THE SPECTRAL DENSITY FUNCTIONS OF THE ADSORPTION SYSTEM K-/112/W AN ATTEMPT OF SURFACE DIFFUSION INVESTIGATION

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THE SPECTRAL DENSITY FUNCTIONS OF THE ADSORPTION SYSTEM K-/112/W AN ATTEMPT

OF SURFACE DIFFUSION INVESTIGATION

J. Beben, Ch. Kleint, R. Meclewski

To cite this version:

J. Beben, Ch. Kleint, R. Meclewski. THE SPECTRAL DENSITY FUNCTIONS OF THE ADSORP- TION SYSTEM K-/112/W AN ATTEMPT OF SURFACE DIFFUSION INVESTIGATION. Journal de Physique Colloques, 1984, 45 (C9), pp.C9-13-C9-16. �10.1051/jphyscol:1984903�. �jpa-00224379�

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JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment au n012, Tome 45, d k e m b r e 1984 page C9-13

THE SPECTRAL DENSITY FUNCTIONS OF THE ADSORPTION SYSTEM K-/112/W AN ATTEMPT OF SURFACE D I F F U S I O N I N V E S T I G A T I O N

J . ~ ~ b e n * , Ch. ~ l e i n t * * , R .

clewsk ski*

* ~ n s t i t u t e of Experimental Physics, University of WrocZaw, PoZand

**Department of Physics of t h e Karl M m x University, Leipzig, G.D.R.

R6sum6 - Les auteurs ont d6termin6 les coefficients de la diffusion superficielle du potassium sur le plan / 1 1 2 / du tungstgne, par la m6thode des fluctuations de 116mission de champ.

Abstract

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An attempt was made f o r determining s u r f a c e d i f f u - s i o n c o e f f i c i e n t s of potassium on t h e /112/ t u n g s t e n plane by means of t h e FE-current f l u c t u a t i o n s method.

I

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INTRODUCTION

A novel method f o r determining s u r f ace d i f f u s i o n c o e f f i c i e n t s of a d s o r b a t e s on s i n g l e c r y s t a l planes of f i e l d e m i t t e r s i n terms of t h e time c o r r e l a t i o n f u n c t i o n , A/?-/, of f i e l d emission c u r r e n t

f l u c t u a t i o n s was presented by Gomer / I / . He obtained t h e c o r r e l a t i o n f u n c t i o n whose forms a r e r a t h e r complicated. The approximate form is:

6 2

where8 C

-

^{i s}a c o n s t a n t .

%=

^rZ/4D, g l ( ~ / ~ o ) - i s a f u n c t i o n eva- l u a t e d numerically by Goner / I / , r,

-

i s a r a d i u s of a c i r c u l a r probed a r e a , ?i

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^{i s}t h e average s u r f a c e c o n c e n t r a t i o n of t h e adsor- b a t e , D

-

^{i s}t h e d i f f u s i o n c o e f f i c i e n t .

I n t h e present paper t h a t form of t h e c o r r e l a t i o n f u n c t i o n was ap- p l i e d t o determine t h e d i f f u s i o n c o e f f i c i e n t and t h e a c t i v a t i o n energy f o r s u r f a c e d i f f u s i o n of potassium on t h e / I 12/ W plane.

Both previous /2/ and new experimental r e s u l t s were used.

I1

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EXPERfa6ENTAL AND RESULTS

F l u c t u a t i o n s measurements a r e c a r r i e d out using two techniques:

I / d i r e c t measurement of A/$/

2/ d i r e c t measurement of t h e s p e c t r a l d e n s i t y f u n c t i o n W/f / /frequency d i s t r i b u t i o n / .

R e s u l t s can be r e p r e s e n t e d i n both forms u s i n g F o u r i e r transforms.

I n t h i s work t h e measurement of W / f / was c a r r i e d out and then t h e c o r r e l a t i o n f u n c t i o n s were c a l c u l a t e d .

The measurements of W/f/ were c a r r i e d out w i t h a n a l l - g l a s s f i e l d emission tube, equipped w i t h a potassium source. The tube and t h e used procedure were described i n d e t a i l elsewhere /2/. Examples of t h e present experimental r e s u l t s a r e shown i n Piga. 1 and 2. W/f/

can be s e e g a s copmplicated. The curves c o n s i s t of e i t h e r one, two o r t h r e e s t r a i g h t l i n e s i n a double l o a r i t h m i c p l o t , s e p a r a t e d by t h e knee. The s i m p l e s t examples of W / f f were chosen and t h e v a l u e s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984903

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JOURNAL DE PHYSIQUE

- - >

FREQUENCY F

F i g . 1 . Spectral density functions F i g . 2. Spectral denaity

a t coverage ⁸^m0.63 functions a t tempera- ture T = 300 K

F i g . 3. The spectral density funotion chosen f o r evaluation of the

correlation function

A/T/

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Fig, $.Pointer the correlation function evaluated from the experi- mental results shown in Fig. 3, Solid ourves: theoretioal oorrelation function oorresponding to two values of D

"':

10"'

' 23 i~ 2'5 2.6 2 7 28 1037 [;('I temperatures,

\

^Q³ ³

ⁱ

'hx

, k

^Fig.^5, Arrheniue plots obtained from the data shown in Fig, 4 and similar results for other

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C9-16 JOURNAL DE PHYSIQUE

of t h e c o r r e l a t i o n f u n c t i o n were evaluated. Pigs. 3 and 4 / p o i n t s / show r e l a t i v e l y simple examples of W / f / and A/Z/, r e s p e c t i v e l y . I n o r d e r t o determine D we t r i e d t o f i t t h e experimental c o r r e l a t i o n f u n c t i o n / p o i n t s i n Fig. 4/ t o t h e t h e o r e t i c a l one corresponding t o t h e above mentioned formula, but unsuccessfully. A t r a c e of a knee seems t o i n d i c a t e t h a t t h e experimental c o r r e l a t i o n f u n c t i o n con- sists of two superposed t h e o r e t i c a l f u n c t i o n s corresponding t o two d i f f e r e n t v a l u e s of D. A sum of them f i t s r a t h e r w e l l t o t h e experimental c o r r e l a t i o n function. The v a l u e s of t h e d i f f u s i o n c o e f f i c i e n t /Dl and D2/ a r e i n d i c a t e d i n Fig. 4. The same procedure was used f o r t h e experimental r e s u l t s corresponding t o o t h e r temperatures /but f o r t h e same coverage, 8 ^a0.63/. Temperature dependence of D1/T/

and D2/T/ i s shown i n Fig. 5. The v a l u e s of t h e a c t i v a t i o n e n e r g i e s a r e Q1 = 0.33

*

^{0.1 eV} ^and ^Q2⁼^0.50 ²0. I eV, r e s p e c t i v e l y , I11

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SHORT DISCUSSION

The e x i s t e n c e of t w o d i f f u s i o n processes w i t h d i f f e r e n t d i f f u s i o n o o e f f i c i e n t s can be explained by t h e anisotropy of t h e atomic s t r u c - t u r e of t h e s u b s t r a t e . Surface d i f f u s i o n p a r a l l e l t o t h e nchannelsn, i.e. a l o n g t h e (111, d i r e c t i o n , is expected t o t a k e place w i t h a lower a c t i v a t i o n energy t h a n t h a t f o r t h e d i f f u s i o n perpendicular t o t h e nahannels" i - e . along t h e < 110 > d i r e c t i o n . Very r e c e n t l y , Bayat and Wasemuth /3/ found s i m i l a r anisotropy i n t h e s u r f a c e d i f - f u s i o n f o r t h e same a d s o r p t i o n system b u t f o r a very low K-aoverage.

Table shows a comparison of t h e r e s u l t s . TABLE

This paper 0.63 ^0.33

REFERENCES

/ I / R. Gomer, Surface Soi. 38 /1973/ 373.

/2/ J.Beben, Ch. K l e i n t and Re Mec?ewski, 26th IFE Symposium, 1979, s e e a l s o : Surface Sof. 93 /1980/ 33, and Proc. 6 t h Seminar Surface Phys., in: Acta U n i v e r s i t a t i s W r a t i s l a v i e n s i s , 455 /19R3/ 47.

/3/ B. Bayat and H-W. Wessmuth, Surface Sci. 133 / 1 9 ~ 3 / 1.