SURFACE LATTICE DYNAMICS OF NICKEL

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SURFACE LATTICE DYNAMICS OF NICKEL

V. Bortolani, A. Franchini, F. Nizzoli, G. Santoro

To cite this version:

JOURNAL DE PHYSIQUE

CoLLoque

suppLPment a& n o

Tome

de'cembre 1981

page

SURFACE LATTICE DYNAMICS OF NICKEL

V.

F.

I s t i t u t o d i F i s i c a and

U n i v e r s i t d d i Modena, 41100 Modena,

I t a l y

Abstract.- In the framework of a central and anqular force constants aode1,we have evaluated the phonon spectrum and the loss function of the Ni(lll) surfa- ce covered with Oxigen. We explain quantitatively the main features of the observed electron enerqy loss spectra.

1. Introduction.- In this work we are interested in the surface optical phonons of

the Ni(lll) surface for which very accurate high resolution electron energy loss ( E E

LS) experiments are available''). The detection of these surface vibrations wrth

E E L S occurs through the dipole coupling. The dipole is provided by fraction of mono-

layers of Oxiqen adsorbed on the metallic surface. As a consequence there are pro- blems of interpretation of the experimental spectra because one has to discrimrnate

between the modes of the substrate and the modes ~nduced by the adsorbate. In order

to solve this problem we show here that a realistic surface phonon calculation is needed. Our results indlcate that the observed peaks relate to the phonons of the substrate for the Rayleiqh wave, but otherwise are due to rhe adsorbed layer. 2. Calculation of the E E L S spectrum.- In the dipole coupling approximation, the EELS scattering cross section has the form:

Here w 1s the normal component of the polarization vector of the excited phononwith

-+

parallel momentun Q, and frequency w . 1 labels the atomic planes and ml is the mass

of the atoms in the 1 plane. It 1s clear from this equation that the rno5es which are

detectable are those having a non zero normal component of the sum of the polariza- tion vectors in the surface unit cell. Tn order to evaluate the surface phonon field of Ni we use the slab method, in the framework of a central and angular force con- stants parametrization(2). We present here the calculations for the measured EELS spectra relatlve to the Ni(ll1) :O ~ ( 2 x 2 ) and to the Ni(ll1) :O ( J ~ X J ~ ) R ~ O ' geometries, depicted in Fiq.1. In both configurations the O x i ~ e n is bound to three Ni in a C

3v position.

We flrstly conslder the ~ ( 2 x 2 ) qeometry. Tn Lhis case the M point of the 2-dinen sional Brillouin zone of the ideal (111) surface is folded in

r ,

the M phonons. The experimental results'') are reported in Fig.2a. Three peaks are

JOURNAL DE PHYSIQUE

Fig. 1 : a ) N i ( 1 11) :O p (2x21 geometry. 0xigen atoms,

@

,

@

,

@

p r e s e n t . The one a t 72 meV, which i s f a r o u t s i d e t h e phonon spectrum o f N i , i s c l e a r - l y due t o t h e motion o f t h e Oxigen r e l a t i v e t o t h e t h r e e c o o r d i n a t e N i atoms. I t c o r - responds t o t h e A l normal mode of a pyramidal x y m o l e c u l e ( 3 ) . A s i t can be s e e n from

3

Fig.3, t h i s mode g i v e s a d i p o l e moment a l o n g t h e C3v a x i s , i . e . t h e s u r f a c e normal. The lowest peak can b e i n t e r p r e t e d i n terms of t h e s u r f a c e phonons of t h e c l e a n N i

(11 1) s u r f a c e ( 2 ) . I n f a c t , n e a r t h i s frequency t h e r e i s t h e Rayleigh wave of t h e M

p o i n t which i s mainly p o l a r i z e d normal t o t h e s u r f a c e . The o t h e r peak a t 32.8 meV, i n s i d e t h e phonon spectrum o f N i , cannot b e e x p l a i n e d i n terms of t h e phonons of t h e c l e a n s u r f a c e . The modes of t h e M p o i n t around t h i s frequency a r e l o n g i t u d i n a l and dc n o t couple with t h e impinging e l e c t r o n s . To c l a r i f y t h e n a t u r e o f t h i s peak we have performed a f u l l c a l c u l a t i o n of t h e phonons of t h e covered s u r f a c e . We have conside- r e d t h e i n t e r a c t i o n of Oxigen w i t h t h e t h r e e n e a r e s t neighbouring N i atoms by i n t r o - ducing one c e n t r a l and one a n g u l a r f o r c e c o n s t a n t . B y any a r b i t r a r y c h o i c e of t h e s e f o r c e c o n s t a n t s t h e c a l c u l a t e d EELS c r o s s s e c t i o n shows t h r e e s t r u c t u r e s . The one a t lowest frequency remains r e l a t e d t o t h e Rayleigh mode o f t h e s u b s t r a t e . The o t h e r two peaks a r e connected w i t h t h e A1 ( h i g h e r frequency peak) and A2 ( c e n t r a l peak) modes of t h e x y molecule. For t h i s molecule, t h e frequency of t h e A1 mode i s mainly d u e t o

3

t h e v a l u e of t h e Ni-0 c e n t r a l f o r c e c o n s t a n t , while t h e frequency of A2 depends on t h e Ni-0-Ni a n g u l a r f o r c e c o n s t a n t . To determine t h e f o r c e c o n s t a n t s o f t h e x y mole-

3 c u l e we n o t e t h a t , even i f t h e f r e e N i 0 molecule does n o t e x i s t , t h e s u r f a c e poten-

3

t i a l i s a b l e t o s t a b i l i z e such a molecule. By using t h e EELS d a t a r e l a t i v e t o a very low d i s o r d e r e d coverage of Oxigen we f i t t h e peak a t 72 meV with t h e c e n t r a l f o r c e c o n s t a n t and t h e peak a t 30 meV with t h e a n g u l a r f o r c e c o n s t a n t . The r e s u l t s obtainec w i t h t h e s e parameters a r e r e p o r t e d i n Fig.2b. The lowest peak i s s t i l l r e l a t e d t o thc Rayleigh wave of t h e c l e a n s u r f a c e . The presence of t h e Oxigen atom does n o t modify t h e frequency and p o l a r i z a t i o n of t h i s mode. The h i g h e s t peak remains a t t h e energy p o s i t i o n of t h e A1 mode of t h e molecule. The o t h e r peak a t 32.8 meV, i n p e r f e c t a g r e - ement w i t h t h e experiment, r e s u l t s s l i g h t l y s h i f t e d with r e s p e c t t o t h e energy of thc A mode of t h e f r e e molecule, w h i i e t h e p o l a r i z a t i o n remains t h e same. The frequency

2

Fiq. 2 : a) and b) experimental and calculated EELS intensities for the ~ ( 2 x 2 ) geometry. c) and d) the same for the (r'3xJ3)~30~ geometry.

strate.

The same analysis has been carried out for the (/3x/3)~30' geometry. The experi-

mental and calculated intensities are

compared in Fiq.2~ and Fig.2d respecti-

vely. The two observed modes are rela-

ted to the A and A modes of the mole-

1 2

cule. The 29.8 mev peak is slightly shifted with respect to the correspon- ding mode of the ~ ( 2 x 2 ) geometry becau*

-.

of the different 0-0 interaction.

In conclusion, we have shown that A1

A2

a detailed calculation allows to explain

the loss spectra of coated systems and Fig. 3 : Normal modes of the x y pyra-

3

midal molecule that contribute to the

to identify the origin of the eperimen-

EELS cross section. tal stuctures in terms of the modes of

the substrate and those of the adsorbate species.

References

1) H Ibach and D Bruchmann, Phys.Rev.Lett.

44,

2) V Bortolani, A Franchini, F Nizzoli and G Santoro, Proccedings of the S m e r S c b l

on the Dynamics of Gas-Surface Interaction, Erice (1981), to be published