Inter-crystallite Bragg scattering decodes the nanostructure of hard carbon for sodium storage and beyond

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Abstract

Characterising short-range ordered structures remains a persistent challenge in materials science. Hard carbon, a predominant anode for sodium-ion batteries, exemplifies this barrier to rational development. Here, we resolved the atomic structure of hard carbon and its sodium storage sites using ex situ and in situ neutron diffraction, underpinned by a theoretical advance in crystallography. We identified inter-crystallite Bragg scattering as a non-negligible contributor to polycrystalline diffraction when crystallite sizes fall below ~10 nm, establishing the corresponding "Randomly Parallel Pairs" model for crystallographic analysis. The nanostructure of hard carbon was quantitatively reconstructed using only 10 isolated atoms, and its evolution during sodiation was decoded. These insights inform three principles for materials design and clarify the mechanistic basis for achieving theoretical capacities up to 744 mAh g⁻¹. More generally, this work demonstrates the applicability of the Rietveld method down to the 1 nm scale, establishing a new paradigm for characterising short-range ordered systems.

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