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Organisationseinheit der BAM
## 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.
Continuing progress in the field of X-ray scattering methods empowers scientists with new possibilities to capture the most important piece of information about the structure of the sample - its 3D electron density.
Although the first methods appeared almost a century ago, recovering the density structure of a sample is still very problematic. Most avail-able imaging techniques transform a 3D electron density of a realspace structure into the 2D Fourier Transform of the intensity of scattered waves in the reciprocal space. This process causes a loss of information.
Firstly, instead of a 3D sample, a 2D image is created, and secondly, the phase information of the scattered waves is lost. The latter is known as the ”phase problem” and poses a serious obstacle on a way to recover a 3D electron density. In this work, we draw attention to the problem of forward and inverse Small Angle X-Ray Scattering. In the first, forward, part, we rethink the existing pipelines to computationally simulate such scattering experiments. Although there are efficient implementations of fast Fourier transformation, they often have some drawbacks. For instance, to calculate a 3D fast Fourier transform it is required to place its density in the RAM. For high-resolution structures of size > 1024 3 , this becomes very problematic, as the whole density structure requires more than 16 GB of memory.
CUDA solution allows for a very fast and parallelizable implementation of high-resolution data on hundreds of last-generation machines.
Such computations are very pricy and inaccessible for most scientists.
To bypass this limitation, we propose a solution for a split-up 3D fast Fourier transform, which is implemented as a sequence of 2D and 1D operations. We compare our implementation on the simulated 3D shapes and show the result of a proof-of-concept on 4096 3 Metallorganic framework density structure. In the second, inverse problem, we train an invertible neural network, that given scattering data can predict the shape and its parameters. The architecture is built such, that the inverse problem is learned together with the forward process - the Fourier Transformation. We achieved very good results with this architecture, nonetheless, further testing is required, as the current training set only encompasses three simple shapes: sphere, hard sphere and cylinder.
All code to reproduce and analyze the results is available at https: //github.com/sofyalaski/SAXS-simulations.