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

R. Evans, P. Lloyd, Mujibur Rahman Mujibur

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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
Volume9
Issue number10
DOIs
Publication statusPublished - 1979

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Phase stability
brasses
Brass
Free energy
Electrons
free energy
Atoms
electrons
Binary alloys
binary alloys
free electrons
pseudopotentials
suggestion
Carrier concentration
atoms
Crystal structure
Crystals
crystal structure
crystals
brass

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Metals and Alloys

Cite this

On the origin of the Hume-Rothery rules for phase stability in α and β brasses. / Evans, R.; Lloyd, P.; Rahman Mujibur, Mujibur.

In: Journal of Physics F: Metal Physics, Vol. 9, No. 10, 006, 1979, p. 1939-1960.

Research output: Contribution to journalArticle

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