Learning lattice parameters from powder X-ray diffraction data using invariants

Hofgard, E.; Min, K.; Segal, N.; Mittan-Moreau, D.W.; Tehrani, A.M.; Oklejas, V.; Gómez-Bombarelli, R.; Nigam, J.; Paley, D.W.; Brewster, A.S.; Smidt, T.

doi:10.1107/S2053273326010284

Figure 4
Example interpolation between a cubic and triclinic lattice and the corresponding change in bispectrum and S⁶ distance. The interpolation parameter α linearly deforms the lattice in real space. While the bispectrum varies smoothly in the Euclidean ( L²) norm along this path, distances computed in reduced-cell representations (e.g. S⁶) can exhibit non-smooth behavior due to changes in the chosen reduced basis during lattice reduction. Note that intermediate lattices are also triclinic, as the interpolation does not enforce any symmetry constraints.

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ISSN: 2053-2733

Volume 83| Part 1| January 2027|

https://doi.org/10.1107/S2053273326010284

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