Real-space tight-binding approach to stability and order in substitutional multicomponent alloys

Abstract

A real-space approach based on the tight-binding approximation for studying electronic structure properties and stability and order in substitutional multicomponent alloys is presented. First, for a chemically random alloy based on a periodic lattice, we show that the coherent potential approximation equations can be solved self-consistently in real space with the same accuracy currently achieved in reciprocal space. The resulting one-electron Green function is given by a continued fraction expansion, and this analytic form can be conveniently used to determine alloy properties, and in particular the energetics. Second, combined with an orbitalpeeling technique, this method allows in a very efficient way the calculation of the effective cluster interactions which enter the expression of the configurational part of the total energy for describing order-disorder phenomena in alloys. Finally, we present some applications and briefly discuss the possible extensions of this approach.

A first-principles approach to modeling alloy phase equilibria

“…6,44 The method provides a formalism for expressing the energy of different atomic arrangements on an underlying lattice framework in terms of an expansion of pair and manybody cluster interaction parameters. These parameters are derived from electronic pertubation theories 1,5,[45][46][47][48][49] or by fitting to results of first-principles calculations of alloy energetics 2-4 . Recently, Zunger, Wolverton, and collaborators developed a first-principles methodology incorporating a model for composition-dependent elastic strain energy (associated with atomic size differences) within the cluster expansion framework for alloy energetics described above.…”

Direct Energy Conversion for Fast Reactors

“…However, more recently, theoretical studies [van Ek, 1996;] have shown that alloying effects could be used to improve the thermoelectric properties of FeSi 2 . Recent developments in theoretical predictions of alloy stability and transport properties [Turchi, 1995[Turchi, , 1997] will allow us to improve the performance at high temperature of pseudo-binary alloys such as (Fe,Os,Ru)Si 2 . The same theoretical technology which is based on a real-space electronic structure description of multi-component alloys, will be also applicable to other geometries such as thin films and quantum wells.…”

“…Recently a real-space version of these tools have been implemented [Turchi, 1995[Turchi, , 1997] to study systems with low symmetry (such as in the presence of interfaces or surfaces) or with no symmetry at all (such as in the case of amorphous materials). These new updates will be efficiently applicable to the prediction of materials properties, and in particular electronic transport, in thin films materials, and in two-dimensional quantum well devices.…”

Tight-binding modeling of interstitial ordering processes in metals: Application to zirconium hydrides

“…The success of the original TB-GPM method then sparked a lot of studies in the alloy literature, among which are various attempts to put together a real-space way of solving the inhomogeneous CPA equations with recursion for both diagonal and off-diagonal disorder (Shiba approximation [19]) and extension to multicomponent alloys and transport (Kubo-Greenwood) [20][21][22]. Indeed, a main advantage of such a real-space approach is that it can be easily applied to finite systems (such as nanoalloys) or amorphous alloys such as NiZr [23].…”