Meng, QingpingWu, LijunWelch, David O.Tang, MingZhu, Yimei2018-07-162018-07-162018Meng, Qingping, Wu, Lijun, Welch, David O., et al.. "Non-uniform Stress-free Strains in a Spherically Symmetrical Nano-sized Particle and Its Applications to Lithium-ion Batteries." <i>Scientific Reports,</i> 8, (2018) Springer Nature: https://doi.org/10.1038/s41598-018-23320-7.https://hdl.handle.net/1911/102440The stress-free strain originated from local chemical composition and phase transformation can significantly alter the microstructures of materials; and then affect their properties. In this paper, we developed an analytical method to calculate stress-strain field due to the non-uniform stress-free strain in a spherically symmetrical particle. Applying the method to a lithium ion (Li-ion) battery electrode, the evolution of Li-ion concentration and strain field during the lithiation process is studied. Our studies reveal that the maximum strain in the electrode generally occurs on surface of sample, and is mainly dependent on the difference of Li-ion concentration of surface and of center in sample. Decreasing the difference of Li-ion concentration can efficiently decrease the maximum strain so that cracks of electrodes can been prevented. Our analytical results provide a useful guidance for practical applications of energy storage materials.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.Journal articlehttps://doi.org/10.1038/s41598-018-23320-7