in addition, fig. 7 shows that the ni-rich particles are surrounded by the o-rich particles, and the o-rich particles are uniformly distributed in the x direction. the average grain size of the linio2 is calculated to be around 20nm, which is smaller than the width of the hexagonal close-packed layer (d) of 11.1 nm. as a result, the energy of the particle would be more easy to release and facilitate the crack propagation. this model is a good explanation to the micro-crack propagations, which could be the crack generation mechanism in the layered nanocrystals that were observed by the previous works [ 25, 26, 27, 28, 29 ]. the average contraction in y direction ( fig. 6f ) is calculated to be ~5.8%, and the contraction in the x direction ( fig. 6g ) is ~3.9%. the nanodomain in the ncm811 is unstable at the delithiated states and cause the nanodomain shrink, which could be the driving force for the crack propagations. the contraction could be the reason for the nanodomain shrink and contribute to the micro-crack generation in this nanostructured material. further, the contraction of ncm811 could cause the disconnection of the nanodomain that could lead to the crack propagation. the contraction in x direction is caused by the rapid phase separation, and the contraction in y direction is caused by the anisotropic phase transformation of ni-rich and o-rich particles. 6f ) is calculated to be ~3.6%, and the contraction in the x direction ( fig. 6g ) is ~5.8%.

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