Effective Cluster Interactions at Disordered Surfaces
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EFFECTIVE CLUSTER INTERACTIONS AT DISORDERED SURFACES V.Drchal,
P.Weinberger, TU Vienna, Austria;
J.Kudrnovsky, LUdvardi,
A.Pasturel,
Domaine University, St.Martin d'Heres, France ABSTRACT Effective
cluster
interactions
alloys are determined systems.
inhomogeneous system.
(ECI)
at
surfaces
Illustrative
results
of
of the
using the generalization
are
disordered
substitutionally
TB-LMTO-CPA method
reported
for
the
(Ag,Pd)
to
alloy
INTRODUCTION properties
Many physical
related to present
or expected
future high
technologies
are conseqences of the semi-inifinite nature of real solid systems. Real in this context means that the top atomic layers of such a system can be formed by a material
(element)
other
than
the
composition of a particular material
bulk in the
material surface
or
also
that
the
near region can
actual
be different
from the one deep inside the system. Many technologically important binary alloys for example show surface segregation, which for different surfaces of one and the same
material
catalytic
can be of different nature. Famous
systems such as for
example Ni/Pt alloys fall in this category. In the present paper methods culate
the
necessary
electronic for
structure and
a statistical
parameters of the
mechanical
study
of alloy
to cal-
effective Ising Hamiltonian surfaces
with concentration
gradients are presented. THEORETICAL APPROACH Let
be the Hamiltonian in the orthogonal muffin-tin orbital (MTO) re-
H L, tL
written usually as
presentation
JL, VL'
H
~~~~ = t
R6SL, /2{S~~ 0 L +AX (-
RL 6
1 •.,%i-L,
^ /2
(1)
XL,,_5tL,
where X denotes atomic sites and L = (1m) angular momenta. The quantities X = C, A, y are the so-called ements X XL
.
potential parameters which are diagonal
matrices
with el-
For z = E - ib, 8 > 0 , the potential function P°(z) is P 0 (z)= (z - C) { A - Y (z - C) }I-.
The canonical structure constants ments SoL,'L' = system and
hence are
presentation
to
So in (1) are represented
(2) by a matrix of ele-
S0(1-l') , which depend only on the lattice structure of the non-random.
the so-called
most
By switching localized
Mat. Res. Soc. Symp. Proc. Vol. 253.
from the
MTO
orthogonal
representation
1992 Materials Research Society
MTO
re-
characterized
370
by a non-random site- and angular momentum diagonal matrix j3 ( P.1 = 1P, V 3 ), the Green's function in the original representation, G(z) = (z - H)" , is related to the Green's function in
the new representation,
g(z), by a simple
scal-
ing transformation [1,2]
g(z) =
(P(z)
-
G(z) = X(z) + p(z) g(z) ii(z) P°(z))', S )" , P(z) = P°(z) (1 - 13
X(z) = A-" 0,111= n I
Let L = {
a lattice
vector
= c
aII E
13)
-
}
lattice
atomic position vector I and
( y
I+ n 2
two-dimensional
primitive
2
L.
S = S°(1
p.(z) = (dP(z)/dz)"/
,
13S')-',
2
(4) (5)
.
be the two-dimensional lattice spanned by the
vectors +
ii(z)
(3)
a I and
a2
.
then
quite
clearly
each
can be expressed in terms of a vector c
a
By neglecting
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