A Tight-Binding-Bond Approach to Interatomic Forces in Disordered Transition Metal Alloys
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A TIGHT-BIDNDING-BOND APPROACH TO INTERATOMIC IFORCES IN DISORDERED TRANSITION METAL ALLOYS A. PASTUREL Laboratoire de Thermodynamique et Physico-Chimie Mdtallurgiques, ENSEEG BP75, 38402 Saint Martin d' H~res, France
ABSTRACT A tight-binding-bond approach to interatomic forces in disordered transition metalAluminium alloys is presented. The bond-order is calculated on a Bethe lattice reference system, well adapted to topologically disordered alloy. It is shown that the bond-order depends strongly on the strength of the pd hybridization in the AB alloy, leading to non additive potentials with a strong preference for the formation of pair of unlike atoms and short bond-distances in the A-B pairs. This is illustrated by studying the structural properties of liquid A18 0 Ni 2 0 and Al8oMn20 alloys using molecular dynamics simulations and by comparing our results with the available experimental ones.
TIGHT-BINDING-BOND APPROACH TO INTERATOMIC FORCES With the development of simulation techniques in the past two decades, there have been many studies of the properties of various liquid systems. However, an accurate simulation of the properties of transition metals and of their alloys is still a challenging problem since bonding is not well described by currently available pair and embedded-atom potentials. Very recently, a bond-order approach to interatomic interactions has been proposed [1]. This bondorder approach is derived from tight-binding Htckel theory in which the quantum-mechanical bond energy in a given pair of atoms i and j is written in the chemically intuitive form:
U',.ni(,j) = aI(a'a(i).fi(j) = 2X Hiajp.ia ,f a ,P
(1)
where Hia.jp is the Slater-Koster bond integral matrix linking the orbitals ct3 on sites i and j together.
e is the corresponding bond-order matrix whose elements give the difference
between the number of electrons in the bonding
-hia + jB)
and anti-bonding-L i't-
jiP)
states. Bond-order potentials are similar to the embedding potentials in that the bond in a given pair of atoms is considered as embedded in and depending on the local atomic environment . Thus eq.(I) represents only formally a pair interaction and depends via the bond-order on many-atom effects. This dependence can be explicitely shown by using the recursion method to write the bond-order as an integral over the imaginary part of the difference of two continued fractions: 3ia1,j
[G0
(E)
with:
G;0(E)IdE -
=
G 0(E)=(W'j(E-HitIj1Y')
(2)
(3)
Mat. Res. Soc. Symp. Proc. Vol. 291. ©1993 Materials Research Society
160
= I-I i ± jf). The continued-fraction representation leads to an expansion of
where I0
the bond-order in terms of many-body cluster interactions. For instance, the first level of the continued fraction corresponds to the bond-order in an isolated dimer, the second level reflects the influence of the first shell neighbors and so on. In their study of structural stability in crystalline transition metals, Pettifor and Aoki [2] have shown that the cubic (bcc) versus cubic (fcc) stability depends on t
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