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Free electron to electride transition in dense liquid potassium

Abstract

At high pressures, simple metals such as potassium have a rich phase diagram including an insulating electride phase in which electrons have a localized, anionic character. Measurements in the liquid phase have shown a transition between two states, but experimental challenges have prevented detailed thermodynamic measurements. Using potassium as an example, we present numerical evidence that the liquid–liquid transition is a continuous transformation from free electron to electride behaviour. We show that the transformation manifests in anomalous diffusivity, thermal expansion, speed of sound, coordination number, reflectivity and heat capacity across a wide range of pressures. The abnormalities stem from a significant change in the local electronic and ionic structure. Although primarily a pressure-induced phenomenon, there is also a thermal expansion anomaly. By establishing the electride nature of the high-pressure liquid phase, we resolve the long-standing mystery of how a liquid can be denser than a close-packed solid. Our work is relevant for high-pressure thermodynamic properties of all alkali metal liquids.

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Fig. 1: Phase diagram of potassium from MLMD simulations.
Fig. 2: Thermodynamic quantities of liquid potassium, shown as a function of pressure for selected temperatures.
Fig. 3: Dynamical properties of liquid potassium from MLMD simulations.
Fig. 4: Structural properties of liquid potassium from AIMD simulations.
Fig. 5: Electronic properties of liquid potassium.

Data availability

All the data presented in Figs. 15 are available as source data. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

Code is available at https://github.com/zhaolongxjtu/KMLP.

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Acknowledgements

H.Z. and G.J.A. acknowledge the ERC project HECATE for funding. V.N.R. thanks the UK’s EPSRC for CM-CDT studentships. H.Z. and X.D. thank the National Natural Science Foundation of China (51931004 and 51871177) and the 111 project 2.0 (BP2018008). We are grateful for computational support from the UK national high performance computing service (ARCHER) and the UK Materials and Molecular Modelling Hub, which is partially funded by EPSRC (EP/P020194), access for both of which was obtained via the UKCP consortium and funded by EPSRC grant no. EP/P022561/1.

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H.Z., V.N.R., A.H. and G.J.A. conceived the research. H.Z., V.N.R., A.H. and L.Z. conducted the simulation. S.S. and G.J.A. created the two-state liquid model. All the authors participated in the analysis and interpretation of the results as well as writing of the manuscript.

Corresponding authors

Correspondence to Long Zhao or Graeme J. Ackland.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Takanori Hattori, Artem Oganov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20 and Notes 1–8.

Supplementary Video 1

Liquid potassium ELF at 22.8 GPa and 650 K. The ELF (0.70) for a liquid is challenging to summarize: here one snapshot is scanned over 100 ELF surfaces along the z direction.

Source data

Source Data Fig. 1

Plotted data points.

Source Data Fig. 2

Plotted data points.

Source Data Fig. 3

Plotted data points.

Source Data Fig. 4

Plotted data points.

Source Data Fig. 5

Plotted data points and single images for Fig. 5c–f.

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Zong, H., Robinson, V.N., Hermann, A. et al. Free electron to electride transition in dense liquid potassium. Nat. Phys. 17, 955–960 (2021). https://doi.org/10.1038/s41567-021-01244-w

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