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From entropy to compression: Competing thermodynamic drivers of structural transitions in transition metals

S. Azadi1,2,3,*, S. M. Vinko2, A. Principi1, T. D. Kühne3,4,5, and M. S. Bahramy1

  • *Contact author: sam.azadi@manchester.ac.uk
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Phys. Rev. Research 8, 043154 – Published 12 November, 2026

DOI: https://doi.org/10.1103/918j-rz63

Abstract

Structural phase transitions in metals are conventionally described in terms of external pressure and density, while electronic entropy is typically regarded as a secondary correction to the free energy. Here, we show that electronic entropy constitutes a thermodynamic control parameter of comparable importance to external pressure in determining structural stability. Using finite-temperature density functional theory, we construct pressure–electronic-temperature phase diagrams for 15 transition metals spanning the hcp, fcc, and bcc families and systematically investigate the competition between compressive and entropic contributions to the free energy. We find that increasing electronic entropy progressively reshapes the free-energy landscape, reducing structural competition and driving universal trends in phase stability across chemically diverse metals. In contrast, external pressure often acts in opposition, stabilizing structures that are suppressed by electronic excitation. The resulting phase behavior cannot be understood from pressure alone but emerges from the balance between these two thermodynamic driving forces. Our results establish a general framework for understanding structural transformations in electronically excited matter, extend the conventional pressure-temperature description of metals by explicitly incorporating electronic entropy, and provide quantitative predictions for ultrafast laser and x-ray free-electron laser experiments operating far from equilibrium.

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Phys. Rev. Research 8, 043154– Published 12 November, 2026
  • Received 18 May 2026
  • Accepted 29 September 2026
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