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