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This talk highlights a proof-of-concept that demonstrates the ability to calculate high-resolution Fourier transforms. These can be combined with multi-scale modeling to simulate scattering over a wide range, from small-angle scattering to XRD and PDF.
The preprint documenting this is available on the ArXiv here:
https://doi.org/10.48550/arXiv.2303.13435
The Jupyter notebook, VASP calculation details and MOUSE measured scattering patterns are available from this Zenodo repository: https://dx.doi.org/10.5281/zenodo.7764045
## Summary:
This notebook and associated datasets (including VASP details) accompany a manuscript available on the ArXiv (https://doi.org/10.48550/arXiv.2303.13435) and hopefully soon in a journal as short communication as well. Most of the details needed to understand this notebook are explained in that paper with the same title as above. For convenience, the abstract is repeated here:
## Paper abstract:
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is presented coupled to the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The ``Ultima Ratio'' strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from $Q<0.01$\,$\mathrm{nm}^{-1}$ up to $Q\approx150$\,$\mathrm{nm}^{-1}$, with a resolution of 0.16\,\AA. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to $8000^3$ voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-$Q$ behaviour.
The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder.
While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is on the same scale as the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The "Ultima Ratio" strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from Q < 0.01 1/nm up to Q < 150 1/nm, with a resolution of 0.16 Angstrom. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to 8000^3 voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-Q behaviour. The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder. While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
he mutual influence of F and OH groups in neighboring sites in topaz (Al2SiO4(F,OH)2) was investigated using magic angle spinning nuclear magnetic resonance (MAS NMR) and Raman spectroscopy. The splitting of 19F and 1H NMR signals, as well as the OH Raman band, provides evidence for hydrogen bond formation within the crystal structure. Depending on whether a given OH group has another OH group or fluoride as its neighbor, two different hydrogen bond constellations may form: either OH···O···HO or F···H···O. The proton accepting oxygen was determined to be part of the SiO4 tetrahedron using 29Si MAS NMR. Comparison of the MAS NMR data between an OH-bearing and an OH-free topaz sample confirms that the 19F signal at −130 ppm stems from F− ions that take part in H···F bonds with a distance of ∼ 2.4 Å, whereas the main signal at −135 ppm belongs to fluoride ions with no immediate OH group neighbors. The Raman OH sub-band at 3644 cm−1 stems from OH groups neighboring other OH groups, whereas the sub-band at 3650 cm−1 stems from OH groups with fluoride neighbors, which are affected by H···F bridging. The integrated intensities of these two sub-bands do not conform to the expected ratios based on probabilistic calculations from the total OH concentration. This can be explained by a difference in the polarizability of the OH bond between the different hydrogen bond constellations or partial order or unmixing of F and OH, or a combination of both. This has implications for the quantitative interpretation of Raman data on OH bonds in general and their potential use as a probe for structural (dis-)order. No indication of tetrahedrally coordinated Al was found with 27Al MAS NMR, suggesting that the investigated samples likely have nearly ideal Al/Si ratios, making them potentially useful as high-density electron microprobe reference materials for Al and Si, as well as for F.
We demonstrate here using a disulfide system the first example of reversible, selective, and quantitative transformation between three crystalline polymorphs by ball mill grinding. This includes the discovery of a previously unknown polymorph. Each polymorph is reproducibly obtained under well-defined neat or liquid-assisted grinding conditions, revealing subtle control over the apparent thermodynamic stability. We discovered that the presence of a contaminant as low as 1.5% mol mol−1 acting as a template is required to enable all these three polymorph transformations. The relative stabilities of the polymorphs are determined by the sizes of the nanocrystals produced under different conditions and by surface interactions with small amounts of added solvent. For the first time, we show evidence that each of the three polymorphs is obtained with a unique and reproducible crystalline size. This mechanochemical approach gives access to bulk quantities of metastable polymorphs that are inaccessible through recrystallisation.