On the origin of the Hume-Rothery rules for phase stability in α and β brasses

R. Evans*, P. Lloyd, Mujibur Rahman Mujibur

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


The authors investigate the Blandin-Heine-Stroud-Ashcroft suggestion that the Hume-Rothery rules for the phase stability of alpha and beta brasses arise as a consequence of the rapid variation of the free electron density response function in the neighbourhood of 2KF. Using pseudopotential theory the authors show that the most structure-sensitive contribution to the free energy of a random binary alloy is the one-electron contribution arising from the virtual crystal bandstructure of neutral pseudo-atoms. The calculated difference in the one-electron contribution to the free energy between different crystal structures shows rapid variations at concentrations which are characterised by particular electron per atom ratios Z for which 2KF is equal to the first or second reciprocal lattice vector of the alloy.

Original languageEnglish
Article number006
Pages (from-to)1939-1960
Number of pages22
JournalJournal of Physics F: Metal Physics
Issue number10
Publication statusPublished - 1979
Externally publishedYes

ASJC Scopus subject areas

  • General Engineering
  • Physics and Astronomy (miscellaneous)
  • Metals and Alloys


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