Fig. 2: Operando visualization of the coexisting phases during the structural phase transformation under lithium intercalation.

a–o The 3D strain field inside a single Li_xNi_0.5Mn_1.5O₄ nanoparticle during the two-phase reaction induced by Li intercalation. The strain maps are extracted by inverting coherent X-ray diffraction data shown in Figs. 1c–j and S4. The semi-transparent isosurface portrays the particle shape, while the colored slices display the strain distribution, ε₁₁₁(r), on three chosen planes. We show the strain field, ε₁₁₁(r), as the local lattice constant compared to the average lattice constant, d_a, of the (111) planes between the fully charged, Li-poor phase (\({d}_{c}=8.00{\text {\AA}}\)) and the partially discharged Li-rich phase (\({d}_{d}=8.10{\rm A}\)), where \({d}_{a}=\left({d}_{c}+{d}_{d}\right)/2=8.05\,{\rm {A}}\) and \({\varepsilon }_{111}\left(r\right)=d\left(r\right)/{d}_{a}-1\). At 0% DoD in a), the particle has a uniform negative strain shown in dark purple, corresponding to the Li-poor phase with a small lattice constant, \({d}_{c}\). At the end of the two-phase reaction around 68.1% DoD in (o), the particle presents a uniform positive strain shown in light yellow, corresponding to the Li-rich phase with a large lattice constant d_d. \({Q}_{111}\) points along z.