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# Three-dimensional atomic packing in amorphous solids with liquid-like structure

## Abstract

Liquids and solids are two fundamental states of matter. However, our understanding of their three-dimensional atomic structure is mostly based on physical models. Here we use atomic electron tomography to experimentally determine the three-dimensional atomic positions of monatomic amorphous solids, namely a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into pentagonal bipyramid networks with medium-range order. Molecular dynamics simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic metallic liquids, which rapidly grow in size and form more icosahedra during the quench from the liquid to the glass state. These results expand our understanding of the atomic structures of amorphous solids and will encourage future studies on amorphous–crystalline phase and glass transitions in non-crystalline materials with three-dimensional atomic resolution.

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• ### Revealing the role of liquid preordering in crystallisation of supercooled liquids

Nature Communications Open Access 04 August 2022

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## Data availability

The raw and processed experimental data are available at https://github.com/AET-AmorphousMaterials/Supplementary-Data-Codes. The 3D atomic coordinates of the Ta thin film and Pd1 and Pd2 nanoparticles have been deposited in the Materials Data Bank (www.materialsdatabank.org) with Materials Data Bank identification numbers TaXX00001, PdXX00001 and PdXX00002, respectively.

## Code availability

The MATLAB source codes for the RESIRE reconstruction and data analysis used in this work are available at https://github.com/AET-AmorphousMaterials/Supplementary-Data-Codes.

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## Acknowledgements

We thank J. Ciston for help with data acquisition and X. Tian for help with data analysis. This work was primarily supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering under award no. DE-SC0010378. We also thank the support by STROBE: a National Science Foundation Science and Technology Center under award no. DMR-1548924. Some of the data analysis was partially supported by the National Science Foundation Designing Materials to Revolutionize and Engineer our Future (DMREF) programme under award no. DMR-1437263 and the Army Research Office Multidisciplinary University Research Initiative (MURI) programme under grant no. W911NF-18-1-0431. The ADF-STEM imaging with TEAM I was performed at the Molecular Foundry, which is supported by the Office of Science, Office of Basic Energy Sciences of the US Department of Energy under contract no. DE-AC02-05CH11231.

## Author information

Authors

### Contributions

J.M. conceived the idea and directed the project; A.K.S. synthesized the amorphous Ta thin film; Y.N. and O.C. synthesized the amorphous Pd nanoparticles; J.Z., A.K.S., P.E. and J.M. discussed and performed the AET experiments of the amorphous materials; and M.P., Y. Yuan, S.J.O. and J.M. developed the 3D reconstruction algorithm. Y. Yuan, D.S.K., D.J.C., F.Z., Y. Yang and J.M. performed image reconstruction and atom tracing, analysed the data and interpreted the results; D.S.K. and J.M. discussed and performed the MD simulations. Y. Yuan, D.S.K. and J.M. wrote the manuscript. All authors commented on the manuscript.

### Corresponding author

Correspondence to Jianwei Miao.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Materials thanks Matthew Kramer and Yong Yang for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Table 1 and Figs. 1–22.

### Supplementary Video 1

Experimental 3D atomic model of the amorphous Ta thin film. The reconstructed volume of the thin film consists of 6,615 disordered atoms (in blue) with several crystal nuclei of 1,669 atoms on the surface (in grey).

### Supplementary Video 2

Experimental 3D atomic model of the amorphous Pd1 nanoparticle. The nanoparticle consists of 51,170 disordered atoms (in green) with several small crystal nuclei of 1,138 atoms on the surface (in grey).

### Supplementary Video 3

Experimental 3D atomic model of the amorphous Pd2 nanoparticle. The nanoparticle consists of 74,893 disordered atoms (in green) with several small crystal nuclei of 1,345 atoms on the surface (in grey).

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Yuan, Y., Kim, D.S., Zhou, J. et al. Three-dimensional atomic packing in amorphous solids with liquid-like structure. Nat. Mater. 21, 95–102 (2022). https://doi.org/10.1038/s41563-021-01114-z

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• DOI: https://doi.org/10.1038/s41563-021-01114-z

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