Surface excess free energies and equilibrium Wulff shapes in variable chemical environments at finite temperatures

Mujan N. Seif, Matthew J. Beck

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Burgeoning interest in nanoparticles across a number of distinct fields has spurred broad investigation into the optimization of particle shape and surface chemistry. Here we demonstrate the application of DFT and DFPT calculations to compute bulk reference free energies and surface excess free energies accounting for vibrational and, where appropriate, configurational entropies of solid particles and particle surfaces. Using these results we construct “particle configuration maps”—graphical maps of the equilibrium shape and surface chemistry of particles over a range of temperatures and environmental conditions. Applied to W particles in O- or Ba/O-containing environments (a model system relevant to thermionic dispenser cathodes with critical applications in vacuum electronic devices) these maps highlight the critical role that Ba plays in controlling both the shape and surface chemistry of W particles in application-relevant conditions. These system-specific findings demonstrate the broad power of DFT+DFPT computed particle configuration maps: revealing connections between and insight into particle behavior and properties as a function of experimentally-relevant conditions.

Original languageEnglish
Article number148383
JournalApplied Surface Science
StatePublished - Feb 28 2021

Bibliographical note

Publisher Copyright:
© 2020


  • Equilibrium Wulff shape
  • High temperature surface energies
  • Surface energy
  • Tungsten

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Surfaces, Coatings and Films
  • Surfaces and Interfaces


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