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The absolute thermoelectric power of liquid metals
Volume 22, number 5
PHYSICS LETTERS
THE A B S O L U T E T H E R M O E L E C T R I C
15 September 1965
PO'WER OF
LIQUID METALS
A. S. MARWAHA
B i r b e c k College, London
and N. E. CUSACK University of E a s t Anglfa Received 28 July 1966
The results of new measurements of the absolute thermoelectric power of ten liquid metals are reported. These measurements extend uptol000OKfor most metals and include A1 and T1, for which there seems to be no other published data.
This l e t t e r p r e s e n t s r e s u l t s of new m e a s u r e m e n t s of the absolute t h e r m o e l e c t r i c p o w e r of ten liquid m e t a l s . The m o s t r e c e n t c o m p a r a b l e v a l ue s a r e those of B r a d l e y [1] and the p r e s e n t w o r k is by a technique d i f f e r e n t f r o m B r a d l e y ' s , c o v e r s a s o m e w h a t w i d e r t e m p e r a t u r e r a n g e and adds v a l u e s f o r the t h e r m o e l e c t r i c p o w e r s of liquid A1 and T1 which a r e the f i r s t a v a i l a b l e as f a r as we know. The b a s i c method was e s s e n t i a l l y that of C u s a c k et al. [2] with s o m e t e c h n i c a l i m p r o v e m e n t s . The S eeb eck v o lt a g e of a t h e r m o c o u p l e c o n s i s t i n g of the liquid m e t a l and a p u r e c o p p e r o r platinum w i r e was m e a s u r e d and fitted by l e a s t s q u a r e s to a p a r a b o l a ; this could always be done within e x p e r i m e n t a l e r r o r l e a v i n g the e x p e r i m e n t a l v a l u e s d i s t r i b u t e d r a n d o m l y about the p a r a b o l a . The t h e r m o e l e c t r i c p o w e r was obtained by d i f f e r e n t i a t i o n with r e s p e c t to t e m p e r a t u r e and the absolute t h e r m o e l e c t r i c p o w e r of Cu or Pt was s u b t r a c t e d . The value used f o r Cu was: SCu = 0.05 + ( 5 . 4 5 × 1 0 - 3 ) T p V / d e g . F o r Pt, v a l u e s given by C u s a c k and Kendall [3] w e r e used. In all c a s e s S could be r e p r e s e n t e d by an empirical formula S = a+bT
#V/deg
w h e r e T is the absolute t e m p e r a t u r e . The v a l u e s obtained w e r e as g i v e n in table 1. The e r r o r in s is difficult to e s t i m a t e but the absolute value should not be in e r r o r by m o r e than + 0.2 /iV/deg. It is p o s s i b l e to c a l c u l a t e a t h e o r e t i c a l value f o r S f r o m Z i m a n ' s t h e o r y as is done by, f o r e x 556
Table 1 Metal
A1 Bi Cd Ga Hg In Pb Sn Tl Zn
S(Tm) a 103b Temperature range (/IV/deg) (#V/deg) (//V/deg2) (OK) Tm to: -2.1 -0.7 0.5 -0.4 -3.5 -I.0 -3.4 -0.5 -0.5 0.1
0 0 0 0 2.00 0 0 0 1.42 -2.94
-2.24 -1.31 0.79 -1.28 -23.33 -2.38 -5.72 -1.03 -3.38 4.42
1250 1O0O 100O 1000 585 1000 1000 I000 1000 1000
a m p l e , Su n d st r o m [4]. F o r this p u r p o s e it is n e c e s s a r y to choose f r o m the l i t e r a t u r e p seu d o p o t e n t i a l m a t r i x e l e m e n t s , U(K), and s t r u c t u r a l inf o r m a t i o n , often r e p r e s e n t e d by the s t r u c t u r e f a c t o r a(K). T h e r e is by now quite a v a r i e t y of U(K) and a(K) to choose f r o m (see f o r e x a m p l e W i s e r [5]) and so s e n s i t i v e to the c h o i c e is the c a l c u l a t e d value of S that we c o n s i d e r it i m p o s s i b l e at p r e s e n t to t e s t the t h e o r y i t s e l f by c o m p a r i n g the e x p e r i m e n t a l and c a l c u l a t e d S. F o r e x a m p l e d i f f e r e n t c h o i c e s of U(K) and a(K) give c a l c u l a t e d v a l u e s of S p b ( T m) equal to -4.4, -0.03, 0.2 and 1.1 /~V/deg. This l a t t e r point and f u r t h e r t e c h n i c a l d e t a i l s of the e x p e r i m e n t will be d i s c u s s e d m o r e fully elsewhere. 1. C.C.Bradley, Phil. Mag. 7 (1962) 1337. 2. N.E.Cusack, P.W. Kendall and A.S.Marwaha, Phil. Mag. 7 (1962) 1745. 3. N.E. Cusack and P.W. Kendall, Proc. Phys. Soc. 72 (1958) 898. 4. L.J.Sundstrom, Phil. Mag. l l (1965) 657. 5. N.Wiser, Phys. Rev. 143 (1966)393.
PHYSICS LETTERS
THE A B S O L U T E T H E R M O E L E C T R I C
15 September 1965
PO'WER OF
LIQUID METALS
A. S. MARWAHA
B i r b e c k College, London
and N. E. CUSACK University of E a s t Anglfa Received 28 July 1966
The results of new measurements of the absolute thermoelectric power of ten liquid metals are reported. These measurements extend uptol000OKfor most metals and include A1 and T1, for which there seems to be no other published data.
This l e t t e r p r e s e n t s r e s u l t s of new m e a s u r e m e n t s of the absolute t h e r m o e l e c t r i c p o w e r of ten liquid m e t a l s . The m o s t r e c e n t c o m p a r a b l e v a l ue s a r e those of B r a d l e y [1] and the p r e s e n t w o r k is by a technique d i f f e r e n t f r o m B r a d l e y ' s , c o v e r s a s o m e w h a t w i d e r t e m p e r a t u r e r a n g e and adds v a l u e s f o r the t h e r m o e l e c t r i c p o w e r s of liquid A1 and T1 which a r e the f i r s t a v a i l a b l e as f a r as we know. The b a s i c method was e s s e n t i a l l y that of C u s a c k et al. [2] with s o m e t e c h n i c a l i m p r o v e m e n t s . The S eeb eck v o lt a g e of a t h e r m o c o u p l e c o n s i s t i n g of the liquid m e t a l and a p u r e c o p p e r o r platinum w i r e was m e a s u r e d and fitted by l e a s t s q u a r e s to a p a r a b o l a ; this could always be done within e x p e r i m e n t a l e r r o r l e a v i n g the e x p e r i m e n t a l v a l u e s d i s t r i b u t e d r a n d o m l y about the p a r a b o l a . The t h e r m o e l e c t r i c p o w e r was obtained by d i f f e r e n t i a t i o n with r e s p e c t to t e m p e r a t u r e and the absolute t h e r m o e l e c t r i c p o w e r of Cu or Pt was s u b t r a c t e d . The value used f o r Cu was: SCu = 0.05 + ( 5 . 4 5 × 1 0 - 3 ) T p V / d e g . F o r Pt, v a l u e s given by C u s a c k and Kendall [3] w e r e used. In all c a s e s S could be r e p r e s e n t e d by an empirical formula S = a+bT
#V/deg
w h e r e T is the absolute t e m p e r a t u r e . The v a l u e s obtained w e r e as g i v e n in table 1. The e r r o r in s is difficult to e s t i m a t e but the absolute value should not be in e r r o r by m o r e than + 0.2 /iV/deg. It is p o s s i b l e to c a l c u l a t e a t h e o r e t i c a l value f o r S f r o m Z i m a n ' s t h e o r y as is done by, f o r e x 556
Table 1 Metal
A1 Bi Cd Ga Hg In Pb Sn Tl Zn
S(Tm) a 103b Temperature range (/IV/deg) (#V/deg) (//V/deg2) (OK) Tm to: -2.1 -0.7 0.5 -0.4 -3.5 -I.0 -3.4 -0.5 -0.5 0.1
0 0 0 0 2.00 0 0 0 1.42 -2.94
-2.24 -1.31 0.79 -1.28 -23.33 -2.38 -5.72 -1.03 -3.38 4.42
1250 1O0O 100O 1000 585 1000 1000 I000 1000 1000
a m p l e , Su n d st r o m [4]. F o r this p u r p o s e it is n e c e s s a r y to choose f r o m the l i t e r a t u r e p seu d o p o t e n t i a l m a t r i x e l e m e n t s , U(K), and s t r u c t u r a l inf o r m a t i o n , often r e p r e s e n t e d by the s t r u c t u r e f a c t o r a(K). T h e r e is by now quite a v a r i e t y of U(K) and a(K) to choose f r o m (see f o r e x a m p l e W i s e r [5]) and so s e n s i t i v e to the c h o i c e is the c a l c u l a t e d value of S that we c o n s i d e r it i m p o s s i b l e at p r e s e n t to t e s t the t h e o r y i t s e l f by c o m p a r i n g the e x p e r i m e n t a l and c a l c u l a t e d S. F o r e x a m p l e d i f f e r e n t c h o i c e s of U(K) and a(K) give c a l c u l a t e d v a l u e s of S p b ( T m) equal to -4.4, -0.03, 0.2 and 1.1 /~V/deg. This l a t t e r point and f u r t h e r t e c h n i c a l d e t a i l s of the e x p e r i m e n t will be d i s c u s s e d m o r e fully elsewhere. 1. C.C.Bradley, Phil. Mag. 7 (1962) 1337. 2. N.E.Cusack, P.W. Kendall and A.S.Marwaha, Phil. Mag. 7 (1962) 1745. 3. N.E. Cusack and P.W. Kendall, Proc. Phys. Soc. 72 (1958) 898. 4. L.J.Sundstrom, Phil. Mag. l l (1965) 657. 5. N.Wiser, Phys. Rev. 143 (1966)393.