensities were fitted to analytical expressions including some fitting parameters, i.e. scale factor, peak positions, peak widths and degree of preferred orientation of the crystallites. All fitting parameters were optimized by the non-linear least-squares procedure. Then the weight fraction of each component was determined from the optimized scale factors. In the present study, well-crystallized binary systems, zinc oxide-zinc sulfide (ZnO-ZnS) and salicylic acid-benzoic acid (SA-BA), were used as the samples. In analysis of the ZnO-ZnS system, the weight fraction of ZnO or ZnS could be determined quantitatively in the range of 5-95% in the case of both powders and tablets. In analysis of the SA-BA systems, the weight fraction of SA or BA could be determined quantitatively in the range of 20-80% in the case of both powders and tablets. Quantitative analysis applying this pattern-fitting procedure showed better reproducibility than other X-ray methods based on the linear or integral intensities of particular diffraction peaks. Analysis using this pattern-fitting procedure also has the advantage that the preferred orientation of the crystallites in solid dosage forms can be also determined in the course of quantitative analysis.

Change of the microstructure of microcrystalline cellulose with grinding and compression

The microstructure of microcrystalline cellulose was investigated by use of a radial distribution function (RDF) based on the intensity of X-ray scattering data. Changes in the microstructure of the cellulose as a result of grinding and compression were detected by use of the RDF. The RDF of intact microcrystalline cellulose had peak maxima corresponding to distances of approximately 1.5, 2.6, 5.0, 8.2, 13.3 and 17.0 A. The first two corresponded to the intramolecular atomic distances; other peaks were attributable to the intermolecular (inter-fibre) atomic distance. Changes in the RDF as a result of grinding indicated that the regular intermolecular atomic arrangement was gradually lost. Compression resulted in formation of long-range (> 20 A) ordering of the intermolecular (inter-fibre) atomic arrangement. These results show that RDF analysis is suitable for monitoring changes in the structure of microcrystalline cellulose which occur as a result of grinding and compression.