Independent component analysis combined with Laplace inversion of spectrally resolved spin-alignment echo/T ₁ 3D ⁷Li NMR of superionic Li₁₀GeP₂S₁₂

Abstract

The use of independent component analysis (ICA) for the analysis of two-dimensional (2D) spin-alignment echo–T 1 7Li NMR correlation data with transient echo detection as a third dimension is demonstrated for the superionic conductor Li10GeP2S12 (LGPS). ICA was combined with Laplace inversion, or discrete inverse Laplace transform (ILT), to obtain spectrally resolved 2D correlation maps. Robust results were obtained with the spectra as well as the vectorized correlation maps as independent components. It was also shown that the order of ICA and ILT steps can be swapped. While performing the ILT step before ICA provided better contrast, a substantial data compression can be achieved if ICA is executed first. Thereby the overall computation time could be reduced by one to two orders of magnitude, since the number of computationally expensive ILT steps is limited to the number of retained independent components. For LGPS, it was demonstrated that physically meaningful independent components and mixing matrices are obtained, which could be correlated with previously investigated material properties yet provided a clearer, better separation of features in the data. LGPS from two different batches was investigated, which showed substantial differences in their spectral and relaxation behavior. While in both cases this could be attributed to ionic mobility, the presented analysis may also clear the way for a more in-depth theoretical analysis based on numerical simulations. The presented method appears to be particularly suitable for samples with at least partially resolved static quadrupolar spectra, such as alkali metal ions in superionic conductors. The good stability of the ICA analysis makes this a prospect algorithm for preprocessing of data for a subsequent automatized analysis using machine learning concepts.