THE FACES ON MICRO-CRYSTALS (FIELD EMITTERS, CATALYST PARTICLES)

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THE FACES ON MICRO-CRYSTALS (FIELD EMITTERS, CATALYST PARTICLES)

M. Drechsler

To cite this version:

M. Drechsler. THE FACES ON MICRO-CRYSTALS (FIELD EMITTERS, CATALYST PARTI- CLES). Journal de Physique Colloques, 1986, 47 (C2), pp.C2-389-C2-391. �10.1051/jphyscol:1986260�.

�jpa-00225694�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°3, Tome 47, mars 1986 page C2-389

THE FACES ON MICRO-CRYSTALS (FIELD EMITTERS, CATALYST PARTICLES)

M. DRECHSLER

CRMC2-CNRS, University Aix-Marseille III, Campus de Luminy, case 913, F-13288 Marseille Cedex 2, France

Résumé - Le diamètre d'une face d'un micro-cristal est décrit comme fonction du rayon de courbure de la surface. Une face hkl apparait seulement si le rayon est supérieur à une valeur limite. Une étude en microscopie ionique confirme ces prédictions. Les faces d'une particule catalytique (Pt) sont déterminées par analyse de l'image électronique du cristal.

Abstract - The diameter of a face on a micro-crystal is described as a function of the surface curvature radius. A face hkl appears only above a special limit radius. A field ion microscope study confirms such predictions.

The faces on a Pt catalyst particle are determined by analysis of an electron micrograph of the crystal.

INTRODUCTION

The basic problem studied in this paper is : what hkl faces are present on a crystal?

For macroscopic polyhedral crystals this problem has been solved in the 19th century.

It is known that the crystal surface is often not a polyhedron, but composed of plane faces and curved regions (see / l / ) . This has been found on field emitter crystals as well as on metal crystals grown on a support. A curved region is composed of many extreme small hkl faces, which is a consequence of the atomic crystal structure. So questions arise as : what hkl faces exist on the curved regions ? What are the diameters of such faces : How does a diameter change with the surface curvature or the crystal diameter ? A special answer to the last question is given by the theory of equilibrium shapes (Gibbs, Wulff), namely : Relative diameters should be indepen- dent of the crystal size. This is true for macroscopic crystals, where a lattice plane distance is practically infinitely small. However, as we will show here for face and bodycentered cubic crystals (fee, bec) on micro-crystals the diameter of a face must change with the crystal size. Furtheron we compare the result with field ion micro- graphs and finally use it for a first attempt to determine the faces on a metal particle of a catalyst (see also / 2 / ) .

THE DIAMETER OF A FACE AS A FUNCTION OF THE SURFACE CURVATURE

In the following it is for simplici ty assumed that the cross section of a curved crystal region has a constant curvature radius r at least along a certain region. This assumption is roughly confirmed by micro-crystal curvature measurements on crystal profile images obtained by transmission or scanning electron microscopes (TEM,SEM).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986260

JOURNAL

DE

PHYSIQUE

Using geometry and s t a t i s t i c s i t can b e shown t h a t t h e mean diameter (2g) of an hkl f a c e of a c u b i c c r y s t a l ( f c c , bcc) i s :

a = l a t t i c e parameter, h k l a r e t h e c r y s t a l l o g r a p h i c f a c e i n d i c e s .

A f a c e can e x i s t only i f i t s diameter i s g r e a t e r than t h e d i s t a n c e ^S between neighbo- r e d atom c h a i n s of t h e o u t e r l a t t i c e p l a n e . Consequently a f a c e h k l can e x i s t o n l y above a l i m i t c u r v a t u r e r a d i u s rm. The v a l u e of rm i s :

2 2 2 112

(2) rm ^% 0.2

c ^-

^{and d =} a / ( h +k +l )

d 3

d = l a t t i c e p l a n e d i s t a n c e of h k l . Q u a n t i t a t i v e d a t a of t h e s e e q u a t i o n s a r e p r e s e n t e d i n diagrams and t a b l e s f o r more than 40 types of f c c and bcc f a c e s .

Some g e n e r a l r e s u l t s a r e :

0

( 1 ) The s u r f a c e of extreme s m a l l c r y s t a l s (< =20 A) i s composed n e a r l y only of c l o s e s t packed f a c e s .

( 2 ) Whena c r y s t a l i s growing from 20 A t o

-

200 A medium index f a c e s ( f o r example

(024)) begin t o appear ( t h e c u r v a t u r e r a d i u s i s assumed t o be i n t h e o r d e r of 0.2 of t h e c r y s t a l d i a m e t e r ) .

( 3 ) High index f a c e s ( f o r example (446)) appear only above

*

200 A c r y s t a l s i z e . (4) Very high index f a c e s o r f a c e s with g r e a t e r s t e p @ s t a n c e s can appear only on r e l a t i v e l y g r e a t c r y s t a l s , f o r exampole f a c e s of

'

20 A s t e p d i s t a n c e on c r y s t a l s g r e a t e r than

-

¹ pm and those of 40 A s t e p d i s t a n c e on c r y s t a l s g r e a t e r t h a n = 10 pm.

(5) P o i n t (4) h a s a consequence f o r t h e e q u i l i b r i u m shapes of c l e a n m e t a l c r y s t a l s . Experimental e q u i l i b r i u m shape s t u d i e s a r e made on c r y s t a l s up t o "10 pm s i z e

including; f i e l d e m i t t e r c r y s t a l s t u d i e s ( s e e / l / ) . Such shapes can n o t e x a c t l y be those c a l c u l a t e d using s u r f a c e f r e e energy a n i s o t r o p i e s . T h e r e a l e q u i l i b r i u m shapes must be rnodified f o r a very small c r y s t a l . For example t h e angle between a c l o s e packed f a c e and i t s n e a r e s t v i c i n a l f a c e can n o t have a c o n s t a n t v a l u e ( i t s v a l u e i s even con- t r o v e r s i a l

131).

Rather t h i s a n g l e must i n c r e a s e w i t h d e c r e a s i n g c r y s t a l s i z e i n a xanner which i s c a l c u l a b l e using d a t a of equ. 1 and 2.

(6) The diameter of a r e a l f a c e i s only one of a c a l c u l a b l e diameter d i s t r i b u t i o n . So a comparison between c a l c u l a t e d and measured d a t a r e q u i r e s s t a t i s t i c a l measure- ments of t h e diameter of one f a c e l e a d i n g t o a diameter d i s t r i b u t i o n and then t h e mean v a l u e of t h i s d i s t r i b u t i o n h a s t o b e compared w i t h t h e c a l c u l a t e d mean diameter.

CONTROL OF THE APPEARENCE AND SIZE OF FACES BY FIELD I O N MICROSCOPY

The c a l c u l a t e d appearences and t h e diameters of the f a c e s can be c o n t r o l e d by f i e l d i o n microscopy (FIM). For such a c o n t r o l it h a s t o be c o n s i d e r e d t h a t t h e c u r v a t u r e r a d i u s along a f i e l d evaporated t i p s u r f a c e v a r i e s i n a s p e c i a l manner, which can be determined by FIM micrograph a n a l y s i s / 4 / . The c o n t r o l h a s been made b a n a l y s i n micrographs of t u n g s t e n t i p s of d i f f e r e n t mean r a d i i (30

H,

60

1,

270

1

^{and 600}

1)

taken by M. AUDIFFREN and J . BARDON i n our l a b o r a t o r y i n t h e course of a former s t u d y . The r e s u l t of many c o n t r o l s i s : A l l f a c e appearences ( l i m i t r a d i i ) and a l l f a c e d i a m e t e r s determined from t h e micrographs a r e i n r e a s o n a b l e agreement with t h e corresponding d a t a c a l c u l a t e d u s i n g e q u a t i o n I and 2.

FACE ANALYSIS BY ELECTRON MICROSCOPY (FIELD EMITTER CRYSTALS, CATALYST PARTICLES) The f a c e s of h e a t e d c r y s t a l s formed by s u r f a c e s e l f - d i f f u s i o n can n o t be analysed

u s i n g t h e FIM. I n such c a s e s t h e a n a l y s i s can be made by measuring s u r f a c e c u r v a t u r e r a d i i along s p e c i a l zones by e l e c t r o n microscopy (TEM, SEM)

111141

and t h e use o f equ. 1 and 2. Recently we have r e a l i z e d a f i r s t a t t e m p t t o analyse f a c e s on much s m a l l e r c r y s t a l s , i . e . on supported platinum

articles

of a c a t a l y s t used i n che- mical i n d u s t r y / 2 / . The p a r t i c l e s were v i s u a l i z e d by TEM (micrographs taken by R.M. RICKARD of our l a b o r a t o r y ) . Then, c u r v a t u r e r a i i u s measurements i n combination w i t h equ. 1 and 2 l e a d t o t h e r e s u l t t h a t on a 20 A p a r t i c l e (zone [220]) only c l o s e packed f a c e s e x i s t ( { 1 1 1 ). and t 0 0 2 ) ) . However, on a 70

1

p a r t i c l e a t l e a s t 11 131 and I331

1

a r e analysed a s a d d i t i o n a l f a c e s . As t h e a d d i t i o n a l f a c e s have c e r t a i n l y a d i f f e r e n t c a t a l y t i c a c t i v i t y , i t can b e supposed t h a t t h e e x p e r i m e n t a l l y known a c t i v i t y change a s a f u n c t i o n of t h e p a r t i c l e s i z e i s a t l e a s t i n some c a s e s a consequence of t h e d e s c r i b e d appearence of a d d i t i o n a l f a c e s . Nevertheless more s t u d i e s i n t h i s d i r e c t i o n a r e r e q u i r e d t o v e r i f y t h i s h y p o t h e s i s .

DISCUSSION

By u s i n g t h e f a c e a n a l y s i s d e s c r i b e d h e r e one should b e aware t h a t t h e i d e a l atomic s u r f a c e s t r u c t u r e of a f a c e i s m o d i f i a b l e by a d s o r b a t e s , r e l a x a t i o n , r e c o n s t r u c t i o n and thermal roughening and t h e i n f o r m a t i o n on such phenomena i s u s u a l l y very poor.

But t h e ignorance of such s t r u c t u r e d e t a i l s does n o t change t h e f a c t t h a t t h e d e t e r - mination of t h e h k l v a l u e s and t h e s i z e of a f a c e i s o f b a s i c importance.

OUTLOOK

The r e s u l t s b r i e f l y d e s c r i b e d h e r e may s t i m u l a t e :

(1) t o improve t h e d e t e r m i n a t i o n of t h e h k l v a l u e s of h i g h index f a c e s i n f i e l d i o n microscopy,

(2) t o v e r i f y e x p e r i m e n t a l l y t h e p r e d i c t e d change of t h e e q u i l i b r i u m shape f o r very s m a l l c r y s t a l s ,

( 3 ) t o s t u d y s y s t e m a t i c a l l y t h e appearence of f a c e s on c a t a l y s t p a r t i c l e s i n view of f u t u r e attemps t o c o r r e l a t e changes of f a c e appearences (due t o p a r t i c l e s i z e changes) w i t h changes i n t h e c a t a l y t i c a c t i v i t y .

REFERENCES

/ l / M. D r e c h s l e r , i n "Surface M o b i l i t i e s on S o l i d Surfaces", ed. Vu Thien Binh, Plenum P r e s s , New York, 1983, p. 405-458

/ 2 / M. D r e c h s l e r : S u r f a c e S c i .

162

(1985) 755-763

/ 3 / C. Rottmann and W. Wortis : S t a t i s t i c a l Mechanics o f Equilibrium Shape C r y s t a l s , p r e p r i n t 1984, Phys. Dep., U n i v e r s i t y of I l l i n o i s a t Urbana-Champaign

/ 4 / M. D r e c h s l e r , P . Wolf : I n t e r n . Conf. E l e c t r o n Microscopy, B e r l i n 1958, Verh.1 (ed. Bargmann e t a l ) , Springer-Verlag, B e r l i n 1960, p. 835

/S/ M. D r e c h s l e r , I n t e r n . F i e l d Emission Symposium, P h i l a d e l p h i a 1983, p . 163-165 (not y e t published i n d e t a i l )