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The thermoelectric power of supercritical fluid mercury
Volume 38A, number 4
THE
THERMOELECTRIC
PHYSICS LETTERS
POWER
OF
14 February 1972
SUPERCRITICAL
FLUID
MERCURY
L. J. DUCKERS and R. G. ROSS School of Mathematics and Physics, University of East Anglia, Norwich NOR 88C, UK Received 20 December 1971
The absolute thermoelectric power of fluid Hg has been determined to beyond the [iquid-vapour critieal point, and a large change has been detected at about the critical density.
Using two d i f f e r e n t types of c e ll , we have made d i r e c t m e a s u r e m e n t s of the S e e b e c k v o l t age, E(T), r e s u l t i n g f r o m a t h e r m o c o u p l e with one limb in the f o r m of a column of fluid Hg d e fined by a c e r a m i c tube, and the o t h e r limb a Pt c o u n t e r - e l e c t r o d e . Our type I c e l l was s i m i l a r to that p r e v i o u s l y used f o r Hg t h e r m o p o w e r m e a s u r e m e n t s [1,2], but in our c a s e the c e r a m ic tube was made of pure r e c r y s t a l l i z e d a l u m i na, Lu cal o x o r B eO and the m e t a l c o n t a i n e r of Mo. In our type II c e l l , the ttg was confined only in Lucalox, with the hot junction t h e r m o c o u p l e and c o u n t e r - e l e c t r o d e p r o t e c t e d by a Mo sheath. In both types of c e l l , Hg and Pt w e r e s e p a r a t e d by a wall of Mo 0.010"-0.015" thick. Cell and s p e c i m e n w e r e s u b j e c t e d to h y d r o s t a t i c p r e s s u r e in an A r g a s - f i l l e d , i n t e r n a l l y - h e a t e d v e s s e l s i m i l a r to that in [3,4] but designed f o r m o r e e x t r e m e conditions. Hot and cold junction t e m p e r a t u r e s w e r e m e a s u r e d with Pt v e r s u s P t l 3 R h t h e r m o c o u p l e s , and the p r e s s u r e was m e a s u r e d with an E t h e r t r a n s d u c e r c a l i b r a t e d a g a i n s t a d e a d - w e i g h t t e s t e r . E(T) m e a s u r e d along i s o b a r s was d i f f e r e n t i a t e d with r e s p e c t to t e m p e r a t u r e , and known v a l u e s f o r the t h e r m o p o w e r , S p t , of p u r e Pt [5] w e r e used to obtain the t h e r m o p o w e r , SHg , of p u r e Hg. The p r e s s u r e d e pendence of Spt ann of the emf of our t h e r m o couples was i g n o r e d o v e r our r a n g e of v a r i a b l e s up to 2kb and 1650°C. At r e l a t i v e l y high Hg d e n s i t i e s , we found SHg to be n eg at i v e, and the v a l u e s we obtained w e r e in r e a s o n a b l e a g r e e m e n t with p r e v i o u s r e s u l t s [1,2, 6]. In the e x t e n s i v e m e a s u r e m e n t s of S c h m u t z l e r and H e n s e l [6] only n e g a t i v e v a l u e s f or SHg w e r e obtained, but in the i m m e d i a t e s u p e r c r i t i c a l r e g i o n , w h e r e they did not r e p o r t data, we find e v i d e n c e of a rapid change of SHg to values ~ 0. Our r e s u l t s , which have a l r e a d y been r e p o r t e d in p r e l i m i n a r y f o r m [7], a r e s u m m a r i z e d ' h e r e in fig. 1.
1.9
/
----'~
IB "~1"7 W U2 1"5 "~oo
/ " ,,so
,~o
,s~
TEM PERATURF_.,°C
Fig. 1. Points of change for E(T) for various conditions and ceils. Type I cell: with A1203 (m,[~), with BeO(x); type II celt (A). Estimated critical point - i - " At the points indicated (m), E(T) and the total r e s i s t a n c e of c e l l + s p e c i m e n jumped s i m u l t a neously and discontinuously to l a r g e v a l u e s as the t e m p e r a t u r e was i n c r e a s e d . Since this b e haviour i n v a r i a b l y o c c u r r e d at p r e s s u r e s l e s s than the c r i t i c a l p r e s s u r e , Pc, r e p o r t e d by p r e vious w o r k e r s [8, 9], we a t t r i b u t e d it to r e a c h i n g the l i q u i d - v a p o u r e q u i l i b r i u m c u r v e at the hot junction of the cell. At t e m p e r a t u r e s ca. 1000°C and below, the vapour p r e s s u r e c u r v e we d e t e r mined by this method was i n d i st i n g u i sh ab l e f r o m that of H e n s e l and F r a n c k [8], but our c u r v e d e viated to t e m p e r a t u r e s of a few tens of d e g r e e s l o w er than t h e i r s n e a r the c r i t i c a l point. This deviation is c o n s i s t e n t with the data of [9]. 291
Volume 38A. n u m b e r 4
PHYSICS
A r o u n d t h e p o i n t s i n d i c a t e d ( ~ , ×, A), a t e m p e r a t u r e c h a n g e of a b o u t 10°C p r o d u c e d a c h a n g e in t h e s i g n of d E / d T r e p r o d u c i b l y on h e a t i n g a n d c o o l i n g . B o t h E(T) a n d t h e t o t a l r e s i s t a n c e of c e l l + s p e c i m e n r e m a i n e d c o n t i n u o u s f u n c t i o n s of temperature. From this continuity, and from the p r e s s u r e s > Pc w h e r e t h i s b e h a v i o u r w a s o b s e r v e d , we c o n c l u d e d t h a t it w a s to b e a s s o ciated with the single-phase supercritical fluid. Since Spt varies smoothly at these temperat u r e s , we i n t e r p r e t o u r r e s u l t s a s i n d i c a t i n g a s u b s t a n t i a l a n d r a p i d c h a n g e in SHg. T o t h e l e f t of t h e p o i n t s s h o w n , SHg w a s ~ - 1 0 0 t~VK -1, a n d to t h e r i g h t it w a s ~ 0. To exclude the possibility that the measured c h a n g e of s i g n of d E / d T is d u e to t h e t h e r m o e l e c t r i c i t y of t h e c e l l , we u s e t h e f o r m u l a f r o m [10] f o r t h e t h e r m o p o w e r , Sc, of c o n d u c t o r s A a n d B in p a r a l l e l .
Sc = ( S A / R A + S B / R B } / ( 1 / R A + 1 / R B ) ;
(1)
SA a n d R A a r e t h e t h e r m o p o w e r a n d r e s i s t a n c e of m a t e r i a l A a n d s i m i l a r l y f o r B. W e a p p l y eq. (1) to o u r t y p e II c e l l w i t h L u c a l o x a n d Hg in parallel. Existing data show that Ssapphire is probably negative above 1200°C [11-15], and so, presuma b l y , i s SLucalo x. A l l o w i n g f o r S p t , we m u s t t h e r e f o r e a t t r i b u t e t h e m e a s u r e d d E / d T to a n e a r z e r o SHg. M e a s u r e m e n t s w i t h B e O a g r e e d within experimental error with those with A 1 2 0 3 , w h i c h a l s o m a k e s it u n l i k e l y t h a t t h e ceramic contribution is predominant under t h e s e c o n d i t i o n s . T h e c o n t r i b u t i o n f r o m t h e Mo w a l l s e p a r a t i n g Hg a n d P t i s too s m a l l in m a g n i t u d e to a c c o u n t f o r t h e o b s e r v a t i o n s , a n d would not give a sharp and reproducible effect. W e c o n c l u d e , t h e r e f o r e , t h a t SHg c h a n g e s f r o m l a r g e n e g a t i v e to n e a r z e r o v a l u e s on h e a t ing a c r o s s t h e l i n e ( [ ~ , × , A ) in fig. 1. T h i s l i n e almost certainly approximates the critical isoc h o r e ( s e e [16] f o r a d i s c u s s i o n of t h i s p o i n t ) .
292
LETTERS
14 F e b r u a r y 1972
From our measurements, we e s t i m a t e T c = 1 4 6 2 ° C , in good a g r e e m e n t w i t h [17] b u t s l i g h t l y l o w e r t h a n [8, 9]. O u r v a l u e Pc = 1513 b a g r e e s w e l l w i t h [8, 9]. We are currently considering the theoretical i n t e r p r e t a t i o n of t h e s e r e s u l t s , a n d t h e i r r e l a t i o n to e x i s t i n g o p t i c a l , e l e c t r i c a l a n d e q u a t i o n of s t a t e d a t a f o r Hg.
References [1] V. Crisp and N.E. Cusaek, Phys. L e t t e r s 28A (1969) 712. [2] V. t{. C. Crisp, N. E. Cusaek and P. W. Kendall, J. Phys. C, Metal Phys. Suppl. no. 1 (1970) $102. [3] D.R.Postill, R.G. Ross and N.E. Cusaek, Adv. Phys. 16 (1967) 493. [4] D.R. Postili, R.G. Ross and N.E. Cusaek, Phil. Mag. 18 (1968) 519. [5] N. Cusaek and P. Kendall, Proe. Phys. Soe. 72 (1958) 898. [6] R. Sehmutzler and F. Hensel, Phys. L e t t e r s 35A (1971) 55. [7] L . J . Duekers and R.G. Ross, 9th Ann. Meeting Eur. High P r e s s . Group, Umea, Sweden, 1971, not published. [8] F. Hensel and E.U. F r a n c k , Ber. Bunsengesellsehaft fiir phys. Chem. 70 (1966) 1154. [9] I. K. Kikoin and A. P. Senehenkov, Phys. Metals and Metall. 24 no. 5 (1967) 74. [ 10] D.K.C. MacDonald, T h e r m o e l e e t r i e i t y (Wiley, 1962) p. 115. [11] D.W. P e t e r s , J. Phys. Chem. Solids 27 (1966) 1560. [12] S. DasGupta and J. Hart. Brit. J. Appl. Phys. 16 (1965) 725. [13] G. M. Stulova and Yu.K. Shalabutov, Soy. Phys. Semicond. 1 (1968) 996. [14] P . J . H a r r o p a n d R.H. C r e a m e r , Brit. J. Appl. Phys. 14 (1963) 335. [ 15] R. R. C r e a m e r , private communication ( 1971). Dr. C r e a m e r has informed us that the value of for sapphire in [14] should be negative, and that it r e f e r s to 1300°C. [16] R.G. Ross and D. A. Greenwood, P r o g r . Mater. Sci. 14 (1969) 173. [17] F. Birch, Phys. Rev. 41 (1932) 641.
THE
THERMOELECTRIC
PHYSICS LETTERS
POWER
OF
14 February 1972
SUPERCRITICAL
FLUID
MERCURY
L. J. DUCKERS and R. G. ROSS School of Mathematics and Physics, University of East Anglia, Norwich NOR 88C, UK Received 20 December 1971
The absolute thermoelectric power of fluid Hg has been determined to beyond the [iquid-vapour critieal point, and a large change has been detected at about the critical density.
Using two d i f f e r e n t types of c e ll , we have made d i r e c t m e a s u r e m e n t s of the S e e b e c k v o l t age, E(T), r e s u l t i n g f r o m a t h e r m o c o u p l e with one limb in the f o r m of a column of fluid Hg d e fined by a c e r a m i c tube, and the o t h e r limb a Pt c o u n t e r - e l e c t r o d e . Our type I c e l l was s i m i l a r to that p r e v i o u s l y used f o r Hg t h e r m o p o w e r m e a s u r e m e n t s [1,2], but in our c a s e the c e r a m ic tube was made of pure r e c r y s t a l l i z e d a l u m i na, Lu cal o x o r B eO and the m e t a l c o n t a i n e r of Mo. In our type II c e l l , the ttg was confined only in Lucalox, with the hot junction t h e r m o c o u p l e and c o u n t e r - e l e c t r o d e p r o t e c t e d by a Mo sheath. In both types of c e l l , Hg and Pt w e r e s e p a r a t e d by a wall of Mo 0.010"-0.015" thick. Cell and s p e c i m e n w e r e s u b j e c t e d to h y d r o s t a t i c p r e s s u r e in an A r g a s - f i l l e d , i n t e r n a l l y - h e a t e d v e s s e l s i m i l a r to that in [3,4] but designed f o r m o r e e x t r e m e conditions. Hot and cold junction t e m p e r a t u r e s w e r e m e a s u r e d with Pt v e r s u s P t l 3 R h t h e r m o c o u p l e s , and the p r e s s u r e was m e a s u r e d with an E t h e r t r a n s d u c e r c a l i b r a t e d a g a i n s t a d e a d - w e i g h t t e s t e r . E(T) m e a s u r e d along i s o b a r s was d i f f e r e n t i a t e d with r e s p e c t to t e m p e r a t u r e , and known v a l u e s f o r the t h e r m o p o w e r , S p t , of p u r e Pt [5] w e r e used to obtain the t h e r m o p o w e r , SHg , of p u r e Hg. The p r e s s u r e d e pendence of Spt ann of the emf of our t h e r m o couples was i g n o r e d o v e r our r a n g e of v a r i a b l e s up to 2kb and 1650°C. At r e l a t i v e l y high Hg d e n s i t i e s , we found SHg to be n eg at i v e, and the v a l u e s we obtained w e r e in r e a s o n a b l e a g r e e m e n t with p r e v i o u s r e s u l t s [1,2, 6]. In the e x t e n s i v e m e a s u r e m e n t s of S c h m u t z l e r and H e n s e l [6] only n e g a t i v e v a l u e s f or SHg w e r e obtained, but in the i m m e d i a t e s u p e r c r i t i c a l r e g i o n , w h e r e they did not r e p o r t data, we find e v i d e n c e of a rapid change of SHg to values ~ 0. Our r e s u l t s , which have a l r e a d y been r e p o r t e d in p r e l i m i n a r y f o r m [7], a r e s u m m a r i z e d ' h e r e in fig. 1.
1.9
/
----'~
IB "~1"7 W U2 1"5 "~oo
/ " ,,so
,~o
,s~
TEM PERATURF_.,°C
Fig. 1. Points of change for E(T) for various conditions and ceils. Type I cell: with A1203 (m,[~), with BeO(x); type II celt (A). Estimated critical point - i - " At the points indicated (m), E(T) and the total r e s i s t a n c e of c e l l + s p e c i m e n jumped s i m u l t a neously and discontinuously to l a r g e v a l u e s as the t e m p e r a t u r e was i n c r e a s e d . Since this b e haviour i n v a r i a b l y o c c u r r e d at p r e s s u r e s l e s s than the c r i t i c a l p r e s s u r e , Pc, r e p o r t e d by p r e vious w o r k e r s [8, 9], we a t t r i b u t e d it to r e a c h i n g the l i q u i d - v a p o u r e q u i l i b r i u m c u r v e at the hot junction of the cell. At t e m p e r a t u r e s ca. 1000°C and below, the vapour p r e s s u r e c u r v e we d e t e r mined by this method was i n d i st i n g u i sh ab l e f r o m that of H e n s e l and F r a n c k [8], but our c u r v e d e viated to t e m p e r a t u r e s of a few tens of d e g r e e s l o w er than t h e i r s n e a r the c r i t i c a l point. This deviation is c o n s i s t e n t with the data of [9]. 291
Volume 38A. n u m b e r 4
PHYSICS
A r o u n d t h e p o i n t s i n d i c a t e d ( ~ , ×, A), a t e m p e r a t u r e c h a n g e of a b o u t 10°C p r o d u c e d a c h a n g e in t h e s i g n of d E / d T r e p r o d u c i b l y on h e a t i n g a n d c o o l i n g . B o t h E(T) a n d t h e t o t a l r e s i s t a n c e of c e l l + s p e c i m e n r e m a i n e d c o n t i n u o u s f u n c t i o n s of temperature. From this continuity, and from the p r e s s u r e s > Pc w h e r e t h i s b e h a v i o u r w a s o b s e r v e d , we c o n c l u d e d t h a t it w a s to b e a s s o ciated with the single-phase supercritical fluid. Since Spt varies smoothly at these temperat u r e s , we i n t e r p r e t o u r r e s u l t s a s i n d i c a t i n g a s u b s t a n t i a l a n d r a p i d c h a n g e in SHg. T o t h e l e f t of t h e p o i n t s s h o w n , SHg w a s ~ - 1 0 0 t~VK -1, a n d to t h e r i g h t it w a s ~ 0. To exclude the possibility that the measured c h a n g e of s i g n of d E / d T is d u e to t h e t h e r m o e l e c t r i c i t y of t h e c e l l , we u s e t h e f o r m u l a f r o m [10] f o r t h e t h e r m o p o w e r , Sc, of c o n d u c t o r s A a n d B in p a r a l l e l .
Sc = ( S A / R A + S B / R B } / ( 1 / R A + 1 / R B ) ;
(1)
SA a n d R A a r e t h e t h e r m o p o w e r a n d r e s i s t a n c e of m a t e r i a l A a n d s i m i l a r l y f o r B. W e a p p l y eq. (1) to o u r t y p e II c e l l w i t h L u c a l o x a n d Hg in parallel. Existing data show that Ssapphire is probably negative above 1200°C [11-15], and so, presuma b l y , i s SLucalo x. A l l o w i n g f o r S p t , we m u s t t h e r e f o r e a t t r i b u t e t h e m e a s u r e d d E / d T to a n e a r z e r o SHg. M e a s u r e m e n t s w i t h B e O a g r e e d within experimental error with those with A 1 2 0 3 , w h i c h a l s o m a k e s it u n l i k e l y t h a t t h e ceramic contribution is predominant under t h e s e c o n d i t i o n s . T h e c o n t r i b u t i o n f r o m t h e Mo w a l l s e p a r a t i n g Hg a n d P t i s too s m a l l in m a g n i t u d e to a c c o u n t f o r t h e o b s e r v a t i o n s , a n d would not give a sharp and reproducible effect. W e c o n c l u d e , t h e r e f o r e , t h a t SHg c h a n g e s f r o m l a r g e n e g a t i v e to n e a r z e r o v a l u e s on h e a t ing a c r o s s t h e l i n e ( [ ~ , × , A ) in fig. 1. T h i s l i n e almost certainly approximates the critical isoc h o r e ( s e e [16] f o r a d i s c u s s i o n of t h i s p o i n t ) .
292
LETTERS
14 F e b r u a r y 1972
From our measurements, we e s t i m a t e T c = 1 4 6 2 ° C , in good a g r e e m e n t w i t h [17] b u t s l i g h t l y l o w e r t h a n [8, 9]. O u r v a l u e Pc = 1513 b a g r e e s w e l l w i t h [8, 9]. We are currently considering the theoretical i n t e r p r e t a t i o n of t h e s e r e s u l t s , a n d t h e i r r e l a t i o n to e x i s t i n g o p t i c a l , e l e c t r i c a l a n d e q u a t i o n of s t a t e d a t a f o r Hg.
References [1] V. Crisp and N.E. Cusaek, Phys. L e t t e r s 28A (1969) 712. [2] V. t{. C. Crisp, N. E. Cusaek and P. W. Kendall, J. Phys. C, Metal Phys. Suppl. no. 1 (1970) $102. [3] D.R.Postill, R.G. Ross and N.E. Cusaek, Adv. Phys. 16 (1967) 493. [4] D.R. Postili, R.G. Ross and N.E. Cusaek, Phil. Mag. 18 (1968) 519. [5] N. Cusaek and P. Kendall, Proe. Phys. Soe. 72 (1958) 898. [6] R. Sehmutzler and F. Hensel, Phys. L e t t e r s 35A (1971) 55. [7] L . J . Duekers and R.G. Ross, 9th Ann. Meeting Eur. High P r e s s . Group, Umea, Sweden, 1971, not published. [8] F. Hensel and E.U. F r a n c k , Ber. Bunsengesellsehaft fiir phys. Chem. 70 (1966) 1154. [9] I. K. Kikoin and A. P. Senehenkov, Phys. Metals and Metall. 24 no. 5 (1967) 74. [ 10] D.K.C. MacDonald, T h e r m o e l e e t r i e i t y (Wiley, 1962) p. 115. [11] D.W. P e t e r s , J. Phys. Chem. Solids 27 (1966) 1560. [12] S. DasGupta and J. Hart. Brit. J. Appl. Phys. 16 (1965) 725. [13] G. M. Stulova and Yu.K. Shalabutov, Soy. Phys. Semicond. 1 (1968) 996. [14] P . J . H a r r o p a n d R.H. C r e a m e r , Brit. J. Appl. Phys. 14 (1963) 335. [ 15] R. R. C r e a m e r , private communication ( 1971). Dr. C r e a m e r has informed us that the value of for sapphire in [14] should be negative, and that it r e f e r s to 1300°C. [16] R.G. Ross and D. A. Greenwood, P r o g r . Mater. Sci. 14 (1969) 173. [17] F. Birch, Phys. Rev. 41 (1932) 641.