THERMAL EXPANSION OF ALKALI-GRAPHITE INTERCALATION COMPOUNDS

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THERMAL EXPANSION OF ALKALI-GRAPHITE INTERCALATION COMPOUNDS

S. Hardcastle, H. Zabel

To cite this version:

S. Hardcastle, H. Zabel. THERMAL EXPANSION OF ALKALI-GRAPHITE INTERCA- LATION COMPOUNDS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-326-C6-328.

�10.1051/jphyscol:1981695�. �jpa-00221632�

JOURNAL DE PHYSIQUE

CoZloque C6, suppldment au n o 12, Tome 42, de'cembre 1981 page C6-326

T H E R M A L EXPANSION O F ALKALI-GRAPHITE INTERCALATION COMPOUNDS

S.E. H a r d c a s t l e and H. Zabel

Loomis Laboratory of Physics and MateriaZs Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, ILL. 61801, U.S.A.

Abstract.-The c - a x i s thermal expansion of s e v e r a l a l k a l i - g r a p h i t e i n t e r c a l - a t i o n compounds has been measured by means of x-ray s c a t t e r i n g between 1 5 and 300 K. The thermal expansion depends s t r o n g l y on t h e s t a g e of t h e compound and i s l a r g e s t f o r CgM (M=K,Rb,Cs) compounds. The d a t a have been analyzed i n terms of a n one-dimensional quasi-harmonic approximation, which y i e l d s Griineisen parameters two o r t h r e e times a s l a r g e a s f o r p r i s t i n e g r a p h i t e .

1. I n t r o d u c t i o n .

-

(n d e s i g n a t e s t h e number of g r a p h i t e p l a n e s between two i n t e r c a l a t e d p l a n e s ) and t h e a l k a l i atoms chosen by means of x-ray Bragg-scattering.

2. Experimental. - Highly o r i e n t e d p y r o l y t i c g r a p h i t e (HOPG) was i n t e r c a l a t e d with a l k a l i atoms by t h e two bulb method i n t h e u s u a l manner.3 The homogeneity and s t a g e of t h e compound was determined by (00.k) scans. The TE was measured between 1 5 and 300 K d u r i n g h e a t i n g and c o o l i n g c y c l e s w i t h MoK r a d i a t i o n . A more d e t a i l e d d e s c r i p t i o n of t h e experimental s e t up w i l l be given elsewhere.

3. R e s u l t s .

-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981695

i n t e r i o r g r a p h i t e p l a n e s .

TEMPERATURE (K

l ~ ' ~ ' ~ ' ~ ' l ' l ' ~ ' ~ l

TEMPERATURE (K

Fig. 1: Thermal expansion of a l k a l i - g r a p h i t e i n t e r c a l a t i o n compounds, ( a ) of s t a g e 1 K , Rb, C s compounds, (b) of s t a g e 2 K, and Rb. I n ( c ) d i f f e r - e n t s t a g e s of K compounds a r e compared.

TEMPERATURE (K

4. Discussion.

-

[001]L modes. The higher modes a r e s e p a r a t e d from r h e lower by a l a r g e frequency gap and can t h e r e f o r e be n e g l e c t e d . 4 It h a s been shown r e c e n t l y t h a t t h e [001]L modes a r e s t r o n g l y i n f l u e n c e d by i n t e r ~ a l a t i o n . ~ The i n t e r p l a n a r coupling c o n s t a n t s a r e changed, and frequency gaps occur a t t h e c e n t e r and boundary of t h e B r i l l o u i n zones, c r e a t i n g new maxima i n t h e d e n s i t y of s t a t e s . There a r e i n p r i n c i p a l two p o s s i b l e r e a s o n s f o r a n i n c r e a s e d TE of A G I C ' s a s compared t o p r i s t i n e g r a p h i t e : e i t h e r t h e phonon d e n s i t y of s t a t e s i n c r e a s e d and/or t h e anharmonicity of t h e v i b r a t i o n a l p o t e n t i a l i s enhanced. To e l u c i d a t e t h e s e p o s s i b i l i t i e s , t h e TE's have been analyzed i n terms of a 1-D quasi-harmonic approximation,6 i n which t h e r e l a t i v e change of t h e c-axis i s g i v e n by:

and t h e thermal energy is:

=

2

.

Etherm 2.rr 2%T

Here y i s t h e m o d e Griineisen parameter, t h e e l a s t i c c o n s t a n t s Cg3 f o r each com- pound have been taken from Ref. 5 , V i s t h e volume of a u n i t c e l l , w i s t h e l a t t i c e v i b r a t i o n a l frequency, and i s t h e Boltzmann c o n s t a n t . The thermal energy h a s been determined by numerical i n t e g r a t i o n over t h e measured 10011L phonon d i s p e r s i o n s .

C6-328 JOURNAL DE PHYSIQUE

I n F i g . 2 t h e TE i s p l o t t e d a g a i n s t t h e t h e r m a l e n e r g y f o r t h e compound C K. From 8

T a b l e 1 Compound Temperature r a n g e

(K) yc

HOPG 1 5

-

1 2 0

-

C8K 1 5

-

125

-

240

-

C24K 1 5

-

1 6 0

-

'3 6K 1 5 - 7 0 - 3 1

90

-

1 9 0

-

8

6

10

0 5 -

* 4 -

Y

a"

1 -

t h e s l o p e , t h e Griineisen p a r a m e t e r h a s been d e r i v e d . I n T a b l e 1 p a r a m e t e r s g a i n e d

- ' HOPG ' C8K

-

. .

.- .. .

.*

-

.-

.*

*...

... .

:-

.. .

-.-:

i n t h i s way f o r K compounds a r e l i s t e d and compared w i t h BOPG. The Griineisen -

5 10 15 20

THERMAL ENERGY (meV) F i g . 2: c - a x i s t h e r m a l ex- p a n s i o n o f s t a g e 1 K and HOPG a g a i n s t t h e r m a l e n e r g y , g a i n e d f ram[ 0011 L phonon d i s - p e r s i o n s .

p a r a m e t e r o f p r i s t i n e g r a p h i t e i s i n good agreement w i t h p u b l i s h e d d a t a . ' The a n h a r m o n i c i t y of t h e l a t t i c e v i b r a t i o n s i n c - d i r e c t i o n seems s e v e r e l y i n f l u e n c e d by t h e i n t e r c a l a t i o n p r o c e s s : s t a g e 1 compounds show a c o n s i d e r a b l y h i g h e r y a t low t e m p e r a t u r e s , which w e n i n c r e a s e s a t h i g h e r t e m p e r a t u r e s . Also, s t a g e 2 and 3 compounds e x h i b i t i n c r e a s e d Grfineisen p a r a m e t e r s . T h e r e f o r e , w e b e l i e v e t h a t t h e dominant e f f e c t f o r t h e l a r g e TE o f AGIC's i s a n i n c r e a s e d a n h a r m o n i c i t y of t h e l a t t i c e v i b r a t i o n s , r a t h e r t h a n t h e h i g h e r d e n s i t y o f s t a t e s i n t h e f r e q u e n c y r e g i o n c o n s i d e r e d h e r e .

We acknowledge v a l u a b l e d i s c u s s i o n w i t h A. Magerl, R. Nicklow and R. F i e d l e r , d o n a t i o n o f HOPG from A. W. Moore, and f u n d i n g from U. S. DOE DE-AC02-76EF.01198, R e s e a r c h C o r p o r a t i o n and t h e U n i v e r s i t y of I l l i n o i s R e s e a r c h Board.

R e f e r e n c e s :

1. T h e r m a l p h y s i c a l P r o p e r t i e s of M a t t e r TPRC Data S e r i e s , Thermal Expansion Non- m e t a l l i c s o l i d s , l3, 8 0 (1977).

2. F o r a r e c e n t r e v i e w s e e : M. S. D r e s s e l h a u s a n d G. D r e s s e l h a u s , Adv. Phys.

30, 139 (1981).

-

3 . A. Hgrold, B u l l . Soc. Chim. Fr.

187,

4 , R. NicWow, N. Wakabayashi, and E. G. Smith, Phys. Rev. B?, 4951 (1972).

5. H. Zabel and A. Magerl, c o n t r i b u t i o n t o t h i s volume and t o b e p u b l i s h e d . 6. G. L e i b f r i e d and W. Ludwig, S o l i d S t a t e P h y s i c s

12,

7. A. C. B a i l e y and B. Y a t e s , J. Appl. Phys.

41,