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Dynamic electron density as an order parameter for phase transitions: Evidence from α−KNO3

Anagha Ghosh1, Somnath Dey2,*, B. Viliam Hakala3, Hend Shahed3, Sander van Smaalen4, and Swastik Mondal1,5,†

  • *Present address: Department of Structure Analysis, Institute of Physics of the Czech Academy of Sciences, Prague 8 18221, Czech Republic.
  • †Contact author: swastik_mondal@cgcri.res.in
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APS Open Sci. 1, 000205 – Published 5 November, 2026

DOI: https://doi.org/10.1103/vjv9-twm9

Abstract

We report that topological features of the dynamic electron density provide a microscopic electronic order parameter that directly reflects the extent of structural change during a phase transition and offers insight into its underlying mechanism. Using multipole electron-density models derived from extensive high-resolution synchrotron x-ray diffraction datasets collected on α−KNO3 at 100, 200, 290, and 380 K, we reconstruct the thermally convoluted dynamic electron density at each temperature. It is found that its temperature evolution quantitatively captures the progressive suppression of local symmetry breaking as the system approaches the α→β phase transition. The topological descriptors of the electron density associated with the nitrate group exhibit a nonmonotonic temperature evolution with the initial inequivalence among the N–O bond electron densities undergoing an order-parameter-like collapse upon heating to 380 K, preceding the actual phase-transition temperature. These findings demonstrate that dynamic electron-density topology can provide valuable microscopic insight into structural phase transitions.

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APS Open Sci. 1, 000205– Published 5 November, 2026
Vol. 1
  • Received 3 February 2026
  • Accepted 13 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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