Electron model for the thermoelectric properties of gold
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I) P R O P O S E D
MODEL
Molt and J o n e s a have shown that a g e n e r a l e x p r e s s i o n f o r the a b s o l u t e t h e r m o e l e c t r i c p o w e r is given by: (1~ / 0 S - 7rZKZT
~ff--v~(E))} E = E F
[1]
w h e r e K is B o l t z m a n n ' s c o n s t a n t , T is the a b s o l u t e t e m p e r a t u r e , a(E) is the e l e c t r i c a l c o n d u c t i v i t y e v a l u a t e d at the F e r m i l e v e l , EF, and e is the c h a r g e on the c a r r i e r . T h u s , S will r e f l e c t c h a n g e s in e l e c t r o n i c s t r u c t u r e b e c a u s e ~r(E) is s e n s i t i v e to this f a c t o r . When cr(E) i s a p p r o x i m a t e d ~ by a(E) = c o n s t . E x
[2]
in the r e g i o n E ~-EF, the a b s o l u t e t h e r m o e l e c t r i c p o w e r is e x p r e s s e d by 7]2 K 2 T
s-
E~ 3e
x
[3]
Mott and J o n e s have shown that the e m p i r i c a l v a l u e s of the c o n s t a n t x r e q u i r e d to f i t the o b s e r v e d b e h a v i o r s D. D. POLLOCK is Professor of Engineering, Faculty of Engineering and Applied Science, State University of New York, Buffalo, N. Y. 14214. Manuscript submitted April 21, 1972. METALLURGICAL TRANSACTIONS
of the noble m e t a l s lie between - 1 . 1 and -1.6,2 d e p e n d ing upon the m e t a l . Eq. [3] p r e d i c t s p o s i t i v e , l i n e a r v a l u e s of S with p o s i t i v e s l o p e s a s functions of t e m p e r a t u r e . T h i s a g r e e s with the o b s e r v e d b e h a v i o r of gold only up to about 400 K. It is c o n s i d e r e d that the d e v i a t i o n s f r o m l i n e a r i t y beyond 400 K i n d i c a t e that c h a n g e s p r o b a b l y take p l a c e in the conduction p r o c e s s . It thus m a y be a s s u m e d that a s i g n i f i c a n t change in the conduction m e c h a n i s m b e c o m e s o p e r a t i v e beyond 400 K. Such a change would be r e q u i r e d to p r o g r e s s i v e l y affect the conduction p r o c e s s with i n c r e a s i n g temperatures. The p r o p o s e d m o d e l for this b e h a v i o r i s obtained by c o n s i d e r i n g the r e l a t i o n s h i p b e t w e e n the 5d and 6s s t a t e s of gold. At low t e m p e r a t u r e s gold p o s s e s s e s the e l e c t r o n i c c o n f i g u r a t i o n c o m m o n l y a s c r i b e d to the noble m e t a l s ; the f i l l e d d band l i e s below the F e r m i l e v e l . A s the t e m p e r a t u r e i n c r e a s e s , and 400 K is a p p r o a c h e d , the top of the d band and the F e r m i l e v e l a r e c o n s i d e r e d to move c l o s e r t o g e t h e r . Up to the point w h e r e the top of the d band l i e s j u s t below EF, the e l e c t r i c a l conduction is e n t i r e l y by the h a l f - f i l l e d s band. E q s . [2] and [3] e m b o d y the e l e c t r o n i c b e h a v i o r in this r a n g e of t e m p e r a t u r e . In the n e i g h b o r h o o d of 400 to 500 K the top of the d band is c o n s i d e r e d to j u s t o v e r l a p the F e r m i l e v e l ; s - d h y b r i d i z a t i
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