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PHONONS IN ALKALI GRAPHITE INTERCALATION COMPOUNDS
H. Zabel, A. Magerl
To cite this version:
H. Zabel, A. Magerl. PHONONS IN ALKALI GRAPHITE INTERCALATION COMPOUNDS.
Journal de Physique Colloques, 1981, 42 (C6), pp.C6-289-C6-291. �10.1051/jphyscol:1981683�. �jpa- 00221619�
JOURNAL DE PHYSIQUE
CoZZoque C6, supple'ment au nO1 2, Tome 42, de'cembre 1981 page c6-289
PHONONS IN ALKALI GRAPHITE INTERCALATION COMPOUNDS
H. Zabel and A . ~ a g e r l *
Loomis Laboratory of Physics and MateriaZs Research Laboratory, University of IZZinois a t Urbana-Champaign, Urbana, 11;. 61801, U.S.A.
I I n s t i t u t Laue-Langevin, 256X, F-38042 GrenobZe-Cedex, France
A b s t r a c t , - The [001]L phonon branches 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 com- pounds CxlI (x=8,24,36; M=K,Rb,Cs) have been measured by means of i n e l a s t i c neutron s c a t t e r i n g experiments. I n a l l c a s e s t h e phonon branches show zone
f o l d i n g e f f e c t s , due t o t h e enlarged u n i t c e l l a s compared t o p r i s t i n e graph- i t e , a l o n g w i t h opening of frequency gaps 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 zone. A l l measured [OOlIL phonon d i s p e r s i o n s a r e d e s c r i b a b l e by one-dimensional s h e l l models w i t h d i f f e r e n t masses and f o r c e c o n s t a n t s t o account f o r t h e g r a p h i t e and a l k a l i area-mass d e n s i t i e s a l o n g t h e c-axis and t h e i r i n t e r p l a n a r i n t e r a c t i o n s .
1. I n t r o d u c t i o n . - Within t h e p a s t y e a r , t h e i n t e r e s t i n t h e s t u d y of low frequency modes i n g r a p h i t e i n t e r c a l a t i o n compounds h a s i n c r e a s e d c o n s i d e r a b l y , u l a f t e r t h e high frequency modes have been i n v e s t i g a t e d e x t e n s i v e l y by Raman spectroscopy and i n f r a r e d r e f l e c t a n c e . / I n p a r t i c u l a r , t h e low l y i n g modes w i t h phonon propagation i n t h e hexagonal c - d i r e c t i o n ([001]L and [001]T) a r e important f o r t h e d e t e r m i n a t i o n of t h e g r a p h i t e - i n t e r c a l a n t i n t e r p l a n a r i n t e r a c t i o n . Knowledge of t h e coupling f o r c e c o n s t a n t s may c o n t r i b u t e t o t h e s o l u t i o n of such important q u e s t i o n s a s t h e o r i g i n of long-range s t a c k i n g o r d e r of g r a p h i t e and i n t e r c a l a t e d p l a n e s and of i n t e r - c a l a n t in-plane o r d e r - d i s o r d e r phase t r a n s i t i o n s . I n a d d i t i o n , t h o s e modes allow t o s t u d y some fundamental a s p e c t s of l a t t i c e dynamics: s i n c e t h e i n t e r p l a n a r d i s - t a n c e s of t h e atoms a r e n o t changed f o r [001] modes, they may b e considered a s t h e movement of a one-dimensional (1-D) a r r a y of r i g i d l a y e r s . The p r o p e r t i e s of t h i s l i n e a r c h a i n of g r a p h i t e and i n t e r c a l a n t p l a n e s can a r t i f i c a l l y b e changed, by changing t h e s t a g e n b f t h e compound (n d e s i g n a t e s t h e number of g r a p h i t e planes between two i n t e r c a l a t e d planes), and/or t h e i n t e r c a l a n t chosen, and e f f e c t s l i k e zone f o l d i n g and opening of frequency gaps a t t h e c e n t e r and t h e boundary of t h e B r i l l o u i n zone can b e s t u d i e d i n a s y s t e m a t i c manner.
I n t h e f o l l o w i n g t h e experimental r e s u l t s o b t a i n e d f o r [001]L modes i n 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 (AGIC's) w i l l b e p r e s e n t e d and l a t t i c e dynamical models w i l l b e d i s c u s s e d . A more d e t a i l e d d i s c u s s i o n i s given i n a s e p a r a t e con-
t r i b u t i o n t o t h i s volume.&/ The [001]T modes, which a r e l e s s a c c e s s i b l e t o i n e l a s - t i c neutron s c a t t e r i n g , have been s t u d i e d by Raman s p e c t r o s c o p y . 5 /
2. Experimental. - The samples were i n t e r c a l a t e d w i t h a l k a l i atoms i n a two-stage f u r n a c e i n t h e u s u a l manner,$/ and homogeneity of each compound was determined by
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981683
C6-290 JOURNAL DE PHYSIQUE
x-ray and n e u t r o n e l a s t i c (0011) s c a n s . Relevant parameters of t h e samples b e f o r e a f t e r i n t e r c a l a t i o n w i l l b e published e l s e w h e r e . l / Constant Q s c a n s were performed, u s i n g t r i p l e - a x i s s p e c t r o m e t e r s a t t h e N a t i o n a l Bureau of Standards r e s e a r c h r e a c t o r , Flashington, D. C.
3. R e s u l t s . - The [001]L phonon e n e r g i e s o b t a i n e d a t C8K, C24K, C36K, C24Xb, C8Cs and CZ4Cs a r e p l o t t e d i n F i g . 1. For t h e s a k e of completeness t h e corresponding modes of C8Rb have a l s o been i n c l u d e d . / The phonon wavevectors a r e given i n u n i t s of t h e i n t e n s i t y p e r i o d C, n e g l e c t i n g any s t a c k i n g sequence of t h e g r a p h i t e and/or a l k a l i planes. Each s t a g e n compounci c o n t a m s n i l p l a n e s p e r u n i t c e l l . Accord- i n g l y , t h e r e a r e n + l phonon b r a n c h e s , which could a l l b e determined: i n each c a s e one
Fig. 1: 1,leasured phonon e n e r g i e s f o r [001]L modes i n 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. The phonon e n e r g i e s of CzRb have been t a k e n from Ref. 8. F u l l l i n e s a r e b e s t f i t s w i t h 1-D i o n - s h e l l models.
a c o u s t i c a l branch and n o p t i c a l b r a n c h e s . Mode s p l i t t i n g s could b e c l e a r l y r e s o l v e d i n most c a s e s , w i t h t h e e x c e p t i o n of C24Cs, where t h e carbon and cesium l a y e r s have al~rrost i d e n t i c a l i n - p l a n e area-mass d e n s i t i e s . Low t e m p e r a t u r e experiments down t o 63 K have been performed a t C36K. The r e s u l t s do n o t i n d i c a t e any change of t h e phonon e n e r g i e s a c r o s s t h e phase t r a n s i t i o n a t around 130 K.?/
4 . D i s c u s s i o n . - The d a t a have been a n a l y z e d by s e v e r a l 1-D l a t t i c e dynamical models. I n o p p o s i t i o n t o p u r e graphite,-/ Born-von arm& t y p e models cannot d e s c r i b e t h e observed [001]L modes of AGIC's. Here a s i m p l e 1-D s h e l l model
Fig. 2: Schematic r e p r e s e n t a t i o n of t h e 1-D i o n - s h e l l model f o r s t a g e n compound d l and d2 a r e t h e d i s t a n c e s between a l k a l i and g r a p h i t e p l a n e s , I c i s t h e r e p e a t d i s - t a n c e of t h e compound i n t h e c - d i r e c t i o n . $11 and M2 a r e t h e a l k a l i and g r a p h i t e area-mass d e n s i t i e s , r e s p . and m i s t h e e l e c t r o n mass d e n s i t y , which is e x t r a p o l a t e d t o z e r o . OK i s t h e c o r e - s h e l l , $$ t h e s h e l l - g r a p h i t e , and $2 t h e i n t e r i o r g r a p h i t e - g r a p h i t e f o r c e c o n s t a n t .
y i e l d s t h e b e s t r e s u l t . I n t h i s model a charged l a y e r h a s been i n t r o d u c e d between a l k a l i and a d j a c e n t g r a p h i t e p l a n e s t o account f o r t h e inhomogeneous charge d i s t r i - b u t i o n a l o n g t h e c-axis ( F i g . 2 ) . B e s t f i t s of t h e s h e l l model t o t h e measured phonon e n e r g i e s y i e l d v a l u e s f o r $K, which a r e roughly an o r d e r of magnitude l a r g e r t h a n t h e f o r c e c o n s t a n t s $S and $ 2 , w h i l e OS i s always l a r g e r t h a n $ 2 , by a b o u t 10- 20%, and $ 2 is almost i d e n t i c a l t o t h e i n t e r p l a n a r c o u p l i n g c o n s t a n t of p r i s t i n e g r a p h i t e .
The a u t h o r s acknowledge v a l u a b l e d i s c u s s i o n s w i t h J. J. Rush and J. TI. Roiie.
T h i s work was s u p p o r t e d i n p a r t by t h e U.S. Department o f Energy under C o n t r a c t DE-AC02-76ER01198, t h e Research 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 Research Board.
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