Low-energy excitation in CuI

SOLID STATE

Solid State lonics 53-56 (1992) 1278-1281 North-Holland

IONICS Low-energy excitation in CuI Takashi Sakuma Department o['Ph)'sics, Faculty (~[Science, lbaraki Universio', Mito 310, Japan

Kaoru Shibata Institutejor Materials Research, ~ibhoku UniversiO,, Sendai 980, Japan

and Sadao Hoshino Institute (~fApplied Physics, University of Ysukuba, Tsukuba 305, Japan

Neutron inelastic scattering of the copper-ion conductor CuI is measured by the time-of-flight (TOF) method at 35, 2011),280 and 360 ° C. The neutron inelastic spectra are analyzed by the use of a model function for the generalized density of states. This model function consists of two components: a low-energy excitation mode and phonon modes due to the transverse acoustic branch. The value of the dispersionless low-energy excitation h~o~ 3.4 meV is almost independent of temperature. The relation between the excitation energy and the mass of the cations can be represented by h(o ~ ( I/M)'/2. The relation could also bc described as a cation plasma model with an appropriate effective charge of the cation.

1. Introduction T h e structures and d y n a m i c a l p r o p e r t i e s o f superionic c o n d u c t o r s h a v e been extensively investigated. C o p p e r i o d i d e ( C u l ) exhibits h i g h - t e m p e r a t u r e phase t r a n s i t i o n s at 3 6 9 ° C (T-I3) and at 4 0 7 ° C ([3ct). T h e high t e m p e r a t u r e [3- and a - p h a s e s are well k n o w n as h a v i n g a high ionic c o n d u c t i v i t y . T h e crystal structures o f C u l h a v e been studied by X-ray [ 13] and n e u t r o n d i f f r a c t i o n m e t h o d s [4]. Low-energy e x c i t a t i o n s h a v e been o b s e r v e d in the n e u t r o n scattering studies o f several cation superionic c o n d u c t o r s [ 5 - 1 0 ]. T h e values o f the low-energy e x c i t a t i o n for Ag-, Na- and C u - i o n s u p e r i o n i c c o n d u c t o r s were f o u n d to be 2 . 0 - 3 . 0 [ 5 - 7 ] , 6.0 [8] and 3.4 [9,10] meV, respectively. In the present study, the inelastic n e u t r o n scattering s p e c t r u m o f CuI was m e a s u r e d at several t e m p e r a t u r e s by the use o f the T O F s p e c t r o m e t e r L A M 40 installed at the pulsed spallation n e u t r o n facility Author to whom correspondence should be addressed.

K E N S . The results o f the m e a s u r e m e n t s are c o m p a r e d with those o f o t h e r s u p e r i o n i c conductors.

2. Experimental Inelastic n e u t r o n scattering m e a s u r e m e n t s were p e r f o r m e d at 25, 200, 280 and 3 0 0 ° C . A p o w d e r s p e c i m e n o f CuI was c o n t a i n e d in a cylindrical alum i n u m tube o f 13 m m d i a m e t e r and 80 m m length with a thin wall. T h e range o f Q ( = 4 ~ sin 0/,2.) cove r e d by this s p e c t r o m e t e r is 0 . 2 - 2 . 5 A-1 a t elastic scattering and the energy resolution was a b o u t 200 i.teV ( F W H M ) . T h e data collection t i m e for each t e m p e r a t u r e was a b o u t 5 h.

3. Results and analysis A low-lying dispersionless excitation near 3.4 meV was o b s e r v e d in the inelastic scattering spectra o f a p o w d e r sample o f C u l o v e r the m e a s u r e d range o f Q.

0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

T. Sakuma et al. / Low-energy excitation in Cul

The observed inelastic scattering spectra I(Q, co) of CuI with Q = 2 . 5 A -~ at various temperatures are shown in fig. 1. The asymmetry of elastic peak profiles is caused by the incident neutron pulse profile. A distinct inelastic peak with a low-energy transfer exists in the observed spectra in fig. 1 though it is fairly damped at 360°C. As the temperature is lowered the excitation near 3.4 meV becomes clear and the intensity of the inelastic scattering spectra in the energy range 1.0-3.0 meV decreases. The analysis of the inelastic scattering spectra was performed in the same manner as that of copper-ion conductors recently carried out by the present authors [10]. Since the diffuse scattering intensity in the powder X-ray diffraction pattern would be mainly produced by the disordered structure of the cations, the observed spectra at Q = 2 . 5 A - ' can be assumed to be due mainly to the contribution from Cu atoms. The relation between the dynamical structure factor S(Q, 09) and the generalized density of states G(Q, co) is as follows [ 5 ]'

G( Q, co ) =S( Q, co)/exp( - 2BQ2 /167t 2) h2Q2 n(co)+ l X

-2M

(co>0)

co

where exp(-BQ2/161t 2) is the Debye-Waller factor, M is the mass of the Cu atom and n(co) is the Bose factor. The G(Q, 09) spectra with Q = 2 . 5 A - ' thus obtained are shown in fig. 2. The values of the temperature factor B, o f CuI used for the calculation were 1.0, 3.0, 6.5 and 13.0 at 25,200, 280 and 360°C, respectively.

Cul ~oo

-

=

Q=2.5 A

4

#

%

I []

80

% ~S

I

I

E] o:/x'c'~

360 'C 280 'C

[] ~:qt,~

200 'c

×

25%

O

[]

~

~

Ld~ 'rtt~ o E : ~ l ~ [i~-E]~C>

60

[] o

~-40~ cu

o

--'~

20 0 2

2~

0 Energy

Transfer

41

16 (meV)

Fig. 1. The observed inelastic neutron scattering spectra of Cul with Q = 2 . 5 A - t at 25,200, 280 and 360°C.

127 9

The model scattering function for the generalized density of states consists of two components: the lowenergy excitation mode and the phonon modes mainly due to the transverse acoustic branch. The model function to fit the density of states is as follows:

coF G( Q' CO) =COF( ( ( CO~_ C O ~ + CO2F2) + g( CO) , g( co ) .~ co2

( co~- O) ,

where co, and F are the frequency and the half-width of the low-energy excitation mode, respectively, and g(co) is the density of states due mainly to the transverse acoustic branch. The results of fitting with the experimental spectra are shown in fig. 2. The values of the fitting parameters obtained for the low-energy excitation mode are displayed in table 1.

4. Discussion It is found from table 1 that the value of low-energy excitation hco~~ 3.4 meV is almost independent of temperature. When the temperature increases, the half-width F of the low-energy excitation mode increases at temperatures above 200 °C. The temperature dependence of the half-width of the low-energy excitation mode could be associated with that of the electrical conductivity. The half-width shows the degree of anharmonicity of thermal vibration, which is proportional to the inverse of the lifetime of the mode. As the thermal vibration becomes large, a mobile ion can easily diffuse over the barrier of the activation energy. In the case of CuI, the measured Debye-Waller factors are extremely large above 200°C in the 7-phase [ 1 ], indicating the strong anharmonic vibration of the atoms at high temperatures. Corresponding to the increase of the thermal vibration of the diffusive ions, the electrical conductivity increases rapidly at temperatures above 200°C [ 11 ]. It is found that most part of the generalized density of states of CuI consists of the low-energy excitation mode from fig. 2. In the case of 13-Cu2Se the generalized densities of states on the lower-energy side was approximated by the low-energy excitation mode and that on the higher-energy side by the phonon modes mainly due to the acoustic branch [ 9 ]. The density of states of Cul which was reported

T. Sakuma et al. / Low-energy excitation in ('ul

1280

fs~

BO

- - - - + - ~

I o

25 C

200 °C

g

60

-

60

C~ cO

40

B

<:£ LO CM

A

4O

3

.< 20

&

S

QD 0

0

<7, (:2B

?

1

T ___J I

2O

3

4

5

6

0

1

ENERGY TRANSFER (meV)

2

3

~

+

--+

-

I

5

6

ENERGY TRANSFER (meV)

(a) 80

4

(©) I

1

80

CO

1

-.~

~

....

~

E

/

4~

o

6o

+t +++ /'

T

I

L ~D

+

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40 T

LC~ ¢XJ

&

:

L 0

1

2

3

4

5

20

I

t 0

ENERGY TRANSFER (meV)

1

2

3

4

5

6

ENERGY TRANSFER (meV)

(c)

(d)

Fig. 2. The generalized density of states G( Q, (o) of CuI. The lines show the fitting results for each mode: solid line, Iow,-cnergy excitation mode+acoustic mode; broken line, low-energy excitation mode; dotted line, acoustic mode. Thc vertical lines with data points show the

statistical errors: (a) 25°C, (b) 200°C, (c) 300°C, (d) 400~C.

Table 1 The values of fitting parameters in the generalized density of slates G( Q, (o). oJ~and Fare the frequency and halt-width respectively of the low-energy excitation mode.

co~ ( m e V ) F (meV)

25~'C

200°C

280¢C

260C

3.5 1.4

3.4 1.4

3.4 1.6

3,4 3.3

from the inelastic neutron scattering measurement with a single crystal has a m a x i m u m peak about 6 meV [12]. The value of g(o)) obtained in fig. 2

agrees qualitatively with that of the former report. The feature of the observed inelastic neutron scattering spectra in fig. 1 is similar to that in the silverion conductor RbAg415 reported by Shapiro et al. [ 7 ]. As the temperature is lowered the excitation near 2.2 m e V becomes clear and the intensity of the inelastic scattering spectrum of RbAg4I 5 in the energy range 1.0-2,0 meV decreases. The temperature-dependenl behavior of the observed spectra in RbAg41s was qualitatively explained by the Brownian motion of the diffusing ion moving in a sinusoidal potential well. However, no detailed treatment of the scattered

T. Sakuma et al. ~Low-energy excitation in Cul n e u t r o n spectra has been performed. As stated in the previous paper [ 10 ], there is a relation between the excitation energy and the mass M of the mobile ion, namely that h¢ooc ( 1 / M ) 1/2. The calculated values of the excitation energy of Ag and Na conductors with this relation when the value of 3.4 meV is fixed for the case of Cu are shown in table 2. As shown in the table, the calculated values almost coincide with the observed values. The calculated value for the Cl-ion conductor is also shown in the table though the m e a s u r e m e n t has not been made so far. In order to confirm the systematic relation between the excitation energy and the mass of the mobile ion, not only for cations but also for anions, inelastic neutron scattering measurements on the chlorine-ion conductor CsPbC13 are now in progress. There are three theoretical models which might be able to explain the relation between the value of lowenergy excitation mode and the mass of cations: ( 1 ) a Brownian motion model, (2) an optical p h o n o n model and (3) an ionic plasma model. The value of the low-energy excitation mode is not sensitive to the crystal structures of superionic conductors with the same mobile cation. In the case of the Brownian motion model, it is not consistent with the observation because the height of the potential barrier in general depends on the given crystal structure. As we treat the low-energy excitation mode as a branch of the optical p h o n o n modes in the case of the optical p h o n o n model, the value of M has to be replaced by the reduced mass of the cation and the anion. However, agreement between the calculation and observation was obtained if the mass of the cation was used. The result that the value of the low-energy excitation mode depends not on the lattice type but on the mass of cation would suggest the possibility of a collective motion in superionic conductors. Recently, an ionic plasma model to describe the low-energy excitation of cation superionic conductors was presented by Kobayashi et al. [13]. The ionic plasma frequency ~Op is given by 'Fable 2 Calculated and observedvaluesof the low-energyexcitation mode for mobile ions.

Ec,~ (meV) Lobs (meV)

Ag

Cu

Na

C1

2.6 2.0-3.0 [5-7]

3.4 ~3.4

5.7 ~6.0 [8]

4.6 -

1281

= ( 4 ~ n ( Z * e ) 2 . ~ '/2 O~p \ %M / ' where n and M are the n u m b e r density and the mass of mobile cations, respectively, Z* is the effective charge, e is the elementary charge and eo is the static dielectric constant. The idea of an ionic plasma was also suggested by Matsubara [ 14 ] to explain the lowenergy excitation in superionic conductors. At present, the value of the effective charge of each substance has not been reported. Therefore, we could not investigate the validity of the ionic plasma model. If we could apply the ionic plasma model to superionic conductors, it might be possible to estimate the value of the effective charge. Further study of theoretical treatments including the temperature dependence of the low-energy excitation mode is necessary.

Acknowledgements The authors would like to thank Professor Y. Izumi and Mr. T. Kaneko for their help in the experiment at KENS. The present work was supported in part by a G r a n t - i n - A i d for Scientific Research from the Ministry of Education, Science and Culture of Japan.

References [ 1] S. Miyake, S. Hoshino and T. Takenaka,J. Phys. Soc. Japan 7 (1952) 19. [2] S. Miyakeand S. Hoshino, Rev. Mod. Phys. 30 ( 1958 ) 172. [ 3 ] T. Sakuma, J. Phys. Soc. Japan 57 ( 1988 ) 565. [4] W. Biihrerand W. H~ilg,Electrochim. Acta 22 (1977) 701. [ 5 ] K. Shibata and S. Hoshino, J. Phys. Soc. Japan 54 ( 1985 ) 3671. [6 ] S. Hoshino,S.M. Shapiroand K. Shibata,J. Phys. Soc. Japan 55 (1986) 3671. [7] S.M. Shapiro, D. Semmingsen and M. Salamon, in: Proc. Intern. Conf. on Lattice Dynamics, ed. M. Balkanski (Flammarion, Paris, 1978). [8 ] D.B. McWhan,S.M. Shapiro, J.P. Remeika and G. Shirane, J. Phys. C 8 ( 1975 ) L487. [9] T. Sakuma and K. Shibata, J. Phys. Soc. Japan 58 (1989) 3061. [ 10] T. Sakuma, T. Shibata and S. Hoshino, Solid State Ionics 40/41 (1990) 337. [ 11 ] T. Matsui and J.B. Wagner,J. Electrochem.Soc. 124 (1977) 300. [ 12 ] B. Hennion and F. Moussa, Phys. Rev. Lett. 28 ( 1972 ) 964. [13] M. Kobayashi, T. Tomoyose and M. Aniya, J. Phys. Soc. Japan 60 (1991) 3742. [ 14] T. Matsubara, private communication.