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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.
Amorphous calcium carbonate (ACC) is an important precursor in the biomineralization of crystalline CaCO3. In nature, it serves as a storage material or as a permanent structural element, whose lifetime is regulated by an organic matrix. The relevance of ACC in materials science is primarily related to our understanding of CaCO3 crystallization pathways and CaCO3/(bio)polymer nanocomposites. ACC can be synthesized by liquid–liquid phase separation, and it is typically stabilized with macromolecules. We have prepared ACC by milling calcite in a planetary ball mill. Phosphate “impurities” were added in the form of monetite (CaHPO4) to substitute the carbonate anions, thereby stabilizing ACC by substitutional disorder. The phosphate anions do not simply replace the carbonate anions. They undergo shear-driven acid/base and condensation reactions, where stoichiometric (10%) phosphate contents are required for the amorphization to be complete. The phosphate anions generate a strained network that hinders ACC recrystallization kinetically. The amorphization reaction and the structure of BM-ACC were studied by quantitative Fourier transform infrared spectroscopy and solid state 31P, 13C, and 1H magic angle spinning nuclear magnetic resonance spectroscopy, which are highly sensitive to symmetry changes of the local environment. In the first—and fast—reaction step, the CO32– anions are protonated by the HPO42– groups. The formation of unprecedented hydrogen carbonate (HCO3–) and orthophosphate anions appears to be the driving force of the reaction, because the phosphate group has a higher Coulomb energy and the tetrahedral PO43– unit can fill space more efficiently. In a competing second—and slow—reaction step, pyrophosphate anions are formed in a condensation reaction. No pyrophosphates are formed at higher carbonate contents. High strain leads to such a large energy barrier that any reaction is suppressed. Our findings aid in the understanding of the mechanochemical amorphization of calcium carbonate and emphasize the effect of impurities for the stabilization of the amorphous phases in general. Our approach allowed the synthesis of new amorphous alkaline earth defect variants containing the unique HCO3– anion. Our approach outlines a general strategy to obtain new amorphous solids for a variety of carbonate/phosphate systems that offer promise as biomaterials for bone regeneration.
Clays are crucial mineral phases in Earth’s weathering engine, but we do not know how they form in surface environments under (near-)ambient pressures and temperatures. Most synthesis routes, attempting to give insights into the plausible mechanisms, rely on hydrothermal conditions, yet many geological studies showed that clays may actually form at moderate temperatures (<100 °C) in most terrestrial settings. Here, we combined high-energy X-ray diffraction, infrared spectroscopy, and transmission electron microscopy to derive the mechanistic pathways of the low-temperature (25–95 °C) crystallization of a synthetic Mg-clay, saponite. Our results reveal that saponite crystallizes via a two stage process: (1) a rapid (several minutes) coprecipitation where ∼20% of the available magnesium becomes incorporated into an aluminosilicate network, followed by (2) a much slower crystallization mechanism (several hours to days) where the remaining magnesium becomes gradually incorporated into the growing saponite sheet structure.