HIGH DENSITY REFRACTIVE INDEX OF XENON

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HIGH DENSITY REFRACTIVE INDEX OF XENON

J. Itie, R. Le Toullec

To cite this version:

J. Itie, R. Le Toullec. HIGH DENSITY REFRACTIVE INDEX OF XENON. Journal de Physique

Colloques, 1984, 45 (C8), pp.C8-53-C8-56. �10.1051/jphyscol:1984810�. �jpa-00224308�

Colloque C8, supplément au n°l 1, Tome 45, novembre 1984 page C8-53

HIGH DENSITY REFRACTIVE INDEX OF XENON

J.P. Itie and R. Le Toullec

Physique des Milieux Très Condensés, Université P. et M. Curie, T1Z E4, 4, Place Jussieu, 75230 Paris Cedex 05, France

Résumé Nous avons mesuré l'indice de réfraction du Xénon sur un grand do- maine de densité (jusqu'à 0,06 mole c m-^ ) . Le facteur de Lorentz-Lorentz décroit fortement quand la densité augmente. Une discussion critique du critère de métallisation d'Herzfeld est faite.

Abstract The refractive index of Xenon is determined over a large range of density (up to 0,06 mole c m- 3) . The Lorentz factor decreases strongly with increasing density. A critical discussion on Herzfeld criterion of metal- lization is made.

Densities of metallization of some dielectrics (Solid Xe, Csl, ..) /I, 2, 3/ are often campared to the results obtained from Herzfeld criterion /4/. Lorentz-Lorenz factor is defined by : 2 ,

r ^ n ., 0 1 / . •,

FL L = TN. « = ^ — p < "

where N is the Avogadro number, a the atomic polarisability, n0 the static re- fractive index and p the molar density. Herzfeld criterion assumes that metalliza- tion occurs at a density pM determined by the relation : F. . p„ - 1, with the hypothesis that F. . remains a constant. To check this hypothesis we have measured the variation of the refractive index of solid Xe with pressure. Solid Xe is a very compressible solid and does not absorb in the visible part of spectrum, even at 50 GPa. We measure the refractive index of Xe by comparison with thoses of some crystals (Mg 0 n = 1,734 ; A1203 n = 1,765 ; Zn 0 n = 2,008).

Experimental method.

Xe and crystals are introduced in a diamond anvil cell /5/. The pressure is measu- red by the ruby fluorescence technic /6/. The cell is setted up under a microscope and the illumination is made by reflection in order to increase the contrast of the interference spectrum of the Fabry-P^rot formed by the diamonds. At index crossing, the contrast obtained in a part of the cell including Xe plus crystal is maximum.

At pressures higher than 10 GPa, because of the deformation of the diamonds we can- not use this method. In this case we observe the optical disappearing of the crys- tal in Xe. To relate pressure to density we have used the 300 K isotherm of Xe /7,8/.

The results are summarized in the table, taking in account the variation of the crystals refractive indices with pressure /9,10/.

P(GPa) p (moles cm"3) nX e at A - 6500 A (E - 1,907 eV) 0,02585* L o w temperature 1 M 6

0 0277] measurements /ll/ ^ ^g,

5,2 u',0419 1,725 ± 0,005 6,8 0,0440 1,755 ± 0,01 26,6 0,0596 1,95 ± 0,03

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984810

C8-54 JOURNAL

DE

PHYSIQUE

D i s c u s s i o n and i n t e r p r e t a t i o n

Using a two o s c i l l a t o r s model, the f i r s t one f o r o u t s h e l l e l e c t r o n s a b s o r p t i o n ( i n - d i c e d b ) , t h e second one f o r c o r e e l e c t r o n s a b s o r p t i o n ( i n d i c e d c ) , we can express the d i e l e c t r i c c o n s t a n t ^E~ i n t h e one e l e c t r o n theory :

w i t h E = Hw plasma energy, E i n c i d e n t photon energy, Eb and Ec e n e r g i e s o f the

P P

o s c i l l a t o r s . We can developp E~ = ~ ~ 4 ! l N e2 m - l f p, where f i s t h e e f f e c t i v e num-

P a

ber o f e l e c t r o n s p e r atom p a r t i c i p a t i n g t o t h e a b s o r p t i o n , and w r i t e :

where A ^I 4ll

H2

Na e2m-l. To r e l a t e € 1 t o the measured r e f r a c t i v e index we have t o take i n t o account the i n t e r a c t i o n s between the e l e c t r o n s . Using the L o r e n t z l o c a l f i e l d t h e o r y we o b t a i n the C l a u s i u s M o s s o t t i r e l a t i o n :

The values o f f c and Ec are d i r e c t l y o b t a i n e d from t h e a b s o r p t i o n spectrum o f Xe ( f = 14

,

^{E =} 100 eV). E' (E = 1,907) i s n e g l i g i b l e i n comparison t o E2

.

We can a l s o n e g l e c t t h e v a r i a t i o n o f E w i t h d e n s i t y and we suppose t h a t f i s i n - dependent o f the d e n s i t y . To a d j u s t fb, we have used low temperature values o f n(P,E) a t two d e n s i t i e s and d i f f e r e n t E values /11/. fb = 5.4. From our h i g h den- s i t i e s values wa can c a l c u l a t e the corresponding values o f Eb(u). I n o r d e r t o i n t e r - p o l a t e our r e s u l t s , E & P ) values were f i t t e d w i t h an e m p i r i c law :

w i t h E o = 12.33 eV po = 0,018 mole ~ r n - ~ B = 1.8 E l = 0,381 eV.

From ( 3 1 , (41, ( 5 ) we can determine t h e v a r i a t i o n o f the r e f r a c t i v e index o f Xe w i t h d e n s i t y . E x t r a p o l a t i o n t o l i q u i d and gas i s i n good agreement w i t h experiment ( f i g . 1 )

From n ( p ) we can c a l c u l a t e the corresponding values o f F ( 0 ) ( f i g . 21 We n o t e t h a t i f F remains n e a r l y c o n s t a n t i n t h e gas, l i q u i d anbLdensity s o l i d phases, i n the h i g h b k n s i t y range FLL decreases s t r o n g l y . Using ( 3 ) and ( 4 ) we can r e l a t e the d i e l e c t r i c constant E = n2 t o the " e f f e c t i v e energy gap" o f ' t h e o u t s h e l l e l e c t r o n s :

d e n s i t y a t E = 1 , 9 0 7 eV. F u l l l i r e v e r s u s d e n s i t y . c a l c u l a t i o n ( . . and I ) e x p e r i m e n t a l

p o i n t s .

w i t h A c l = A ~ , O E ~ - ' and E 2 = E;

-

Afb p ( 3 - A E , ) - ' 9

E a s y c a l c u l a t i o n s show t h a t a t E = U , Eg

=

0 i s e q u i v a l e n t t o FCLp = 1.

I n f i g . 3 we show t h e v a r i a t i o n

300 - -

w i t h d e n s i t y o f E,, and

E' ( 3 - ~ ~ 1 )-! I f we s u p p o s e FLL P

c o n s t a n t , which means C b c o n s - t a n t , w e o b t a i n t h e d e n s i t y o f

200 - ^-

m e t a l l i z a t i o n p a t t h e c r o s -

s i n g p o i n t o f t!e two c u r v e s .

0

2

I f we e x t r a p o l a t e o u r r e s u l t s

N- o b t a i n e d up t o U,06 mole ~ m - ~

W t o h i g h e r d e n s i t y , we s e e no

I c r o s s i n g which means t h a t t h e r e

100 - -

i s no m e t a l l i z a t i o n (Eg > 0 ) .

I I n f a c t t h i s model n e g l e c t s t h e

1

b r o a d e n i n g o f a b s o r p t i o n band

I and s u p p o s e v a l i d t h e L o r e n t z - I Lorenz l o c a l f i e l d t h e o r y up

I t o m e t a l l i z a t i o n .

2 4 6 8 &

P (la2rno~e

F i g . 3 - V a r i a t i o n o f E i and Afb p ( 3 - ~ p l ) - ' w i t h d e n s i t y . Dashed l i n e : FLL = c s t .

D e n s i t y o f m e t a l l i z a t i o n % i s d e t e r m i n e d by t h e c r o s s i n g p o i n t .

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C o n c l u s i o n

We have measured a l a r g e v a r i a t i o n o f t h e r e f r a c t i v e i n d e x o f Xe ( f r o m 1 t o 1,95) o v e r a l a r g e range o f d e n s i t y ( f r o m 0,02 t o 0,06 mole ~ r n - ~ ) . I n t h i s d e n s i t y r a n g e L o r e n t z - L o r e n z f a c t o r FLL decreases s t r o n g l y , b u t an e x t r a p o l a t i o n o f t h i s r e s u l t s i s n o t j u s t i f i e d , i n r e s p e c t t o t h e s i m p l i c i t y o f t h e model. H e r z f e l d c r i t e r i o n must be u s e v e r y c a r e f u l l y and c a n n o t p r o v i d e an a b s o l u t e jauge t o d e t e r m i n e t h e d e n s i t y o f m e t a l l i z a t i o n . F o r s u c h d e t e r m i n a t i o n more s o p h y s t i c a t e d methods a r e n e c e s s a r y , l i k e o p t i c a l a b s o r p t i o n o r r e s i s t i v i t y measurements u n d e r h i g h p r e s s u r e .

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