Adsorbate induced reconstruction of Ni (100)

Journal of Electron Spectroscopy and Related Phenomena, 38 (1986) 45-54 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

ADSORBATE

INDUCED RECONSTRUCTION

T.S. RAHMANI,

of Physics,

lDepartment *IGV/KFA

M. ROCCA*',

JUlich,

OF Ni( 100)

S. LEHWALD',

H. IBACH'

Kansas State University,

Postfach

1913,

45

D-5170

Jijlich

Manhattan

KS 66506, USA

(F.R. Germany)

ABSTRACT We have carried out a systematic lattice dynamical study of the ~(2x2) overlayer of oxygen, sulfur and carbon (nitrogen) on Ni(lOO). The model consists of nearest neighbour interactions between all atoms and an additional (attractive) interaction between the adsorbate atoms and the second neighbour substrate atom directly below, which consequently introduces internal stresses. We show that the relative strength of the internal stress and the coupling between the first and second layer nickel atoms determine whether the Ni(lOO) surface will reconstruct. The presence of the attractive force between the adsorbate atoms and the second layer nickel atoms allows us to explain the observed anomaly in the dispersion of the Rayleigh wave for the oxygen overlayer on Ni(lOO) and leads to a natural explanation for the reconstruction pattern observed in the presence of the carbon and nitrogen overlayers via softening of a substrate phonon.

1. INTRODUCTION In the past several years a number of experimental on the structure

and dynamics of the Ni(lOO) surface,

or in the presence

of ordered overlayers

we will be concerned

with two particular

which are (i) the anomalous

low freqency

and theoretical

have become available. intriguing

aspects

of the Rayleigh

In this paper

of these studies

surface phonon at the

zone boundary when the surface is covered with a ~(2x2) overlayer (ref. 1) and (ii) the reconstruction layer of carbon ysis

(ref. 2) and nitrogen

interaction

between the adsorbate

of the adsorbate

teraction

controls

of oxygen

of the nickel surface with a ~(2x2) over(ref. 3). Using a lattice

it will be shown that both phenomena

distance

studies

either in the clean form

have a common origin

dynamical

atom and the second layer substrate

to the surface and the strength

whether the phonon spectrum displays

anal-

in an attractive atom. The

of the attractive

anomalies

in-

or the sur-

face reconstructs. In previous

lattice dynamical

face phonon branches

*Permanent

address:

0368-2048/86/$03.50

a nearest

analyses

neighbour

of the experimentally central force model

observed

sur-

(ref. 4,5) was

Dipartimento di Fisica, Universitl degli Studi di Genova, Via Dodecanso 33, I-16100 Genova, Italy

0 1986 Elsevier Science Publishers B.V.

46 used. Within this model the softening could be described

of the Rayleigh wave at the zone boundary

by making the force constant

between the nickel atoms in the

first layer and the nickel atoms in the second layer rather small, namely 30 % of the bulk force constant. the dispersion

curves was obtained.

found necessary

surface

at the X-point

a reasonable

No reduction

of this force constant was

discovered

corresponds

of the surface

that the p4g(2x2)

to the displacement Brillouin

interactions

reconstruction

of sul-

of the car-

pattern of the A2-eigenmode

zone of the unreconstructed

face (ref. 5). Within this simple lattice dynamical neighbour

overall fit of

in order to reproduce the data for a ~(2x2) overlayer

fur. It was furthermore bon covered

With this assumption

~(2x2) sur-

model involving

nearest

only, this mode would become soft when the force con-

stant between the first layer nickel atoms and the second layer nickel atoms approaches

zero. While this simple lattice dynamical

lish a connection

between

remained problematic reduction

in the force constant.

bour interactions longer

the observed

in its physical

phonon anomaly

picture

with additional

attractive

propensity struction

parameter

of the adsorbate

when the distance

The paper is organized description

Green's

the results for the dispersion

and eventually becomes

on Ni(lOO).

spectral

is described

densities

section

to the discussion of the structure

2. (2x2) STRUCTURES Ordered

sponding

dynamiFourier

In section

of the reconstruction.

of (2x2) overlayers

These overlayers

We now turn to a surface.

of 25 % and 50 % of

with ~(2x2) overlayers

may be obtained

genides Te, Se, S and 0, each being positioned

(save for an overall

vertical

in the fourfold

is that of a ~(2x2) structure.

relaxation

corre-

with the chalcohollow site as

shown in Fig. la. Since the nickel atoms remain at their positions

tion pattern

nickel sur-

study. The final

on the Ni(lOO)

on Ni(lOO) are formed with coverages

Here we will be only concerned

to 50 % coverage.

clean surface

4

ON Ni(lOO)

structures

the adsorbate.

The lattice by employing

curves for the ~(2x2) oxygen covered

and compared to results of the previous

brief description

recon-

smaller.

in the third section.

face are presented is devoted

our study

of the surface

In the next section we provide a brief

of (2x2) overlayers

functions

no

layer. As will be seen the

of the adsorbate

cal model and our method of calculating transformed

the behaviour

phonon anomalies

as follows.

of the geometry

interactions

nickel atoms and the

small. Furthermore

controlling

from the surface

of the surface to display increases

it

second nearest neigh-

(and repulsive)

between the surface

next layer nickel atoms to become unphysically

is the distance

and the reconstruction

because of the required drastic

The new model involving

requires the force constant

will show that an important

model was able to estab-

as for the

(ref. 6)) the diffrac-

The unit cell of this structure

47

L

t1001 [llOl

/ \\ //

Fi

ElII 'R '\ t /' \/

b

a

Fig. 1. a) (100) surface with a ~(2x2) overlayer. The dashed line is the surface unit cell. b) Brillouin zone for the clean and ~(2x2) surface (full and dashed line, respectively).

contains

one adsorbate

face Brillouin

the chalcogenides both adsorbates

atom and two nickel atoms in each nickel layer. The sur-

zone is depicted

in Fig. lb. Overlayers

of the same type as with

can also be formed with carbon and nitrogen.

the nickel surface

reconstructs

to form a p4g(2x2)

(ref. 2,3). The unit cell is now as with a (2x2) overlayer. tions in the diffraction dicular

pattern

glide planes oriented

ture as originally

proposed

indicate the presence

extinc-

of two mutually

perpen-

The geometric

struc-

et al. (ref. 2) is shown in Fig. 2. AS

can be seen from the figure the reconstruction and clockwise

structure

Systematic

along the [loo] direction.

by Onuferko

However with

consists

of a counter

clockwise

rotation

of the nickel atoms around the adsorbate

atoms. Experi-

mental and theoretical

studies of the surface phonon dispersion

of this struc-

ture have been performed.

These results will be reported

tion. Here we are concerned

with the lattice dynamics

and the forces which drive the surface

in a separate

publica-

of the ~(2x2) structure

into the observed

reconstruction.

48 3. THE LATTICE

DYNAMICAL

The lattice proximation

dynamics

MODEL of the nickel surface

The Hamiltonian

using pair potentials.

where uu is the ath Cartesian K in the layer arbitrarily

component

tz with the position

chosen

pair potential

origin,

is treated

in the harmonic

therefore

of the displacement

vector LI connecting

ap-

assumes the form

of the atom labeled

the unit cell with an

M is the mass of the atom and P its momentum.

The

is given by

o,,(ij) = 6ij z, Ka,(ij')

- (I-'ij) K,B(ij)

J with the effective

K,,(ij)

=

L

force constant

K as

6as + (‘Pyj -'j

Iri

I

Here oij and myj are the first and second derivations

of the pair potential

and

fi is the unit vector from atom i to atom j. As in the previous interactions

only are assumed

Equilibrium tential

conditions

vanishes,

the minimum

of the pair potential

by including

connecting

for a reasonable

the second

of the pair poposition

neighbour

interaction

bility criterion

of the bulk phonon spectrum

ferent atoms.

(ref. 7)

between the adsorbate

atom and

With such second neighbour

interac-

of the potentials

need no longer vanish.

The sta-

that the net force on each atom must vanish generates

between the first derivatives

at

the atom to its next neighbour.

representation

layer nickel atom underneath.

tions the first derivatives

neighbour

for atoms in the second nickel layer and below.

then require that the first derivative

For atoms near the surface we go beyond this simple model

the second

relations

study of this system nearest

i.e. each atom in the bulk has its equilibrium

This model suffices of nickel.

lattice dynamical

of the pair potentials

In our model we assume an attractive

interaction

a set of

connecting

dif-

between the ad-

sorbate and the second layer nickel atom (vi2 > 0). This requires a repulsive interaction

between

the adsorbate

atom and the first layer nickel atom ($2

<

0) (Fig. 3). The force on the first layer nickel atoms then needs to be balanced by a repulsive may proceed

interaction

in two different

to nickel atoms in the second layer. Now, one

ways.

In order to balance the force on the first

nickel layer atoms one could introduce layer. These would then require further

a cp'to all nickel atoms in the second 9' to atoms below and so forth. A par-

49

,,~

layer Iqa

Fig. 3. The figure illustrates the force constants which couple the adatom in layer 0 (labelled as +) among each other (p;O), to the first layer nickel atoms (qbI, cpjjl), and to the second layer nickel atoms (f&s @2)s and also-the force constants coupling the first layer nickel atoms to atoms in the second layer via as seen in sectional view AA' or as seen in sectional view BB'. further discussion.

0 1

/’

layer 2

88’

sde

9

“lew

CR\

'\

'\ ,/ '\\,/ b

titularly

hyer 1

(9

‘+ ,/' '\ /' u

layer 2

simple choice of balancing

the force is to connect

the first layer

nickel atoms with 9' only to the second layer nickel atoms below the adsorbate atom

(Fig. 3). The three equations

for having no net forces on the adsorbate,

first layer nickel atom and second layer nickel atom in z-direction

then read

4qbl n,(Ol) + 'pb2 n,(O2) = 0

(4)

2Pbl

(5)

n,(lO)

+ 2$2

Vb2 nZ(20) + 4$2

n,(12) n,(21)

= 0

(6)

= 0

where n,(ij) is the z-component three equations

which

are fulfilled

of the unit vector from atom i to atom j. These

with

leaves the force between the adsorbate

as the only free parameter x and y-direction

of the potentials.

the net forces on the atoms vanish because

choice of balancing have however

and the second layer nickel atom

for the first derivative

the forces as described

also explored

anced in the alternative

procedure

of symmetry.

above is particularly

the lattice dynamics as described

For the The

simple. We

of the system with forces balabove. No significant

differ-

50 curves were found. We note further that our model with

ences in the dispersion internal

stresses

would be compatible

sition of the nickel atoms, Since no such detailed

with adsorbate

in particular

data is available

induced shifts of the po-

with a buckling

of the second layer.

on the surface structure

we kept the

atoms at their bulk positions. The lattice Green's

dynamical

functions

model

constructed

is evaluated

with the aid of Fourier

transformed

from the eigenvectors

*

U

(eZ~;L;~‘;Q,~)

a6

=

ei(Ql;fzK)ei(Ql;f;K’)

1

2 w -

S

where ei(QII;IZ~) is the ath Cartesian s, with Q, the wave-vector the displacement eigenfrequency function

component

of the atom

K

(9)

ag(Q,) component parallel

of the eigenvector

to the surface

for the mode

associated

with

in the unit cell in the layer P.z, m,(Q,) is the

and w is the frequency.

The equation

of motion

for the Green's

is

with the dynamical

Matrix iQ,,[Ro(fraZK)-Ro(L;$KI1)]

@aB(tIEzK,g;t;K”)

Das(QI;tZ~;ll;~“)

= 1

.

a'; [M(L~K)M(~;K”)]~‘~

As can be seen the equations ed from the eigenvectors

e

of motions

couples the Green's

of the atoms in a particular

function

(11)

construct-

layer to the displacement

of atoms in layers above and below. Here we discuss sagittal

solutions

plane is a symmetry

even and odd solutions. ceeding spectral

as described

along the ry

plane the equations

The resulting

equations

separate

direction.

into two subsets for

are solved analytical

in ref. 4. Phonon dispersion

Since the

curves are obtained

by profrom the

densities

Pa&~ZK,+‘;QIW)

=g

for Q, oriented

= 1 $(Ql,‘lZK)e;(Q,f$K’) * G-w,(Q,)) S

[Uas(fz ~,Li~';Q,,w+ic)

A detailed

account

- U

aB

(!2 K,&;K';Qp,w-ie)] z

for the equations

odd modes will be presented

.

for the Green's functions

in a separate

publication.

(12) for the even and

51 4. APPLICATION

TO THE ~(2x2) OXYGEN OVERLAYER

In this section we present overlayer

obtained

tions and compare bour coupling.

with our new model which includes the results to those previously

Before we proceed

fect of the proposed layer substrate frequency

attractive

interac-

with nearest neigh-

to demonstrate

the ef-

atom and the second

with (pi*. For this purpose we calculate

the

modes of the system at 7 and at 51 as a func-

force pb2 keeping

all other parameters

of the modes for which the calculation

w IE,r)

second neighbour

obtained

it may be illuminating

of a few characteristic

Fig. 4. We take the remaining

curves for the oxygen

force between the adsorbate

atom parametrized

tion of the attractive vectors

results for the dispersion

parameters

is performed

fixed. The eigen-

are displayed

in

as: (p;;T= 2.43; g:. = 0; ml2 = 0;

‘00’013

lpamllel

w,lE.jo Iparallel adsorbate

Fig. 4. Eigenvectors for a few characteristic the high symmetry points r and X.

model

0000

modes of the ~(2x2) overlayer

in

= 1, in units of the bulk nickel force constant. The mass Ma and the vertiq1;2 cal distance R, for the adsorbate atom are taken so as to simulate oxygen (MA = 16, RI = 0.9 8). The results for frequencies lel adsorbate o(Al,x) cantly

are little affected.

The vertical

adsorbate

reduced. One has to keep in mind, however,

In a physical effect

are plotted

modes w(E,T) and u2(E,?) and the vertical

realistic

observed nonzero.

is the Rayleigh

reduction

mode o(Al,.)

which

of the frequency

wave at the zone boundary.

of the frequency

mode at 7 is signifi-

that mb2 is kept zero here.

model mi2 should increase with %2

of 'pb2 on UI(A~,T). A large reduction

w~(E,X) which

in Fig. 5. The paraladsorbate

balances

the

occurs with

This shows that the

of the mode is an indication

of q)b2 being

Fig. 5. Characteristic frequencies of the ~(2x2) surface as a function of the attractive interaction between the adsorbate and the second layer atom.

%‘a0

We now compare overlayer

the results for the dispersion

obtained

in our present

calculation,

with those in Ref. 1. The parameters bour interaction

and the attractive

layer we choose

stress included,

used in the old model with nearest

neigh-

only (Fig. 5a) are miI = 2.43; o;O = 0.23, mi2 = 0.3 in units

of the bulk force constant. teraction

curve of the ~(2x2) oxygen

with internal

For the new model with second nearest force between the adsorbate

neighbour

~6~ = 2.5; qi2 = 0.7; $jo = 0.28; gy2 = 0.8 and pi2 = 0.35a.

with a, = 2.49 R the surface models the intralayer

lattice constant

coupling

constant

of the clean surface.

between the nickel surface

For both atoms (pi1

was kept at the bulk value. As can be seen from Fig. 6 the model provides slightly

better fit to the data in tracking

closely.

Here, we have made no attempt to model the upwards

cal branch near l' by including

dipole-dipole

the vertical

interactions

tage of the new model

is that it no longer requires

the nearest

model.

neighbour

straightforward

in-

atom and the second

and physical

The main advantage appealing

served with carbon and nitrogen

branch more

shift of the verti-

(ref. 4). The advan-

my2 to be as small as with

is, however,

explanation

overlayers.

adsorbate

a

that it provides

for the reconstruction

ob-

a

53

wthoutmternal

stress

wtihmternalstress

5w~l5

- 15

500-

100

0

0.5

F

1.0

the frequencies

1.0

seen in Fig. 5 the most dramatic

is with the A2-mode

actually

to reconstruction equation

0.5

TO THE RECONSTRUCTION

As was already

the A2-mode

0

x

g=Q,ll.26 A-'

5. APPLICATION

Fig. 6. The dispersion curves for surface modes and resonances calculated in the nearest neighbour model (left) and with second nearest neighbour interaction and internal stresses.

3

of motion

is (in our model)

becomes soft and the surface

to a p4g(2x2)

structure

for the A2-mode entirely

effect

of the force '~6~ on

at y. For gb2 exceeding becomes

value

instable with respect

(compare Fig. 4 and Fig. 2). The

at x is particularly

localized

a particular

simple since the mode

to the first nickel layer.

Its frequency

is

MSu

2

which

2 = '~1;~+ 'Pi2/ao + 2~;I(a,/2

using

2 -I/2 + RI)

(I31

(7) and (8) becomes

(I41 Obviously

this mode becomes soft when

(I51

54 This is the stability the phase boundary perature

phase diagram.

bility of structures physical

picture

particular

construction

criteria

The three overlayers

interaction

tation as to why the surface the phonon anomaly

parameters

should vary in a

of sulfur, oxygen and carbon differ

is not known). As can be seen from the stahas a larger propensity

RI is, even with $,2 kept constant.

The model presented

for the sta-

which are 1.35 8; 0.9 8 and 0.1 8, respec-

(15) the ~(2x2) overlayer

the smaller

it marks

in a zero tem-

have been derived earlier

as to why particular

the distance

As an equation structure

W(100)surface (ref. 8). There, however, no

RI of the adsorbate

larger attractive surface.

Similar

was provided

(for nitrogen

bility criterion

for the ~(2x2) surface.

on the clean

direction.

in the distances tively

criterion

between the ~(2x2) and the p4g(2x2)

pi2 is expected here therefore behaves

when the adatom

provides

towards

In addition,

is closer to the

a very appealing

normal with a sulfur overlayer,

with oxygen and reconstructs

rea

interpredisplays

with carbon.

ACKNOWLEDGEMENTS The work of T.S. Rahman was partially Foundation

under Contract

from NATO Research

No. DMR-8402850.

supported

by the National

We also acknowledge

Science

travel support

Grant No. 075/84.

REFERENCES 1 2 3 4 5 6 7 8

J.M. Szeftel, S. Lehwald, H. Ibach, T.S. Rahman, J.E. Black and D.L. Mills, Phys. Rev. Lett. 51 (1983) 268 J.H. Onuferko, D.P. Woodruff, B.W. Holland, Surface Sci. 131 (1983) 245 W. Daum, to be published T.S. Rahman, D.L. Mills, J.E. Black, J.E. Szeftel, S. Lehwald and H. Ibach, Phys. Rev. B 30 (1984) 589 S. Lehwald, M. Rocca, H. Ibach and T.S. Rahman, Phys. Rev. B 31 (1985) 3477 J.W.M. Frenken, J.F. von der Veen and 6. Allan, Phys. Rev. Lett. 51 (1983) 1876 A similar model has also been proposed by S.C. Ying in these Proceedings A. Fasolino, G. Santoro and E. Tosatti, Phys. Rev. Lett. 44 (1980) 1684