Modelling and Theories of Alloy Phase Behavior

  • R. E. Watson
  • J. W. Davenport
  • M. Weinert
  • L. H. Bennett
Part of the NATO ASI Series book series (ASIC, volume 286)


It has been recognized since the early work of Hume-Rothery and others that many trends in alloy phase formation are readily understood in terms of physically plausible atomic parameters. For example, a substitutional alloy can only occur if there is not too great a difference in the sizes of the alloy constituents, so as not to require too great a cost in the elastic energy associated with deforming the lattice. This has led, in turn, to the introduction of so-called structural maps where two (or more) such atomic parameters are employed as the coordinates and well defined regions are observed to be associated with particular crystalline phases. These coordinates sometimes involve the difference in atomic parameters, such as the difference in the sizes of the constituent atoms, and sometimes involve an average, such as the average d-band occupancy of constituent transition element metals. An alternative approach to the emphasis on atomic parameters has been the consideration, as pioneered by Pearson, of how atoms are packed in some crystal structure and how this controls what the constituent atoms may be. Recently this has led to the utilization of Wigner-Seitz (sometimes called Voronoi or Dirichlet) constructs of the atomic cells in a crystal structure and, in turn, to the observation that sometimes two crystals which are nominally considered to have the same crystal structure according to normal crystallographic designation should, in fact, be considered to be different. The Wigner-Seitz cell constructs have also offered a framework for understanding trends in the magnetic and chemical properties of particular phases as well as making coordination between crystalline and glassy structures. Neither of the above approaches—correlations with atomic parameters or with packing considerations—provide numerical estimates of quantities of thermodynamic interest such as heats of formation. Such heats are being calculated with varying rigor and varying computational complexity ranging from model Hamiltonians employing atomic parameters to intricate electron band theory calculations. This chapter will attempt to provide the reader with a sense of some of successes and some of the problems when employing the above approaches to trace out trends in alloy phase behavior. Because of space limitations, this review will be highly selective.


Bond Line Atomic Parameter Interstitial Region Band Theory Total Energy Calculation 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • R. E. Watson
    • 1
  • J. W. Davenport
    • 1
  • M. Weinert
    • 1
  • L. H. Bennett
    • 2
  1. 1.Department of PhysicsBrookhaven National LaboratoryUptonUSA
  2. 2.National Bureau of StandardsGaithersburgUSA

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