X-ray Powder Diffraction Intensities Research Articles

Understanding extended homometry based on complementary crystallographic orbit sets.

Extended homometry is a phenomenon in which distinct structures have the same X-ray diffraction (XRD) intensities, which may lead to incorrect results of structural analysis based on XRD methods. It is proposed and proved herein that half of a crystallographic orbit has the same powder X-ray diffraction intensity as its complementary set; three more theorems are deduced. These results are conducive to understanding the formation of extended homometric structures. Also analyzed are some reported or potential homometric or weakly homometric structures in the Inorganic Crystal Structure Database to confirm the theorems. This work presents a quick approach to analyze and construct extended homometric structures based on crystallographic orbits.

Powder X-ray diffraction intensities of corundum calculated by conventional and density functional theory methods and extracted by deconvolutional treatment on experimental data

Least-squares analysis on the diffraction intensity values certified for NIST SRM676a and SRM1976c α-Al2O3 (corundum) have shown that the intensities of SRM1976c can be simulated by the March-Dollase preferred orientation model along the (001)-direction. Diffraction intensities of randomly oriented corundum crystallites have been calculated from electron density data obtained by conventional and density functional theory (DFT) calculations, on the assumption of independent and similar atomic displacements for Al and O atoms. The results of DFT calculations support that the strongest peak of randomly oriented α-Al2O3 crystalline powder should be 113-reflection, though the intensities simulated by DFT calculations are not closer to NIST SRM676a intensities than those expected for a fully ionized model ${\rm Al}_2^{3 + } {\rm O}_3^{2-}$. Diffraction data of two types of relatively fine (nominally 2–3 μm and ca 0.3 μm) α-Al2O3 powder have been collected and processed by a deconvolutional treatment (DCT). Integrated peak intensities extracted from the DCT data by an individual peak profile fitting method also support that the 113-reflection is the strongest reflection of randomly oriented α-Al2O3 crystalline powder.

Sodium rare earth metal amides Na3 RE(NH2)6 (RE = La–Nd, Er, Yb) from ammonothermal synthesis

Abstract The amides Na3 RE(NH2)6 have been obtained from the metals in supercritical ammonia under ammonobasic conditions at 573 K and 70 MPa for RE = La–Nd, and at 473 K and 40 MPa for RE = Er, Yb. All compounds are formed in the hot zone within a temperature gradient, indicating a retrograde solubility under the applied process conditions. These amides represent soluble intermediates in ammonothermal binary rare earth metal nitride synthesis. All compounds were obtained as microcrystalline powders, while single crystals of those amides containing the heavier rare earth metals could be isolated. The crystal structures were solved and refined from single-crystal and powder X-ray diffraction intensity data. The results of vibrational spectroscopy are reported. Thermal analysis measurements under inert gas atmosphere demonstrated a decomposition to the respective black binary rare earth metal nitrides REN1−δ .

Utilizing a unified structure model in (3 + 1)-dimensional superspace to identify a homologous phase (Ga1−αAlα)2O3(ZnO)min ZnO-based thermoelectric composites

A unified structure model in (3 + 1)-dimensional superspace proved suitable for identification of a homologous phase (Ga1−αAlα)2O3(ZnO)mby the profile fitting of powder X-ray diffraction intensities for thermoelectric composite materials in the pseudoternary system ZnO–Al2O3–Ga2O3. A homologous compound of the phase parameterm≃ 37 was found to coexist with (Al,Ga)-doped ZnO in samples sintered at 1723 K in air. The thermoelectric properties of the composite materials were closely related to the phase fractions. The higher the phase fraction of (Al,Ga)-doped ZnO with the wurtzite structure, the higher the electrical conductivity. On the other hand, the homologous compound with the long-period structure was effective in lowering the thermal conductivity of the materials.

Optimization of the synthesis of SBA-3 mesoporous materials by experimental design

SBA-3 mesoporous materials are characterized by hexagonal regular arrangements of channels with diameters >2 nm, high specific surface areas and high specific pore volumes. In the work reported herein, experimental design-response surface methodology (RSM) is used to model and optimize the synthesis conditions for SBA-3 mesoporous materials. In this study, we evaluate the influences of surfactant/silica source molar ratios, aging times, temperature and pH on the synthesis of SBA-3 mesoporous materials by analyzing the XRD intensities pertaining to the [100] signal. Response surfaces were obtained using the Box–Behnken design, and the combination of reaction parameters was optimized. By applying statistical methodology, higher levels of the objective function (XRD intensities pertaining to the [100] signal) were obtained using cetyltrimethylammonium bromide (CTAB)/tetraethyl orthosilicate (TEOS) molar ratios of 0.07 and 0.16, HCl/TEOS molar ratios of 8 and 11, reaction temperatures of 35 and 45 °C and aging times of 12–24 h. The mesoporous SBA-3 samples obtained were characterized using small-angle X-ray powder diffraction (XRD), BET, FTIR and 29Si NMR-MAS, scanning electron microscopy (SEM) and transmission electron microscopy (TEM).

Effect of organic ligands (l-Proline and l-Methionine) on growth, structural, vibrational, crystalline perfection, SHG efficiency, microscopic and optical properties of KDP single crystals

The effect of l-Proline (LP) and l-Methionine (LM) doping on the various properties of KDP single crystals grown by slow evaporation solution technique has been investigated. The external morphology of the grown crystals was found to vary due to different dopants and doping concentrations. The change in powder X-ray diffraction intensity patterns due to doping shows the lattice distortion within resolution limit and confirms that there is no extra phase. Further, the same was confirmed by FT-Raman analysis. Infra red microscopic study also exhibits the effectiveness of doping in terms of varying surface morphology. Crystalline perfection of KDP crystals with LP and LM doping was examined by high-resolution X-ray diffraction. This shows very interesting features on the ability of accommodating the dopants in the crystalline matrix. Second harmonic generation efficiency was also found to be in similar fashion as of crystalline perfection. The optical transparency of doped crystals was tested.

Unfolding a two-dimensional powder diffraction image: conformal mapping

A new procedure aimed at unfolding a two-dimensional powder diffraction image into both a one-dimensional azimuthal and a radial scan is presented. In this approach, the sample-to-detector distance is the only parameter that must be adjusted in a separate step by using a standard sample. The technique consists of three steps: tracking the beam centre as the local maximum of the self-convolution of the original two-dimensional map, detector tilt and rotation determination by an intensity-tensor diagonalization, and azimuthal/radial intensity integration by a conformal mapping of the original two-dimensional powder diffraction image. The X-ray powder diffraction (XRPD) intensity profile of the NIST Si 640c standard sample is used to test the performance. The results show the robustness of the method and its capability of efficiently tagging the pixels in a two-dimensional readout system by matching the ideal geometry of the detector to the real beam–sample–detector frame. The technique is a fast, versatile and user-friendly tool for the simultaneous analysis of both azimuthal and radial spectra of two-dimensional XRPD images.

X-ray diffraction studies on (NaCl) x(NaBr) y−x(NaI) 1−y crystals

We have grown (NaCl) x (NaBr) y − x (NaI) 1− y crystals by the melt method for various values of x and y. Thermal parameters like Debye–Waller factor, Debye temperature, mean square amplitude of vibration and Debye frequency were determined using the X-ray powder diffraction intensity data. The results obtained are reported here.

Studies on multiphased mixed crystals grown from NaBr and KCl

We have grown multiphased binary and ternary mixed crystals by the melt method using the miscible alkali halides, viz. NaBr and KCl and physically characterized. Thermal parameters like Debye–Waller factor, Debye temperature, Debye frequency and mean square amplitude of vibration were determined using the X-ray powder diffraction intensity data. DC and AC electrical measurements were carried out by using the parallel plate capacitor method at various temperatures. Activation energies (DC and AC), mean jump frequency, compressibility and mean sound velocity were also determined. The results obtained are reported here.

Application of the HLSVD Technique to the Filtering of X-Ray Diffraction Data

A filter based on the Hankel-Lanczos singular value decomposition (HLSVD) technique is presented and applied for the first time to X-ray diffraction (XRD) data. Synthetic and real powder XRD intensity profiles of nanocrystals are used to study the filter performances with different noise levels. Results show the robustness of the HLSVD filter and its capability to extract easily and effciently the useful crystallographic information. These characteristics make the filter an interesting and user-friendly tool for processing of XRD data.

KNd(MoO4)2: A New Incommensurate Modulated Structure in the Scheelite Family.

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Folding a two-dimensional powder diffraction image into a one-dimensional scan: a new procedure

A new procedure aimed at folding a two-dimensional powder diffraction pattern into a one-dimensional scan is presented. The sample-to-detector distance is the only parameter that, in this approach, needs to be adjusted in a separate step by using the `standard' sample. The technique consists of three steps: tracking the beam centre by means of simulated annealing of the diffraction rings along the same axis, detector tilt and rotation determination by a Hankel Lanczos singular value decomposition and intensity integration by an adaptive binning algorithm. The X-ray powder diffraction (XRPD) intensity profile of the standard NIST Si 640c sample is used to test the performance. Results show the robustness of the method and its capability of efficiently tagging the pixels in a two-dimensional readout system by matching the ideal geometry of the detector to the real beam–sample–detector frame. The technique is a versatile and user-friendly tool for the one-dimensional folding of two-dimensional XRPD images.

KNd(MoO4)2: A New Incommensurate Modulated Structure in the Scheelite Family

Potassium neodymium molybdenum oxide, KNd(MoO4)2, has been synthesized by the solid-state method. The structure and microstructure have been studied by X-ray powder diffraction and transmission electron microscopy (TEM). TEM revealed that the KNd(MoO4)2 structure is incommensurately modulated. The scheelite-like structure of KNd(MoO4)2 has been refined from X-ray powder diffraction intensities in the (3 + 1)D superspace group I2/b(αβ0)00 with a = 5.5202(2) Å, b = 5.33376(5) Å, c = 11.8977(3) Å, γ = 90.9591(7)°, and modulation vector q = 0.57789(4)a* − 0.14748(6)b* (RP = 3.09%, RwP = 4.04%). The ordering of the K and Nd cations appears to be the primary parameter of the structure modulations. The compositional wave of the {KMoO4} and {NdMoO4} distribution is observed in the ab structure projection. The incommensurability of the compositional wave direction with respect to the a and b lattice constants is regarded as the origin of the incommensurate structure modulations.

A new position sensitive area detector for high-speed and high-sensitivity X-ray diffraction analysis

A state-of-art semiconductor technology-based position sensitive area detector, namely D/teX-25, has recently been developed for high-speed and high-sensitivity X-ray diffraction (XRD) analysis of materials. X-ray powder diffraction intensities obtained by a D/teX-25 detector were found to over 50 times higher than those by a conventional scintillation counter. A D/teX-25 detector mounted on a conventional 2 kW XRD system has been used to collect ultrafast XRD data with scanning speeds up to 160°2θ per minute. Ultrahigh-speed XRD is particularly useful for time-resolved dynamical and in-situ studies. A D/teX-25 detector was successfully used on a Rigaku XRD differential scanning calorimetry (DSC) system for simultaneous measurements of XRD and DSC data under controlled temperature and humidity conditions. This has made possible the study of complex and rapid phase transformations of pharmaceutical terfenadine. The D/teX-25 area detector has also been used for recording two-dimensional XRD patterns showing the particle-size effects on α-quartz powder intensities and to obtain digital X-ray topographic images of a complex dislocation network in a Si wafer.

An Analytical Approach to Determine the Pore Shape and Size of MCM-41 Materials from X-ray Diffraction Data

The pore shape and size of MCM-41 were studied analytically by comparing the observed powder X-ray diffraction intensities with that derived from the MCM-41 crystal structure models, with two different pore shapes, a hexagon and a circle. The powder diffraction patterns from the as-synthesized and the calcined MCM-41 were measured by a synchrotron radiation at SPring-8, Japan. The MCM-41 structure with circular and hexagonal pore shapes explains well for the as-synthesized and the calcined MCM-41 crystals, respectively. The pore size and boundary obtained by this approach agree with those obtained from an N2 gas adsorption measurement combined with the Fourier synthesized density map.

Model independent pre-processing of X-ray powder diffraction profiles

Precise knowledge of X-ray diffraction profile shape is crucial in the investigation of the properties of matter in crystals powder. Line-broadening analysis is the fourth pre-processing step in most of the full powder pattern fitting softwares. The final result of line-broadening analysis strongly depends on three further steps: noise filtering, removal of background signal, and peak fitting. In this work a new model independent procedure for two of the aforementioned steps (background suppression and peak fitting) is presented. The former is dealt with by using morphological mathematics, while the latter relies on the Hankel-Lanczos singular value decomposition technique. Real X-ray powder diffraction (XRPD) intensity profiles of Ceria samples are used to test the performance of the proposed procedure. Results show the robustness of this approach and its capability of efficiently improving the disentangling of instrumental broadening. These features make the proposed approach an interesting and user-friendly tool for the pre-processing of XRPD data.

Growth and characterization of multiphased mixed crystals of KCl, KBr and KI:1. Growth and X-ray diffraction studies

The mixed and impurity-added (doped) crystals of alkali halides are found to be harder than the end members and so they are more useful. In view of this, it becomes necessary and useful to prepare binary- and ternary-mixed crystals regardless of miscibility problem and characterize them by measuring their physical properties. In the present work, we have grown (KCl) x (KBr) y − x (KI) 1− y crystals for various values of x and y by the melt method and physically characterized. Bulk composition of the crystals was measured using the measured density and refractive index values. X-ray diffraction analysis indicates the existence of two phases in the mixed crystals. Thermal parameters were determined using the X-ray powder diffraction intensity data.

Disentangling instrumental broadening

A new procedure aimed at disentangling the instrumental profile broadening and the relevant X-ray powder diffraction (XRPD) profile shape is presented. The technique consists of three steps: de-noising by means of wavelet transforms, background suppression by morphological functions and deblurring by a Lucy–Richardson damped deconvolution algorithm. Real XRPD intensity profiles of ceria samples are used to test the performance. Results show the robustness of the method and its capability of efficiently disentangling the instrumental broadening affecting the measurement of the intrinsic physical line profile. These features make the whole procedure an interesting and user-friendly tool for the pre-processing of XRPD data.

Theophylline particle design using chitosan by the spray drying

Solid dispersions of theophylline with chitosan as a carrier were prepared using a spray-drying method. Chitosan dissolved in an acid solution forms a gel, but it does not dissolve in an alkaline solution. Therefore, drugs which form composite particles with chitosan would gradually be released in an acid solution, and are expected to have considerably sustained release in an alkaline solution. In this study, we aimed to apply this ability to sustained release pharmaceutics. In this study, we used theophylline as a model drug and chitosan as a carrier. Mixtures of chitosan and the drug in prescribed ratios were dissolved in an acid solution. The physicochemical properties of the solid dispersions obtained were investigated by powder X-ray diffraction, differential scanning calorimetry, and dissolution rate analyses, with a view to clarify the effect of crystallinity on the dissolution rate. Furthermore, the interaction between the drug and the carrier was investigated by FT-IR analysis. The powder X-ray diffraction intensity of the drug in the spray-dried samples decreased with an increase in chitosan contents, which also caused changes from crystalline to amorphous forms. These results indicated that the system formed a solid dispersion. The dissolution profiles of the drug from the physical mixtures and solid dispersions were almost the same at pH 1.2. However, at pH 6.8, the release from the solid dispersions was sustained more than that from the physical mixtures. The FT-IR spectroscopy for the theophylline solid dispersions suggested that the carbonyl group of theophylline and the amino group of chitosan formed a hydrogen bond. Mass median aerodynamic diameter (MMAD) was measured by using a cascade impactor to evaluate the possibility of solid dispersions as dry powder inhalations. The MMAD of the spray-dried theophylline-chitosan systems were 4.5–5.0 μm. The results suggested that the spray-drying method is usefull to produce dry powders for inhalation.

Modeling of Transmitted X-ray Intensity Variation with Sample Thickness and Solid Fraction in Glycine Compacts

The previous paper in this series introduced an X‐ray diffraction quantitation method for the polymorphic content in tablets made of pure components. Before the method could be transferred, further studies were required to explain the commonly observed X‐ray intensity variation in analyzing compacts. The literature typically attributes the variation to partial amorphization under compression and/or to preferred orientation, without much viable explanation or compelling evidence. In this study, changes in intensity in compacts analyzed in transmission geometry were found to be primarily a function of sample thickness and solid fraction. A theoretical model was developed to describe the X‐ray powder diffraction (XRPD) intensity as a function of solid fraction, mass absorption coefficient, and thickness. The model was tested on two sets of glycine compacts: one with varying thickness at constant solid fraction, and the other with various solid fractions at a given thickness. The results show that the model predicts the XRPD intensity at any given sample thickness and solid fraction. With this model, the intensity variation of compacts made under different compression conditions can be normalized, making the method transferable to various tablet geometries and facilitating the analysis over expected ranges of formulation and process variation. © 2003 Wiley‐Liss, Inc. and the American Pharmacists Association J Pharm Sci 92:2345–2353, 2003