Diffractometer Geometry Research Articles

A diffractometer project for Brazilian Multipurpose Reactor (RMB): McStas simulations and instrument optimization

High-resolution diffractometer is one of the first instruments of the set of 15 priority neutron scattering instruments to be installed at the Brazilian Multipurpose Reactor (RMB). A basic project of this instrument consists of the existence of three guides through which neutrons pass from source to sample to guarantee maximum neutron flux at the sample position. In this study, we investigate guide geometry performance considering fixed diffractometer geometry and spatial arrangement. Comparisons between different guide shapes and supermirrors are performed using software based on the Monte Carlo method, McStas. Our conclusion shows that a better solution is splitting the initial flux into two different guides to obtain the maximum flux at the sample position.

Reliable structural data from Rietveld refinementsviarestraint consistency

A new approach is proposed for assessment of the quality of restrained Rietveld refinement. As the first step, we require the consistency of the restraints and diffraction data: namely, the absence of outliers in the distribution of the bond length deviations from the target values. This condition is tested using a simple and robust outlier detection criterion and can be reached for any correct structure. Then, the range of restraint variation where the model remains consistent (uncertainty window) is calculated. This metric is indicative of the combined model and data quality. The average half uncertainty window (HUW) can serve as an estimate of the effective bond precision; HUW < 0.04 Å is reachable for highly crystalline powders, and HUW exceeds 0.3 Å for unacceptable models. A round-robin involving the most popular laboratory diffractometer geometries and an analysis of literature examples show that HUW, unlike `classic'Rvalues, is instrument independent and versatile.

Synchrotron X-Ray Reflectivity Study of Ni-Oxide-Passive-Layer-and-Water Interface and Yttrium-Stabilized-Zirconia-and-Water Interface

The hydration and water interaction at Ni-oxide-water interface and yttrium-stabilized-zirconia (YSZ)-water interface, respectively, have been investigated with synchrotron X-ray reflectivity. For the nickel-oxide-water interface, a thin passive oxide layer was grown on a single crystal Ni(110) substrate in ultra-high vacuum chamber by blowing in pure O2 gas at room temperature after several cycles of sputtering-and-annealing treatment. The high-resolution specular X-ray reflectivity from the passive oxide layer as grown on the single crystal metal substrate was measured in He environment at room temperature to characterize the thin film thickness and the atomic correlations within the oxide thin film. The detailed interfacial structure and the substrate relaxation with a subatomic resolution could be derived based on the measured X-ray reflectivity in terms of the laterally averaged electron density profile in surface normal direction. The virgin passive oxide layer then exposed to pure water, the effect of hydration was observed with the subsequent reflectivity measurement at the same diffractometer geometry. The resultant X-ray reflectivity data showed drastic changes from the original reflectivity data, which indicates a substantial influence of water interaction on the surface termination of the passive layer. On the other hand, single crystal YSZ-water interfaces were studied as representing the most stable ZrO2 phase and water interface system. The three major crystallographic orientations, (111), (110), and (100), were measured and analyzed for the interfacial hydration structures. The studies eventually aim at fundamental understanding of the water interaction on passive oxide layer of metal alloy surface in nuclear power plant environment. Before directly approaching to the simulated reaction in hot pressurized water, the current study provides the reference data to be compared to.

Stress Development and Adhesion in Hydrogenated Nano-Columnar Pd and Pd/Ti Ultra-Thin Films

Stress development upon hydrogenation of about 100 nm thick palladium layers on thermally oxidized silicon wafers with and without an intermediate Ti layer is studied. Stress developed is investigated by in-situ XRD in H2/N2(hydrogenation) and N2(dehydrogenation) gas at RT. The method adopted to measure residual stress involved specimen omega- (ω) and psi- (ψ) tilting, on two different diffractometer geometries (focusing and parallel). For the stress analysis, the presence of intrinsic elastic anisotropy of the film is considered. Upon hydrogenation α-Pd transformation to β-PdHoccurs and because of the constrained in-plane expansion a large compressive stress develops. Scanning electron microscopy shows that films with a Ti intermediate layer adhere better to the substrate upon hydrogen cycling, whereas, pure Pd film start cracking and buckling.

Towards general diffractometry. III. Beyond the normal-beam geometry

The concept of a general four-circle diffractometer has been realised by introducing axial misalignments into mathematical formulae describing the diffractometer geometry. The advantage of using the described diffractometer formalism for routine measurements is discussed. Transformations of the setting angles of the reflections between different diffractometers, as well as the propagation of errors arising from the misalignment of axes, are taken into account.

Study of the reflectivity of a pyrolytic graphite crystal in a neutron diffractometer geometry

The computer program TISTA, developed previously, has been used to study the characteristics of pyrolytic graphite (PG) crystal plane (002) as a monochromator of a neutron diffractometer. The calculations have been carried out considering the geometry of the proposed neutron diffractometer at a radial beam port at the TRIGA Mark II research reactor of AERE, Savar, Bangladesh. This program may be used for any other diffractometer geometries. The results obtained will be useful in selecting PG(002) monochromators with optimum mosaic spread and thickness. They will also help to set up experiments with maximum flux density for desired resolutions.

Wide-Angle X-Ray, Densitometric and Microscopical Studies on Injection Molded Polypropylene Disks

Abstract Circular disks (280 mm diameter, 2 mm thickness) were injection molded from two grades of isotactic polypropylene under systematic variation of processing parameters (melt temperature, mold temperature, flow rate, packing pressure, and packing time) according to a two-level fractional factorial design. The disks showed ring-shaped zones (“halos”) of enhanced turbidity. The wide-angle X-ray scattering of the disks was measured as a function of the distance from the gate at 13 positions along the radius, using a diffractometer and reflection geometry. These measurements yielded radial profiles of the orientation of α-PP and of the distribution of β-PP crystallites. Both kinds of profiles revealed clear correlations with the polymer grade and with the melt and/or mold temperature. Radial profiles of optical turbidity of the disks were obtained by means of a microdensitometer. Pronounced maxima of turbidity were found to coincide with the maxima observed in the radial distribution of β-PP. An analysis of variance (ANOVA) of the experiments showed that the mass temperature has the greatest influence on the radial distances of the maxima of turbidity. Increasing mass temperature led to decreasing radial distances of the turbidity maxima, whereas the mold temperature as well as the flow rate only had a small influence on the radial positions of the turbidity maxima. The investigation of cross-sections, which were taken from some disks at selected distances from gate, by means of optical microscopy using polarized light revealed significant changes in the morphology with increasing distance from gate, e.g., changes in the size and distribution of β-PP spherulites.

Particle statistics in quantitative X-ray diffractometry

Particle statistics in quantitative X-ray diffractometry relates to the number of particles (crystallites) contributing to the diffracted intensity for a given line. Variations in line intensity between replicate preparations of the same sample arise from statistical variations in the number of diffracting particles. The uncertainty in line intensity, and hence in quantitative estimates of analyte concentration, is termed the particle statistics error. A theoretical estimate of the error for stationary samples qives σPS=ξ[μ*〈v〉/c]1/2, where μ* is the mass absorption coefficient of the mixture, and 〈v〉 and c are the mean particle volume and mass concentration respectively of the analyte. The factor ξ is a function mainly of diffractometer geometry, but also contains contributions from rocking angle and reflection multiplicity. For measurements of the (112) quartz line with a Philips PW1050 vertical goniometer with 2o divergence slit and 0.3 mm receiving slit, ξ was calculated to be 116 g1/2 cm−5/2 for stationary samples. Three close-cut size fractions of quartz were prepared at various concentrations in a calcium carbonate matrix. Replicate preparations were measured and the standard deviation obtained as a function of particle volume and concentration. After correction for other contributing errors, including counting statistics and thermal fluctuations, the experimental value ξ=122±10 g1/2 cm−5/2 was obtained. The effect of sample spinning is considered briefly and predicted to reduce σPS by a factor of about 5. Experimentally, a reduction in σPS of about this order is observed, but the effect is rather variable.

SBGBBG, a program to evaluate the macroscopic strain/stress tensor of a polycrystalline sample from X-ray reflection positions

The evaluation of the strain/stress tensor from strain measured by X-ray diffraction requires a transformation from the sample system S to the laboratory system L. The transformation matrix A depends on the diffractometer geometry and the sample tilting. The conversion from strain to stress relies on poly-crystal elastic compliances S′mnop. The averaging is done about the orientation of the diffracting crystallites. The orientation distribution function (ODF) serves as weighting function. The computer program SBGBBG carries out these calculations.

Potential of the INEL X-ray position-sensitive detector: a general study of the Debye–Scherrer setting

The INEL diffractometer, equipped with a CPS120 curved detector and set up in a Debye-Scherrer geometry, is a unique tool for carrying out powder diffraction studies on air-sensitive and/or small-volume samples. Although it has routinely been used in powder diffractometry because of its minute acquisition times, its accuracy in d-spacing and intensity measurements has not been clearly demonstrated before now. Concerning the d spacings, proper linearization of the CPS120 with a cubic Na2Ca3Al2F14 standard allowed a mean δ2θ difference of 0.006°. Intensity accuracy was measured with different highly and poorly absorbing samples. The accuracy is fairly good for the latter but poor for the former, except when special procedures such as the dilution of the sample with boron powder are used. A Rietveld calculation carried out on TI4V207 showed a very good agreement between the INEL Debye-Scherrer-geometry results and those obtained with a Philips diffractometer and Bragg-Brentano geometry.

Impact of clay particle orientation on quantitative clay diffractometry

AbstractPreferred orientation of clay particles in various clay mounts was measured with an X-ray texture diffractometer. Pole distributions are approximately symmetrical about the normal to the sample. Particle orientation is characterized by standard deviations ranging from 7° for thin sedimented layers, to 20° and more for dry-pressed samples, the latter showing less dependence on particle size. The orientation of the reflecting particles may span a considerable angular range affecting the intensities of diffraction peaks observed on contemporary powder diffractometers, even those with moderate axial divergence. A theory based on the diffractometer geometry was developed to calculate the effect of particle orientation. Results are presented as modified Lorentz factors for orientations deduced from experimental observations. In qualitative X-ray diffractometry of clays, preference must be given to preparation techniques which ensure a high degree of preferred orientation and therefore strong enhancement of basal reflections. In quantitative X-ray diffractometry, the main factor is the reproducibility of particle orientation, and suction and dry pressing are promising methods of sample preparation.

High Quality X-Ray Diffraction Data Using an Adjustable Divergence Slit and Thin Samples

AbstractIn the Bragg-Brentano X-ray powder diffractometer geometry the Automatic Divergence Slit (ADS) provides a fixed area of illumination on a flat specimen. For this case, the “constant volume” diffraction, appropriate for a Constant Divergence Slit (CDS) diffractometer, is not applicable and intensities must be corrected by a sinθ factor before comparison to CDS data.It is shown that for thin layers the diffraction pattern may be treated as a “constant volume” diffraction case when the ADS is used. Moreover, the derivation of the unit cell dimensions using a common least-square procedure can result in excellent lattice parameters without using internal standards, because the transparency aberrations are minimized.ADS data were obtained for a variety of reference materials including several NBS SRM powders. It was found that thin samples made of powder mixed with vaseline gave “constant volume” diffraction, less angular aberration, and yet had line intensities only somewhat less than bulk samples.Three main benefits arise using a combination of thin layers and ADS: (a) The amount of material needed for routine chracterization is small, (b) The relative experimental intensities are approximately the same as those obtained from bulk specimens using a CDS. (c) The measured (Bragg) scattering angles are more accurate compared with those measured from bulk specimens.

Structure of pivaloyloxymethyl (3S,5R,6S)-6-bromopenicillanate

C~4H20BrNOsS, M,=394.3, monoclinic, P21, a = 5.949 (1), b= 10.470 (1), c= 14.299 (1) A, fl= 94.56 (2) °, V= 887.8 A 3, Z = 2, Dx= 1.475 gcm -3, 2(Cu Ka) = 1.5418/~, # = 42.0 cm -1, F(000) = 404, room temperature, final R = 0.069 for 1305 independent reflections. The thiazolidine ring is slightly puckered, with the C(3) atom, which is attached to the pivaloyl side chain, 0.47 (1)/~ out of the plane formed by the remaining atoms. The nitrogen atom is 0.37 (1)/k above the plane defined by the three atoms to which it is bonded. Molecular packing results from normal van der Waals interactions. Introduction. As pointed out in previous papers of this series, a crystal-structure determination of several penam derivatives was undertaken in our laboratory to establish the influence of 1,6-substituents on the conformation of the molecular nucleus. As part of these studies, the structure of the title compound was determined and is presented here. Experimental. Crystallized by slow evaporation from methanol, colourless irregular-shaped crystal, approxi- mate dimensions 0.25 x 0.22 × 0.07 mm; automatic four-circle Huber diffractometer; Ni-filtered CuKct radiation; co scans; integrated intensities as described by Lehmann & Larsen (1974); lattice parameters from setting angles of 20 reflections with 20 values between 60 and 75°; space group P2~ (No. 4); Lorentz- polarization and empirical absorption (see Alzari, Rivero, Punte & Ronco, 1986) corrections; min., max. transmission factors 1.00, 1.58; data collected to 20ma x = 120°; index range -6 to 6, 0 to 11, 0 to 16 for h,k,l respectively; 1362 unique reflections (not obscured by diffractometer geometry) measured, of which 1305 with I> 2a(I) considered observed; three standard reflections showed no significant fluctuations. Structure solved by Patterson and difference Fourier methods; refined by full-matrix least squares based on F's; weighting scheme: w = 1/(a2(F) + 0.0137Fq; H atoms stereochemically positioned with isotropic thermal parameters (not refined) equal to those of their bonded C atoms; all methyl groups refined as rigid bodies;

Accuracy of crystal structure error estimates

A statistical analysis of 100 crystal structures retrieved from the Cambridge Structural Database is reported. Each structure has been determined independently by two different research groups. Comparison of the independent results leads to the following conclusions: (a) The e.s.d.'s of non-hydrogen-atom positional parameters are almost invariably too small. Typically, they are underestimated by a factor of 1.4-1-45. (b) The extent to which e.s.d.'s are underestimated varies significantly from structure to structure and from atom to atom within a structure. (c) Errors in the positional parameters of atoms belonging to the same chemical residue tend to be positively correlated. (d) The e.s.d.'s of heavy-atom positions are less reliable than those of light-atom positions. (e) Experimental errors in atomic positional parameters are normally, or approximately normally, distributed. (f) The e.s.d.'s of cell parameters are grossly underestimated, by an average factor of about 5 for cell lengths and 2.5 for cell angles. There is marginal evidence that the accuracy of atomic-coordinate e.s.d.'s also depends on diffractometer geometry, refinement procedure, whether or not the structure has a centre of symmetry, and the degree of precision attained in the structure determination.

Angle and index calculations for `z-axis' X-ray diffractometer

Closed formulas are given for the calculation of the orientation matrix and the angles for a given reflection in a `z-axis' diffractometer geometry. These equations are derived for the conditions where the angle of incidence of the primary beam to the surface of the crystal is specified. Comparison is made with the standard four-circle configuration and the differences between these two geometries are evaluated. Some further applications are discussed.

Experimental improvements in analysis of aerosol samples by X-ray powder diffraction

Instrumental modifications of Bragg-Brentano diffractometer geometry to obtain more complete data on aerosol samples were studied. The conventionally used graphite crystal monochromator was replaced by an ideally focusing Johansson-type quartz crystal, which resolved overlapping peaks and eliminated the K α 2 component from the diffraction patterns. The commonly used copper target X-ray tube was replaced by a longer wavelength chromium tube which gives better peaks separation. The optimum step size is also discussed. These parameters are compared in a study on aerosol samples generated by the manual metal arc welding of mild steel, the purpose being to reveal the complex spinel structure assumed to be contained in the samples.

The approximation of asymmetric neutron powder diffraction peaks by sums of Gaussians

Neutron powder diffractometers operating with large vertical counter acceptance angles produce diffraction patterns in which the peaks are shifted and broadened, and may become distinctly asymmetric. It is shown that a sum of Gaussians generally provides a good approximation to these peaks. The sum of Gaussians has been included as an optional description of the profile within an existing profile refinement program. In this application, the sum incorporates a single asymmetry parameter which can be estimated from the diffractometer geometry or determined in the refinement. It is recommended that, in describing asymmetric peaks, the sum of Gaussians be used in place of the simple Gaussian multiplied by Rietveld's semi-empirical asymmetry factor.

Calibration of the Diffractometer at Low Values of Two Theta

A set of experimentally obtained “d” values is subject to a variety of random and systematic errors, some of which are inherent to a given diffractometer configuration and some of which may result from incorrect alignment of the diffractometer or technique in establishing peak positions and subsequent calculation of “d” values. In a previous paper (1) we have discussed the problems involved in the identification and control of errors in the computer controlled diffractometer and in that paper we indicated that it is useful to differentiate between different types of two-theta values. Firstly the Theoretical 20 values are those values which are dependant only on the size and distribution of atoms in the unit cell of the phase. The Practical 20 values on the other hand result when aberrations inherent in a given diffractometer geometry are convoluted with the Theoretical 20 values. In terms of their typical magnitudes the most important of these aberrations in decreasing order are: Specimen Displacement, Axial Divergence, Flat Specimen and Transparency Errors. Other inherent errors include refraction and the effects of focal line and receiving slit widths etc., but these latter effects are generally considered small. At the second level, Experimental 20 values also depend on misalignment errors. The third level errors accrue in the conversion of the experimental 20 value to “d” spacing. These errors may arise simply from round-off errors or from more fundamental reasons arising from the polychromatic nature of the source and uncertainties in the wavelength of the diffracted radiation.

50-kilobar gasketed diamond anvil cell for single-crystal x-ray diffractometer use with the crystal structure of Sb up to 26 kilobars as a test problem

A single-crystal gasketed diamond anvil cell of a new design for use on a diffractometer is described. It has achieved hydrostatic pressures of 50 kilobars as determined from the ruby fluorescence shift. The design combines several advantages. Nearly half the area of the Ewald sphere is available without having to remount the crystal. For reflecting planes nearly parallel to the diamond anvil faces, all reflections in the angular range ∼4°⩽ϑ⩽85° can be observed. Alignment of the diamonds, as well as loading and alignment of the sample crystals, is very simple and quick. The diffractometer geometry allows accurate measurements of weak reflections as well as accurate determinations of the x-ray absorption corrections for the cell. The materials of construction are nontoxic except for one diamond mount, a small beryllium cylinder situated so that it is never touched, scraped, or rubbed. As a test problem, the z parameter of antimony has been found to increase linearly from z=0.23357 at 1 bar to z =0.2380±0.0005 at 26 kilobars.

A method of increasing the detected intensity in X-ray powder diffractometers

It is known that errors are introduced in an X-ray powder diffractometer experiment due to instrument parameters such as the divergence of the incident X-ray beam, the width of the detector slit and the spacing of the Soller slits. A method to correct for these errors is developed. This allows the use of larger slit widths and incident divergence, leading to increased detected intensities. The method will be of use in powder line profile analysis and particularly in the study of liquids and amorphous solids. The errors introduced in the measured intensity are corrected by expanding the scattered intensity as a power series in the scattering angle. The theory for the simple case of a one-dimensional spectrum, scanned by a one-dimensional slit, is developed. In this case, to the second order, the required correction to the measured intensity, is proportional to its second Taylor coefficient. The efficiency of the correction technique is studied through computer studies on model intensity profiles. Some results on an experimental line profile are also presented. Finally, the correction formula for the case of the general powder diffractometer geometry is derived.