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## 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.
Systematic errors in the evaluation of uncorrected data from thermographic lock-in measurements
(2018)
Lock-in thermography (LT) is based on the correct evaluation of phase differences between the temperature oscillations at different surface regions of the object under test during periodic heating. Since the usual heating procedures contain a DC component, the actual heating pattern achieved is not harmonic. This causes systematic deviations when phase differences are determined by means of harmonic analysis, e.g. with FFT analysis. The resulting errors depend clearly on the ratio between DC and AC amplitude, which is demonstrated at simulated and experimentally recorded temperature transients. Further experimental LT data obtained by different oscillating energy inputs showed a variety of possible shapes of transients with different DC components.
Systematic errors in the evaluation of uncorrected data from thermographic lock-in measurements
(2018)
Lock-in thermography (LT) is based on the correct evaluation of phase differences between the temperature oscillations at different surface regions of the object under test during periodic heating. Since the usual heating procedures contain a DC component, the actual heating pattern achieved is not harmonic. This causes systematic deviations when phase differences are determined by means of harmonic analysis, e.g. with FFT analysis. The resulting errors depend clearly on the ratio between DC and AC amplitude, which is demonstrated at simulated and experimentally recorded temperature transients. Further experimental LT data obtained by different oscillating energy inputs showed a variety of possible shapes of transients with different DC components.