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Composition and electronic structure of stage II BF4- intercalated graphite
Solid State Communications, Vol.55,No.5, pp.40]-403, ]985. Printed in Great Britain.
COMPOSITION
AND
ELECTRONIC H.
Department
STRUCTURE
Zaleski,
of P h y s i c s ,
P.K.
McMaster
(Received
1 March
OF STAGE Ummat
II BF 4- I N T E R C A L A T E D
a n d W.R.
University, 1985
0038-]098/85 $3.00 + .00 Pergamon Press Ltd.
b y M.
GRAPHITE
Datars
Hamilton,
Canada,
L8S 4M1
F. C o l l i n s )
G r a p h i t e w a s r e a c t e d w i t h s o l i d n i t r y l t e t r a f l u o r o b o r a t e to f o r m a s t a g e II c o m p o u n d . T h e e x p e r i m e n t a l de H a a s - v a n A l p h e n f r e q u e n c i e s a n d c y c l o t r o n m a s s e s a r e in a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s of the r i g i d b a n d m o d e l w i t h the F e r m i e n e r g y e q u a l to -0.96 eV. T h e c h a r g e t r a n s f e r is o n e e l e m e n t a r y c h a r g e per 41.5 c a r b o n atoms.
Introduction
nitryl tetrafluoroborate. A large charge transfer results from chemical oxidation of c a r b o n b y the n i t r y l ion (NO2+). T h e c o m p o u n d is c h a r a c t e r i z e d b y w e i g h t uptake and X-ray diffraction. The band p a r a m e t e r s a r e o b t a i n e d f r o m de H a a s - v a n A l p h e n (dHvA) e f f e c t m e a s u r e m e n t s which also provide additional information a b o u t the s t r u c t u r e and the c o m p o s i t i o n of the c o m p o u n d .
Graphite intercalation compounds (GIC) a r e s y n t h e t i c c o n d u c t o r s w h o s e s t r u c t u r e c o n s i s t s of a r e g u l a r s e q u e n c e of a l t e r n a t i n g m o n o l a y e r s of i n t e r c a l a t e a n d n l a y e r s of carbon, w h e r e n is the s t a g e index. T h e s e m a t e r i a l s e x h i b i t m e t a l l i c c o n d u c t i v i t y d u e to c h a r g e t r a n s f e r b e t w e e n c a r b o n and i n t e r c a l a t e that i n c r e a s e s the n u m b e r of c a r r i e r s in c a r b o n layers. T h e c o m p o u n d s h a v e u s u a l l y a l a r g e n u m b e r of a t o m s per u n i t cell t h a t m a k e s f i r s t - p r i n c i p l e b a n d structure calculations difficult. Instead, p h e n o m e n o l o g i c a l rigid band m o d e l s h a v e b e e n d e v e l o p e d l,z,3. T h e y a s s u m e that the e l e c t r o n i c s t r u c t u r e of G I C c a n b e a p p r o x i m a t e d b y the s t r u c t u r e of n g r a p h e n e l a y e r s for a s t a g e n c o m p o u n d . T h e F e r m i e n e r g y is a d j u s t e d to a c c o m m o d a t e c a r r i e r s c o m i n g f r o m the intercalate. The simplest band structure model based on a tight binding nearest neighbor approximation has been proposed b y B l i n o w s k i et al I . T h e m o d e l h a s b e e n s u c c e s s f u l l y u s e d to e x p l a i n o p t i c a l p r o p e r t i e s of s o m e a c c e p t o r G I C 1,5. However, quantum oscillatory phenomena measurements 6 showed a discrepancy b e t w e e n t h e o r e t i c a l p r e d i c t i o n s and e x p e r i m e n t a l d a t a that p r o m p t e d the a u t h o r s to s u g g e s t a v a r i a t i o n of i n t e r a t o m i c i n t e r a c t i o n s as a f u n c t i o n of c h a r g e t r a n s f e r . R e c e n t l y , the a n a l y s i s of de H a a s v a n A l p h e n d a t a of SbCI 5 s t a g e I a n d II and S b F 6- s t a g e I c o m p o u n d s 7 s h o w e d t h e i m p o r t a n c e of m o r e d i s t a n t n e i g h b o r i n t e r a c t i o n s and, in fact, g o o d agreement was obtained between data and the r i g i d b a n d m o d e l p r o p o s e d b y Holzwarth 3 . In this w o r k w e r e e x a m i n e the validity of the rigid band model of H o l z w a r t h for the d e s c r i p t i o n of the e l e c t r o n i c s t r u c t u r e of the s t a g e II BF 4- c o m p o u n d . T h e c o m p o u n d is p r e p a r e d b y a r e a c t i o n of g r a p h i t e w i t h s o l i d
Experimental P i e c e s of p y r o l i t i c g r a p h i t e (HOPG) w e r e p u t i n t o a g l a s s t u b e in c o n t a c t w i t h s o l i d N O 2 B F 4 salt. T h e t u b e w a s e v a c u a t e d , s e a l e d and p u t i n t o an o v e n at 85 °C for o n e day. A b l a c k c o m p o u n d with greenish shade was obtained. S a m p l e s w e r e put i n t o a v a c u u m t i g h t h o l d e r and p l a c e d in the d H v A a p p a r a t u s . Different samples cooled from room t e m p e r a t u r e to 77 K s l o w l y (~12 hrs) a n d q u i c k l y (~lhr) g a v e the s a m e d H v A spectrum. The dHvA effect measured by the m o d u l a t i o n t e c h n i q u e w a s p e r f o r m e d w i t h e a c h s a m p l e ' s c - a x i s p a r a l l e l to t h e d i r e c t i o n of t h e m a g n e t i c f i e l d of a superconducting selenoid. The signal was s a m p l e d a n d a n a l y z e d b y an a q u i s i t i o n s y s t e m c o n n e c t e d to a m i c r o c o m p u t e r . T h e cyclotron masses were determined from the t e m p e r a t u r e d e p e n d e n c e of the d H v A a m p l i t u d e s b e t w e e n 1.3 and 4.2 K. Results
and
Discussion
T h e (OO1) X - r a y d i f f r a c t i o n p a t t e r n s h o w e d that a p u r e s t a g e II c o m p o u n d w a s obtained. The c-axis identity period w a s I c = 1 1 . 1 3 + 0.02 A. T h e w e i g h t u p t a k e d u r i n g the r e a c t i o n w a s 68 + 3 %. T h e B F 4- ion w a s p r e v i o u s l y i n t e r c a l a t e d b y r e a c t i o n of n i t r y l t e t r a f l u o r o b o r a t e d i s s o l v e d in d r y n i t r o m e t h a n e 8 a n d b y a c t i o n of g a s e o u s p r o d u c t s of t h e r m a l decomposition of N O 2 B F 4 s a l t 9. T h e I c v a l u e of t h i s w o r k is s l i g h t l y s m a l l e r t h a n t h a t o b t a i n e d in s o l u t i o n a n d g a s p h a s e r e a c t i o n s . T h e w e i g h t u p t a k e is 401
STAGE II BF 4- INTERCALATED GRAPHITE
402
l a r g e r t h a n t h a t in t h e o t h e r m e t h o d s o f preparation. A t y p i c a l F o u r i e r t r a n s f o r m of the d e H a a s - v a n A l p h e n d a t a is s h o w n in F i g u r e i. T h e r e a r e p e a k s at f r e q u e n c i e s o f 5 2 3 + i, 8 5 7 + 2, 1 0 4 4 + 2, 1 3 7 7 + 2 a n d 1895 + 4 Tesla. A s t a g e II c o m p o u n d is e x p e c t e d to h a v e t w o b a s i c g r a p h i t i c b a n d s 1,3. W e i d e n t i f y p e a k s at F 1 = 523 T and F 2 = 1377 T with these bands. The o t h e r f r e q u e n c i e s c o r r e s p o n d to F 2 - F I, 2F 1 a n d F 1 + F 2. T h e c y c l o t r o n m a s s e s c o r r e s p o n d i n g to F 1 a n d F 2 a r e 0.162 _+ 0 . 0 0 1 m 0 a n d 0 . 2 8 + 0.01 m 0, r e s p e c t i v e l y , w h e r e m 0 is the free e l e c t r o n mass. The carrier concentration can be e a s i l y c a l c u l a t e d f r o m the d H v A data. T h e n u m b e r o f c a r r i e r s p e r u n i t c e l l is e q u a l t o 2 V F / V B w h e r e V F is t h e r e c i p r o c a l s p a c e v o l u m e of the F e r m i s u r f a c e a n d V B is the r e c i p r o c a l s p a c e v o l u m e of the B r i l l o u i n zone. In a t w o d i m e n s i o n a l s y s t e m the r a t i o of v o l u m e s is e q u a l to the r a t i o of c o r r e s p o n d i n g areas. T h e F e r m i s u r f a c e a r e a A F i is d i r e c t l y p r o p o r t i o n a l to the d H v A frequency A F i = 2~e d%c
Fi
AB =
I
2
(2)
x = (F 1 + F 2 ) / 7 8 9 1 4
(3)
where F 1 and F 2 are the frequencies of basic oscillations in Tesla. S u b s t i t u t i n g our v a l u e s of F 1 a n d F 2 i n t o (3) o n e o b t a i n s x = 0 . 0 2 4 1 o r o n e e l e m e n t a r y c h a r g e p e r 41.5 c a r b o n a t o m s for the c o m p o u n d studied. T h e c h e m i c a l a n a l y s i s of the BF 4- c o m p o u n d p r e p a r e d f r o m t h e r m a l d e c o m p o s i t i o n of n i t r y l t e t r a f l u o r o b o r a t e 9 s h o w e d that e a c h B F 4ion is a c c o m p a n i e d b y t w o n e u t r a l m o l e c u l e s of N O 2 B F 4. C o m b i n i n g this i n f o r m a t i o n w i t h the c h a r g e t r a n s f e r from our dHvA data one expects the f o r m u l a C 4 1 . 5 B F 4 (NO2BF4) 2 for the c o m p o u n d s t u d i e d . T h e w e i g h t u p t a k e for the a b o v e f o r m u l a is 70.7 % w h i c h a g r e e s w i t h the m e a s u r e d o n e of 68 + 3 %. T h e c h a r g e p e r c a r b o n a t o m in this w o r k is l a r g e r t h a n t h a t o b t a i n e d b y b o t h p r e v i o u s m e t h o d s 8,9. In fact it is l a r g e r t h a n in t h e m o s t s t a g e II a c c e p t o r c o m p o u n d s I0. It is t h e r e f o r e a g o o d c a s e to t e s t c h a r g e t r a n s f e r
w h e r e F i is t h e d H v A f r e q u e n c y o f t h e band. T h e a r e a of the B r i l l o u i n z o n e is
I
(2n)2/~a
T h e t o t a l n u m b e r of c a r r i e r s p e r c a r b o n a t o m is e q u a l t o t h e s u m o f c o n c e n t r a t i o n s for all b a n d s d i v i d e d b y four a t o m s p e r u n i t c e l l in a s t a g e II compound. Numerically one obtains
(i)
I
Vol. 55, No. 5
I
I
I
I
I
I
bH
Z >(I ~-H m (I W (3 H _J O_ (I (~ W H nO L~_ I
I
I
I
I
I
I
!
I
200
40O
G00
800
i000
1200
1400
1600
1800
FREOUENCY
( TESLIq )
F i g u r e I. T h e F o u r i e r t r a n s f o r m d H v A s i g n a l of s t a g e II BF 4intercalation compound.
of
the
2000
Vol. 55, No. 5
R A G E II BF 4
related d e v i a t i o n s from the rigid band m o d e l s of the e l e c t r o n i c s t r u c t u r e of g r a p h i t e i n t e r c a l a t i o n compounds. The e x p e r i m e n t a l b a n d p a r a m e t e r s are c o m p a r e d to the t h e o r e t i c a l c a l c u l a t i o n s b a s e d on the theory of H o l z w a r t h 3,4 The F e r m i e n e r g y is a d j u s t e d to fit the o b s e r v e d d H v A frequencies F 1 and F 2. The best fit is o b t a i n e d for the value of -0.96 eV relative to the m a x i m u m energy of the valence band. The fitted f r e q u e n c i e s of 520 a n d 1392 T e s l a a r e w i t h i n 1 % of the e x p e r i m e n t a l l y o b s e r v e d values of F 1 and F 2, respectively. The t h e o r e t i c a l c y c l o t r o n mass value of 0.16 m 0 m a t c h e s the e x p e r i m e n t a l one for the F 1 frequency. For F 2 the t h e o r e t i c a l p r e d i c t i o n of 0.30 m 0 is s l i g h t l y larger than the o b s e r v e d mass of 0.28 m 0. The good a g r e e m e n t b e t w e e n the rigid band theory and e x p e r i m e n t s h o w s that the interaction between carbon atoms remain intact upon intercalation. This is s u r p r i s i n g e s p e c i a l l y for i n t e r p l a n a r i n t e r a c t i o n w h e r e w e a k g r a p h i t i c bonds c o m p e t e w i t h strong e l e c t r o s t a t i c a t t r a c t i o n b e t w e e n c a r b o n a t o m s and intercalate. Conclusions Stage II BF 4 i n t e r c a l a t i o n c o m p o u n d was o b t a i n e d by r e a c t i o n of g r a p h i t e
403
INTERCALATED GRAPHITE
w i t h solid nitryl t e t r a f l u o r o b o r a t e . The i n t e r c a l a t e c o n c e n t r a t i o n is larger than that in the c o m p o u n d s p r e p a r e d by r e a c t i o n of d i s s o l v e d and t h e r m a l l y d e c o m p o s e d nitryl t e t r a f l u o r o b o r a t e 8 , 9. The charge t r a n s f e r o b t a i n e d from de H a a s - v a n A l p h e n m e a s u r e m e n t s was used to p r e d i c t the c o m p o s i t i o n of the compound. The c a l c u l a t e d w e i g h t uptake c o r r e s p o n d i n g to that c o m p o s i t i o n was in a g r e e m e n t w i t h the m e a s u r e d one. T h e r i g i d b a n d m o d e l of the e l e c t r o n i c s t r u c t u r e of g r a p h i t e i n t e r c a l a t i o n c o m p o u n d s was found valid to d e s c r i b e q u a n t i t a t i v e l y the band p a r a m e t e r s of the compound. The e x p e r i m e n t a l d H v A f r e q u e n c i e s and c y c l o t r o n m a s s e s w e r e fitted w i t h the Fermi e n e r g y as the only a d j u s t a b l e parameter. The good a g r e e m e n t d e m o n s t r a t e s that the d e v i a t i o n s from the rigid b a n d model are n e g l i g i b l y s m a l l for a h i g h c a r b o n c h a r g e s t a t e of the stage II BF 4- compound.
A c k n o w l e d g e m e n t - The r e s e a r c h was s u p p o r t e d f i n a n c i a l l y by the N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h Council of Canada. W e thank Dr A.W. Moore for s u p p l y i n g HOPG graphite.
References i. J. B l i n o w s k i , N q u y e n H y Hau, C. R i g a u x , J.P. V i e r e n , R. Le T o u l l e c , G. F u r d i n , A. H e r o l d a n d J. M e l i n , J. P h y s i q u e 41, 47 (1980) 2. G. D r e s s e l h a u s a n d S.Y. L e u n g , Solid State Commun. 35, 819 (1980) 3. N.A.W. H o l z w a r t h , 3665 (1980)
Phys.
Rev. B 2 1 ,
4. W e h a v e u s e d the v a l u e of -0.01 eV for the m a t r i x e l e m e n t ----M~0 instead of -0.02 given in Ref.3 b e c a u s e there is only one n e i g h b o r i n g g r a p h e n e layer in the stage II compound. For j~i the H a m i l t o n i a n m a t r i x e l e m e n t H ~ ( k ) does not have to be real. In this case the correct form is
H ~'('k )
=
1 M nbb m(i-j [ '--2-r, nm
)~m(k)
5. R.E. H e i n z , G. Doll, P. C h a r r o n a n d P.C. E k l u n d , Mat. Sci. Soc. S y m p . Proc. 20, " I n t e r c a l a t e d graphite", 87 (1983)
6. R.S. M a r k i e w i c z , H.R. Hart, Jr., L.V. I n t e r r a n t e , J.S. K a s p e r , S o l i d State Commun. 35, 513 (1980) 7. H. Z a l e s k i , P.K. U m m a t a n d W.R. D a t a r s , J. Phys. C17, 3167 (1980): H. Z a l e s k i , P.K. U m m a t a n d W.R. Datars, E x t e n d e d A b s t r a c t s "Graphite I n t e r c a l a t i o n Compounds", P r o c e e d i n g s of S y m p o s i u m I 1984 Fall M e e t i n g of the M a t e r i a l s R e s e a r c h Society, Nov 28-30, Boston, USA, p45 8. D. B i l l a u d , A. P r o n a n d F. L i n c o l n V o g e l , S y n t h . Met. 2, 177 (1980) 9. D. B i l l a u d , A. C h e n i t e , Bull. 18, I001 (1983)
Mat.
Res.
IO.R.S. Markiewicz, C. L o p a t i n a n d C. Z a h o p o u l o s , Mat. Sci. Soc. Symp. Proc. 20, " I n t e r c a l a t e d graphite", 135 (1983)
COMPOSITION
AND
ELECTRONIC H.
Department
STRUCTURE
Zaleski,
of P h y s i c s ,
P.K.
McMaster
(Received
1 March
OF STAGE Ummat
II BF 4- I N T E R C A L A T E D
a n d W.R.
University, 1985
0038-]098/85 $3.00 + .00 Pergamon Press Ltd.
b y M.
GRAPHITE
Datars
Hamilton,
Canada,
L8S 4M1
F. C o l l i n s )
G r a p h i t e w a s r e a c t e d w i t h s o l i d n i t r y l t e t r a f l u o r o b o r a t e to f o r m a s t a g e II c o m p o u n d . T h e e x p e r i m e n t a l de H a a s - v a n A l p h e n f r e q u e n c i e s a n d c y c l o t r o n m a s s e s a r e in a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s of the r i g i d b a n d m o d e l w i t h the F e r m i e n e r g y e q u a l to -0.96 eV. T h e c h a r g e t r a n s f e r is o n e e l e m e n t a r y c h a r g e per 41.5 c a r b o n atoms.
Introduction
nitryl tetrafluoroborate. A large charge transfer results from chemical oxidation of c a r b o n b y the n i t r y l ion (NO2+). T h e c o m p o u n d is c h a r a c t e r i z e d b y w e i g h t uptake and X-ray diffraction. The band p a r a m e t e r s a r e o b t a i n e d f r o m de H a a s - v a n A l p h e n (dHvA) e f f e c t m e a s u r e m e n t s which also provide additional information a b o u t the s t r u c t u r e and the c o m p o s i t i o n of the c o m p o u n d .
Graphite intercalation compounds (GIC) a r e s y n t h e t i c c o n d u c t o r s w h o s e s t r u c t u r e c o n s i s t s of a r e g u l a r s e q u e n c e of a l t e r n a t i n g m o n o l a y e r s of i n t e r c a l a t e a n d n l a y e r s of carbon, w h e r e n is the s t a g e index. T h e s e m a t e r i a l s e x h i b i t m e t a l l i c c o n d u c t i v i t y d u e to c h a r g e t r a n s f e r b e t w e e n c a r b o n and i n t e r c a l a t e that i n c r e a s e s the n u m b e r of c a r r i e r s in c a r b o n layers. T h e c o m p o u n d s h a v e u s u a l l y a l a r g e n u m b e r of a t o m s per u n i t cell t h a t m a k e s f i r s t - p r i n c i p l e b a n d structure calculations difficult. Instead, p h e n o m e n o l o g i c a l rigid band m o d e l s h a v e b e e n d e v e l o p e d l,z,3. T h e y a s s u m e that the e l e c t r o n i c s t r u c t u r e of G I C c a n b e a p p r o x i m a t e d b y the s t r u c t u r e of n g r a p h e n e l a y e r s for a s t a g e n c o m p o u n d . T h e F e r m i e n e r g y is a d j u s t e d to a c c o m m o d a t e c a r r i e r s c o m i n g f r o m the intercalate. The simplest band structure model based on a tight binding nearest neighbor approximation has been proposed b y B l i n o w s k i et al I . T h e m o d e l h a s b e e n s u c c e s s f u l l y u s e d to e x p l a i n o p t i c a l p r o p e r t i e s of s o m e a c c e p t o r G I C 1,5. However, quantum oscillatory phenomena measurements 6 showed a discrepancy b e t w e e n t h e o r e t i c a l p r e d i c t i o n s and e x p e r i m e n t a l d a t a that p r o m p t e d the a u t h o r s to s u g g e s t a v a r i a t i o n of i n t e r a t o m i c i n t e r a c t i o n s as a f u n c t i o n of c h a r g e t r a n s f e r . R e c e n t l y , the a n a l y s i s of de H a a s v a n A l p h e n d a t a of SbCI 5 s t a g e I a n d II and S b F 6- s t a g e I c o m p o u n d s 7 s h o w e d t h e i m p o r t a n c e of m o r e d i s t a n t n e i g h b o r i n t e r a c t i o n s and, in fact, g o o d agreement was obtained between data and the r i g i d b a n d m o d e l p r o p o s e d b y Holzwarth 3 . In this w o r k w e r e e x a m i n e the validity of the rigid band model of H o l z w a r t h for the d e s c r i p t i o n of the e l e c t r o n i c s t r u c t u r e of the s t a g e II BF 4- c o m p o u n d . T h e c o m p o u n d is p r e p a r e d b y a r e a c t i o n of g r a p h i t e w i t h s o l i d
Experimental P i e c e s of p y r o l i t i c g r a p h i t e (HOPG) w e r e p u t i n t o a g l a s s t u b e in c o n t a c t w i t h s o l i d N O 2 B F 4 salt. T h e t u b e w a s e v a c u a t e d , s e a l e d and p u t i n t o an o v e n at 85 °C for o n e day. A b l a c k c o m p o u n d with greenish shade was obtained. S a m p l e s w e r e put i n t o a v a c u u m t i g h t h o l d e r and p l a c e d in the d H v A a p p a r a t u s . Different samples cooled from room t e m p e r a t u r e to 77 K s l o w l y (~12 hrs) a n d q u i c k l y (~lhr) g a v e the s a m e d H v A spectrum. The dHvA effect measured by the m o d u l a t i o n t e c h n i q u e w a s p e r f o r m e d w i t h e a c h s a m p l e ' s c - a x i s p a r a l l e l to t h e d i r e c t i o n of t h e m a g n e t i c f i e l d of a superconducting selenoid. The signal was s a m p l e d a n d a n a l y z e d b y an a q u i s i t i o n s y s t e m c o n n e c t e d to a m i c r o c o m p u t e r . T h e cyclotron masses were determined from the t e m p e r a t u r e d e p e n d e n c e of the d H v A a m p l i t u d e s b e t w e e n 1.3 and 4.2 K. Results
and
Discussion
T h e (OO1) X - r a y d i f f r a c t i o n p a t t e r n s h o w e d that a p u r e s t a g e II c o m p o u n d w a s obtained. The c-axis identity period w a s I c = 1 1 . 1 3 + 0.02 A. T h e w e i g h t u p t a k e d u r i n g the r e a c t i o n w a s 68 + 3 %. T h e B F 4- ion w a s p r e v i o u s l y i n t e r c a l a t e d b y r e a c t i o n of n i t r y l t e t r a f l u o r o b o r a t e d i s s o l v e d in d r y n i t r o m e t h a n e 8 a n d b y a c t i o n of g a s e o u s p r o d u c t s of t h e r m a l decomposition of N O 2 B F 4 s a l t 9. T h e I c v a l u e of t h i s w o r k is s l i g h t l y s m a l l e r t h a n t h a t o b t a i n e d in s o l u t i o n a n d g a s p h a s e r e a c t i o n s . T h e w e i g h t u p t a k e is 401
STAGE II BF 4- INTERCALATED GRAPHITE
402
l a r g e r t h a n t h a t in t h e o t h e r m e t h o d s o f preparation. A t y p i c a l F o u r i e r t r a n s f o r m of the d e H a a s - v a n A l p h e n d a t a is s h o w n in F i g u r e i. T h e r e a r e p e a k s at f r e q u e n c i e s o f 5 2 3 + i, 8 5 7 + 2, 1 0 4 4 + 2, 1 3 7 7 + 2 a n d 1895 + 4 Tesla. A s t a g e II c o m p o u n d is e x p e c t e d to h a v e t w o b a s i c g r a p h i t i c b a n d s 1,3. W e i d e n t i f y p e a k s at F 1 = 523 T and F 2 = 1377 T with these bands. The o t h e r f r e q u e n c i e s c o r r e s p o n d to F 2 - F I, 2F 1 a n d F 1 + F 2. T h e c y c l o t r o n m a s s e s c o r r e s p o n d i n g to F 1 a n d F 2 a r e 0.162 _+ 0 . 0 0 1 m 0 a n d 0 . 2 8 + 0.01 m 0, r e s p e c t i v e l y , w h e r e m 0 is the free e l e c t r o n mass. The carrier concentration can be e a s i l y c a l c u l a t e d f r o m the d H v A data. T h e n u m b e r o f c a r r i e r s p e r u n i t c e l l is e q u a l t o 2 V F / V B w h e r e V F is t h e r e c i p r o c a l s p a c e v o l u m e of the F e r m i s u r f a c e a n d V B is the r e c i p r o c a l s p a c e v o l u m e of the B r i l l o u i n zone. In a t w o d i m e n s i o n a l s y s t e m the r a t i o of v o l u m e s is e q u a l to the r a t i o of c o r r e s p o n d i n g areas. T h e F e r m i s u r f a c e a r e a A F i is d i r e c t l y p r o p o r t i o n a l to the d H v A frequency A F i = 2~e d%c
Fi
AB =
I
2
(2)
x = (F 1 + F 2 ) / 7 8 9 1 4
(3)
where F 1 and F 2 are the frequencies of basic oscillations in Tesla. S u b s t i t u t i n g our v a l u e s of F 1 a n d F 2 i n t o (3) o n e o b t a i n s x = 0 . 0 2 4 1 o r o n e e l e m e n t a r y c h a r g e p e r 41.5 c a r b o n a t o m s for the c o m p o u n d studied. T h e c h e m i c a l a n a l y s i s of the BF 4- c o m p o u n d p r e p a r e d f r o m t h e r m a l d e c o m p o s i t i o n of n i t r y l t e t r a f l u o r o b o r a t e 9 s h o w e d that e a c h B F 4ion is a c c o m p a n i e d b y t w o n e u t r a l m o l e c u l e s of N O 2 B F 4. C o m b i n i n g this i n f o r m a t i o n w i t h the c h a r g e t r a n s f e r from our dHvA data one expects the f o r m u l a C 4 1 . 5 B F 4 (NO2BF4) 2 for the c o m p o u n d s t u d i e d . T h e w e i g h t u p t a k e for the a b o v e f o r m u l a is 70.7 % w h i c h a g r e e s w i t h the m e a s u r e d o n e of 68 + 3 %. T h e c h a r g e p e r c a r b o n a t o m in this w o r k is l a r g e r t h a n t h a t o b t a i n e d b y b o t h p r e v i o u s m e t h o d s 8,9. In fact it is l a r g e r t h a n in t h e m o s t s t a g e II a c c e p t o r c o m p o u n d s I0. It is t h e r e f o r e a g o o d c a s e to t e s t c h a r g e t r a n s f e r
w h e r e F i is t h e d H v A f r e q u e n c y o f t h e band. T h e a r e a of the B r i l l o u i n z o n e is
I
(2n)2/~a
T h e t o t a l n u m b e r of c a r r i e r s p e r c a r b o n a t o m is e q u a l t o t h e s u m o f c o n c e n t r a t i o n s for all b a n d s d i v i d e d b y four a t o m s p e r u n i t c e l l in a s t a g e II compound. Numerically one obtains
(i)
I
Vol. 55, No. 5
I
I
I
I
I
I
bH
Z >(I ~-H m (I W (3 H _J O_ (I (~ W H nO L~_ I
I
I
I
I
I
I
!
I
200
40O
G00
800
i000
1200
1400
1600
1800
FREOUENCY
( TESLIq )
F i g u r e I. T h e F o u r i e r t r a n s f o r m d H v A s i g n a l of s t a g e II BF 4intercalation compound.
of
the
2000
Vol. 55, No. 5
R A G E II BF 4
related d e v i a t i o n s from the rigid band m o d e l s of the e l e c t r o n i c s t r u c t u r e of g r a p h i t e i n t e r c a l a t i o n compounds. The e x p e r i m e n t a l b a n d p a r a m e t e r s are c o m p a r e d to the t h e o r e t i c a l c a l c u l a t i o n s b a s e d on the theory of H o l z w a r t h 3,4 The F e r m i e n e r g y is a d j u s t e d to fit the o b s e r v e d d H v A frequencies F 1 and F 2. The best fit is o b t a i n e d for the value of -0.96 eV relative to the m a x i m u m energy of the valence band. The fitted f r e q u e n c i e s of 520 a n d 1392 T e s l a a r e w i t h i n 1 % of the e x p e r i m e n t a l l y o b s e r v e d values of F 1 and F 2, respectively. The t h e o r e t i c a l c y c l o t r o n mass value of 0.16 m 0 m a t c h e s the e x p e r i m e n t a l one for the F 1 frequency. For F 2 the t h e o r e t i c a l p r e d i c t i o n of 0.30 m 0 is s l i g h t l y larger than the o b s e r v e d mass of 0.28 m 0. The good a g r e e m e n t b e t w e e n the rigid band theory and e x p e r i m e n t s h o w s that the interaction between carbon atoms remain intact upon intercalation. This is s u r p r i s i n g e s p e c i a l l y for i n t e r p l a n a r i n t e r a c t i o n w h e r e w e a k g r a p h i t i c bonds c o m p e t e w i t h strong e l e c t r o s t a t i c a t t r a c t i o n b e t w e e n c a r b o n a t o m s and intercalate. Conclusions Stage II BF 4 i n t e r c a l a t i o n c o m p o u n d was o b t a i n e d by r e a c t i o n of g r a p h i t e
403
INTERCALATED GRAPHITE
w i t h solid nitryl t e t r a f l u o r o b o r a t e . The i n t e r c a l a t e c o n c e n t r a t i o n is larger than that in the c o m p o u n d s p r e p a r e d by r e a c t i o n of d i s s o l v e d and t h e r m a l l y d e c o m p o s e d nitryl t e t r a f l u o r o b o r a t e 8 , 9. The charge t r a n s f e r o b t a i n e d from de H a a s - v a n A l p h e n m e a s u r e m e n t s was used to p r e d i c t the c o m p o s i t i o n of the compound. The c a l c u l a t e d w e i g h t uptake c o r r e s p o n d i n g to that c o m p o s i t i o n was in a g r e e m e n t w i t h the m e a s u r e d one. T h e r i g i d b a n d m o d e l of the e l e c t r o n i c s t r u c t u r e of g r a p h i t e i n t e r c a l a t i o n c o m p o u n d s was found valid to d e s c r i b e q u a n t i t a t i v e l y the band p a r a m e t e r s of the compound. The e x p e r i m e n t a l d H v A f r e q u e n c i e s and c y c l o t r o n m a s s e s w e r e fitted w i t h the Fermi e n e r g y as the only a d j u s t a b l e parameter. The good a g r e e m e n t d e m o n s t r a t e s that the d e v i a t i o n s from the rigid b a n d model are n e g l i g i b l y s m a l l for a h i g h c a r b o n c h a r g e s t a t e of the stage II BF 4- compound.
A c k n o w l e d g e m e n t - The r e s e a r c h was s u p p o r t e d f i n a n c i a l l y by the N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h Council of Canada. W e thank Dr A.W. Moore for s u p p l y i n g HOPG graphite.
References i. J. B l i n o w s k i , N q u y e n H y Hau, C. R i g a u x , J.P. V i e r e n , R. Le T o u l l e c , G. F u r d i n , A. H e r o l d a n d J. M e l i n , J. P h y s i q u e 41, 47 (1980) 2. G. D r e s s e l h a u s a n d S.Y. L e u n g , Solid State Commun. 35, 819 (1980) 3. N.A.W. H o l z w a r t h , 3665 (1980)
Phys.
Rev. B 2 1 ,
4. W e h a v e u s e d the v a l u e of -0.01 eV for the m a t r i x e l e m e n t ----M~0 instead of -0.02 given in Ref.3 b e c a u s e there is only one n e i g h b o r i n g g r a p h e n e layer in the stage II compound. For j~i the H a m i l t o n i a n m a t r i x e l e m e n t H ~ ( k ) does not have to be real. In this case the correct form is
H ~'('k )
=
1 M nbb m(i-j [ '--2-r, nm
)~m(k)
5. R.E. H e i n z , G. Doll, P. C h a r r o n a n d P.C. E k l u n d , Mat. Sci. Soc. S y m p . Proc. 20, " I n t e r c a l a t e d graphite", 87 (1983)
6. R.S. M a r k i e w i c z , H.R. Hart, Jr., L.V. I n t e r r a n t e , J.S. K a s p e r , S o l i d State Commun. 35, 513 (1980) 7. H. Z a l e s k i , P.K. U m m a t a n d W.R. D a t a r s , J. Phys. C17, 3167 (1980): H. Z a l e s k i , P.K. U m m a t a n d W.R. Datars, E x t e n d e d A b s t r a c t s "Graphite I n t e r c a l a t i o n Compounds", P r o c e e d i n g s of S y m p o s i u m I 1984 Fall M e e t i n g of the M a t e r i a l s R e s e a r c h Society, Nov 28-30, Boston, USA, p45 8. D. B i l l a u d , A. P r o n a n d F. L i n c o l n V o g e l , S y n t h . Met. 2, 177 (1980) 9. D. B i l l a u d , A. C h e n i t e , Bull. 18, I001 (1983)
Mat.
Res.
IO.R.S. Markiewicz, C. L o p a t i n a n d C. Z a h o p o u l o s , Mat. Sci. Soc. Symp. Proc. 20, " I n t e r c a l a t e d graphite", 135 (1983)