INSTABILITY AND RECONSTRUCTION OF THE W (001) SURFACE

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Submitted on 1 Jan 1984

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INSTABILITY AND RECONSTRUCTION OF THE W (001) SURFACE

M. Tomá¡ek, S. Pick

To cite this version:

M. Tomá¡ek, S. Pick. INSTABILITY AND RECONSTRUCTION OF THE W (001) SURFACE.

Journal de Physique Colloques, 1984, 45 (C5), pp.C5-125-C5-129. �10.1051/jphyscol:1984518�. �jpa- 00224136�

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Colloque C5, suppl6ment au n04, Tome 45, avril 1984 page C5-125

INSTABILITY AND RECONSTRUCTION OF THE W (001) SURFACE

M. ~orn6;ek and 5. Pick

J . Heyrovskg I n s t i t u t e of Physicat Chemistry and EZectrochemistry, CzeckosZovak Academy of Sciences, Mcickova 7 , 121 38 Prague 2, CzechosZovakia

R6sumg - Nous introduisons une approche simple et qualitative du type Jahn-Teller pour dgcrire la reconstruction de la surface (001) du W e t nous l'appliquons 2 l'gtude des modes de dgformation de haute symgtrie.

Ceux-ci sont 26pargs en deux groupes ("in-plane" et "buckled"), le mode d u type M5 6tant le plus favorable.

Abstract.-A simple q u a l i t a t i v e pseudo J a h n d e l l e r approach t o t h e r e c o n s t r u c t i o n of t h e W (001) s u r f a c e is introduced and the r e s u l t s of i t s a p p l i c a t i o n t o high-symmetry deformation modes a r e presented.

They a r e s p l i t i n t o in-plane and buckled modes,the M5 zig-zag mode being most promising.

1. Introduction.-Interest i n r e c o n s t r u c t i o n of the \V and Mo (001) sur'face and e f f o r t s invested l e d t o t h e c l a r i f i c a t i o n of problems involved and c r y s t a l l i z a t i o n of main ideas behind it /1-4/.Contro- v e r s i a l p o i n t s between experiment and theory s t i l l remain /5,6/ and i t i s not c l e a r whether t h e phenomenon is t h e r e s u l t of a general i n s t a b i l i t y of t h e (001) surface o r whether t h e r e e x i s t s a pronounced s i n g l e def ormat ion mode .However, l o c a l theory i s g e t t i n g more popula- r i t y now than i n t h e p a s t a s i t i s not s u r p r i s i n g with metals exhi- b i t i n g a covalent component of bonding.Such a theory has t o r e f l e c t c o r r e c t l y l o c a l f e a t u r e s of t h e e l e c t r o n i c s t r u c t u r e and exhibit t h e inherent l o c a l symnetry.bor t h e W and Mo (001) surface,these l o c a l f e a t u r e s a r e ascribed t o Shockley s u r f a c e s t a t e s (dangling bonds,SS) a t EF /7-lO/,also c a l l e d the " c e n t r a l " peak /11/ i n t h e l o c a l densi- t y of states.Loca1 symmetry of t h e surface,of main importance here, i s given by t h e symmetry of the o r b i t a l s forming t h e s e SS,and by t h e p o t e n t i a l a c t i n g upon them.The above requirements a r e not met by e a r l i e r one-band (1 o r b i t a l ) t h e o r i e s t h a t can use s e l e c t i o n r u l e s based on t r a n s l a n t i o n a l symmetry only and a r e l i m i t e d t o the P e i e r l s mechanism.The d i e l e c t r i c response c a l c u l a t i o n s /2,12,13/ a l s o do not o f f e r f u l l q u a l i t a t i v e information on t h e r e c o n s t r u c t i o n mechanism.

Naturally, two-band (2 o r b i t a l ) models /14,15/ grasp chemistry and l o c a l p r o p e r t i e s (symmetry) of t h e surface b e t t e r and can lead t o a r i c h e r scope of q u a l i t a t i v e conclusions than one-band models /16/.

Due t o t h e important r o l e of dangling bonds i n surface e l e c t r o n i c p r o p e r t i e s , t h e i n t r o d u c t i o n of t h e concept of "broken covalency"

/17-19/ appears t o be n a t u r a l here.As a r u l e , t h e l a t t e r i s used when i n t r i n s i c l a t t i c e i n s t a b i l i t y l e a d s t o t h e loosening of elec- t r o n s from old bonds and so enables the e l e c t r o n s t o couple i n a new way.Here,the loosening i s done by a mechanical process c r e a t i n g t h e surf ace.

2.Local model of t h e electron-phonon interaction.-In t h e present work,electron-phonon coupling i s considered c r u c i a l f o r t h e reconstruction.SS a r e supposed t o be t h e main e l e c t r o n i c ingredient i n t h i s coupling.Al1 t h e experimental and t h e o r e t i c a l information pre- s e n t l y a v a i l a b l e shows t h a t t h e r e a r e two almost degenerated bands

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984518

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C5-126 JOURNAL DE PHYSIQUE

of SS a t E on the2W and Mo (001) surface stemming from t h e hybridi- z a t i o n of $he x2-y and xy o r b i t a l s with t h e appropriate l i n e a r corn- b i n a t i o n s of xz and yz orbitals.Resulting surface hybrids a r e non- bonding with r e s p e c t t o t h e bulk,since i n each hybridizing p a i r , t h e f u n c t i o n s have opposite p a r i t y with respect t r f l e c t i o n i n t h e surface plane /2O/.hccording t o / l O , l l / , t h e x8-yb o r b i t a l i s well l o - c a l i z e d i n t h e surface l a y e r while t h e xy o r b i t a l shows /11/ some i n - t e r a c t i o n with t h e subsurfgce l a y e r and can be s e n s i t i v e t o i n t e r p l a - n a r deformations ( s e e t h e

r

mode below).

Following P r i e d e l / ~ l / , a t o z s i n a two-dimensional l a y e r provide a sharp "central" peak only i f t h e i r i n t e r a c t i o n s with t h e neighbours superpose coherently,which i s possible f o r a l a y e r with highly sym- m e t r i c a l geometry.!Che l a t t e r imposes severe r e s t r i c t i o n s on t h e va- l u e s of orbital-based matrix elements.If one atom i n t h e surface i s displaced perpendicularly,the symmetry of i t s neighbourhood i s pre- served and no d r a s t i c change i n t h e " c e n t r a l v peak occurs.However,if t h e l a t t e r geometry i s l o c a l l y destroyed by one atom displacement p a r a l l e l t o t h e c r y s t a l s u r f a c e , t h e coherence e f f e c t disappears and t h e "central" peak i s s p l i t . T h i s l e a d s t o t h e decrease 8 E of t h e e l e c t r o n i c energy

i n t h e pseudo ~ a h n - ~ e l i e r (vibronic ) theory /21,22/, according t o which t h e most perspective deformation modes

3

a r e estimated here.

The l a t t e r w i l l give t h e l a r g e a t change i n t h e form of t h e l l c e n t r a l n peak. a ) , l b ) , ~ , and E a r e t h e wave functions and energies of occu- pied

1 ^?)

and empty (by SS of t h e o r i g i n a l (unreconstructed) system, and w 1s t h e f i r s t derivative of t h e e l e c t r o n i c energy ( p o t e n t i a l function) with r e s p e c t to,

a

. A s seen from ( l ) , "broken covalency1*

y i e l d i n g a global band of angling bond s t a t e s around Ep i d e a l l y f i t s t h e general i n s t a b i l i t y condition saying t h a t t h e r e should e- x i s t " s o f t n excited s t a t e s with symmetry lower than t h a t of t h e

ound state.Via t h e electron-phonon matrix element Wab= (a1 wlb)

,

1 ) e x p l o i t s the symmetry f u l l y s i n c e wab r e p r e s e n t s a s e l e c t i o n ru-

P

l e .Rsmely, f o r some deformations ,web contains a much l a r g e r amount

fi

of new non-zero orbital-based ma rix elements, t h a n f o r o t h e r ,$

.

This simple behaviour prompts one t o introduce /22/ a purely lo- c a l molecular f i e l d model which considers only one s i n g l e atom car- r y i n g t h e mentioned f o u r d - o r b i t a l s from Ep giving r i s e t o t h e "cen- t r a l " peak.

For in-plane deformations

(G5,z

) t o be considered below /22/, t h e change of t h e molecular f ~ e l ~ ' 4 p o t e n t i a l &Y behaves l i k e x o r x+y and hence,leads t o t h e r e p u l s i o n i n t h e p a i r s of o r b i t a l s f o r - ming t h e SS-This i s a s o r t of "rehybridization" t h a t can be looked upon a s a r e s u l t of the new bonding mechanism o f t h e reconstructed

surface i n which (slsaturated") dangling bonds a r e now engaged.

On t h e o t h e r hand,for buckled modes, bV i s e i t h e r f u l l symmetric (El) o r behaves like_x2-y2

(zl

⁾.Theref ore,no repulsion d l ) o r only a s l i g h t s p l i t t i n g (X ) of xz,gz o r b i t a l s i s t o be expected /22/.

3,Considerations of %he k-s ace s metry.-There e x i s t s a r e l a t i o n - s h i p 22/ between ~ e i e r l s mEchanlb and' t h e pseudo Jahn-Teller ef- f e t 'in t h e delocalized Bloch f u n c t i o n (BF) picture.Consider t h e

( d x ~ ) R 4 5 0 r e c o n s t r u c t i o n which occurs both f o r buckled %_and zig-zag modes .Of s p e c i a l importanse here a r e d i r e c t i o n s ^f4

11

[l,

a

and

%,-J

, t h e c e n t r e s x4 and

x2

of which f a l l on t h e bounds- r y of t h e new-surface B r i l l o u i n zone.Due t o purely t r a n s l a t i o n a l symmetry ,f o r M each SS branch i s s p l i t i n ?! ^'4% p o i n t s .Hence, one could assume t h a t buckled deformations would be well d z s c r i b ~ d by the-BF picture.If

D,1]

holds, t h e same i s t r u e f o r M5 i n

xi .

I n Xa ,however,no s p l i t t i n g occurs f o r m5 and a s i n g l e SS band.

Owing t o t h e presence of a g l i d e plane,the folded SS branches a r e pinned

/lo/

i n t h e 2-dim. p r o j e c t i v e i r r e d u c i b l e r e p r e s e n t a t i o n 'P

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of the original (lxl) surface,repulsi@ns invoked by symmetry also appear.Fron this one infers,that it is important to include a larger number of orbitals on the atom than one.

4.Enumeration of reconstruction-active surface modes /22f.-Let us enumerate all the transitions (deformation modes) which,due to the change of scalar parameters,the (1x1) surface can undergo continu- ously according to the Landau theory /23/.0nly deformations in the surface layer will be considered and the surface relaxation (

P1)

will be omitted.The latter theory singles out the oints

7

($=( 0'0) 1

-

X (k = q / a (1,0),k2=a/a (0,I)) and

a

(&=%/a (1,lP) from the surface

~ridouiri zone an2 considera the following Lrreducible representati- ons (IR) as the only candidates for the transition ( yk=coa

- a).

IR Basis sign^ Structure Atoms witki different

of IR environments :

Surf ace Subsurf ace 75

; Y g +

^(1x1) no no

;Y:, -

^(1x1) ^no ^no

-

1

+

⁽2x2

1

Yes no

-

⁽^2x1⁾ ^Yes ^no

-

^A

*4 YY,kl) ⁺ ^(2x2) ^no ^Yes

2 yg2 -

⁽^2x1 ^no ^no

-

4

M1

;Y&

(nxf?!)~45~ Yes no

-

^A

_Yk' ₊

( flxC)~45O no no

M5 ,,

-

Y Y 1 ,

-

( G x m ~ 4 5 O no no

- - - Note that for 2-dim. IR,it is necessary to add the sign of the cubic

anisotropy term h( l4

+

Q 4 ) in the thermodynamical potential ex- pansion to fully spe

%

ify the deformation mode.

One remarks,that for s o m e ~ , a t o m s in the surface and subsurface layer exist which differ by the geometry of their environment,so fa- vouring a partial charge transfer.Por such situations,one can sus- pect that ionic superlattices can emerge /16/ which are generally not advantageous on energetical grounds for metals (naturally in the absence of adsorbates or external electric fields) .Hence,the

e5

^and

deformations should be more advantageous.They exhibit an interes-

5%

extremal property ,namely, that

r

(rigid shift ) maximalizes the interplanar d e f o q t i o n as compare2 with the surface one,the opposite being true for M5.In particular,for a coordinate system con- nected with-a surface atom and for a suitable normalization,the equation _R(M

)=Ft(x3 )+5(X4)

holds for the displacsments-of the first surface neiJbours of thls atom and similarly ,r(M5)

= ; ( x ~ ) = , ~ ( X ~

⁾is true Tor displacements of its subsurface neighbours.

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C5-128 JOURNAL DE _PHYSIQUE

5,Phenomenological phonon model.-As has been found /24,25/,the ide- ally terminated (OOL) surface of' W exhibits a rich scone of surface phohons which lower their frequencies simultaneously /25,26/-and thus-can be considered as candidates for reconstruction.The M1,5 and X3 modes are the most promising /25,27/ of them (the T 5 mode does not appear in this particular model),They are expected to soften earlier than the remaining Xl,4 ones.Reaults obtained for W and Pe show that there are no marked qualitative differences between these two systems /24,25/.0ne concludes,that to discover such differences ,the surface electronic factor has to be included explicitly. 6.Discussion.-The present simple and heuristic approach leads to the following conclusions:

Local featiires of SS cause a genuine splitting of deformations on the W (001) surface into buckled and in-plane ones.For the latter, local electronic properties appear to be decisive whereas for the former,the BF-picture seems suitable.Most promising is the M5 (and perhaps the r g ) mode,although a globs1 lowering of stability of the (001) surface is to be expected.The

r

mode oan intervene in the optiaalization of surface-eubsurf ace 'interact ions if relaxat ion is not sufficient /28/.Under special exper&nental conditions,also the

-

Ml and Xg modes could be important.For M1,this can happen i n field- ion emission where this mode can be energetically stabilized by the external electric field, especially due to the presence of the T a m surface state at EF /16,29/.However,this state is insensitive to the reconstruction~accor~ing to photoemission results /30/],which shows a preference of the 1 5 mode under normal conditions (absence of electric field) .The X3 reconstructioa, in its turn, can be accoaing to Willis /1/ induced by the adsorption.The importance of the 1 5 mode is supported also by the results on hydrogen chemisorption. Natu- rally,the sign of the cubic ani~lotropy constant Achanges as a re- sult of chemisorption /3,4/.

As far as the weakly incommensurate Mo (001) reconstruction is concerned /3l/,symmetry reasons prevent a strict separation of in- plane and buckled modes in this case.However,the situation will not lie far froa the comiiensurate one of W (001).

Recent calculation,similar i n spirit to /14/,was performed for the W and Ta (001) surface /32/.It includes explicitly correlation ef- fects and leads to conclusions in some controversion to the cornon- ly accepted point of view.Xaturally,correlation in surfaces is a difficult problem which is still at the very beginning.

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INSTABILITY AND RECONSTRUCTION OF THE W (001) SURFACE

HAL Id: jpa-00224136

https://hal.archives-ouvertes.fr/jpa-00224136