Petroleum Derived Carbons

29

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on October 13, 2015 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0021.ch029

Free Carrier Plasma in Graphite Compounds JOHN E. FISCHER, THOMAS E. THOMPSON, and F. LINCOLN VOGEL Moore School of Electrical Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Penn. 19174

The intercalation compounds of graphite are materials in which layers of atoms or molecules lie between aromatic layers of carbon atoms. (1) (2) Systematic x-ray studies (2) (3) have shown that each layer of carbon atoms retains the original hexa gonal lattice of graphite with little or no change in the carbon carbon bond distance but the distance between the carbon layers, i.e. the separation distance along the c-axis, is altered to allow for the insertion of the intercalate. Such compounds can exist in different stages of intercalation: stage one where the intercalated specie lies between every other layer of carbon atoms, stage two where there are two layers of carbon atoms be tween the intercalate layers, stage Ν where there are Ν carbon layers between the intercalate layers, etc. As an example we show the structure of the first stage compoundC Kin Figure 1. A number of graphite intercalation compounds are metallic in nature (5) (6) as indicated by their paramagnetism and electri cal conductivities (pristine graphite is a diamagnetic semimetal.) Whereas the room-temperature electrical conductivity of stress -annealedpyrolytic graphite parallel to the basal planes (per pendicular to the c-axis) can be 1/25 of the electrical conduc tivity of OFHC copper (or better), the conductivities of some graphite intercalation compounds are an order of magnitude higher, approaching half that of Cu. This is the case, for instance, for the intercalates of sulfuric and nitric acid. The increase in basal plane conductivity can be explained in terms of increased carrier concentration in the graphite layers due to charge trans fer between the intercalate and the host lattice. At room temper ature crystalline graphite has a carrier concentration (Ν = P, since its a semimetal) of approximately 10 cm" (compared to 10 cm" for Cu) and an average basal plane mobility of 10* cm / Vs (compared to 35 cm/Vs for Cu). Hall effect measurements in dicate that a fractional charge transfer occurs when sulfuric or nitric acid is intercalated into graphite leaving the graphite layers with additional holes and, therefore, an increased con ductivity. This fact raises the obvious question: Can one find 8

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23

3

3

1

2

418

In Petroleum Derived Carbons; Deviney, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

2


29.

FISCHER E T

AL.

Free Carrier

Plasma

419

an i n t e r c a l a t e which w i l l give enough o f a c a r r i e r i n c r e a s e to make the c o n d u c t i v i t y even b e t t e r than t h a t o f Cu? Since a charge t r a n s f e r mechanism i s involved, perhaps a stronger a c i d , one with more i o n i z i n g a b i l i t y , would be most e f f e c t i v e . The work o f Vogel (7) has given some i n d i c a t i o n that t h i s i s indeed the case. Despite a large amount of e f f o r t on the synthesis and p h y s i c a l measurements of graphite i n t e r c a l a t i o n compounds, the d e t a i l e d i n f l u e n c e o f the i n t e r c a l a t e on the e l e c t r o n i c p r o p e r t i e s of the r e s u l t i n g compound remains l a r g e l y unexplained. One would hope t o be able t o understand the e l e c t r i c a l conduction i n terms o f such f a m i l i a r concepts as c a r r i e r d e n s i t y , m o b i l i t y and energy band s t r u c t u r e . Measurements of c o n d u c t i v i t y , H a l l e f f e c t and magnetoresistance have not provided a general model or set of models to describe the i n t e r p l a y between charge t r a n s f e r and changes i n m o b i l i t y . To our knowledge, the Shubnikov-deHaas experiment o f Bender and Young (8) on d i l u t e bromine-graphite i s the only case where a d e t a i l e d c o r r e l a t i o n can be made between i n t e r c a l a t i o n and the e l e c t r o n i c s t r u c t u r e . The research reported here are some i n i t i a l r e s u l t s of a program of experiments designed t o probe the e l e c t r o n i c s t r u c t u r e and conduction processes o f these s y n t h e t i c metals. One component of t h i s program i s o p t i c a l and modulation spectroscopy, the goals o f which are t o observe plasma o s c i l l a t i o n s a s s o c i a t e d with conduction e l e c t r o n s and/or h o l e s , and t o f o l l o w key i n t e r band t r a n s i t i o n s versus i n t e r c a l a t i o n i n order t o deduce Fermi l e v e l s h i f t s , changes i n bandwidths, and c o n t r i b u t i o n s of new bands derived from the i n t e r c a l a t i n g specie. We have begun t h i s work with a study of the o p t i c a l r e f l e c t i v i t y and thermoreflectance of graphite i n t e r c a l a t e d with HNO3 and SbFs. In the f o l l o w i n g s e c t i o n we present some ideas on the e f f e c t of i n t e r c a l a t i o n on the conduction processes i n g r a p h i t e compounds. T h i s i s followed by a d e s c r i p t i o n o f the r e l a t i o n s h i p between o p t i c a l r e f l e c t i v i t y and e l e c t r o n i c conduction. Following t h i s i s a d e s c r i p t i o n of our experiments with a summary and conclusions. Conductivity

- A Simple Model

One of the most s t r i k i n g features of i n t e r c a l a t i o n compounds i s the large increase i n a-axis (basal plane) c o n d u c t i v i t y r e l a t i v e to that o f pure graphite. (5)(6) I t i s o f fundamental importance t o understand the dependence o f c o n d u c t i v i t y on i n t e r c a l a t i n g specie and concentration. In t h i s s e c t i o n we present a simple model f o r the concentration dependence which, d e s p i t e i t s l i m i t a t i o n s , b r i n g s out two important f e a t u r e s : the i n t e r p l a y between increases i n f r e e c a r r i e r d e n s i t y and e l e c t r o n phonon s c a t t e r i n g r a t e , and the i n f l u e n c e o f d i m e n s i o n a l i t y . The dc c o n d u c t i v i t y of a simple f r e e - e l e c t r o n metal i s


PETROLEUM

420 given

by σ = Ney


DERIVED CARBONS

= Ne

τ/m*

(1)

where Ν i s the c a r r i e r d e n s i t y , μ i s the m o b i l i t y , τ i s the mean time between c o l l i s i o n s and m* the e f f e c t i v e mass. At room tem perature the c o n d u c t i v i t y o f most metals i s l i m i t e d by c o l l i s i o n s with thermal v i b r a t i o n s o f the l a t t i c e atoms (phonons), so the s c a t t e r i n g r a t e l/τ i s governed by the net i n t e r a c t i o n between a l l the e l e c t r o n s and phonons i n the system. The e f f e c t i v e mass accounts approximately f o r the i n f l u e n c e o f the p e r i o d i c c r y s t a l p o t e n t i a l on e l e c t r o n motion. In f r e e space m* = me, the t r u e e l e c t r o n mass, whereas e l e c t r o n s i n s o l i d s can have m* g r e a t e r o r l e s s than me« Since m* depends on c r y s t a l p o t e n t i a l i t can be a n i s o t r o p i c and lead t o anisotropy i n σ through Eq. (1). The energy band s t r u c t u r e determines the parameters Ν, τ and m* so once we assume a model f o r the e f f e c t o f i n t e r c a l a t i o n on band s t r u c t u r e , we can use i t t o estimate the change i n conduc t i v i t y . The e l e c t r o n d e n s i t y Ν i s p r o p o r t i o n a l t o the k-space volume enclosed by the Fermi s u r f a c e ; i f Ν increases (e.g. upon i n t e r c a l a t i o n ) , t h i s volume, hence the Fermi energy Ef, i n c r e a s e s . The electron-phonon s c a t t e r i n g r a t e l/τ i s determined by the num bers o f e l e c t r o n s and phonons that are able t o i n t e r a c t while simultaneously conserving energy and momentum. Since phonon energies are small compared t o the Fermi energy, and s i n c e the Fermi-Dirac d i s t r i b u t i o n f u n c t i o n governs e l e c t r o n occupancy, only e l e c t r o n s w i t h i n a few kT o f E f p a r t i c i p a t e i n c o l l i s i o n s with phonons. Thus l/τ i s roughly p r o p o r t i o n a l to the area o f the Fermi s u r f a c e . The e f f e c t i v e mass m* i s i n v e r s e l y p r o p o r t i o n a l t o the curvature o f the energy bands, which i n t u r n i s determined by the c r y s t a l p o t e n t i a l . In g r a p h i t e , the strong s p bonds with i n the sheets g i v e a large energy bandwidth, which leads t o a small m* and t h e r e f o r e a l a r g e σ, f o r e l e c t r o n motion p a r a l l e l t o the sheets. The much weaker p overlap between sheets g i v e s a b i g g e r mass, hence lower σ f o r motion along the c-axis ( a d d i t i o n a l anisotropy i n the s c a t t e r i n g r a t e f u r t h e r enhances the anisotropy in σ). Consider f i r s t a c r y s t a l with simple i s o t r o p i c energy bands such that E(R) = fi ic /2m*. The Fermi s u r f a c e f o r t h i s case i s s p h e r i c a l , with a radius given by k f = (2m* E f / f i ) * . The e l e c t r o n d e n s i t y i s p r o p o r t i o n a l to the volume: 2

z

2

2

2

3

(2) while the s c a t t e r i n g r a t e goes as the l/τ «

area:

2

k . f

(3)

Suppose we " i n t e r c a l a t e " with donors, o b t a i n i n g one a d d i t i o n a l e l e c t r o n f o r each i n t e r c a l a t e d ion dependent of concentration X.


29.

421

Free Carrier Plasma

FISCHER E T A L .

The F e x m i s u r f a c e w i l l g r o w t o accomodate t h e added e l e c t r o n s . I f Ν = N + X , the Fermi radius increases k f « ( N + X ) / , ac cording t o (2). A t t h e same t i m e , t h e s c a t t e r i n g r a t e w i l l i n c r e a s e due t o t h e l a r g e r number o f e l e c t r o n s w i t h e n e r g i e s kT a b o u t E f . N e g l e c t i n g c h a n g e s i n t h e phonon d e n s i t y o f s t a t e s we have from (3) t h a t 1 / τ « ( N + X ) / . A s s u m i n g m* i s u n c h a n g e d , t h e n e t dependence on c o n c e n t r a t i o n i s 1

0

3

0

2

3


0

σ

3 0

(Χ) « (N

o

+

X)

1

/

3

.

(4)

We now c o n s i d e r t h e e f f e c t s o f a n i s o t r o p y . The F e r m i s u r f a c e f o r a t w o - d i m e n s i o n a l o r l a y e r s t r u c t u r e c r y s t a l c a n be a p p r o x i mated b y a c y l i n d e r , t h e component o f t h e m* t e n s o r p e r p e n d i c u l a r to the layers being very large. I f the m a t e r i a l remains twod i m e n s i o n a l a f t e r i n t e r c a l a t i o n , we h a v e Ν = No + X 4ΤΓ k f H , where 4 π k f i s t h e c r o s s - s e c t i o n a l a r e a and Η t h e h e i g h t o f t h e F e r m i c y l i n d e r (H » k f ) . Now t h e s c a t t e r i n g r a t e goes as l/τ 2 π k f H α ( N + X ) / , a n d t h e n e t dependence becomes Œ

2

2

œ

1

2

0

σ

2 β

(Χ) « (N

o

- X ) \

(5)

a more r a p i d i n c r e a s e w i t h X t h a n t h e i s o t r o p i c c a s e , E q . ( 4 ) . S i m i l a r l y , o n e - d i m e n s i o n a l s o l i d s ( s u c h as t h e c h a r g e t r a n s f e r s a l t T T F : TCNQ o r t h e l i n e a r c h a i n p o l y m e r ( S N ) ) m i g h t be e x p e c t e d t o behave a s : X

σ

1 β

(Χ) « (N

o

+ X),

(6)

t h e s t r o n g e s t d e p e n d e n c e o f a l l . The i m p l i c a t i o n i s q u i t e straightforward: I n o r d e r t o m a x i m i z e c o n d u c t i v i t y by a c c e p t i n g the s m a l l e s t degradation i n τ f o r a g i v e n i n c r e a s e i n N , the low est d i m e n s i o n a l i t y should give the best r e s u l t . The above m o d e l i s b a s e d o n many a s s u m p t i o n s , n o t a l l o f which are j u s t i f i e d i n the s p e c i f i c case o f g r a p h i t e . E q . (1) assumes t h a t o n l y one t y p e o f c a r r i e r i s i m p o r t a n t . This i s c e r t a i n l y not t r u e f o r pure g r a p h i t e , i n which the c o n d u c t i v i t y i s t h e sum o f r o u g h l y e q u a l c o n t r i b u t i o n s f r o m e l e c t r o n s and h o l e s , h o w e v e r i n l o w s t a g e compounds where t h e c o n d u c t i v i t y has i n c r e a s e d b y an o r d e r o f m a g n i t u d e t h e c a r r i e r d e n s i t y must be more t h a n t e n t i m e s t h e i n i t i a l v a l u e s i n c e τ i s c e r t a i n l y l o w e r (as w i l l b e shown l a t e r ) . Thus we c a n assume t h a t one t y p e o f c a r r i e r w i l l d o m i n a t e σ i n t h e compounds. The a s s u m p t i o n t h a t t h e f r a c t i o n a l charge t r a n s f e r per i o n (or degree o f i o n i z a t i o n ) i s i n dependent o f c o n c e n t r a t i o n i s p r o b a b l y t h e l e a s t j u s t i f i e d . This a s s u m p t i o n p l a c e s two u n r e a l i s t i c c o n s t r a i n t s on t h e band s t r u c t u r e o f t h e compound: t h e e n e r g y l e v e l s i n t r o d u c e d b y t h e i n t e r c a l a n t must be f a r i n e n e r g y from E f s o t h e y do n o t h y b r i d i z e w i t h t h e c a r b o n bands n e a r E f , and t h e c a r b o n b a n d s t r u c t u r e must i t s e l f b e u n c h a n g e d b y i n t e r c a l a t i o n . The l a t t e r i s p a r t i c u l a r l y weak, s i n c e t h e i n t e r p l a n a r s e p a r a t i o n changes b y more t h a n a



422

PETROLEUM

DERIVED

CARBONS

f a c t o r o f two i n some cases, which w i l l have a profound i n f l u e n c e on the bandwidths along the c - a x i s . The change i n bandwidth w i l l a l s o change m*, contrary to another o f our assumptions. Changes i n phonon d e n s i t y o f s t a t e s are probably n e g l i g i b l e t o f i r s t order, s i n c e even i n stage 1 compounds 75% or more o f the bonds are e s s e n t i a l l y u n a f f e c t e d (the b a s a l plane l a t t i c e parameter changes by only a few p e r c e n t ) . The f i n a l a r b i t e r o f our simple p i c t u r e i s o f course comparis i o n with experiment. Ubbelohde and co-workers have p u b l i s h e d σ(χ) data f o r many i n t e r c a l a t i n g species i n g r a p h i t e , most o f which show r a p i d i n c r e a s e s i n σ up t o stage 4 or 5, followed by s a t u r a t i o n o r even decreases upon f u r t h e r i n t e r c a l a t i o n . A most curious r e s u l t i s t h a t IC£ i n t e r c a l a t i o n approximately f o l l o w s our f r e e - e l e c t r o n , σ~Χ*$ p r e d i c t i o n while the c h e m i c a l l y s i m i l a r Br2 system reaches i t s maximum c o n d u c t i v i t y at about stage 5 and then s a t u r a t e s . I t ' s c l e a r that many s u b t l e e f f e c t s p l a y a r o l e , and t h e r e f o r e a more p e n e t r a t i n g t h e o r e t i c a l e f f o r t i s required. Conduction Processes

from O p t i c a l R e f l e c t i v i t y

R e f l e c t i o n o f l i g h t from a non-magnetic conducting s u r f a c e i s a c l a s s i c a l electromagnetic f i e l d problem. The r e f l e c t i v i t y ( f r a c t i o n of energy r e f l e c t e d from the surface) can be w r i t t e n i n terms o f a complex d i e l e c t r i c f u n c t i o n and/or a complex r e f r a c t i o n index. The complex d i e l e c t r i c response f u n c t i o n ε(ω) i s d e f i n e d by one o f Maxwell's equations: cVxH = 4ÏÏJ +

9 0

9Ε

/ 3 τ = ε(ω) /9τ .

(7)

i a j t

Assuming a s i n u s o i d a l time dependence e ~ , a free c a r r i e r current l i n e a r l y dependent on the e l e c t r i c f i e l d J = σΕ, and that the p o l a r i z a t i o n o f the l a t t i c e can be d e s c r i b e d by a l a t t i c e d i e l e c t r i c constant D = ε E, the d i e l e c t r i c f u n c t i o n takes the form 0

ε (ω) * ε + ι4πσ/ω. ο

(8)

The complex d i e l e c t r i c f u n c t i o n i s simply r e l a t e d to the complex index o f r e f r a c t i o n ε = (η + i k ) , and the normal i n c i d e n c e r e f l e c t i o n i s g i v e n by F r e s n e l ' s equation: 2

_ (η - η ' )

" Tn

2

+ (k - k ' )

η )* + (k -

W

2

>

C) 9

where the primed i n d i c e s r e f e r t o the medium o u t s i d e the conductor. For r e f l e c t i o n from a sample i n vacuum η'= 1 and k'= 0. Within the r e l a x a t i o n time approximation the s i n g l e c a r r i e r ac c o n d u c t i v i t y i s given:


29.

Free Carrier

FISCHER E T A L .

423

Plasma

2

m

°

Ne T/m* (1 + ιωτ)

( 1 0 ) 1

J


S u b s t i t u t i o n o f (8) and (10) i n t o F r e s n e l ' s equation r e s u l t s i n a d i s t i n c t i v e shape f o r r e f l e c t i v i t y versus photon energy: R * 100% at low energy, then drops a b r u p t l y t o a small v a l u e , the drop occuring over an energy range governed by εο and Η/τ, and l o c a t e d i n the v i c i n i t y o f the "plasma frequency" given by ω

2

= (4TT Ne /m*)^,

ρ

(11)

i f εο i s not much g r e a t e r than u n i t y . By f i t t i n g the F r e s n e l ' s equation t o experimental r e f l e c t i v i t y data, values f o r εο, τ and 0)p can be obtained. From these parameters the c o n d u c t i v i t y can be found: σ = αν> τ/4π. I f the e f f e c t i v e mass i s known, these parameters can oe f u r t h e r r e l a t e d t o the c a r r i e r c o n c e n t r a t i o n and m o b i l i t y : Ν = ω ρ m* (4π e ) " , μ = e τ/m*. In t h i s paper we analyze the o p t i c a l r e f l e c t i v i t y data o f s e v e r a l g r a p h i t e i n t e r c a l a t i o n compounds i n the v i c i n i t y o f the plasma edge i n order t o determine the e f f e c t o f i n t e r c a l a t i o n on the conduction processes. Even though we are not c e r t a i n as t o the exact value o f m*, we can i d e n t i f y trends i n σ among v a r i o u s compounds from o p t i c a l measurements alone, a great h e l p given the d i f f i c u l t y o f accurate and r e l i a b l e σ measurements on these highly anisotropic crystals. One c o m p l i c a t i o n i n our a n a l y s i s a r i s e s from the f a c t t h a t εο i s frequency dependent due t o resonances o r interband t r a n s i t i o n s a s s o c i a t e d with the e l e c t r o n s on the i o n core. Such e f f e c t s , however, don't mask the b a s i c "edge" i n r e f l e c t i v i t y at the plasma frequency. 2

2

2

1

Experimental Methods and Results In t h i s s e c t i o n we present r e s u l t s o f o p t i c a l r e f l e c t a n c e and thermoreflectance experiments on s e v e r a l a c i d i n t e r c a l a t i o n com pounds. These provide i n f o r m a t i o n on c o n d u c t i v i t y changes v i a Eq. 11 and a l s o g i v e c l u e s concerning band s t r u c t u r e and Fermi l e v e l p o s i t i o n i n the compounds. Sample P r e p a r a t i o n . I n t e r c a l a t i o n compounds were made from stress-annealed pyrol y t i c g r a p h i t e ( 9 ) , which c o n s i s t s o f 1-10 micron c r y s t a l l i t e s with t h e i r c-axes a l i g n e d t o w i t h i n a f r a c t i o n o f a degree, a l though the a-axes o f the i n d i v i d u a l c r y s t a l l i t e s are randomly o r i e n t e d i n the b a s a l plane. Rectangular bars were cut from l a r g e r p l a t e s u s i n g a diamond wire saw. I n t e r c a l a t i o n was per formed by immersing the bars i n red fuming n i t r i c a c i d at room temperature f o r s e v e r a l hours. Expansion along the c-axis was dramatic and r e a d i l y observable. While i n the a c i d , the bars


P E T R O L E U M DERIVED CARBONS

424

separated i n t o 50-100μπι t h i c k sheets; the c-faces thus exposed were b l o t t e d dry a n d used d i r e c t l y f o r o p t i c a l measurements. X-ray d i f f T a c t o m e t e r data i n d i c a t e d a w e l l - d e f i n e d s i n g l e phase stage 4 compound ( c - a x i s repeat d i s t a n c e 17.8&). The i n t e r c a l a t i o n s p e c i e h a s p r e v i o u l s y been proposed (10) as N03".3HN0 . I n t e r c a l a t i o n with SbF$ w a s c a r r i e d out (11) i n sealed copper tubes c o n t a i n i n g g r a p h i t e bars and a preweighed amount of l i q u i d SDF5. The tubes were heated t o 500K f o r s e v e r a l hours. The superacid HSbF^ w a s made by condensing HF g a s i n t o a Kel-F tube, then adding an equal mole f r a c t i o n o f l i q u i d SbFg. Graphite bars were immersed d i r e c t l y i n t h i s mixture f o r s e v e r a l hours at 300K. X-ray a n a l y s i s i n d i c a t e d stage 1 with c - a x i s repeat d i s tance 8.38 8, v e r y c l o s e t o the 8.4lR value reported by M e l i n and Herold (12) f o r SbF i n t e r c a l a t i o n without HF. This i s larger than the 7.75A value f o r stage 1 n i t r a t e and i s c o n s i s t e n t with SbFfc" as the i n t e r c a l a t e d s p e c i e , s i n c e NO3" i s p l a n a r whereas S b F ~ i s o c t a h e d r a l (13). To the best of our knowledge, t h i s i s the f i r s t example o f g r a p h i t e i n t e r c a l a t e d with a mixture o f a Lewis a c i d and a Bronsted a c i d (13)


3

5

6

O p t i c a l Reflectance Spectra. Reflectance s p e c t r a were measured u s i n g a prism monochromator i n t e r f a c e d t o a programmable c a l c u l a t o r . For r e f l e c t a n c e s p e c t r a , the r e f l e c t e d i n t e n s i t y was measured at up t o 500 energy v a l u e s , f i r s t from the sample, then from an aluminum m i r r o r . The r a t i o was then c a l c u l a t e d and p l o t t e d a u t o m a t i c a l l y . Once the data was obtained, f u r t h e r p r o c e s s i n g such as smoothing, d i f f e r e n t i a t i o n , m u l t i p l e p l o t s e t c . could be performed. Experiments were mostly l i m i t e d t o room temperature s i n c e our c o o l i n g system r e q u i r e s t h a t the sample be i n a vacuum environment. T h i s w a s found t o lead t o r a p i d degradation o f the a c i d i n t e r c a l a t i o n compounds. The sample space was thus f i l l e d with dry N2 gas. Unpolarized l i g h t at near-normal i n c i d e n c e on t o b a s a l planes correspond t o the e l e c t r i c f i e l d being p e r p e n d i c u l a r t o the c-axis f o r a l l data reported here. Figure 2 shows the 300K r e f l e c t a n c e o f stage 4 g r a p h i t e n i t r a t e . The r e f l e c t a n c e o f pure g r a p h i t e i s roughly constant at 40% i n t h i s r e g i o n . We a s s o c i a t e the minimum near l . l e V with a plasma o s c i l l a t i o n o f f r e e h o l e s . The o r i g i n o f the minimum at 0.5eV i s n ' t c l e a r ; i t s p o s i t i o n and s t r e n g t h v a r y from sample to sample. Included i n F i g u r e 2 i s a t h e o r e t i c a l curve based on Eqs. (8), (9) and (10), with the parameters ϋωρ = 3.2 eV, O U T = 25 and εο = 10. Comparisons with theory are only u s e f u l f o r i l l u s t r a t i n g trends and should not be regarded as curve f i t s i n the u s u a l sense. The comparison i s q u i t e good a t low energy and i n the edge r e g i o n . Near 0.5eV, the comparison suggests a second ab s o r p t i o n process which produces a n e g a t i v e peak i n the m e t a l l i c r e f l e c t a n c e . The i n c r e a s e i n R above the plasma minimum can be explained by the onset o f interband t r a n s i t i o n s , which l e a d t o a


29.

FISCHER E T A L .

9

~rv—ν:

' : Ο!

:0 'Jo

SO ; j Q

Free Carrier Plasma

425

q


^5 :0

Q

a - axis

ι

·

Figure 1. The first stage compound C K (after Réf. 4) 8




426

frequency dependent εο. F i g u r e 3 compares s p e c t r a from s e v e r a l SbV$ compounds, with and without HF. V a r i a t i o n s i n absolute r e f l e c t a n c e are probably due t o v a r i a t i o n s i n f l a t n e s s and s u r f a c e q u a l i t y . The r e f l e c tance minimum s h i f t s s y s t e m a t i c a l l y t o h i g h e r energy with i n c r e a s i n g a c i d s t r e n g t h . We a l s o s t u d i e d the s e n s i t i v i t y o f the SbFs+HF compound t o ambient a i r ; a f u r t h e r i n c r e a s e i n the energy o f the r e f l e c t a n c e minimum was n o t i c e d when the sample was t r a n s f e r r e d i n t o the spectrometer under N2 gas. The low energy s t r u c t u r e i s seen t o be q u i t e v a r i a b l e i n amplitude and energy, being almost absent i n the unexposed s u p e r a c i d sample. Table I summarizes the parameters obtained from p r e l i m i n a r y a n a l y s i s o f r e f l e c t a n c e s p e c t r a . Comparative values Hu>p and τ i n T a b l e I were obtained f o r the v a r i o u s compounds keeping εο = 10L Trends among the compounds are more s i g n i f i c a n t than absolute v a l u e s . The l a s t t h r e e e n t r i e s were obtained from the same i n t e r c a l a t e d sample; the r e f l e c t a n c e o f the f r e e s u r f a c e i n contact with the a c i d was very low, but the r e f l e c t a n c e minimum occurred a t 2 eV. The v a r i a t i o n i n ωρ among the l a s t t h r e e samples i s most l i k e l y due t o nonuniform i n t e r c a l a n t c o n c e n t r a t i o n a r i s i n g from an incomplete chemical r e a c t i o n . (12) One would l i k e f i r s t o f a l l t o compare values i n Table I with the corresponding values f o r pure g r a p h i t e . T h i s i s n ' t s t r i c t l y p o s s i b l e because the expected plasma edge a s s o c i a t e d with the 10 cnf f r e e e l e c t r o n s and holes i s obscured i n r e f l e c t i v i t y by strong interband t r a n s i t i o n s . (This p o i n t i s d i s c u s s e d more f u l l y i n the next s e c t i o n . ) We can, however, estimate ωρ and oyr from measured values o f N,P, m* and τ. Such an estimate shows that ωρ increases and τ decreases with i n t e r c a l a t i o n , as expected from our e a r l i e r a n a l y s i s . D e t a i l e d comparisons are unwise due t o the f a c t that σ becomes complex and s t r o n g l y frequency-dependent f o r frequencies near and above ωρ. 1 9

3

Thermoreflectance Spectra. Thermoreflectance, the d e r i v a t i v e of the r e f l e c t i v i t y with respect t o temperature, was measured by the d i r e c t heating method whereby a square wave current waveform was passed through the sample, producing peak J o u l e heating of approximately 0.2 W which gives an a l t e r n a t i n g ΔΤ o f the o r d e r o f IK and an average tempera t u r e i n c r e a s e o f 5K. The modulating frequency was 13 Hz. Optical and e l e c t r o n i c d e t a i l s a r e given elsewhere (14). These e x p e r i ments were a l s o c a r r i e d out a t room temperature with near-normalincidence u n p o l a r i z e d l i g h t . Thermoreflectance experiments were undertaken i n order t o study v a r i a t i o n s i n π bandwidth due to i n t e r c a l a t i o n . In pure g r a p h i t e the e l e c t r o n i c band s t r u c t u r e near the Fermi energy, E f , c o n s i s t s o f t h r e e overlapping bands which have t h e i r o r i g i n i n the 2p atomic wave f u n c t i o n s o f the carbon atoms, the π e l e c t r o n s . The i n t e r a c t i o n between carbon l a y e r s s p l i t s the degeneracy o f 2


29.

AL.

Free Carrier

427

Plasma

these bands, g i v i n g the energy vs c r y s t a l momentum curves shown i n F i g u r e 4. The π bandwidth i s thus a measure o f the i n n e r p l a n a r i n t e r a c t i o n o f the carbon l a y e r s . The energies E i and E2 shown on F i g u r e 4 represent t r a n s i t i o n s from the bottom o f the 1^2 band to E f and from E f t o the top o f the πι band, r e s p e c t i v e l y . Thus l 2 4γ gives a d i r e c t measure o f the π bandwidth. F i g u r e 5a i s a thermoreflectance spectrum o f one o f our pure graphite samples. T h i s data agrees with the r e s u l t s o f G u i z z e t t i et a l . (15), g i v i n g a value γι = 0.4eV. F i g u r e 5b shows a thermo r e f l e c t a n c e spectrum f o r a stage 4 n i t r a t e compound. The spectrum i s dominated by the thermal d e r i v a t i v e o f the plasma edge at l . l e V (see F i g u r e 2) with weaker s t r u c t u r e below (0.6 and 0.7 eV) and above (1.7 and 2.1 eV). The two lower peaks might be i n t e r p r e t e d as analogs o f E j and E , g i v i n g = 0.32eV f o r stage 4 n i t r a t e . T h i s suggestion must remain t e n t a t i v e , pending a systematic study o f a range o f compounds o f v a r y i n g stage and d spacing. The shape o f the down-up s t r u c t u r e at l . l e V i n F i g . 5b agrees well with that p r e d i c t e d from the temperature d e r i v a t i v e o f the r e f l e c t a n c e equation, supporting the i d e n t i f i c a t i o n o f t h i s s t r u c t u r e (and the a s s o c i a t e d minimum i n r e f l e c t a n c e ) as a plasma edge. F i g u r e 6 shows the l o g a r i t h m i c d e r i v a t i v e with respect t o energy, d ( l n R)/dE, obtained by the c a l c u l a t o r from the data o f F i g u r e 2 (stage 4 n i t r a t e ) . Comparing the plasma response near l . l e V with the corresponding thermoreflectance spectrum i n F i g . 5b, we n o t i c e t h a t the p o s i t i v e peak i s l a r g e r r e l a t i v e t o the negative peak i n d ( l n R)/dE than i n AR/R (thermo.). T h i s i s be cause the former i n c l u d e s the e f f e c t o f interband t r a n s i t i o n s a s s o c i a t e d with the i n c r e a s e i n R above l . l e V whereas these t r a n s i t i o n s do not c o n t r i b u t e s t r o n g l y t o thermoreflectance s i n c e they are not a s s o c i a t e d with high-symmetry p o i n t s i n the zone. The v a l u e o f such d a t a i s twofold. F i r s t , the amplitude o f the nega t i v e peak gives an accurate d i r e c t measure o f τ i f a>pT > 5, with out recourse t o d e t a i l e d curve f i t t i n g . Second, d e t a i l e d study o f secondary s t r u c t u r e ( i . e . 0.45 eV i n F i g u r e 6) i s g r e a t l y aided by d e r i v a t i v e techniques s i n c e i t i s now well-separated from the main response. I t i s somewhat d i s t u r b i n g that the o t h e r peaks i n Figure 5b don't show up i n d ( l n R)/dE, which makes t h e i r i n t e r p r e t a t i o n even more t e n t a t i v e . E


FISCHER E T

+

E

=

2

D i s c u s s i o n and Conclusions The p r i n c i p a l r e s u l t o f t h i s paper i s the observation o f m e t a l l i c edges i n r e f l e c t a n c e s p e c t r a o f i n t e r c a l a t i o n compounds. These are r e l a t e d t o the "transmission windows reported by Hennig (16). The plasma edge i n t e r p r e t a t i o n i s based upon the f o l l o w i n g arguments: 1) general agreement with the shape p r e d i c t e d by the Drude equation; 2) a temperature c o e f f i c i e n t du>p/dT o f - 3 x l 0 ~ eV/K, c o n s i s t e n t with the i n f l u e n c e o f l a t t i c e d i l a t i o n on c a r r i e r d e n s i t y i n simple metals; 3) thermoreflectance lineshapes 11

4



428

PETROLEUM DERIVED CARBONS


FISCHER E T A L .

Free Carrier Plasma


29.

PHOTON ENERGY (eV) Figure 5b.

Thermoreflectance of graphite nitrate


429



Figure 6.

Computer derivative of Figure 2


29.

FISCHER E T A L .

Free Carrier

431

Plasma

i n agreement with the temperature d e r i v a t i v e o f the Drude equa t i o n , 4) a higher plasma frequency i n t h e SbF compound compared t o n i t r a t e , c o n s i s t e n t with p r e l i m i n a r y measurements (7) which i n d i c a t e t h a t the former has higher c o n d u c t i v i t y . An i n t e r e s t i n g r e s u l t i s obtained by comparing SDF5+HF with HNO3 compounds v i a Table I and Eqs. (1) and (11): 5

o(SbF +HF) Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on October 13, 2015 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0021.ch029

5

σ(ΗΝ0 )

2

=

ω τ (SbF^+HF) ω

3

2 ρ

,

τ

(

1

2

)

(ΗΝ0 ) 3

2 =3

5

• ·· According t o Ubbelohde (6), σ ( Η Ν 0 ) / o(graphite) = 12, thus t h e implied c o n d u c t i v i t y increase f o r stage 1 SbFs+HF i s 3.5 χ 12 = 42 times. Since o(copper)/ o(graphite) = 30, t h i s i n t u r n im p l i e s t h a t a(SbF +HF) i s 40% higher than that o f copper, l a r g e r than any value reported f o r g r a p h i t e i n t e r c a l a t i o n compounds, or indeed f o r any s y n t h e t i c metal. T h i s r e s u l t i s independent o f the d e t a i l s o f the r e f l e c t i v i t y f i t s as long as εο i s approxi mately the same f o r t h e two compounds, because t h e r e f l e c t a n c e minimum ω i s given by ω ρ = ω * εο. T h i s p r e d i c t i o n i s o f course amenable t o t e s t by d i r e c t c o n d u c t i v i t y measurements. The o p t i c a l experiment has t h e advantages t h a t contacts are not r e quired and the r e s u l t s are not a f f e c t e d by anisotropy. It would be premature at t h i s p o i n t t o attempt t o p a r t i t i o n the ωρ i n c r e a s e between Ν and m*. We c e r t a i n l y expect Ν t o i n crease upon i n t e r c a l a t i o n , but the behavior o f m* i s l e s s pre d i c t a b l e . For example, the above comparison between SDF5+HF (stage 1) and HNO3 (stage 4) could n a i v e l y be i n t e r p r e t e d as an increase i n Ν o f a f a c t o r 3.5, c l o s e t o the v a l u e 4 which would be obtained i f the degree o f i o n i z a t i o n and the d e n s i t y o f ions w i t h i n a plane are both independent o f c o n c e n t r a t i o n . (Neither o f these suppositions are j u s t i f i e d . ) Furthermore, Ubbelohde has shown t h a t σ(ΗΝ03) decreases s l i g h t l y f o r concentrations beyond stage 4. A c l u e can be obtained as f o l l o w s . In pure g r a p h i t e , t h e f r e e c a r r i e r plasma i s obscured by interband t r a n s i t i o n s , but the π valence (bound) e l e c t r o n s e x h i b i t a resonance at 7eV. I f we suppose t h a t t h e 6eV plasma frequency f o r the stage 1 SbF5+HF com pound represents 1 f r e e hole p e r 8 carbon atoms, then we can e s t i mate (accounting f o r the decreased d e n s i t y o f carbon atoms) t h a t the average m* f o r t h i s compound i s roughly 0.1 m . I f the charge t r a n s f e r i s l e s s than 1 p e r i n t e r c a l a n t molecule, m* becomes even smaller. I t appears, t h e r e f o r e , t h a t m* i n the compounds remains s u b s t a n t i a l l y s m a l l e r than the f r e e - e l e c t r o n value, con t r a r y t o a suggestion by Hennig (16). The u l t i m a t e usefulness o f f r e e - c a r r i e r plasma a n a l y s i s w i l l come from a combination o f experiments which g i v e an overdetermi3

5

2

0

0

e


432


TABLE I


C-I-C Distance

HN0

3

air-exposed

7.75

3.2

3 χ 10"

1 5

air-exposed

8.41

3.5

3 χ 10"

1 5

air-exposed

8.38

4.0

6 χ 10

Stage 4 SbF

5

SbF

5

1

+ HF

Stage 1 No gas ambient

center o f bar

4.7

j u s t below surface

4.9

original surface

6

C K 8

3 χK f

1/30

HN0 BF

3

-

stage 1

1/6

-

stage 4

1/3

?

3

SbF

5

+ HF

predicted

-

5/6

stage 1

from

L

15

σ/σ(eu) a-axis 30ΌΚ

graphite

r

5

"3 χ 1 0 " -

Table I I Material

1

(1.4)*

ω


1

5


29.

FISCHER E T A L .

433

Free Carrier Plasma

ned set o f one-electron parameters. T h i s procedure w i l l be necessary t o p r o v i d e j u s t i f i c a t i o n f o r t h e use o f s i n g l e - p a r t i c l e theory i n t h e f i r s t p l a c e . ( I t may t u r n out that the d.é. cond u c t i v i t y i s enhanced by c o l l e c t i v e phenomena.) We have noted p r e v i o u s l y that the f r e e c a r r i e r plasma i n pure g r a p h i t e does not produce t h e expected Drude edge i n r e f l e c tance. P h y s i c a l l y , t h i s a r i s e s from the f a c t that t h e t h r e s h o l d f o r interband t r a n s i t i o n s i n only 0.02eV so t h e interband strength i s very l a r g e by t h e time ω reaches 0.4eV, t h e l o c a t i o n o f t h e expected minimum. A n a l y t i c a l l y t h e e f f e c t o f a complex ε i s i d e n t i c a l t o a very small τ i n Eq. (10), such that t h e resonance i s broadened out. The observation o f plasma edges i n reflectance* s p e c t r a o f i n t e r c a l a t i o n compounds thus i m p l i e s that t h e interband strength i s q u i t e small f o r ω below 1.2eV. The r e d u c t i o n i n band width mentioned e a r l i e r would oppose t h i s e f f e c t ; t h e n e t r e s u l t must be due t o the s h i f t i n E f . The present work, coupled with e a r l i e r s t u d i e s by Vogel on BF compounds, c l e a r l y demonstrates that strong a c i d s lead t o l a r g e r c o n d u c t i v i t y i n c r e a s e s than reported h e r e t o f o r e . I t would be extremely i n t e r e s t i n g t o l e a r n t o what extent t h i s i s due t o l a r g e r f r a c t i o n a l charge t r a n s f e r and/or t o l a r g e d-spacing hence a l a r g e d e n s i t y o f s t a t e s at the Fermi l e v e l . I t w i l l a l s o be important t o f i n d out i f there are any r e a l d i f f e r e n c e s between SbF5 alone and w i t h HF. The d-spacings a r e q u i t e s i m i l a r , and the d i f f e r e n c e s i n plasma energies shown i n Figure 3 c o u l d i n p r i n c i p l e be due t o contamination e f f e c t s . The bandwidth hypoth e s i s could be t e s t e d on stage 1 SbCils f o r which d=9.3o8 (although t h i s compound may be d i f f i c u l t t o s y n t h e s i z e ) . Table I I summarizes t h e 300K c o n d u c t i v i t i e s o f s e v e r a l com pounds. Values are given r e l a t i v e t o copper t o emphasize t h e p r a c t i c a l p o s s i b i l i t i e s . At t h i s p o i n t we cannot estimate the maximum c o n d u c t i v i t y achievable v i a i n t e r c a l a t e d g r a p h i t e , be cause we have y e t t o i d e n t i f y t h e l i m i t i n g f a c t o r s and appropriate models. 0

3

Supported i n p a r t by ARPA Order 2380, DOD Grant DAHC15-73G14; by ONR Grant NOOO14-75C-0751; and by t h e Pennsylvania Science and Engineering Foundation.

Literature Cited (1) . Hennig, G.R., Progress in Inorganic Chemistry, edited by F. A. Cotton (Interscience, New York, 1959), Vol. I, p. 125. (2) . Rüdorff, W., Advances in Inorganic Chemistry and Radiochemistry, edited by H. J. Emeleus and A. G. Sharpe (Academic Press, New York, 1959), Vol. 1, p. 223. (3) . Nixon, D. E. and Parry, G. S., J. Phys. C 2, 1732 (1969). (4) . Rüdorff, W. and Schulze, Ε., Z. Anorg. Allgem. Chem. 277, 156 (1954). (5) . Ubbelohde, A. R., Proc. Roy. Soc. (London) A 309, 297 (1969). (6) . Ubbelohde, A. R., Proc. Roy Soc. (London) A 327, 289 (1972).



434


(7) . Vogel, F. L., (Unpublished). (8) . Bender, A. S. and Young, D. Α., J. Phys. C 5, 2163 (1972). (9) . Moore, A. W., Chemistry and Physics of Carbon, edited by P. L. Walker and P. A. Thrower (Marcel Dekker Inc., New York, 1973), Vol. 11, p. 69. We are grateful to Dr. Moore of Union Carbide for providing us with aligned graphite specimens. (10) . Ubbelohde, A. R., Proc. Roy. Soc., A 304, 25, (1968). (11) . La Lancette, J. M. and La Fontaine, J., Chem. Commun. 815, (1973). (12) . Mélin, J. and Herold, Α., C. R. Acad. Sc. Paris 280, 641 (1975). (13) . Gillespie, R. J. and Peel, T. E., Advances in Physical and Organic Chemistry (Academic Press, New York, 1971), Vol. 9, p. 1. (14) . Loughin, S., Yang, C. Y. and Fischer, J. E., Appl. Opt. 14, 1373 (1975). (15) . Guizzetti, G. Nosenzo, L., Reguzzoni, E. and Samoggia, G., Phys. Rev. Letters 31, 154 (1973). (16) . Hennig, G. R., J. Chem. Phys. 43, 1201 (1965).


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