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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.
Iron nitride (Fe3N) and iron carbide (Fe3C) nanoparticles can be prepared via sol−gel synthesis. While sol−gel methods are simple, it can be difficult to control the crystalline composition, i.e., to achieve a Rietveld-pure product. In a previous in situ synchrotron study of the sol−gel synthesis of Fe3N/Fe3C, we showed that the reaction proceeds as follows:
Fe3O4 → FeOx → Fe3N → Fe3C. There was considerable overlap between the different phases, but we were unable to ascertain whether this was due to the experimental setup (side-on heating of a quartz capillary which could lead to thermal gradients) or whether individual particle reactions proceed at different rates. In this paper, we use in situ wide- and small-angle X-ray scattering (wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS)) to demonstrate that the overlapping phases are indeed due to variable reaction rates. While the initial oxide nanoparticles have a small range of diameters, the size range expands considerably and very rapidly during the oxide−nitride transition. This has implications for the isolation of Rietveld-pure Fe3N, and in an extensive laboratory study, we were indeed unable to isolate phasepure Fe3N. However, we made the surprising discovery that Rietveld-pure Fe3C nanoparticles can be produced at 500 °C with a sufficient furnace dwell time. This is considerably lower than the previous reports of the sol−gel synthesis of Fe3C nanoparticles.
n this work, three new pharmaceutical hydrated salts of ciprofloxacin with selected derivatives of benzoic acid, namely 4-hydroxybenzoic acid, 4-aminobenzoic acid and gallic acid, were obtained and systematically investigated by several solid-state analytical techniques. In situ Raman spectroscopy was applied to elucidate the alternative pathways of the solid forms' formation under mechanochemical conditions. Crystal structure analysis and a CSD survey allowed us to establish a distinct supramolecular motif formed by infinite columnar stacks of ciprofloxacin dimers arranged in the “head-to-tail” manner. An alternative “head-to-head” packing arrangement was only observed in the crystal of the hydrated ciprofloxacin salt with 4-aminobenzoic acid. In addition, the pH-solubility behavior of the solid forms was thoroughly investigated. Furthermore, a distinct structure–property relationship between the specific features of the supramolecular organization of the hydrated salts and their solubility was observed and discussed.
Ca-, Sr-, and Ba-Based coordination polymers (CPs) were prepared mechanochemically by milling metal-hydroxide samples with anthranilic acid (oABAH). {[Ca(oABA)2(H2O)3]}n consists of one-dimensional polymeric chains that are further connected by a hydrogen-bonding network. {[Sr(oABA)2(H2O)2]·H2O}n is a one-dimensional CP in which water molecules bridge Sr2+ ions and increase the dimensionality by building an extended network. {[Ba(oABA)2(H2O)]}n crystallizes as a two-dimensional CP comprising one bridging water molecule. The cation radii influence the inorganic connectivity and dimensionality of the resulting crystal structures. The crystal structures were refined from powder X-ray diffraction data using the Rietveld method. The local coordination environments were studied via extended X-ray absorption fine structure (EXAFS) measurements. The compounds were further characterized using comprehensive analytical methods such as elemental analysis, thermal analysis, MAS NMR, imaging, and dynamic vapor sorption (DVS) measurements. Compounds 1, 2, and 3 exhibit small surface areas which decrease further after thermal annealing experiments. All compounds exhibit a phase transformation upon heating, which is only reversible in 3.
Ball mass is an important parameter that is known to have an influence on the outcome of a mechanochemical reaction induced by ball-milling. A standard way of modifying the ball mass is to change the size of the ball made of the same material. In this case, however, a change in mass is accompanied by a simulatneous change in the ball size. It is therefore not possible to disentangle the effects of mass and Surface area in these cases. In the present work we report the results of experiments with specially designed and manufactured balls in which (1) milling ball mass is held constant, but their size differs, and (2) the ball mass is altered, with the diameter of the milling ball being held constant. Using the cocrystallisation of theophylline + nicotinamide as a case study it was found that both diameter and ball mass play crucial roles in determining the rate of a mechanochemical reaction. For comparison, we have also used milling balls with the same size (different mass), and others with the same mass (different size) made of different materials, as would be “traditional”. It was found that, despite having the same size, the lightest milling ball (nylon) was the most efficient in initiating the co-crystallisation, presumably due to the sorption of EtOH. Hence, the results of this manuscript also demonstrate how milling ball material can in fact be the most influential parameter, and potentially counterintuitive to classical mechanics.
Mechanochemistry is a fast and efficient method applicable for the synthesis of new organic[1], metal-organic[2], and inorganic[3] compounds. The direct monitoring of milling reactions is still challenging. The underlying reaction mechanisms remain often unclear. In the last years, have established a tandem in situ approach for investigating mechanochemical reactions using time-resolved in situ XRD coupled with Raman spectroscopy.[4] Here, we present an in situ coupling of synchrotron XRD, Raman spectroscopy, and thermography allowing the observation of mechanochemical reactions in real time.[5] Information on the crystalline, molecular, and temperature state of the materials during grinding could be collected. The chemical composition of the reaction mixture was found to be directly correlated with changes in the temperature profile of the reaction. Furthermore, the presented setup allows the detection of crystalline, amorphous, eutectic as well as liquid intermediates. The resulting deeper kinetic and thermodynamic understanding of milling processes is the key for future optimization of mechanochemical syntheses.
We present naproxen/proline cocrystals discovered when combining enantiopure and racemic naproxen and proline. Using liquid-assisted grinding as the main method to explore the variety of crystal forms in this system, we found 17 cocrystals, of which the structures of only four of them were previously known. The naproxen/proline system exhibited multiple polymorphs of 1 : 1 stoichiometry as well as more rare cocrystals with 1 : 2 and 2 : 3 stoichiometries, two cocrystal hydrates and one cocrystal solvate. In situ ballmilling, used to monitor liquid-assisted grinding reactions, revealed that the solvent dictates the reaction intermediates even if the final reaction product stays the same. Synchrotron X-ray diffraction data collected in situ upon heating allowed us to monitor directly the phase changes upon heating and gave access to pure diffraction patterns of several cocrystals, thus enabling their structure determination from powder X-ray diffraction data; this method also confirmed the formation of a conglomerate in the RS-naproxen/DL-proline system. Proline in cocrystals kept its ability to form charge-assisted head-to-tail
N-H⋯O hydrogen bonds, typical of pure crystalline amino acids, thus increasing the percentage of strong chargeassisted interactions in the structure and consequently providing some of the cocrystals with higher melting points as compared to pure naproxen. The majority of drugs are chiral, and hence, these data are of importance to the pharmaceutical industry as they provide insight into the challenges of chiral cocrystallization.
Two divalent manganese aminophosphonates, manganese mono (nitrilotrimethylphosphonate) (MnNP3) and manganese bis N-(carboxymethyl)iminodi(methylphosphonate)) (Mn(NP2AH)2), have been prepared by mechanochemical synthesis and characterized by powder X-ray diffraction (PXRD). The structure of the novel compound Mn(NP2AH)2 was determined from PXRD data. MnNP3 as well as Mn(NP2AH)2 exhibits a chain-like structure.
In both cases, the manganese atom is coordinated by six oxygen atoms in a distorted octahedron. The local coordination around Mn was further characterized by extended X-ray absorption fine structure. The synthesis process was followed in situ by synchrotron X-ray diffraction revealing a three-step reaction mechanism. The asprepared manganese(II) phosphonates were calcined on air.
All samples were successfully tested for their suitability as catalyst material in the oxygen evolution reaction.
The syntheses and crystal structures of two cerium(IV) phosphonates are presented. Cerium(IV) bis(phenylphosphonate) Ce(O3PC6H5)2 1 can be formed from precipitation and mechanochemical reaction, whereas cerium(IV) bis(carboxymethylphosphonate) monohydrate Ce(O3PCH2COOH)2 H2O 2 is only accessible via ball milling. All reactions proceed very fast and are completed within a short time span. In situ measurements for the syntheses of 1 show that the product occurs within seconds or a few minutes, respectively. The structures were solved from powder X-ray diffraction data.
A series of Ca-based coordination polymers were prepared mechanochemically by milling Ca(OH)2 with phthalic acid (H2oBDC), isophthalic acid (H2mBDC), and terephthalic acid (H2pBDC). The hydrated compounds [Ca(oBDC)(H2O)], [Ca(mBDC)(H2O)3.4], and [Ca(pBDC)(H2O)3] were prepared for the first time via mechanochemical routes. The refined structures were validated by extended X-ray absorption data. The new dehydrated compound [Ca(oBDC)] (1-H2O), obtained after the thermal post-treatment of 1 in a reversible phase transition process, was determined ab initio based on the powder X-ray diffraction (PXRD) data. The materials were thoroughly characterized using elemental analysis, thermal analysis, and spectroscopic methods: magic-angle spinning NMR and attenuated total reflection-infrared spectroscopy. The specific surface areas and sorption properties of the hydrated and dehydrated samples were determined using the isotherms of gas sorption and dynamic vapor sorption measurements.