EQUATION OF STATE OF SOLID CHLORINE AND BROMINE

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EQUATION OF STATE OF SOLID CHLORINE AND BROMINE

E.-Fr. Düsing, W. Grosshans, W. Holzapfel

To cite this version:

E.-Fr. Düsing, W. Grosshans, W. Holzapfel. EQUATION OF STATE OF SOLID CHLO- RINE AND BROMINE. Journal de Physique Colloques, 1984, 45 (C8), pp.C8-203-C8-206.

�10.1051/jphyscol:1984837�. �jpa-00224337�

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Colloque CS, supplément au n°l 1, Tome 45, novembre 1984 page C8-203

EQUATION OF STATE OF SOLID CHLORINE AND BROMLNE

E . - F r . B u s i n g , W.A. Grosshans and W.B. HoLzapfel

Fachbepcich Physik, Univepsitat-GH-PeLdepbovn, D-4790 Padevfaorn, F.R.G.

Résumé - Le chlore et le brome ont été étudiés par rayons X en dispersion d'énergie & des pressions jusqu'à 45 SPa à 300 K. Leurs pressions de dissocia- t i o n moléculaire sont estimées en comparant nos mesures avec les résultats déjà publiés.

A b s t r a c t - C h l o r i n e and bromine have been s t u d i e d by energy d i s p e r s i v e X-ray d i f f r a c t i o n under pressure up t o 45 GPa a t room temperature- A comparison o f these data w i t h the e a r l i e r r e s u l t s f o r i o d i n e i s used f o r an estimate o f the molecular d i s s o c i a t i o n pressures Pt f o r bromine and c h l o r i n e .

INTRODUCTION

C h l o r i n e , bromine and i o d i n e c r y s t a l l i z e a t room temperature and about 4 GPa i n the same orthorhombic s t r u c t u r e ( D j ^ - Cmca) and are normally considered as simple molecular c r y s t a l s ( 1 ) .

E a r l i e r i n v e s t i g a t i o n s o f i o d i n e under pressure r e p o r t two t r a n s i t i o n s up t o 30 GPa:

I ) a continuous t r a n s i t i o n i n t o a m e t a l l i c s t a t e ( 2 - 6 ) around 18 GPa and I I ) a f i r s t o r d e r s t r u c t u r a l t r a n s i t i o n a t 20 GPa w i t h molecular d i s s o c i a t i o n to a monoatomic form ( 7 , 8 ) . A s i m i l a r behaviour can be expected also f o r bromine and c h l o r i n e and the present study intends to give f i r s t estimates f o r the r e s p e c t i v e t r a n s i t i o n pressures i n these substances.

EXPERIMENTAL

C h l o r i n e and bromine were i n v e s t i g a t e d up t o 45 GPa i n a gasketed diamond a n v i l c e l l by energy d i s p e r s i v e X-ray d i f f r a c t i o n w i t h synchrotron r a d i a t i o n . The ex- perimental techniques have been described i n d e t a i l elsewhere ( 9 ) . The s o l i d samples o f c h l o r i n e and bromine were f i l l e d i n t o the gasket a t l i q u i d n i t r o g e n temperatures ( 1 0 ) . The use o f n i t r o g e n as pressure t r a n s m i t t i n g medium leads t o n e a r l y h y d r o s t a t i c c o n d i t i o n s over the whole pressure range ( 9 ) . The pressure was measured by the Ruby R i - f l u o r e s c e n c e method w i t h the c a l i b r a t i o n constant o f 365pm/GPa ( 1 1 ) .

RESaTS

N e i t h e r c h l o r i n e n o r bromine show phase t r a n s i t i o n s i n the pressure range up t o 45 GPa a t room temperature. The compression o f c h l o r i n e and bromine i s represented i n f i g . 1 t o g e t h e r w i t h previous data ( 8 ) f o r i o d i n e , whereby the u n i t c e l l volume V f o r each element j s scaled by the bond length L o f the f r e e molecules t o a r r i v e a t scaled volumina V = V / L3, which a l l o w f o r a b e t t e r comparison i n corresponding s t a t e s .

I f one f i t s these room temperature equation o f s t a t e data w i t h the two parameter B i r c h equation (12) using the known scaled volume a t ambient c o n d i t i o n VS-r, one obtains f o r the bulk moduli a t ambient c o n d i t i o n Bj!T and f o r t h e i r

pressure dependences B0' the values which are given i n the second and t h i r d column o f t a b l e 1 .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984837

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t

Iodine

6

-

(Takernun et al. 1982)

10 20 30 40

Pressure/GPa

F i g . 1: Room temperature equations o f s t a t e f o r s o l i d c h l o r i n e , bromine and i o d i n e . The broken l i n e s represent the l i q u i d phase. The dashed-dotted l i n e i n d i c a t e s t h e volume f o r t h e molecular d i s s o c i a t i o n i n i o d i n e .

Table 1: Comparison o f b u l k moduli.

1

Two parameter f i t

i

The l a r g e s t a t i s t i c a l egrors o f these values i n t a b l e 1 r e s u l t from a s t r o n g c o r r e l a t i o n o f B0 and B i n a B i r c h f i t . These c o r r e l a t i o n s are i l l u s t r a t e d i n f i g . 2, which represents the l o c i o f constant standard d e v i a t i o n s as " e r r o r e l l i p s o i d s " . Thia f i g u r ~ , shows more c l e a r l y than t a b . 1 t h a t t h e expected systematics of B and B may be j u s t masked by t h e i r s t r o n g c o r r e l a t i o n s . I t appears t h e r e f o r e more reasonable t o compare t h e B0 -values, whdfh a r e obtained by a one parameter f i t u s i n g a c o n s t a n t avegpge RTvalue f o r B

,

as i n d i c a t e d by t h e v e r t i c a l l i n e i n f i g . 2. The value B = 5.2 leads then t o the data i n the f o u r t h column o f t a b l e 1. Since t h e m e l t i n g temperatures o f c h l o r i n e and bromine a r e below room temperature a t ambient pressure, one may want t o compare t h e b u l k moduli o f these elements a t z e j o pressure and temperature:

.

These values a r e d e r i v e d from the values o f BRT by c o r r e c t i o n s f o r the thermal pressure and a r e compiled i n t h e l a s t column o f tab. 1, which shows apparently t h e same systematic v a r i a t i o n o f the as f o r B i T

,

however, s t i l l w i t h l a r g e u n c e r t a i n t i e s .

One parameter f i t w i t h 8'' = 5.2

Since t h e approach t o the monoatomic phase i s c h a r a c t e r i z e d f i r s t o f a l l by a continuous decrease o f the asymmetry i n the bonding w i t h i n the b - c - p l a i n o f t h e o r t h o r ombic l a t t i c e _(C/4L)

5'

_{] ] I 2}

_-

_1, which tends t o zero when a l l t h e bonds i n the b - c - p l a i n o f t h e (8), one can d e f i n e an asymmetry parameter A = [ ( b / 2 ~ ) ~

+

C1 B r I

BO'

4.3(9) 5.6(8) 5.2(7)

B

: / GPa

13.1(9) 14.3(7) 14.5(3) B & / G P a

ii

B i T / G P a

I I

14.2(24)

i!

11.7(9)

12.2(20)

j

13.3(7)

13.6(11) 13.6(2)

F i g . 2: Contours o f constant standard

d e v i a t i o n f o r the b u l k moduli Fig. 3: V a r i a t i o n o f the asymmetry parameter A f o r c h l o r i n e , bromine and i o d i n e w i t h respect t o the scaled vol umi na V.

0 . 5

0 . 4

0.3

0.2

A

o,;

O r

orthorhombic l a t t i c e would approach t h e value L o f t h e f r e e molecules. F i g . 3 shows i n f a c t t h a t t h i s parameter decreases s t r o n g l y i n i o d i n e under pressure down t o a c r i t i c a l value A t = 0.11 a t the f i r s t o r d e r phase t r a n s i t i o n t o t h e monoatomic phase. For a reasonable comparison w i t h bromine and c h l o r i n e , f i g . 3 represents the v a r i a t i o n o f these asymmetry parameters w i t h r e s p e c t t o the scaled volumina V.

Apparently f i g . 3 shows a common v a r i a t i o n f o r a1 1 t h r e e substances and one may t h e r e f o r e speculate t h a t a l s o bromine t r a n s f o r m a t t h e same value a t = 0.11 i n t o monoatomic phases. This assumption gives as f i r s t estimates f o r these t r a n s i t i o n pressures P t = 58(6) GPa f o r bromine and P t = 140(30) GPa f o r c h l o r i n e i n good agreement w i t h r e c e n t Raman s t u d i e s on these substances (13).

This work was performed w i t h synchrotron r a d i a t i o n a t HASYLAB, DESY and supported i n p a r t by t h e Bundesministerium f u r Forschung und Technologie.

ii=v/L3

OGPa --,

"-OGPa

Chlorine

4 i ~ ~ a - - ~ ~ ~ ~ ~ ~

Bromine

.'

45GPa-. ' lodiie - ....- - . - - .Z-ZOGP,

1 0 2 0

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