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Quasicrystal stability and nucleation kinetics from density functional theory

Nature Physics volume 21, pages 980–987 (2025)Cite this article

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Abstract

The aperiodic order of quasicrystals bridges the amorphous and crystalline regime, so it has remained unclear whether quasicrystals are metastable or stable phases of matter. Density functional theory is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing size, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases, thus revealing that translational symmetry is not a necessary condition for the zero-temperature stability of inorganic solids. Although we found the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is limited by nucleation, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques broadly open the door to first-principles investigations into the structure–bonding–stability relationships of aperiodic materials.

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Fig. 1: Bulk and surface energies of iQCs from scooped nanospheres.
Fig. 2: DFT-calculated convex hull stability of iQCs.
Fig. 3: Size-dependent stability of iQC-ScZn7.33.
Fig. 4: Mixed thermodynamic and kinetic phase diagrams of competitive nucleation in the Sc–Zn system.

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Data availability

Raw DFT-FE input and output files for the large nanoparticle clusters have been deposited on the NOMAD repository at https://nomad-lab.eu/prod/v1/gui/search/entries/entry/id/Iy5_-DeDSoejmoOw7kuJ0mGgfp_u. All other data mentioned in the text are available in the manuscript or in the Supplementary Information.

Code availability

The DFT-FE is open-source code available via https://sites.google.com/umich.edu/dftfe.

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Acknowledgements

W.B. acknowledges H. Takakura and T. Yamada for providing atomistic structures of ScZn7.33 and YbCd5.7 quasicrystals. The work by W.B., S.T. and W.S. was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (Award No. DE-SC0021130). V.G. and S.D. give thanks for the support of the DOE, Basic Energy Sciences (Grant No. DE-SC0008637), which supported the development of DFT-FE. We acknowledge the Texas Advanced Computing Center at the University of Texas at Austin, which uses Grant Award TG-MAT210016 from the Extreme Science and Engineering Discovery Environment and Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support, National Energy Research Scientific Computing Center at Lawrence Berkeley National Laboratory, which is supported by the Office of Science of the DOE (Contract No. DE-AC02-05CH11231 using Award No. BES-ERCAP0020148), and the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE (Contract No. DE-AC05-00OR22725), for providing high-performance computing resources that have contributed to the research results.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

    Woohyeon Baek, Shibo Tan, Vikram Gavini & Wenhao Sun

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

    Sambit Das & Vikram Gavini

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  1. Woohyeon Baek
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  2. Sambit Das
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Contributions

Conceptualization: W.B. and W.S. Methodology: W.B., S.D., S.T., V.G. and W.S. Investigation: W.B., S.D. and S.T. Visualization: W.B. and S.T. Funding acquisition: W.S. and V.G. Supervision: W.S. Writing—original draft: W.B., S.T. and W.S. Writing—review and editing: W.B., S.D., S.T., V.G. and W.S.

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Correspondence to Wenhao Sun.

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Supplementary Information (download PDF )

Supplementary sections 1–12, Figs. 1–19 and Tables 1–6.

Supplementary Data (download ZIP )

Supplementary Data 1 Raw and relaxed crystal structure data and scooped nanospheres of Sc–Zn and Yb–Cd crystalline phases. Supplementary Data 2 Optimized norm-conserving Vanderbilt pseudopotential files used in this study for DFT simulation. Supplementary Data 3 Raw and relaxed atomic coordination data of scooped ScZn7.33 and YbCd5.7 nanospheres. Supplementary Data 4 Refined structure data of ScZn7.33 and YbCd5.7.

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Baek, W., Das, S., Tan, S. et al. Quasicrystal stability and nucleation kinetics from density functional theory. Nat. Phys. 21, 980–987 (2025). https://doi.org/10.1038/s41567-025-02925-6

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