Fig. 3

Activeness of each particle. a Voxel segmentation to define individual particles. Scale bar, 500 nm. b Volume distributions (black solid line with scatter) of individual particles shown in Fig. 2 and the fraction (bar plot) of inactive (magenta bar, <15% of Li _β FePO₄) and active (olive bar, 15–100% of Li _β FePO₄) particles as a function of particle volume with an increment of 200 voxels’ volume. Averaged particle volume in each range also shown. Each voxel has a volume of 6.7 × 6.7 × 6.7 nm³. The experimental error bars are calculated assuming a binomial distribution (active or inactive) taken at one standard deviation. c Compositional analysis based on the dimensions of each plate, comparing the facet area with thickness. The optical densities (ODs) of voxels along the particle thickness direction were averaged out across whole large facet. The thickness of the particle was calculated by the full-width-half-maxima of the averaged OD. The bar plots have the same color definition as b