Nickel-rich layered oxide cathodes promise ultrahigh energy density but is plagued by the mechanical failure of the secondary particle upon (de)lithiation. Existing approaches for alleviating the structural degradation could retard pulverization, yet fail to tune the stress distribution and root out the formation of cracks. Herein, we report a unique strategy to uniformize the stress distribution in secondary particle via Kirkendall effect to stabilize the core region during electrochemical cycling. Exotic metal/metalloid oxides (such as Al₂O₃ or SiO₂) is introduced as the heterogeneous nucleation seeds for the preferential growth of the precursor. The calcination treatment afterwards generates a dopant-rich interior structure with central Kirkendall void, due to the different diffusivity between the exotic element and nickel atom. The resulting cathode material exhibits superior structural and electrochemical reversibility, thus contributing to a high specific energy density (based on cathode) of 660 Wh kg⁻¹ after 500 cycles with a retention rate of 86%. This study suggests that uniformizing stress distribution represents a promising pathway to tackle the structural instability facing nickel-rich layered oxide cathodes.

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. However, current GNN implementations assume ideal distributed scenarios and ignore link fluctuations that occur due to environment or human factors. In these situations, the GNN fails to address its distributed task if the topological randomness is not considered accordingly. To overcome this issue, we put forth the stochastic graph neural network (SGNN) model: a GNN where the distributed graph convolutional operator is modified to account for the network changes. Since stochasticity brings in a new paradigm, we develop a novel learning process for the SGNN and introduce the stochastic gradient descent (SGD) algorithm to estimate the parameters. We prove through the SGD that the SGNN learning process converges to a stationary point under mild Lipschitz assumptions. Numerical simulations corroborate the proposed theory and show an improved performance of the SGNN compared with the conventional GNN when operating over random time varying graphs.