Interfacial tension in a phase-separated 3He-4He mixture

Volume 32A, number 6

INTERFACIAL

PHYSICS LETTERS

TENSION

24 August 1970

IN A PHASE-SEPARATED

3HE-4HE

MIXTURE

D. P. E. DICKSON, D. CAROLINE and E. MENDOZA

Depart~nent of Physics, University College of North Wales, Bangor, Caernaruonshire, UK Received 21 July 1970

The interfacial tension in a phase-separated 3He-4He mixture has been determined between 0.33 K and 0.68 K. The results are consistent with Brouwer and Pathria's estimate of 0.10 erg/cm2 for the interfacial tension at absolute zero.

C l a s s i c a l l y i n t e r f a c i a l t e n s i o n s m a y be obt a i n e d f r o m A n t o n o v ' s r u l e [1]. Applying this d i r e c t l y g i v e s 0.21 e r g / c m z f o r the i n t e r r a c i a l t e n s i o n of a p h a s e - s e p a r a t e d 3He-4He m i x t u r e at 0 K. H o w e v e r , it has b e e n shown [2,3] that the s u r f a c e t e n s i o n of liquid h e l i u m can be e x p r e s s e d as the sum of the i n t r i n s i c s u r f a c e t e n sion, a r i s i n g f r o m the s t r u c t u r a l e n e r g y of the f r e e s u r f a c e , and the c o n t r i b u t i o n f r o m the qua nt i zed v i b r a t i o n a l m o d e s of the s u r f a c e . B r o u w e r and P a t h r i a [4] point out that the i n t e r f a c i a l t e n s i o n should be e x p r e s s e d s i m i l a r l y . A n t o n o v ' s r u l e m a y be applied only to the int r i n s i c i n t e r f a c i a l t e n s i o n , giving a value of 0.094 e r g / c m 2 at 0 K. The z e r o - p o i n t e n e r g y of the v i b r a t i o n a l m o d e s of the i n t e r f a c e [4] c o n t r i b ute 0.007 e r g / c m 2. T h i s g i v e s 0.10 e r g / c m 2 for the total i n t e r f a c i a l t e n s i o n at 0 K, a p p r o x i m a t e ly one half of the c l a s s i c a l e s t i m a t e . It has b e e n s u g g e s t e d [4] that an e x t r a p o l a t i o n of e x p e r i m e n t a l d e t e r m i n a t i o n s should enable one to decide between the two e s t i m a t e s , and f u r t h e r justify the i n c l u s i o n of a c o n t r i b u t i o n f r o m the v i b r a t i o n a l s u r f a c e m o d e s in the s u r f a c e t e n s io n of a quantum liquid. The i n t e r f a c i a l t e n s i o n was d e t e r m i n e d by the c a p i l l a r y r i s e in the n a r r o w gap b e t w e e n the p l a t e s of a v e r t i c a l c y l i n d r i c a l c a p a c i t o r which c o n t r o l l e d the f r e q u e n c y of an o s c i l l a t o r . The c a p i l l a r y r i s e was obtained f r o m the f r e q u e n c i e s c o r r e s p o n d i n g to the t h r e e c o n f i g u r a t i o n s of fig.1. T h i s method of e l e c t r o n i c a l l y m o n i t o r e d c a p i l l a r y r i s e was i n i t i a l l y ap p li e d to d e t e r m i n e the s u r f a c e t e n s i o n of liquid 4He, and gave r e s u l t s in good a g r e e m e n t with a c c e p t e d v a l u e s . The r e s u l t s of the i n t e r f a c i a l t e n s i o n m e a s u r e m e n t a r e d i s p l a y e d in fig. 2. A s well as the r a n dom e r r o r i n d i c a t e d at e a c h point t h e r e i s a s y s t e m a t i c e r r o r of + 0.01 e r g / c m 2. The r a t h e r

Cb)

(c)

Fig. 1. The capacitor in vertical cross-section. a) Empty b) full of non phase-separated mixture c) full of phase-separated mixture.

l a r g e e r r o r s follow m a i n l y f r o m the i n d i r e c t n a t u r e of the method. The r e s u l t s give an i n t e r f a c i a l t en si o n of (0.10 + 0.02) e r g / c m 2 at 0.33 K, i n c r e a s i n g to (0.15 + 0.02) e r g / c m 2 at 0.44 K and then falling to z e r o at the p h a s e - s e p a r a t i o n t e m perature. While the e x p e r i m e n t a l v a l u e s do not allow a r e l i a b l e e x t r a p o l a t i o n to find the i n t e r f a c i a l tension at 0 K they a r e c l e a r l y m o r e c o n s i s t e n t with the e s t i m a t e of 0.10 e r g / c m 2 than with the 0.21 e r g / c m 2 that would be e x p e c t e d c l a s s i c a l l y . The r e s u l t s t h e r e f o r e a p p e a r to c o n f i r m the v a l i d i t y

u

g ~O'lC ~5

~

0-0~

_z

'0-'2 ' #4 'o!6 TEMPERATURE(K)

'o."

Fig. 2. Plot of interfacial tension versus temperature. 419

Volume 32A, number 6

PHYSICS

e x p r e s s i n g the s u r f a c e t e n s i o n of a quantum liquid in t e r m s of an i n t r i n s i c s u r f a c e t e n s i o n p l u s a c o n t r i b u t i o n f r o m the v i b r a t i o n a l s u r f a c e modes. An i n t e r f a c i a l t e n s i o n m a x i m u m o c c u r s at 0.44 K. A m a x i m u m has a l s o been o b s e r v e d [5] in the c u r v e of s u r f a c e t e n s i o n against t e m p e r a t u r e for dilute s o l u t i o n s of 3He in 4He, a phenomenon i n t e r p r e t e d in t e r m s of the p r e s e n c e of i m p u r i t y e n e r g y l e v e l s n e a r the s u r f a c e [6].

EXPERIMENTAL OF

STUDY NEUTRAL

LETTERS

24 August 1970

References [1] G. N. Antonov, J. Chem. Phys. 5(1907) 372. [2] K. R. Atkins, Can. J. Phys. 31 (1953) 1165. [3] W. Brouwer and R. K. Pathria, Phys. Rev. 163 (1967) 200. [4] W. Brouwer and R. K. Pathria, Phys. Rev. 179 (1969) 209. [5] K. N. Zinov'eva and S. T. Boldarev, Soviet Phys.JETP 29 (1969) 585. [6] A. F. Andreev, Soviet Phys. - JETP 23 (1966) 939.

OF THE STARK BROADENING CHLORINE LINES*

N. KONJEVIC, M. P L A T I ~ A and J. L A B A T Institute of Physics, Beograd, P.O.B. 57, Yugoslavia Received 10 June 1970

Half widths of six Stark broadened neutral chlorine lines have been measured in a Z-pinch plasma. Measured broadening parameters are in favorable agreement with those calculated by Roberts.

The Stark b r o a d e n i n g of i s o l a t e d n e u t r a l atom l i n e s w as m e a s u r e d fo r a n u m b e r of a t o m s [1] and f a v o r a b l y c o m p a r e d with e x i s t i n g t h e o r y [2]. The e x t r e m e e x c e p t i o n w e r e n e a r i n f r a r e d C1 I l i n e s w h e r e the e x p e r i m e n t a l half widths d i f f e r f or f a c t o r of ten f r o m t h e o r e t i c a l ones [3]. In the m e n t i o n e d p a p e r [3] b r o a d e n i n g p a r a m e t e r s w e r e m e a s u r e d f r o m t i m e r e s o l v e d s p e c t r a of r a d i a tion e m i t t e d f r o m an e q u i l i b r i u m p l a s m a , cons i s t e d of neon with s p e c t r o s c o p i c a d d i t i v e s of c a r b o n , h y d r o g e n and c h l o r i n e , behind the r e f l e c t e d shock wave in a p r e s s u r e d r i v e n shock tube. The e l e c t r o n d e n s it y (4 - 9 × 1016 c m -3) w a s d e t e r m i n e d by m e a s u r i n g p r e s s u r e and t e m p e r a t u r e (10500 ° - 12000°K). H o w e v e r , the diff e r e n c e between c a l c u l a t e d and e x p e r i m e n t a l widths h as been r e d u c e d to a f a c t o r of 2 ( t h e o r e t i c a l v a l u e s being two t i m e s s m a l l e r than e x p e r i me nta l) within the l i m i t s of the p r e s e n t t h e o r y [4]. T he a i m of this l e t t e r i s to p r o v i d e new e x p e r i m e n t a l r e s u l t s of the Stark b r o a d e n i n g of n e u t r a l c h l o r i n e l i n e s and to c o m p a r e t h e m with the t h e o r y and o t h e r e x p e r i m e n t a l r e s u l t s . T h e p l a s m a s o u r c e was Z - p i n c h o p e r a t e d in d i c h l o r o d i f l u o r o m e t h a n e . It c o n s i s t e d of q u a r t z tube (id 13.5 m m * This work was partially supported by Federal Fund for Scientific Research. 420

or 25.4 m m ) with d i s t a n c e between e l e c t r o d e s of about 20 cm. The d i s c h a r g e was d r i v e n by 150 ~ F c o n d e u s o r bank c h a r g e d to 1.0 and 1.2 kV. D u r i n g the e x p e r i m e n t a continuous flow of d i c h l o r o d i f l u o r o m e t h a n e was s u s t a i n e d at a p r e s s u r e of about 0.1 t o r r . F o r d e t e r m i n a t i o n of axial e l e c t r o n d en si t y (range 0.7 - 1.2 × 1017 c m -3) a l a s e r i n t e r f e r o m e t r y [5] at one w a v e l e n g t h was e m ployed. I n t e r f e r o m e t r i c f r i n g e s at 6328 ~, w e r e d e t e c t e d by m e a n s of p h o t o m u l t i p l i e r p l a c e d b e hind the l a s e r . The light f r o m Z - p i n c h (end on) w as o b s e r v e d by the p h o t o m u l t i p l i e r (EMI 9529,S10 photocathode) - g r a t i n g m o n o c h r o m a t o r ( Z e i s s SPM 2, i n v e r s e l i n e a r d i s p e r s i o n 40 ~ / m m ) s y s t e m , whose output was d i s p l a y e d on a double b e a m o s c i l l o s c o p e and photographed to a n a l y z e . Another p h o t o m u l t i p l i e r (RCA 1P28) w as u s e d s i m u l t a n e o u s l y as a m o n i t o r of i n t e g r a l r a d i a t i o n f r o m the p l a s m a " (side on). The o b s e r v e d light i n t e n s i t i e s w e r e a l ways n o r m a l i z e d to the m o n i t o r s i g n a l s , although the r e p r o d u c i b i l i t y was b e t t e r than 5%. All s i g nals w e r e a n a l y z e d at a d i f f e r e n t t i m e s during p l a s m a decay. A g r e a t c a r e was taken to e n s u r e that t h e r e was no a p p r e c i a b l e s e l f a b s o r p t i o n which could affect the m e a s u r e d b r o a d e n i n g p a r a m e t e r s of i n v e s t i g a t e d l i n e s . In o r d e r to obtain Stark p r o f i l e s of C1 I l i n e s f r o m e x p e r i m e n -