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Rayleigh scattering by SF6 in the critical region
Volume 32A. number 6
PHYSICS L E T T E R S
growths together with temperature which app e a r s p u z z l i n g in t h e o r t h o d o x t h e o r y s i n c e t h e r e r e p r e s e n t s t h e a m p l i t u d e of t h e c o r r e l a t i o n . In o u r c a s e t h e w e i g h t W(To) i n c r e a s e s w i t h t e m perature since then the small fluctuations prev a i l and m a y c o m p e n s a t e t h e s i m u l t a n e o u s d e c r e a s e of t h e f a c t o r A / ~ 1 l e a d i n g to t h e i n c r e a s e of r~ 2. F o r l a r g e q t h e d e p e n d e n c e of t h e c r o s s s e c t i o n on the d i r e c t i o n of q with r e s p e c t to
24 August 1970
crystal axes remains. This consequence is e a s i l y a c c e s s i b l e to e x p e r i m e n t a l t e s t .
Refere~wzs [1] S. Sponer and B. L. Averbach, Phys. Rev. 142 (1966) 291. [2] D. Bally. B. Grabcev, A.M. Lungu. M. Popovici and M. Totia, J. Phys. Chem. Solids 28 (1967) 1947. [3] J. Kochiski, J. Phys. Chem. Solids 26 (1965) 895.
*****
RAYLEIGH
SCATTERING
BY
SF 6 IN
THE
CRITICAL
REGION*
P. B R A U N , D. H A M M E R . W. T S C H A R N U T E R and P. W E I N Z I E R L Institut f l i t Experimentall)hysik H, Technische Hochschule Wien und I. Physikalisches Institul der Universitiit Wien, Vienna, Austria Received 7 July 1970
Scattering data at 7.5 ° and 90 ° were fitted to the Boteh-Fixman equation. Values for the critical exponent of the thermal diffusivity and the long range correlation length were obtained.
The self-beat-spectrometer w a s f i r s t u s e d by F o r d and B e n e d e k [1] f o r e x t r e m e l y high r e s o l u t i o n a n a l y s i s of l i g h t s c a t t e r e d by t h e r m a l f l u c tuations near Tc. We also applied this technique to s t u d y t h e R a y l e i g h l i n e w i d t h in SF 6 a l o n g the c r i t i c a l i s o c h o r e f o r a t e m p e r a t u r e r a n g e 0.04 < T - T c < 2 . 5 o c , and a l o n g the c o e x i s t e n c e l i n e f o r a t e m p e r a t u r e r a n g e 0.015 < T c - T < 4 . 4 o c . T h e s c a t t e r i n g c e l l (height 1 c m , w i d t h 2 c m , l e n g t h 3.5 c m ) w a s f i l l e d with SF 6 c o n t a i n i n g l e s s than 30 p p m i m p u r i t i e s and i m m e r s e d in a w a t e r bath. T h e t e m p e r a t u r e w a s s t a b l e w i t h i n a few m i l l i d e g r e e s p e r day. By o b s e r v i n g the m o v e m e n t of the m e n i s c u s n e a r T c , the c r i t i c a l d e n s i t y w a s e s t a b l i s h e d with an a c c u r a c y of 0.3%. T h e b e a m of a H e - N e L a s e r ( S p e c t r a p h y s i c s M o d e l 122) w a s f o c u s e d n e a r the c e n t e r of the c e l l . T h e s c a t t e r i n g v o l u m e (1 m m in l e n g t h , 0.05 m m in d i a m e t e r ) w a s i m a g e d w i t h an a p e r t u r e of f : 65 on a p h o t o m u l t i p l i e r (EMI 9558B). W e u s e d f o r the a n a l y s i s of t h e p h o t o c u r r e n t a Radiometer FRA 3 Wave Analysator. The spectra obtained were least square fitted to a L o r e n t z i a n c u r v e . F u r t h e r e v a l u a t i o n w a s
d o n e , s t a r t i n g f r o m the B o t c h - F i x m a n [2] e q u a tion f o r the t h e r m a l d i f f u s i v i t y : × = Xo(T - T c ) ~ ( 1 + ~2(T - T c ) - 2 V k 2 ) . F o r the 7.5 ° s c a t t e r i n g d a t a , the F i x m a n c o r r e c t i o n can b e n e g l e c t e d . A l e a s t s q u a r e logar i t h m i c fit f o r t h e r e m a i n i n g p a r a m e t e r s 7,o, T c and ~ = y - ~ y i e l d e d the r e s u l t s shown in fig. 1 and fig. 2. T h e t h e r m a l d i f f u s i v i t y i s : a l o n g the
x10-6 20 ¢m2xse¢-! 10
o x
:
e:,o.____
390
x
.~.~
s
~
.:oa,=oo,
i
10"2
* This r e s e a r c h is supported by the Austrian 'Fonds zur Ft)rderung der wissenschaftlichen Forschung'.
/
I0 -I
t
r-r c
Fig. 1. Thermal diffusivity of SF 6 along the critical isochore at 7.5 ° and 90 ° scattering angle.
*C
PHYSICS
Volume 32A, number 6
LETTERS
I00 ' c n ) 2 z sec*l
xlO-6 50
20 tO
PGas
:
~m8.~.02
x
]
2 -
"C
rc-r
!
l i m i t s ) a s e x p e c t e d f r o m s c a l i n g l a w s [6]. T h e d a t a a b o v e T c d i s a g r e e , h o w e v e r , with t h o s e by S a x m a n n and B e n e d e k [7] (g = 1.26 ±0.02). T h e v a l u e o b t a i n e d f o r ~ a g r e e s w i t h i n the s t a n d a r d d e v i a t i o n w i t h that r e p o r t e d by P u g l i e l l i and F o r d [3] on S F 6. T h e e x p o n e n t s of × d e r i v e d h e r e , a r e s o m e w h a t h i g h e r than t h o s e o b t a i n e d in s e v e r a l o t h e r e x p e r i m e n t s both in CO 2 [8] and b i n a r y m i x t u r e s [9, 10].
=~ ",,,
tO
24 August 1970
IO'!
The authors thankfully acknowledge the acad e m i c h o s p i t a l i t y e x t e n d e d to one of t h e m (D. H.) by P r o f e s s o r B e n e d e k d u r i n g the s u m m e r 1968.
i
10"2
R e f e~'ences
Fig. 2. Thermal diffusivity of SF 6 along the coexistence line at 7.5o scattering angle. c r i t i c a l i s o c h o r e X = (11.2 + 0.5) × 10 -6 × { T - (45.576 + 0.02)} 0"89-~0"07 c m 2 / s , a l o n g the c o e x i s t e n c e l i n e f o r the g a s s i d e × = (35.2 + 0 . 4 ) × I0 -6 ×{(45,575 ± 0.002) - T} 0.88~0.02 c m 2 / s and for the liquid side × = ( 3 2 . 8 + 1 . 5 ) × i 0 - 6 × {(4 5.571 ± 0.003) - T}0.83=e0-04 cm2/s, Using the values for Tc and g from the 7.5 ° scattering data, × and ~ were obtained by a least square logarithmic fit of the 90° data. A v a r i a tion of v yielded vaiues which agree within an e r r o r of ± 20% with theoretical and experimental [ 3 , 4 ] v a l u e s c l o s e to ~. W e t h e r e f o r e a s s u m e d v =~ f o r the e v a l u a t i o n of o u r data. T h e r e s u l t s a r e ~ = (104 ± 21). ( T - Tc) 2/~ A and Xo = 11.3 ± 1.4. T h e l a t t e r i s in good a g r e e m e n t with t h e c o r r e spondent small angle value. P r e l i m i n a r y r e s u l t s [5] a l o n g the c r i t i c a l i s o c h o r e l e a d to g = 0 . 7 8 ± 0 . 0 5 . F u r t h e r m e a s u r e m e n t s c o m p r i s i n g a l s o t h e c o e x i s t e n c e l i n e and improved data evaluation yielded the g-values q u o t e d a b o v e , w h i c h a r e s y m m e t r i c h with r e s p e c t to t h e c r i t i c a l i s o t h e r m (within t h e e r r o r
[1] N. C. Ford and G.B. Benedek, Phys. Rev. Letters 15 (1965) 649. [2] M. Fixman. J. Chem. Phys. 33 (1960) 1357, 1363; W. D. Botch and M. Fixman, J. Chem. Phys. 42 (1965) 199; W.D. Botch. P h . D . dissertation, Univ. of Oregon, 1963, unpublished. [3] V. G. Puglielli and N. C. Ford J r . , Turbidity m e a s urements in SF 6 near its critical point, to be published. [4] M. Gigiio and G. B. Benedek. Phys. Rev. Letters 23 (1969) 1145. [5] P. Braun, D. Hammer and P. Weinzier[, Conf. German and Austrian Physical Societies. Salzburg, Oct. 1969. [6] Kadanoff et al., Rev. Mod. Phys. 39 (1967) 395. [7] G, B. Benedek, Statistical physics, phase transitions and superfluidity (Gordonand Breach) Vo].II pp. 1-98. G. B. Benedek, Polarization, matter and radiation, P r e s s e s Universitaires de France pp. 49-84. [8] H. L. Swinney and H. Z.Cummins, Phys. Rev. 171 (1968) 152. [9] B. Chu and F. J. Schoenes, Phys. Rev. Letters 21 (1968) 6. [10] P. Berge and B. Voloehine, Phys. Letters 26A (1968) 267.
*****
391
PHYSICS L E T T E R S
growths together with temperature which app e a r s p u z z l i n g in t h e o r t h o d o x t h e o r y s i n c e t h e r e r e p r e s e n t s t h e a m p l i t u d e of t h e c o r r e l a t i o n . In o u r c a s e t h e w e i g h t W(To) i n c r e a s e s w i t h t e m perature since then the small fluctuations prev a i l and m a y c o m p e n s a t e t h e s i m u l t a n e o u s d e c r e a s e of t h e f a c t o r A / ~ 1 l e a d i n g to t h e i n c r e a s e of r~ 2. F o r l a r g e q t h e d e p e n d e n c e of t h e c r o s s s e c t i o n on the d i r e c t i o n of q with r e s p e c t to
24 August 1970
crystal axes remains. This consequence is e a s i l y a c c e s s i b l e to e x p e r i m e n t a l t e s t .
Refere~wzs [1] S. Sponer and B. L. Averbach, Phys. Rev. 142 (1966) 291. [2] D. Bally. B. Grabcev, A.M. Lungu. M. Popovici and M. Totia, J. Phys. Chem. Solids 28 (1967) 1947. [3] J. Kochiski, J. Phys. Chem. Solids 26 (1965) 895.
*****
RAYLEIGH
SCATTERING
BY
SF 6 IN
THE
CRITICAL
REGION*
P. B R A U N , D. H A M M E R . W. T S C H A R N U T E R and P. W E I N Z I E R L Institut f l i t Experimentall)hysik H, Technische Hochschule Wien und I. Physikalisches Institul der Universitiit Wien, Vienna, Austria Received 7 July 1970
Scattering data at 7.5 ° and 90 ° were fitted to the Boteh-Fixman equation. Values for the critical exponent of the thermal diffusivity and the long range correlation length were obtained.
The self-beat-spectrometer w a s f i r s t u s e d by F o r d and B e n e d e k [1] f o r e x t r e m e l y high r e s o l u t i o n a n a l y s i s of l i g h t s c a t t e r e d by t h e r m a l f l u c tuations near Tc. We also applied this technique to s t u d y t h e R a y l e i g h l i n e w i d t h in SF 6 a l o n g the c r i t i c a l i s o c h o r e f o r a t e m p e r a t u r e r a n g e 0.04 < T - T c < 2 . 5 o c , and a l o n g the c o e x i s t e n c e l i n e f o r a t e m p e r a t u r e r a n g e 0.015 < T c - T < 4 . 4 o c . T h e s c a t t e r i n g c e l l (height 1 c m , w i d t h 2 c m , l e n g t h 3.5 c m ) w a s f i l l e d with SF 6 c o n t a i n i n g l e s s than 30 p p m i m p u r i t i e s and i m m e r s e d in a w a t e r bath. T h e t e m p e r a t u r e w a s s t a b l e w i t h i n a few m i l l i d e g r e e s p e r day. By o b s e r v i n g the m o v e m e n t of the m e n i s c u s n e a r T c , the c r i t i c a l d e n s i t y w a s e s t a b l i s h e d with an a c c u r a c y of 0.3%. T h e b e a m of a H e - N e L a s e r ( S p e c t r a p h y s i c s M o d e l 122) w a s f o c u s e d n e a r the c e n t e r of the c e l l . T h e s c a t t e r i n g v o l u m e (1 m m in l e n g t h , 0.05 m m in d i a m e t e r ) w a s i m a g e d w i t h an a p e r t u r e of f : 65 on a p h o t o m u l t i p l i e r (EMI 9558B). W e u s e d f o r the a n a l y s i s of t h e p h o t o c u r r e n t a Radiometer FRA 3 Wave Analysator. The spectra obtained were least square fitted to a L o r e n t z i a n c u r v e . F u r t h e r e v a l u a t i o n w a s
d o n e , s t a r t i n g f r o m the B o t c h - F i x m a n [2] e q u a tion f o r the t h e r m a l d i f f u s i v i t y : × = Xo(T - T c ) ~ ( 1 + ~2(T - T c ) - 2 V k 2 ) . F o r the 7.5 ° s c a t t e r i n g d a t a , the F i x m a n c o r r e c t i o n can b e n e g l e c t e d . A l e a s t s q u a r e logar i t h m i c fit f o r t h e r e m a i n i n g p a r a m e t e r s 7,o, T c and ~ = y - ~ y i e l d e d the r e s u l t s shown in fig. 1 and fig. 2. T h e t h e r m a l d i f f u s i v i t y i s : a l o n g the
x10-6 20 ¢m2xse¢-! 10
o x
:
e:,o.____
390
x
.~.~
s
~
.:oa,=oo,
i
10"2
* This r e s e a r c h is supported by the Austrian 'Fonds zur Ft)rderung der wissenschaftlichen Forschung'.
/
I0 -I
t
r-r c
Fig. 1. Thermal diffusivity of SF 6 along the critical isochore at 7.5 ° and 90 ° scattering angle.
*C
PHYSICS
Volume 32A, number 6
LETTERS
I00 ' c n ) 2 z sec*l
xlO-6 50
20 tO
PGas
:
~m8.~.02
x
]
2 -
"C
rc-r
!
l i m i t s ) a s e x p e c t e d f r o m s c a l i n g l a w s [6]. T h e d a t a a b o v e T c d i s a g r e e , h o w e v e r , with t h o s e by S a x m a n n and B e n e d e k [7] (g = 1.26 ±0.02). T h e v a l u e o b t a i n e d f o r ~ a g r e e s w i t h i n the s t a n d a r d d e v i a t i o n w i t h that r e p o r t e d by P u g l i e l l i and F o r d [3] on S F 6. T h e e x p o n e n t s of × d e r i v e d h e r e , a r e s o m e w h a t h i g h e r than t h o s e o b t a i n e d in s e v e r a l o t h e r e x p e r i m e n t s both in CO 2 [8] and b i n a r y m i x t u r e s [9, 10].
=~ ",,,
tO
24 August 1970
IO'!
The authors thankfully acknowledge the acad e m i c h o s p i t a l i t y e x t e n d e d to one of t h e m (D. H.) by P r o f e s s o r B e n e d e k d u r i n g the s u m m e r 1968.
i
10"2
R e f e~'ences
Fig. 2. Thermal diffusivity of SF 6 along the coexistence line at 7.5o scattering angle. c r i t i c a l i s o c h o r e X = (11.2 + 0.5) × 10 -6 × { T - (45.576 + 0.02)} 0"89-~0"07 c m 2 / s , a l o n g the c o e x i s t e n c e l i n e f o r the g a s s i d e × = (35.2 + 0 . 4 ) × I0 -6 ×{(45,575 ± 0.002) - T} 0.88~0.02 c m 2 / s and for the liquid side × = ( 3 2 . 8 + 1 . 5 ) × i 0 - 6 × {(4 5.571 ± 0.003) - T}0.83=e0-04 cm2/s, Using the values for Tc and g from the 7.5 ° scattering data, × and ~ were obtained by a least square logarithmic fit of the 90° data. A v a r i a tion of v yielded vaiues which agree within an e r r o r of ± 20% with theoretical and experimental [ 3 , 4 ] v a l u e s c l o s e to ~. W e t h e r e f o r e a s s u m e d v =~ f o r the e v a l u a t i o n of o u r data. T h e r e s u l t s a r e ~ = (104 ± 21). ( T - Tc) 2/~ A and Xo = 11.3 ± 1.4. T h e l a t t e r i s in good a g r e e m e n t with t h e c o r r e spondent small angle value. P r e l i m i n a r y r e s u l t s [5] a l o n g the c r i t i c a l i s o c h o r e l e a d to g = 0 . 7 8 ± 0 . 0 5 . F u r t h e r m e a s u r e m e n t s c o m p r i s i n g a l s o t h e c o e x i s t e n c e l i n e and improved data evaluation yielded the g-values q u o t e d a b o v e , w h i c h a r e s y m m e t r i c h with r e s p e c t to t h e c r i t i c a l i s o t h e r m (within t h e e r r o r
[1] N. C. Ford and G.B. Benedek, Phys. Rev. Letters 15 (1965) 649. [2] M. Fixman. J. Chem. Phys. 33 (1960) 1357, 1363; W. D. Botch and M. Fixman, J. Chem. Phys. 42 (1965) 199; W.D. Botch. P h . D . dissertation, Univ. of Oregon, 1963, unpublished. [3] V. G. Puglielli and N. C. Ford J r . , Turbidity m e a s urements in SF 6 near its critical point, to be published. [4] M. Gigiio and G. B. Benedek. Phys. Rev. Letters 23 (1969) 1145. [5] P. Braun, D. Hammer and P. Weinzier[, Conf. German and Austrian Physical Societies. Salzburg, Oct. 1969. [6] Kadanoff et al., Rev. Mod. Phys. 39 (1967) 395. [7] G, B. Benedek, Statistical physics, phase transitions and superfluidity (Gordonand Breach) Vo].II pp. 1-98. G. B. Benedek, Polarization, matter and radiation, P r e s s e s Universitaires de France pp. 49-84. [8] H. L. Swinney and H. Z.Cummins, Phys. Rev. 171 (1968) 152. [9] B. Chu and F. J. Schoenes, Phys. Rev. Letters 21 (1968) 6. [10] P. Berge and B. Voloehine, Phys. Letters 26A (1968) 267.
*****
391