A machine learning protocol for revealing ion transport mechanisms from dynamic NMR shifts in paramagnetic battery materials

Abstract

Solid-state nuclear magnetic resonance (ssNMR) provides local environments and dynamic fingerprints of alkali ions in paramagnetic battery materials. Linking the local ionic environments and NMR signals requires expensive first-principles computational tools that have been developed for over a decade. Nevertheless, the assignment of the dynamic NMR spectra of high-rate battery materials is still challenging because the local structures and dynamic information of alkali ions are highly correlated and difficult to acquire. Herein, we develop a novel machine learning (ML) protocol that could not only quickly sample atomic configurations but also predict chemical shifts efficiently, which enables us to calculate dynamic NMR shifts with the accuracy of density functional theory (DFT). Using structurally well-defined P2-type Na_2/3(Mg_1/3Mn_2/3)O₂ as an example, we validate the ML protocol and show the significance of dynamic effects on chemical shifts. Moreover, with the protocol, it is demonstrated that the two experimental ²³Na shifts (1406 and 1493 ppm) of P2-type Na_2/3(Ni_1/3Mn_2/3)O₂ originate from two stacking sequences of transition metal (TM) layers for the first time, which correspond to space groups P6₃/mcm and P6₃22, respectively. This ML protocol could help to correlate dynamic ssNMR spectra with the local structures and fast transport of alkali ions and is expected to be applicable to a wide range of fast dynamic systems.

Fig. 1. Schematic illustration of the machine learning (ML) protocol for calculating the dynamic NMR chemical shifts.

Fig. 2. (a) Illustration of the NN-NMR model for predicting chemical shifts. A Na⁺ local environment in the supercell model of P6₃/mcm Na_2/3(Mg_1/3Mn_2/3)O₂ is shown as an example, and the No. of nodes in each layer of the NN-NMR model was labeled. (b) The testing set RMSEs between ²³Na δ_DFT and δ_NN of P2-Na_2/3(Mg_1/3Mn_2/3)O₂ evolute with the No. of dataset structures. The black error bars indicate the standard deviations (STDs) of the RMSEs. (c) The correlation of ²³Na δ_DFT and δ_NN. The dashed black line indicates a perfect correlation.

Fig. 3. (a) Histograms of the ²³Na δ_NN distribution of Na sites in P2-Na_2/3(Mg_1/3Mn_2/3)O₂. The black curves indicate the histogram outlines of the ²³Na δ_NN of P6₃/mcm and P6₃22 Na_2/3(Mg_1/3Mn_2/3)O₂. The local structures of Na sites are inseted along with their shift histogram, and a scaled histogram for highlighting Na_Mg–Mg sites is also inseted. The averaged ²³Na δ_NN of space groups is indicated by the black vertical lines. The averaged δ_NN of the Na site and space group is labeled, and the occupation fractions of Na sites were labeled with numbers in brackets. The xy-plane ²³Na δ_NN distribution maps of (b) P6₃/mcm and (c) P6₃22 Na_2/3(Mg_1/3Mn_2/3)O₂. The dotted circles and rhombi indicate Na sites and unit cells, respectively.

Fig. 4. (a) PXRD of P2-type Na_2/3(Ni_1/3Mn_2/3)O₂ and its refinement. The fitting good parameters R_p and R_wp are labeled. (b) The ²³Na MAS ssNMR spectra of P2-type Na_2/3(Ni_1/3Mn_2/3)O₂ and fitting curves, in which the peaks of isotropic shifts are labeled with “+”, and the shift and its fractions are labeled with colored numbers without and with brackets, respectively. (c) Supercell structures of Na_2/3(Ni_1/3Mn_2/3)O₂ and their relative total energies (RTEs). For clarification, only underlayer Na prisms were shown in all structures.

Fig. 5. (a) Histograms of the ²³Na δ_NN distribution of Na sites in P2-Na_2/3(Ni_1/3Mn_2/3)O₂. The black curves indicate the histogram outlines of the ²³Na δ_NN of P6₃/mcm and P6₃22 Na_2/3(Ni_1/3Mn_2/3)O₂. The local structures of Na sites are inseted along with its shift histogram. The averaged ²³Na δ_NN of space group is indicated by black vertical lines. The number of averaged δ_NN for the Na site and space group is labeled, and the occupation fractions of Na sites are labeled with the numbers in brackets. The xy-plane ²³Na shift distribution maps of (b) P6₃/mcm and (c) P6₃22 of P2-Na_2/3(Ni_1/3Mn_2/3)O₂. The dotted circles and rhombi indicate Na sites and unit cells, respectively.