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NEUTRON SPECTROSCOPY OF PHONONS IN RbC8
W. Kamitakahara, N. Wada, S. Solin
To cite this version:
W. Kamitakahara, N. Wada, S. Solin. NEUTRON SPECTROSCOPY OF PHONONS IN RbC8.
Journal de Physique Colloques, 1981, 42 (C6), pp.C6-311-C6-313. �10.1051/jphyscol:1981690�. �jpa- 00221627�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZJment au nO1 2, Tome 42, dJcembre 1981 page C6-311
NEUTRON SPECTROSCOPY OF PHONONS I N RbC8
x * ?+ -x
W.A. Kamitakahara, N. Wada and S.A. S o l i n
Ames Laboratory-USDOE and Department of Physics, Iowa S t a t e University, Ames, Ioua 50011, U.S.A.
* ~ a m e s Franck I n s t i t u t e , University of Chicago, Chicago, IZZinois 60637, U. S. A.
* * ~ e ~ a r t m e n t o f Physics, Michigan S t a t e University, East Lansing, Michigan 48824, U. S. A.
Abstract.- Neutron s c a t t e r i n g methods have been used t o i n v e s t i g a t e t h e l a t t i c e dynamics of stage-one Rb g r a p h i t e . I n t e r c a l a t e (Rb) modes w i t h p o l a r i z a t i o n s and wave v e c t o r s p a r a l l e l t o t h e b a s a l p l a n e have been ob- served f o r t h e f i r s t time. The e x p e r i m e n t a l l y d e r i v e d p a r t i a l phonon d e n s i t y of s t a t e s f o r i n t e r c a l a t e modes is compared with model calcula- t i o n s . Phonon d i s p e r s i o n curves have been measured f o r l o n g i t u d i n a l c- a x i s modes and f o r some t r a n s v e r s e modes propagating i n t h e b a s a l plane.
1. Experiment.- A l a r g e ( 6 em3) sample was prepared by t h e u s u a l two-bulb method1 from Union Carbide ZYH p y r o l i t i c g r a p h i t e . The c r y s t a l l i t e s i n such a
sample a r e a l i g n e d w i t h a common c-axis b u t a r e randomly o r i e n t e d i n t h e ab plane. A t r i p l e - a x i s spectrometer a t t h e Oak Ridge Research Reactor was used t o c a r r y out t h e neutron s c a t t e r i n g measurements.
2. I n t e r c a l a t e Modes.- By t h e s e we mean phonons f o r which t h e motions involved a r e almost completely t h o s e of t h e i n t e r c a l a t e (Rb) atoms, w i t h wave v e c t o r s and displacements p a r a l l e l t o t h e b a s a l plane. By averaging s p e c t r a f o r a number of wave v e c t o r t r a n s f e r s Q i n t h e b a s a l plane, we have been a b l e t o o b t a i n a par- t i a l phonon d e n s i t y of s t a t e s f o r t h e i n t e r c a l a t e modes, as shown i n Fig. 1. I n t h e low-energy r e g i o n shown, f o r such s c a n s w i t h -4 p a r a l l e l t o t h e b a s a l plane, t h e g r a p h i t e h o s t responds only v e r y weakly because of t h e very s t r o n g f o r c e s opposing i n t r a l a y e r in-plane displacements of C atoms. The g e n e r a l room back- ground and i n e l a s t i c s c a t t e r i n g from t h e g r a p h i t e p l a n e s (determined by a s c a n on pure p y r o l i t i c g r a p h i t e ) gave a smooth, g e n t l y s l o p i n g c o n t r i b u t i o n t o t h e observed s p e c t r a which was s u b t r a c t e d o f f i n o r d e r t o o b t a i n t h e i n t e r c a l a t e mode spectrum. The l a t t e r was t h e n converted t o a phonon d e n s i t y of s t a t e s by d i v i d i n g by well-known f a c t o r s i n t h e one-pbonon neutron c r o s s s e c t i o n .
The d a t a shown i n Fig. 1 were compared w i t h s e v e r a l model c a l c u l a t i o n s . I n no case were we a b l e t o o b t a i n good agreement w i t h models c o n s i d e r i n g o n l y
x P r e s e n t a d d r e s s : M a t e r i a l s Research Laboratory, U n i v e r s i t y of I l l i n o i s , Urbana, I l l i n o i s 61801, U.S.A.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981690
C6-3 12 JOURNAL DE PHYSIQUE
Fig. 1 : Points are the experi- mentally-derived partial phonon
density of states for inter- calate modes. Calculation NN results from a two-dimensional
(2D) nearest-neighbor force model, while C represents a 3D unscreened Coulomb force model.
FREQUENCY v(THz1
short-range (i.e., nearest-neighbor) forces between Rb atoms. On the other hand, it was found that a model in which the Rb-Rb forces were simply the unscreened Coulomb interactions between +1 ions gave a good description of the intercalate mode phonon density of states (see curve C in Fig. 1). This model has only one adjustable parameter, representing the short-range C-Rb forces, which creates a low-frequency cutoff to the spectrum, and shifts all modes to
somewhat higher frequencies. The overall shape of the spectrum and the general magnitude of the frequencies arise from the crystal structure and the Coulomb
interaction, for which we need to introduce no additional parameters. The good agreement with experiment shows that conduction electron screening of the Rb motions, although it must be present, has a much less important effect on the
intercalate phonon spectrum in RbC8 than on the lattice dynamics of pure Rb meta1.2~3 The unusual order-disorder phase transformations which occur495 in RbCg and similar5 compounds must closely involve the iaercalate-intercalate and intercalate-graphite interactions about which we have obtained detailed information through our experiment and its analysis.
3. Phonon Dispersion Curves.- In addition to our observations of intercalate modes, we have also made measurements on phonon dispersion in RbC8. The longitudinal interlayer frequencies for modes propagating along the c-axis are in generally good agreement with the previous measurements of Ellenson et Dispersion curves for transverse modes with polarization perpendicular to the basal plane, but with wave vector in the basal plane, were also measured, and are shown in the right hand side of Fig. 2. Because our sample is c-oriented and not a single crystal, these dispersion relations are averages over all directions in the basal plane. However, as in pure graphife,6 w($) is bound to be rather isotropic for in the basal plane. The lowest of these transverse branches lies substantially lower than in pure graphite,6 despite the fact that the strong intralayer C-C forces which largely determine these modes in pure graphite are unlikely to be much different in RbC8. Qualitatively, this points to a disproportionate participation of Rb motions (i.e., large Rb phonon
"
0.2 0.1 0 0 .I 0.2 s~bnlls 2 ~ 1 ~ 1 ( units 4r/a a ) +
Fig. 2 : Phonon d i s p e r s i o n c u r v e s f o r RbC 8'
e i g e n v e c t o r s ) f o r t h e s e modes i n t h e i n t e r c a l a t i o n compound. R e c e n t l y proposed l a t t i c e dynamical should be u s e f u l i n a n a l y s i n g o u r r e s u l t s .
The Ames Laboratory is o p e r a t e d f o r t h e U.S. Department of Energy by Iowa S t a t e U n i v e r s i t y under c o n t r a c t no. W-7405-Eng-82. T h i s r e s e a r c h was supported by t h e O f f i c e of B a s i c Energy S c i e n c e s , WPAS-KC-02-02-01. SAS was supported by t h e U.S. Army Research O f f i c e under g r a n t no. DAAG-29-80-K-0003.
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