All codes necessary are available via GitHub (https://github.com/liushuhui84/CalculateStrain).

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Author notes

1. These authors contributed equally: Weijue Wang, Hongbin Xu

Authors and Affiliations

1. State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

   Weijue Wang  (王玮珏), Xiaofeng Yang  (杨小峰), Wei Liu  (刘伟), Yanqiang Huang  (黄延强) & Tao Zhang  (张涛)

2. University of Chinese Academy of Sciences, Beijing, China

   Weijue Wang  (王玮珏), Xiaofeng Yang  (杨小峰), Wei Liu  (刘伟), Yanqiang Huang  (黄延强) & Tao Zhang  (张涛)

3. Department of Chemistry and Guangdong Provincial Key Laboratory of Catalytic Chemistry, Southern University of Science and Technology, Shenzhen, China

   Hongbin Xu  (许泓斌) & Yang-Gang Wang  (王阳刚)

4. School of Railway Intelligent Engineering, Dalian Jiaotong University, Dalian, China

   Shuhui Liu  (刘淑慧)

Contributions

W.L., Y.H. and T.Z. conceived this project and supervised the study. W.W. performed the material synthesis, microscopy, spectroscopy and other experiments. W.W., X.Y. and W.L. performed the data analysis. H.X. and Y.-G.W. conducted DFT calculations. S.L. and W.L. developed the method for atom displacement analysis. W.W., X.Y., W.L., Y.-G.W. and Y.H. wrote the manuscript, with the help of the other authors.

Corresponding authors

Correspondence to Wei Liu  (刘伟), Yang-Gang Wang  (王阳刚), Yanqiang Huang  (黄延强) or Tao Zhang  (张涛).

Competing interests

The authors declare no competing interests.

Peer review information

Nature thanks Gianfranco Pacchioni, Marc Willinger and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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