A fast X-ray-diffraction-based method for the determination of crystal size distributions (FXD-CSD)

2018 ◽  
Vol 51 (5) ◽  
pp. 1352-1371 ◽  
Author(s):  
Sigmund H. Neher ◽  
Helmut Klein ◽  
Werner F. Kuhs
Keyword(s):  
Size Distribution ◽  
Chemical Engineering ◽  
Crystal Size ◽  
Crystal Size Distribution ◽  
Polycrystalline Materials ◽  
Distribution Analysis ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Intensity Scaling

A procedure for a fast X-ray-diffraction-based crystal size distribution analysis, named FXD-CSD, is presented. The method enables the user, with minimal sample preparation, to determine the crystal size distribution (CSD) of crystalline powders or polycrystalline materials, derivedviaan intensity scaling procedure from the diffraction intensities of single Bragg spots measured in spotty diffraction patterns with a two-dimensional detector. The method can be implemented on any single-crystal laboratory diffractometer and any synchrotron-based instrument with a fast-readout two-dimensional detector and a precise sample scanning axis. The intensity scaling is achievedviathe measurement of areferencesample with known CSD under identical conditions; the only other prerequisite is that the structure (factors) of bothsampleandreferencematerial must be known. The data analysis is done with a software package written in Python. A detailed account is given of each step of the procedure, including the measurement strategy and the demands on the spottiness of the diffraction rings, the data reduction and the intensity corrections needed, and the data evaluation and the requirements for the reference material. Using commercial laboratory X-ray equipment, several corundum crystal size fractions with precisely known CSD were measured and analysed to verify the accuracy and precision of the FXD-CSD method; a comparison of known and deduced CSDs shows good agreement both in mean size and in the shape of the size distribution. For the used material and diffractometer setup, the crystal size application range is one to several tens of micrometres; this range is highly material and X-ray source dependent and can easily be extended on synchrotron sources to cover the range from below 0.5 µm to over 100 µm. FXD-CSD has the potential to become a generally applicable method for CSD determination in the field of materials science and pharmaceutics, including development and quality management, as well as in various areas of fundamental research in physics, chemistry, chemical engineering, crystallography, the geological sciences and bio-crystallization. It can be used also underin situconditions for studying crystal coarsening phenomena, and delivers precise and accurate CSDs, permitting experimental tests of various theories developed to predict their evolution.

scholarly journals Determination of crystal size distribution by two-dimensional X-ray diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C1131-C1131
Author(s):  
Alejandro Rodriguez-Navarro ◽  
Krzysztof Kudłacz
Keyword(s):  
Size Distribution ◽  
Crystal Size ◽  
High Sensitivity ◽  
Crystal Size Distribution ◽  
Polycrystalline Materials ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Area Detector ◽  
Diffraction Patterns

Polycrystalline materials properties and behaviour are ultimately determined by their crystallinity, phase composition and microstructure (i.e., crystal size, preferential orientation). Two-dimensional (2D) diffraction patterns collected with an area detector (i.e., CDD), available in modern X-ray diffractometers, contain detailed information about all these important material characteristics. Furthermore, recent advances in detector technologies permits the collection of high resolution diffraction patterns in which the microstructure of the material can be directly imaged. If the size of beam relative to the crystal size in the sample is adequately choosen, the diffraction pattern produced will have spotty rings in which the spots are the diffracted images of individual grains. The resolution of the image is mainly dependent on the characteristics of the X-ray beam (i.e., diameter, angular divergence), which can be modulated by X-ray optics, sample to detector distance, the pixel size of the detector and the sharpness of the point spread function. From these patterns, the crystal size distribution of different crystalline phases present in the sample can be independently determined using specialized software capable of extracting and combining the information contained in these patterns. This technique is applicable to materials with crystal sizes ranging from submicron to mm sizes and is complementary to techniques based on peak profile analyses (i.e., Scherrer method) which are applicable only to nanocrystalline materials. Finally, given the high sensitivity of current detectors, crystal size evolution can be followed in real-time to study important transformation processes such as crystallization, annealing, etc. The use of 2D X-ray diffraction as applied to microstructure characterization will be illustrated through several examples.

High Resolution Synchrotron X-Ray Diffraction Tomography Of Large-Grained Samples

1996 ◽  
Vol 437 ◽  
Author(s):  
D.P. Piotrowski ◽  
S.R. Stock ◽  
A. Guvenilir ◽  
J.D. Haase ◽  
Z.U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Dimensional Distribution

AbstractIn order to understand the macroscopic response of polycrystalline structural materials to loading, it is frequently essential to know the spatial distribution of strain as well as the variation of micro-texture on the scale of 100 μm. The methods must be nondestructive, however, if the three-dimensional evolution of strain is to be studied. This paper describes an approach to high resolution synchrotron x-ray diffraction tomography of polycrystalline materials. Results from model samples of randomly-packed, millimeter-sized pieces of Si wafers and of similarly sized single-crystal Al blocks have been obtained which indicate that polychromatic beams collimated to 30 μm diameter can be used to determine the depth of diffracting volume elements within ± 70 μm. The variation in the two-dimensional distribution of diffracted intensity with changing sample to detector separation is recorded on image storage plates and used to infer the depth of diffracting volume elements.

scholarly journals A Novel Shadowgraphic Inline Measurement Technique for Image-Based Crystal Size Distribution Analysis

Crystals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 740 ◽  
Author(s):  
Dominic Wirz ◽  
Marc Hofmann ◽  
Heike Lorenz ◽  
Hans-Jörg Bart ◽  
Andreas Seidel-Morgenstern ◽  
...  
Keyword(s):  
Size Distribution ◽  
Crystal Size ◽  
Elevated Temperatures ◽  
Measurement Techniques ◽  
Potassium Dihydrogen Phosphate ◽  
Crystal Size Distribution ◽  
Thiamine Hydrochloride ◽  
Dihydrogen Phosphate ◽  
Distribution Analysis ◽  
Inline Measurement

A novel shadowgraphic inline probe to measure crystal size distributions (CSD), based on acquired greyscale images, is evaluated in terms of elevated temperatures and fragile crystals, and compared to well-established, alternative online and offline measurement techniques, i.e., sieving analysis and online microscopy. Additionally, the operation limits, with respect to temperature, supersaturation, suspension, and optical density, are investigated. Two different substance systems, potassium dihydrogen phosphate (prisms) and thiamine hydrochloride (needles), are crystallized for this purpose at 25 L scale. Crystal phases of the well-known KH2PO4/H2O system are measured continuously by the inline probe and in a bypass by the online microscope during cooling crystallizations. Both measurement techniques show similar results with respect to the crystal size distribution, except for higher temperatures, where the bypass variant tends to fail due to blockage. Thiamine hydrochloride, a substance forming long and fragile needles in aqueous solutions, is solidified with an anti-solvent crystallization with ethanol. The novel inline probe could identify a new field of application for image-based crystal size distribution measurements, with respect to difficult particle shapes (needles) and elevated temperatures, which cannot be evaluated with common techniques.

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