Surface, interface and bulk electronic structure of some Pd-Ti systems by a tight-binding method

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Surface, interface and bulk electronic structure of some Pd-Ti systems by a tight-binding method

Š. Pick, P. Mikušik

To cite this version:

Š. Pick, P. Mikušik. Surface, interface and bulk electronic structure of some Pd-Ti systems by a tight- binding method. Journal de Physique I, EDP Sciences, 1992, 2 (1), pp.121-133. �10.1051/jp1:1992128�.

�jpa-00246457�

Classification Physics Abstracts

71.20C 73.60D 73.90

Surface, interface and bulk electronic structure of

_some

Pd-Ti

systems by

_a

tight-binding method

I.

Pick and P. Miku§ik

J.

Heyrovskj

Institute of

Physical Chemistry

and

Electrochemistry,

Czechoslovak Academy of Sciences,

Dolej§kova

3, 182 23

Prague

8, Czechoslovakia

(Received J7 June J99J, revised

J9August

J99J,

accepted

J3 September J99J)

Abstract.

Properties

of the bulk and (lll) surface of the Pd3Ti

alloy

and _some related Ti-Pd systems are studied

by using

_a

simple

LCAO model. The

sign

and

magnitude

of _core level shifts (CLS) at

particular

atoms are correlated with initial state effects. Considerable

positive

CLS _are

predicted

for the surface and

especially

for the bulk Ti and Pd atoms,

respectively,

in the Pd3Ti

phase. Origin

of these CLS _as well _as their relation to

experimental findings

_are discussed. Local

densities of electronic states _are also

presented.

An attempt to draw _some

general

conclusions

conceming

other bimetallic systems with

split

d-bands is made.

1. Introduction.

The _structure and behaviour of transition and noble metal

overlayers

_on another transition metal surface have been studied most

intensively during

several last years,

especially

for late

transition metals

deposited

_on substrates from the central part ^{of the Periodic Table}

[1-7].

It

seems that gross trends _can be often rationaliZed

by using

rules derived from the

corresponding

elemental metal

properties

and from their mutual

alloying ability [8-9]. Yet,

the present state of the art in this respect is not able _{to cover} the

variety

of all the effects

revealed

by experiments.

In the present paper, we address _a

problem

which is in _a certain _sense reversed.

Namely,

_we

are interested in the

deposition

of Ti atoms _on the late transition metal Pd surface and _we consider also _{a more}

general

_scope of

questions

of methodical character related _to it. It is

clear, however,

that the _two kinds of systems have _a number of

properties

in _common. Let _us

mention

positive

_core level shifts

(CLS)

and

depletion

of d-states _at the Fermi level for the late transition metal atoms.

A combined

XPS,

UPS and XAES

experiment [10]

^revealed

(especially

in the Ti _on Pd

case)

well marked

changes

in the valence

region

characterized

by

more or less

split

d-bands and

accompanied by large

CLS for both kinds of atoms. To

explain

this

situation,

formation of the

Pd3Ti alloy

at the

early

_stages of Ti

deposition

has been

suggested

in reference

[10].

The

argument

was the

similarity

with the

spectra

of bulk

alloy samples

found

by

other authors

[11, 12].

There is another _reason which makes Pd-Ti systems

interesting. They belong

to the

large

class of

split

d-band

alloys (I.e. alloys

^of

early

and late transition metal elements

[13])

electronic

properties

of which show distinct similarities, For

example,

for

alloys

of

Ni, Pd,

Pt and noble metals with the

early

transition

elements, significant positive

bulk CLS _on both

constituting

atoms _are

reported

in wide range of concentrations.

Although representative

bulk electronic structure calculations

[14, 15]

and

experimental

data

[13, 16]

_are

available,

the

underlying physics

is not

completely

understood. The

corresponding

information _on surface and interface

properties

of similar systems ^is more modest and is restricted

essentially

to the

systems

quoted

at the

beginning

of this section. To get an

insight

in the

problem,

the present authors

performed simplified

d-band

tight-binding

calculations of the bulk and surface electronic _structure for several Ti-Pd systems. ^Some

preliminary

results for

Pd~Ti

_are

presented

in

[17]. Similarly

_as other authors

[7, 13, 16, 18, 19],

_{we suppose} that there is _a close correlation between CLS and initial state effects in the

photoemission,

which is controlled

mainly by

the

change

^of the local electrostatic

potential.

The local densities of valence electronic states

(LDOS)

for bulk and for surface _{atoms are} also

given.

The

picture

we obtain

shows marked

regularities

and _we

hope

that

they

_can be

helpful

also in elucidation of

properties

of other

alloys

with

split

d-bands.

2. The model.

2.I GEOMETRICAL CONSIDERATIONS. Since the geometry ^{of Ti adatoms} on the Pd

polycrystal

is _not

known,

we have _to make _a choice of structures to be studied. Due to its

high stability,

the dense

(ill)

surface arrangement ^is

likely

to be

statistically significant

for the

polycrystalline

Pd

sample. Below, only

the

(I

I

I)

surface is considered. It is natural to start up with _a

pseudomorphic (I

x

I)

Ti

monolayer

_on

Pd(I II).

Since the metallic radius of Ti is about 6 fb

bigger

than the Pd

radius,

the

overlayer

^will be strained. To reduce the surface-

subsurface stress, we suppose that the surface Ti subsurface Pd _nearest

neighbour

distance is

equal

_to the _sum of the

corresponding

atomic radii

(Vegard's law).

The _same

assumption

is

made also in other _cases

presented

below. It is

beyond

the scope of the present

study

to

suggest

any rearrangement ^{of the Ti}

monolayer

^{with the} surface

compressive

stress reduced.

Note that for the above ratio of metallic

radii,

the

(I

x

I) overlayer

_can still

be, generally speaking,

stable

[8, 9].

For methodical _{reasons, we} find useful _to consider also the

(I

x

I)

Pd

overlayer

on the

(I II)

face of the

hypothetical

fcc Ti

crystal.

Now, the Pd

overlayer

is

expected

to be under tensile stress.

To _assess the idea of surface

alloy formation,

_we have studied also the

Pd~Ti monolayer

deposited

_on

Pd(I

II

).

The

geometry

^{of the}

monolayer

is identical to that of the

(I II)

surface of the

Pd~Ti alloy (Fig. I),

which is also considered. The latter

point

needs _an

explanation.

There is _a

family

^of

closely

related

A~B

structures which differ

by stacking

of the

(I II) A~B planes [20, 21].

The

Pd3Ti crystal belongs

to the

long-period D024

class with the

combined

fcc&hcp stacking (-A-B-C-B-A-).

It is

accepted [14, 15]

that the DO

~~

phase

is well

approximated by

_{a more}

simple L12

structure with the fcc

stacking (-A-B-C-A-),

and _we

adopt

this

point

of view. Let _us mention that the latter

geometry

^{is stabilized for the}

Pd4Ti stoichiometry [20, 21].

Interatomic distances in the

Pd~Ti

intermetallic

compound

are the

same as in the Pd

crystal.

This fact

points

to a strong ^{Pd-Ti bond}

forrnation,

which is confirrned also

by

the considerable

energetical

stabilization

0.8eVlatom [22]

due to the

alloying. Naturally,

_one should admit that among the above surface structures _some may be

unstable with respect to either

segregation

_{or some} ^kind of surface reconstruction.

Nevertheless,

_our results _can shed

light

on the

interpretation

of

experimental

data and _are of methodical interest. To enable CLS

interpretation,

calculations for the semiinfinite

Pd(I II)

crystal

^{and bulk}

hcp

^{Ti metal} were also

perforrned.

o o

O .

O

. o

o O

Fig.

I. The (III) surface cell of the

A3B alloy

in the

Ll~ phase

(see the text). Atoms in the second and third

layer, respectively,

_are

represented by

circles of reduced size.

2.2 THE _{METHOD oF} CALCULATION. The well known d-band model of transition metals

and

alloys [9]

_was

employed

and studied

by

the standard recursion method

technique [23].

Twelve _moments of the electronic Hamiltonian _were evaluated

exactly (I.e.

without

being

influenced

by

_any kind of

simplifying boundary conditions)

for all orbitals of interest. The Hamiltonian of Pettifor

[24]

_was rescaled to obtain the correct Ti and Pd bandwidth

[25].

We

suppose the

R~~

_distance

dependence

of matrix

elements,

and the matrix elements

H~B

between two different atoms are

given by

the formula

[9]

HAB (R

₌

(HAA (R ) HBB (R

)~'~

(l)

In

(semi) empirical schemes,

_an

uncertainty

about the d-electron count at

particular

atoms is

present.

^For

Pd,

the proper choice

giving

the _correct

position

of the Fermi energy

E~

with respect to the bulk

density

of electronic states is

N~

= 9.4

[26] (in

Ref.

[3],

N~

=

9.5 is

used).

For

Ti,

the LMTO

theory [27] predicts N~

~

2.5. It is

possible, however,

that the choice

N~

3 is more convenient

[28]

in LCAO models. We have

accomplished

the

analysis

for both the above values. Since the results do _not differ

essentially, only

the

N~(Ti)

= 3 _case is

presented

in detail below.

Before the self-consistent

procedure

is

described,

one should touch upon the

ionicity problem.

There is _no doubt that _some

charge

transfer takes

place

in transition metal

alloys, although

it is believed to be small. Its

quantification

is obscured

by

the presence of

charge

in the

out-of-sphere region

_as well _as

by

the

long-range

tail of _some orbitals. Hence, to

interpret

the results of elaborate

calculations,

_{one must} be very careful _not to get

picture

which is at variance with the traditional lore

[29].

It is

postulated

in _a

large

class of models that the

charge

transfer _can be treated

by changing-self-consistently

the local atomic d-levels

(diagonal

matrix elements of the

Hamiltonian)

_e,

by

the term, say,

&e,

₌

UQI,

where

Q;

is the

charge

at the site I

(cf.

Refs.

[3, 30]).

Needless to say that _on

empirical

level, this

approach

^is not free from

some

ambiguity,

and this flaw is reinforced for semiinfinite

crystals

where it

leads,

_{as a}

rule,

_to

presence of extended

charged regions. Here,

we

adopt

another

approximation (minimal

polarity hypothesis [30]) imposing

the local

neutrality

condition

Q,

= 0

[9].

The

charge neutrality

is achieved

by adjusting self-consistently

the values _e~ of the local atomic levels. In

analogy

with

Rh3Ti

system, we expect ^the

highest (positive) charge

on Ti _atoms

(0.3

in

[15]).

However, there is _a very

high density

of Ti electronic _states n;

(E~)

at

E~ [14] (see

also

below)

and the obvious guess

&e; Q,/n,(E~)

shows that the

corresponding

corrections _are very small. More

dangerous

in this respect are rather Pd _atoms in

Pd~Ti,

both in the bulk and _at the

surface,

due to the low

density

of electronic Pd states at

E~.

Technically,

all the levels _e, in first four atomic

layers parallel

to the surface _are

adjusted

self-consistently,

and the values from the fourth

layer

are transferred _to

deeper layers.

In other

words,

_we treat the fourth

layer

as bulk. This

approximation,

which is

quite

reasonable

in the

light

of available

models,

is further

justified

_a

posteriori by finding

small differences for third and fourth

layer

CLS in most _cases.

Depending

on the number of

nonequivalent

atoms at the

surface,

four _or

eight

_{parameters are} to be found

self-consistently

in _our model. We fix e~ m 0 for bulk atoms

(Pd

_atoms in the

alloy).

In every self-consistent

cycle,

_we find first

E~ by iterating

the

equation AE~

=

AN~/n~(E~)

for the bulk atom unless the accuracy AN ~ ^~ 0.005 is reached,

Here,

AN

~ is the _error in the

occupation

number. In the _case of the

Pd~Ti

_{systems, seven}

independent

_e, values _are found

by iterating

the guess

he,

=

c

AN,/n, (E~)

unless

£ AN,

_~

K,

where K

=

0.03,

and similar

procedure

^with K

=

0.02 is

applied

_to the other systems. ^{The choice} c~ I is recommended _to reduce the

danger

of oscillations in the iteration process. For too

large

values of

he,

and

AE~,

_a cut-off is

imposed

from the _{same reason.} The convergency was not too sensitive to the

input

_guess of

e;-values.

2.3 COMMENTS _oN THE ELECTRONIC STRUCTURE. Transition metal

binary alloys

with

split

d-bands represent an

intensively

studied group of materials. It appears that

LDOS,

which is

dominated

by d-electrons,

has _an universal character

[14, 15].

The

minority

atom LDOS

forms _a

high-density partly occupied peak.

These B-states do _not resemble _{a «} textbook _» resonance,

however,

since B-derived features

originating

from the A-B

hybridization

_are well apparent ^{in the}

occupied

A-band

region.

The two band systems are

separated by

a

dip

in LDOS

which, similarly

as for many other

alloys

and

compounds, points

to the A-B bond

formation. The late element LDOS is

pushed

to lower

energies

which is

again

_an indicative of the covalent bond

component [31].

It should not be overlooked that _a part ^{of the A-atom}

LDOS appears well above

E~

due _to the A-B interaction. A similar behaviour of the

overlayer

LDOS is

typical apparently

^{also for} the systems ^mentioned in the Introduction. The reduced local

density

of electronic states at

E~

_can cause a

drop

in the surface chemical

reactivity [2].

Let _us

shortly

dwell _on the well known

expression [32]

E~

&E,

=

E

&n, (E )

^dE

(e, N~, ) (2)

for the electronic

(or band)

energy

E, change

at the site I. In

equation (2),

_{n, is} ^the d-electron

LDOS, N~,

is the d-electron

number,

and e; is the local atomic level

(Coulomb integral)

at the

atom I. It is obvious that the electronic energy can not be obtained

correctly by

^{this forrnula} for late transition

elements,

for which the

sp-d hybridization

is essential

[32, 33]. Nevertheless,

there is _some indication

[5, 13]

that the energy of

alloying

_can be assessed within the d-band model

by using

the

equation (2).

Let _us mention that for the systems we

study,

Ti _{atoms are}

compressed,

_{as a} rule, due to a misfit between the Ti and Pd covalent radii.

Neglecting

this

fact,

_an overestimation of the energy

gain

due to

particular

structure forrnation is

expected.

2.4 CORE LEVEL SHIFTS,

Analysis

of _core level shifts offers _an invaluable tool of local

chemical and

physical analysis

of solids and molecules. It is

embarrassing

that _some

points

essential for CLS

interpretation

_are still not settled. The

opinion

is

widespread relating

CLS to initial state effects

[7, 8, 13, 18, 19, 34]. According

to this

approach,

CLS reflect

mainly

the local

change

of the electrostatic

potential.

If it is

really

_so, the electrons in the

highest

core

level _states of transition metal atoms should

experience

similar effects like the localized valence d-electrons

[13, 34],

_see also

[16].

In

tight-binding models,

the local

potential changes

coincide with the shift of local atomic levels

(Coulomb integrals) &e,

^{introduced in the section 2.2. Since} core electron

binding

energies

are measured with respect to

E~,

we

identify

CLS with the

quantity (e; E~).

The

negative sign

_respects the convention

ascribing positive

value _to CLS to

higher binding

energy, Another successful

empirical theory [8, 35]

based _{on a}

therrnodynamic

Bom-Haber

cycle

takes into account the hole

screening

in the final

photoemission

state. It has been

argued [18, 19], however,

that _a

reinterpretation

is

possible

that

brings

this

theory

back to initial state

effects. To

summarize,

in the absence of _{consensus on} the CLS

interpretation

_we

employ

_one

of the two most

popular

and fruitful

approaches,

which is known to

yield

_as a rule

satisfactory

results.

Within the framework

just specified,

the clue to CLS

understanding

lies in the valence d- state behaviour. To describe

it,

_a

picture

based _on low order _moments of the electronic

Hamiltonian

[23]

is

proposed

here. When scrutinized

merciless,

it _can appear ^to be

simplistic

since the

density

of electronic states

undergoes

^{rather drastic}

changes

_as a result of

alloying.

We

believe, nevertheless,

that basic

qualitative

features may be

grasped

in this way.

First,

let _us consider the local d-band width _at the atom A. It is known that

effectively

it is

proportional

to the square ^root of the

(centered)

second moment

m~=£H(B.

If

B

m~ is reduced e.g. due _{to a} lower

coordination,

the band _narrows and the electronic

charge

on atom A from the

right (left)

part ^{of the Periodic}

System

tends _to be increased

(decreased).

The

corresponding

CLS _oppose the

charge

transfer. This is

precisely

the surface band

narrowing

effect described

by

a number of authors

[8, 18].

For

alloys,

one should

keep

in mind that the band

narrowing (or widening)

is controlled also

by

the

possible

nearest

neighbour

distance variation and

by

^the

H~B magnitude (see Eq. (I))

which _can differ _a

good

deal from the

respective

elemental metal values.

The even-order moment m~ bears inforrnation

only

_on those local d-band features which

are

symmetric

with respect to the _centre of

gravity

of the

corresponding

LDOS. For

compounds

and

alloys

with

split

bands such _a symmetry ^{is violated much} more than for

elemental metals. The

antisymmetric

component ^{of the LDOS}

shape

is described

by

odd-

order _moments of energy. In the most

simple approximation,

the asymmetry ^{and the local}

geometry are linked

together by

the third _moment m~

[25].

^The

antisymmetric changes

are,

generally speaking,

most

pronounced

in the off-centre

region

of the LDOS. If the

density,

say, narrows in its lower

part

^due to the m~

change,

^{it is widened} on the

opposite

^{side. To} get

some idea _on the direction of these

effects,

formal mathematical

manipulations

_{are necessary.}

Let _us chose _a

neighbour

B of the atom

A,

and let _us make its

potential

_more

repulsive by increasing

the parameter _e~

by &eB~0, keeping

the

remaining

_parameters fixed. As _a consequence, m~

(evaluated

at the site

A)

will increase

by H(B &eB.

^The

physical

intuition suggests ^{that the}

charge

_on atom A should increase and that is

undoubtedly

true for

E~

situated well inside the d-band of atom A. More

formally,

this conclusion is corroborated

by

the so-called odd-order

generalized

^HUckel rule

[36]

valid for systems ^with

roughly

half-

filled set of electronic levels.

(This

rule _can be

readily expressed

in _terms of the _moments

[37].)

On the other

hand,

the theorem of reference

[38]

_proves that it _{can not} be the case for

general position

^of

E~. Namely,

the theorem asserts that the

charge

variation

&N~

at the site A caused

by _&m~ changes

the

sign

twice

(at least)

when it is considered to be _a function of

E~.

This result is

equivalent

to the

picture

when the induced

change

of LDOS is _an

antisymmetric (see above)

function of energy and has three _zeros inside the allowed energy interval.

Naturally,

the mathematical theorem

gives

_no hint about the _moment when switch from the _« normal _»

(&N~/&eB

_~

0)

to the _« anomalous _»

(&N~/&eB

_~

0) charge

redistribu- tion takes

place.

To avoid _a

confusion,

let _{us note} that in

two-component systems,

^{both these}

altematives _{can occur}

simultaneously

for either kind of atoms. This is because

together

with the interatomic

charge transfer,

also a redistribution between

occupied

and empty states

breaking

the

global charge neutrality

takes

place

if _not corrected

self-consistently.

On the basis of several numerical tests, we

expect

^{that the} « anomalous _» mechanism in systems ^with

split

d-bands _can be

operative

for _a limited number of transition metal atoms such _as those from the very

fight

of the Periodic Table

(and perhaps

also for noble

metals).

Namely, by replacing

Ti _atoms

by

atoms with

higher N~ value,

and

especially by substituting

atoms with

N~

= 9 at Pd

sites,

the

positive

CLS at Pd-like _{atoms are} reduced _{or even}

change

the

sign.

Both the above

changes

_suppress the

m~-value

^{and the}

N~(Pd )

reduction

brings

_one

closer _to the _« normal _»

charge

redistribution

region.

For

example,

for

Pt~Ti

^with

N~(Pt)

=

9,

_we find CLS 0,I eV and 0.2eV _at the surface and _at the bulk Pt atom,

respectively (cf.

Tab. I for

Pd3Ti values).

The CLS values at Ti _{atoms seem} to be less sensitive. The trend

just

described agrees with the

experimentally

observed CLS

[7, 13, 16].

The _« anomalous _» mechanism represents a

specific

kind of «band

widening».

In the

situation described

above,

certain amount of electronic states from

vicinity

of the upper

edge

of the _atom A d-band is

«pumped»

into the _atom B band above

E~

due to the A-B

hybridization.

As _a consequence, the atom A is bereft of some

charge.

_« Normal _{» or}

« anomalous _» CLS

correspond

to the self-consistent corrections &e~

bringing

the _atom back to the

approximate charge neutrality.

Let _{us stress}

that, generally,

both the second and third

order moment effects _{are to} be considered at

equal footing.

Table I. Core level

shifts (in eV) for

^Pd and Ti _atoms in

layers

1-4

for

the systems considered in the present paper. For the

Pd3TilPd

II

I)

_system and

layers 2-4,

the Ti _rows

correspond

to

Pd atoms in the Ti-like

positions

in the

L12

structure

(Fig. I).

For

shills

to

higher binding

energies,

^{the values}

of

CLS _are

positive.

Layer

Pd

(

I I I TilPd I I I Pd/fcc Ti

(

I I I

Pd~Ti (

I I

1) Pd3TilPd (1 11)

0.2 0.3 0,I Ti IA IA

Pd 0.5 0,1

2 0 0.3 0.3 Ti 1.6 0.4

Pd 0.8 0,1

3 0 0,1 0 Ti 1.6 0.2

Pd 0.9 0,1

4 0 0 0 Ti 1.6 0

Pd 0.9 0

3. Results and discussion.

In

figures 2-7,

LDOS for various Ti-Pd systems are

presented. They correspond

to the d- electron

occupation N~

=

3 for

Ti, although

for

N~

₌ 2.5 the results _are

quite

similar. The LDOS _we have obtained conform with the situation sketched in section 2.3

nevertheless,

several

points

are worth of further discussion.

For the

Pd3Ti alloy,

we find _a very

high

Ti LDOS _at

E~.

A similar feature is obtained also

by

other authors

[14].

The Ti LDOS value _at

E~

shown in

figures

3 and 4 _can

hardly

be

accurate due _to the

semiempirical

character of _our model. On the

contrary,

^{the Pd LDOS} at

E~

^is very

low,

both for the bulk and surface. In

analogy

to

[2]

_{one can}

speculate

that the

%RMl

~'~

~RMI

~

L£4L

>

I

fl

~

~s

>

m @

~i ~

O $

O -, q/

~ , tn

, , O

, , a

, ~

, , ,

i ,

, '

-4 -2

E(eV) -4 -2

E(eV)

~~~. ~.

Fig.

^3.

Fig.

2. The local

density

of electronic states (LDOS) for the bulk (full line) and (III) surface

layer

(dashed line) of Pd.

Fig.

3. Bulk LDOS on the Pd (full line) and Ti (dashed line) _atoms in the Pd~Ti

alloy.

FERMI LEVEL

~

~s

'

§

fl ₎₍

3 ii

$

a

~ ~j

E(eV)

Fig.

4. Surface LDOS _on the (I II) Pd (full line) and Ti (dashed line) atoms in the Pd3Ti

alloy.

resulting

chemical reactivities of Pd and Ti _{atoms at} the

Pd~Ti(

II

I)

surface _are much different

mutually.

There is _a surface

s~ift

_{of Pd LDOS to}

higher energies

as

compared

with the bulk

Pd~Ti (cf. Figs.

³ and

4)

^{which is} apparent ^{for the surface feature} at about 1.5 eV below

E~.

We suggest

tentatively

that to these LDOS

changes

contributes also _an

occupied

^surface

state band formation. Accurate location

(or lack)

of similar features at

alloy

surfaces in

angle-

resolved

photoemission

spectra ^{would be}

helpful

for

understanding

the surface electronic

-4

E(eV)

Fig. 5. LDOS _on the surface Pd (full line) and Ti (dashed line) atoms in the Pd3Ti

monolayer

_on the Pd I I I) surface.

~RMI L£4L

~s>

@' m ,,

@ ,

, '

~ ,

3 '

m ,' ,

~"

, ,

, ,

Ul _,

O _,

a '

~ "~~" '_,"

' ,

,' _,

, '

-4 -2

E(eV)

Fig.

6. LDOS _on the surface Ti (dashed line) and subsurface Pd (full line) atoms in the system TilPd (I Ii).

properties.

We have found for the intermetallic

compound Pd~Ti

marked

positive

CLS for both bulk and surface atoms, in

rough agreement

^{with the available}

experimental

data

[10- l2]. Nevertheless,

the

surface component

^of core level shifts is

negative (I,e,

the

positive

CLS at the surface are smaller than those in the

bulk)

in

analogy

to the late transition metal

crystals [39-41].

For these

crystals,

Tamm surface states

split

off from the top ^{of flat d-bands due} to the surface

potential change [40].

Hence, one can

speculate

that similar surface _states could

exist below

E~

at

Pd~Ti

surfaces _as well. This

hypothesis

is corroborated

by

several _reasons

I)

flat d-bands and _a

dip

in LDOS above them exist for

A3B alloys [15], 2)

the formation of

surface _states is

usually

facilitated

by

the A-B interaction in similar situations

[42], 3)

similar surface _{states are} found also for the ordered NiAl

[43]

and Cu-rich CuAl

[44] alloy

surfaces.

For all systems ^considered

here,

^the Pd LDOS from the

E~ vicinity

is

pushed

to lower

energies.

This is _a behaviour

indicating

that Pd states are

becoming bonding

with respect to

the Pd-Ti interaction. A

specific

^LDOS modification is found for the bulk

(and

^also

~RMI LEVEL

>~s

~'

m

$~

~ "

m ' '

~" J ',~

' j

tn _,

O i

O '

~ ' ,

" i

,' _,

," ,

-2

E(eV)

Fig. 7. LDOS _on the surface Pd (full line) and subsurface Ti (dashed line) atoms in the system Pd/fcc Ti ( II1).

subsurface)

Pd atoms in

Pd~Ti only. Namely,

the lower dominant Pd

crystal

LDOS structure at 3 eV below

E~

is shifted due _to

alloying

_to

considerably higher binding energies (the

lower

maximum _more than

by

I

eV,

cf.

Figs.

3 and

4)

and is widened.

Up

to a small

discrepancy conceming

the

positions

of the two above

peaks

below

E~,

the behaviour

just

described was

observed in the

photoelectron spectra [10]

after Ti

deposition

_on the

polycrystalline

Pd

surface. When

comparing

calculated and

experimental

LDOS one should realize that

photoionization

_cross section for Pd 4d electrons is

by

two orders of

magnitude larger

than for the Ti 3d _ones

[45].

The electronic epergy values based _on

equation (2) point

to a considerable energy

stabilization due _to the Pd-Ti interaction. For

example,

we

get

a rather stabilization 0.8 eV per ^atom due to the

Pd~Ti alloy formation,

in

agreement

^{with the available data}

[22].

The CLS obtained for

N~(Ti)

=

3 _are

given

in table I.

(For N~(Ti)

=

2.5,

_we find in the

Pd~Ti alloy

the value 1.6 and 1.7eV for Ti _atoms in the surface and in

deeper layers, respectively.

^Other differences _are

small.) Below,

we argue ^{that the} basic trends

displayed

ⁱⁿ table I follow the concepts ^{introduced in the}

preceding paragraph.

To this

goal,

let _{us note} that the Pd-Ti matrix elements for the

alloy

_are about 25 fb

bigger

than the Pd-Pd _ones for the

palladium metal,

and

they

are

roughly

the _{same as} the matrix elements for the elemental Ti.

These data follow from

equation (I)

and from the fact that the Pd-Ti nearest

neighbour

distance is

practically

the _{same as} in the Pd

crystal [21].

On the fcc

Ti(I II) surface,

the interaction between Pd adatoms is reduced due _{to a}

larger

metallic Ti

radius,

and

just

reversed situation takes

place

for Ti _on

Pd(I II).

^As a consequence, the second _moment m~ and the local bandwidth _are

enlarged

for Pd and

essentially

conserved for Ti bulk _atom in

Pd~Ti,

_as

compared

^{with the} _pure ^{Pd and Ti} _case,

respectively.

For Pd atoms on

Ti(I

II

),

_we have _an essential band

narrowing,

with _{more or} less moderate

changes

at surface atoms in the

other Pd-Ti systems ^{considered here. If there} were no other

effects,

the _common band

narrowing (and widening) arguments

^would

predict positive

CLS for Pd bulk _atoms in the

alloy

and for Ti adatoms _on Pd and

Pd3Ti(1II) surfaces,

whereas

negative

CLS would be

expected

for surface Pd atoms,

especially

in the

Pd/TI(I II)

_case.

Actually,

this

picture

is correct

only

for the

Pd(I II)

surface

[8, 18].

The bandwidth

change

considerations have to be combined with the

charge

redistribution effects associated above with the third _moment m~. For

Ti,

_we have the normal situation consistent with the traditional

electronegativity

arguments, ^{and for Pd} atoms the _« anomalous _» mechanism is

operative. (Roughly speaking,

the

charge

^tends to flow from Ti _onto Pd atoms, and from Pd _atoms it is

pushed

into empty

states above

E~

when Pd and Ti _are

brought

into

contact.) Hence, positive

contributions _to CLS

(making

the local

potential

more

attractive)

_appear for both Pd and Ti _to prevent a

pronounced charge neutrality

violation. At

particular

atom, this contribution increases with the number of unlike

neighbours

it has.

Inspecting

the table

I,

_we check that

taking

into

account the _two mechanism

proposed,

all the gross features arrived at can be understood.

Let _us tum now to the

comparison

with the

experimental

data.

According

_to references

[I1,

12, 16],

CLS for the bulk Pd and Ti _atoms in

Pd~Ti

_are 0.6-1.3 eV and

0.5-0.9eV,

respectively.

This is in

approximate

_agreement with the results

given

in table I.

(By allowing

some

charge

transfer from Ti _onto Pd atoms, we should obtain somewhat smaller CLS at

Ti, together

with _some CLS increase _at Pd

atoms.)

A

comparison

with

experimental

CLS data shows that _our results _can also have

bearing

_on the

systems

^{mentioned in the} Introduction. As it _can be inferred from the _recent literature

(see,

_e-g.

[46, 47])

CLS

interpretation

is _a rather

demanding

task for

complex

systems, ^{and in this} respect our results _are

encouraging.

Note that in references

[11, 12],

discussion of CLS in

Pd~Ti

based _on the Bom-Haber

cycle

and

screening ability

^of electrons in the

alloy, respectively,

is

given.

In the

study

of Ti _on Pd

[10],

the measured CLS _are 1.2 eV and 1.3 eV for Pd 3d and Ti

2p levels, respectively.

Constant and

equal

^FWHM

(full

^width at half

maximum)

^of the two Pd

3d5/2 Peak

_components

(separated by

1.2 eV for all Ti

coverages)

make presence of _a

highly irregular

structure

unlikely.

Note also that the

Auger

_spectra

interpretation [10]

is consistent with the

prevailing

contribution to CLS from the initial _state effects. The

computed

CLS

(Tab. I) prefer clearly

the existence of _a

(possibly thin)

Pd-Ti

alloy

^film at the Pd surface in the

experiment [10]. Supposing

that the

Pd~Ti phase

_or another

phase

with similar

stoichiometry

not considered here is

formed,

we

predict pronounced positive

CLS for both Pd and Ti in agreement with the

experimental findings.

All these facts corroborate the idea

[10]

about _a kind of Pd-Ti

alloy

formation _on Pd surfaces. Also other

arguments

^{in its favour} can be

given.

Surface

alloy

formation is

physically

well

possible

mechanism

[9],

cf, also the situation in the Pt _on Re system

II-

It is

interesting

that model calculations

(see

Tab,12 of

[9]) predict

Pd-Ti

alloying

_at

Pd(001).

The

comparatively large

covalent radius of Ti _can be another factor

discriminating

the pure surface Ti

phase

in thin films. Surface

alloying

in similar systems ^is

probable, although

it is

generally expected

to commence at

temperatures higher [1, 48]

than the _room temperature

conditions of the

experiment [10].

Comments _on the kinetic side of the

problem

_are,

unfortunately,

out of reach of _our methods.

We _were

suggested by

_one of the referees to consider also the _case of isolated adatoms. This is _a

good

^idea

enabling

_us further illustration of the m~ role. We consider

Pd/fcc Ti(

II

I)

and

TilPd(ill)

_systems with

quasiisolated

adatoms

(0.25 monolayer coverage) forming

the

p(2

_x

2)

pattem

(«black» positions

in

Fig. I).

The

corresponding

LDOS _are

given

in

figures

8 and 9. The

high

LDOS at

E~

for Ti adatoms _on

Pd(I II) points clearly

to their

high reactivity.

In this _case,

roughly speaking,

_a surface d-resonance is formed _on adatoms

[3]

and this _process is dominated

by

the band

narrowing,

the

signs

of CLS

obeying

the

corresponding

predictions.

For Pd adatom _on

Ti,

_we find

negative

CLS 0.5 eV and for Ti _on Pd the

positive

value 1.2 eV is obtained. CLS _on the

Pd(I

II substrate surface _are 0.5 eV for Pd atoms with _no Ti _nearest

neighbours,

and 0. I eV for Pd adatoms

adjacent

to Ti _atoms. At the Ti subsurface _we find the value 0.25 eV for all surface _atoms

(with respect

to the bulk _atom in the fcc

structure).

One _can

speculate

about the d-electron count rise _at Pd adatoms due _to

e.g.

ionicity,

which in tum would make the

corresponding

CLS less

negative

_{or even}

positive.

This

effect,

if strong

enough,

would lead to a

large

downward shift of the d-resonance

[3].

It is clear,

however,

that the

comparison

with the

experiment [10]

is _not favourable. We

speculate

rather that adatoms at low coverage form islands _{or some} kind of surface clusters

including

perhaps

also the substrate atoms.

-2

E(eV)

Fig.

8. LDOS _on the Pd adatom (full line), on the substrate Ti _atom

adjacent

to it

(long-dashed

line) and _on the surface Ti atom with _no Pd

neighbour

(short-dashed line) in the system p(2 _x 2)/fcc Ti II1).

12

(

~s

' fl

$

$

~'

O

a Ii

~ l I

,,J

J

/ '

/ /

-4 -2

E(eV)

Fig.

9. LDOS _on the Ti adatom (short-dashed line), _on the substrate Pd atom

adjacent

to it (full line) and _on the surface Pd atom with _no Ti

neighbour (long-dashed

line) in the system

p(2

_x 2)/Pd (111).

The

qualitative picture emerging

from _our models is in agreement ^{with results of other} authors

[7, 13, 16].

We expect ^{in bimetallic} systems

generally non-negligible positive

CLS _on

Ni, Pt,

noble

metal,

and

especially

_on Pd atoms

supposing

that the other constituent _atom

belongs

_to the left-hand part of the Periodic Table. No

charge

transfer

(ionicity)

is

assumed, although

the latter effect could be

important

in _an accurate CLS evaluation. Some other

trends in CLS behaviour _can be rationalized

by using

the above m~ and m~

analysis.

Note added in

proofs

In both the Pd adatom _on Ti and the Ti adatom _on Pd

systems

we have verified that CLS and adatom

binding energies

are

practically

the _same for fcc and

hcp adsorption

^sites.

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