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Submitted on 1 Jan 1978
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DESORPTION HEAT CAPACITY OF 3He
ADSORBED ON SOLID NEON
P. Wennerström, A. Törne, T. Lindqvist
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6, suppl6ment au no
8, Tome 39, aoiir 1978, page C6-328
DESORPTION HEAT CAPACITY O F
3 ~ eADSORBED ON SOLID NEON
P. WennerstrEm, A. T E r e and T. L i n d q v i s t
Department
of
Technology, University
of
Uppsala, UppsaZa, Sweden
RQsum6.- On a mesurd l a c h a l e u r s p 6 c i f i q u e d e d 6 s o r p t i o n d e s couches s u c c e s s i v e s de 3 ~ e a d s o r b 6 s u r n6on s o l i d e . Un modsle de bande r i g i d e pour l a d 5 s o r p t i o n e s t p r 6 s e n t 6 , q u i permet d e r e n d r e compte d e s e x p b r i e n c e s .
A b s t r a c t . - The d e s o r p t i o n h e a t c a p a c i t y o f s u c c e s s i v e monolayers o f 3 ~ e adsorbed on s o l i d neon i s mea- s u r e d . A r i g i d band model f o r t h e d e s o r p t i o n i s s e t up t o i n t e r p r e t t h e measurements.
DESORPTION EXPERIMENT.- I n t h i s r e p o r t we p r e s e n t h e a t c a p a c i t y measurements and a s i m p l e t h e o r e t i c a l model f o r 3 ~ e adsorbed on s o l i d neon. The calorime- t e r c o n s i s t e d of a copper can c o n t a i n i n g a b o u t 50km of copper w i r e a c t i n g a s t h e b a s e f o r t h e neon sub- s t r a t e . The c a l o r i m e t e r was f i l l e d w i t h 1.24
.
l o 2 ' neon atoms, which formed about 12 l a y e r s . E i g h t e e n d i f f e r e n t coverages of 3 ~ e from a b o u t 0.05 monolayer t o more t h a n 4 monolayers of 'He were measured ( s e e f i g u r e 1 ) . A r a p i d i n c r e a s e i n t h e vapour p r e s s u r el a y e r s .
DESORPTION ENERGY.- An a n a l y s i s of t h e d e s o r p t i o n c u r v e s shows t h a t t h e d e s o r p t i o n energy depends on coverage i n t h e f o l l o w i n g way. The d e s o r p t i o n e n e r -
gy f o r t h e f i r s t atom i s 55 K and i t d r o p s r a p i d l y down t o about 1 1 K when t h e f i r s t l a y e r i s completed. It s t a y s c o n s t a n t d u r i n g t h e b u i l d up of t h e second l a y e r , a f t e r which i t d r o p s t o a new l e v e l , about 4 K, d u r i n g t h e b u i l d up of t h e t h i r d l a y e r . No d i s - t i n c t drop i n t h e d e s o r p t i o n energy i s observed a f - t e r t h e t h i r d l a y e r , which can b e i n t e r p r e t e d a s a g r a d u a l change of t h e adsorbed l a y e r s i n t o t h e b u l k l i q u i d s t a t e . The l a t e n t h e a t of l i q u i d 3 ~ e a t 0.5K i s about 3.6 K (30 J / m o l e ) , s e e / I / .
DESORPTION MODEL.- A model i s now s u g g e s t e d f o r t h e d e s o r p t i o n where i t i s assuued t h a t t h e 3 ~ e atoms a r e n o n - l o c a l i z e d and t h a t t h e e n e r g i e s of t h e ada- toms a r e d i s t r i b u t e d w i t h i n a "band" f o r each l a y e r . F u r t h e r i t i s assumed t h a t t h e c o r r e s p o n d i n g d e n s i t y of s t a t e s , D(E) i s independent of coverage and tem- p e r a t u r e ( t h e s p i n - f a c t o r gN i s i n c l u d e d ) and t h a t t h e 3 ~ e adatoms can b e r e p r e s e n t e d by f e r m i o n p a r t i - c l e s . The t o t a l number of 3 ~ e atoms g i v e s t h e chemi- c a l p o t e n t i a l p (T) i m p l i c i t l y . For a thorough ana-
N
l y s i s of an e q u i v a l e n t s y s t e m / 2 / . The chemical po- t e n t i a l p (0) d e t e r m i n e s t h e o n s e t of t h e d e s o r p t i o n
N
peak which can b e r a t h e r a c c u r a t e l y determined expe- r i m e n t a l l y . Because t h e t o t a l number of adatom s t a - t e s i n t h e band i s c o n s t a n t , Ll ( 0 ) i s
F i g . 1 : Heat c a p a c i t y f o r 18 d i f f e r e n t c o v e r a g e s N
of 3 ~ e adsorbed on s o l i d Ne. u n i q u e l y determined by t h e t o t a l number of atoms i n each coverage. Thus t h e band edges must b e chosen was o b s e r v e d a t t h e low t e m p e r a t u r e s i d e of each t o g i v e a good f i t t o t h e o n s e t of d e s o r p t i o n i n peak i n f i g u r e 1 . We t h e r e f o r e i n t e r p r e t t h e peaks a l l e x p e r i m e n t a l c u r v e s . The parameters used i n t h e
as r e p r e s e n t i n g t h e d e s o r p t i o n of c o n s e c u t i v e 3 ~ e c a l c u l a t i o n a r e l i s t e d i n t h e t a b l e . The h e a t capa- c i t y f o r t h i s model i s shown i n f i g u r e 2 f o r some of
A c a l c u l a t i o n of t h e d e n s i t y of s t a t e s f o r a r e c t a n - g u l a r energy d i s t r i b u t i o n g i v e s D(E) = 2.2 x 1 0 1 8 ~ - ' The w i d t h of t h e energy d i s t r i b u t i o n f o r t h e f i r s t l a y e r w i l l b e A
2
35 K . T h i s a g r e e s v e r y w e l l w i t hZZ
t h e w i d t h o b t a i n e d from t h e d e s o r p t i o n model c a l c u -3
l a t i o n .E
-
0
References/ I
/
Keller,W.E., Helium-3 and Helium-4, (PlenumO
1
2
3
4
5
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P r e s s , New York) 1969T [K)
/ 2 / Dash,J.G. and Bretz,M., Phys. Rev.174
(1968) 247 F i g . 2 : Comparison between t h e o r e t i c a l d e s o r p t i o n model and e x p e r i m e n t a l h e a t c a p a c i t y p o i n t s f o r 3 c o v e r a g e s . t h e coverages t o g e t h e r w i t h e x p e r i m e n t a l h e a t capa- c i t y p o i n t s .Lower band Upper band Number of Band
edge (K) e d g e (K) s i t e s
DISCUSSION.- I f one a p p l i e s t h e t h e o r y of an i d e a l Fermi gas and c a l c u l a t e s an e f f e c t i v e mass from
