ELSEVIER Physica B 219&220 (1996) 460-462

Low energy excitation in cation superionic conductors

Michisuke Kobayashi a, ,, Tomozo Tomoyose b, Masaru Aniya c

a Department of Physics, Niioata University, Niioata 950-21, Japan b Department of Physics, Division of General Education, Ryukyu University, Okinawa 903-01, Japan

e Department of Physics, Faculty of General Education, Kumamoto University, Kumamoto 860, Japan

Abstract

The temperature dependence of the low energy excitation (LEE) mode in cation superionic conductors is explained based upon an ionic plasma model. We regard the lattice ions as a uniform negative charge distribution and consider the LEE mode as a plasma oscillation of cations under the anion background. The model explains qualitatively the characteristic features of the LEE mode. A comparison with the boson peak observed in amorphous solids is also presented.

Superionic conductors form a particular class of solid materials characterized by ionic conductivities of an order of magnitude as is usually found in molten salts. There, the high ionic conductivity is due to the movement of one kind of ions between sites provided by the immobile ion sublattice.

A low energy excitation (LEE) mode has been observed in many cation superionic conductors (SIC) by making use of inelastic neutron scattering experiments [1]. A computer simulation has also detected this mode [2]. The frequency co/ of LEE mode has the following characteristics: (1) co~ is optic-like, (2) cot is almost independent of wave number, (3) coe is proportional to M -~/2, where M is the mass of a mobile ion, (4) ¢o~ is not sensitive to the crystal structure of SIC with the same mobile ions, (5) coe apparently decreases with increasing temperature.

These results show that the LEE mode should be ex- plained by an universal model independent of the local struc- ture of SIC.

Hoshino [3] has investigated the LEE mode of Ag3SI in its three different phases and regarded it as a softening of the optical mode connected with the migration of mo- bile ions. He has noted also that the LEE mode might be one of the characteristic features of a solid electrolyte mate- rial. The LEE mode appears at low temperatures where the substance shows no ionic conduction yet. Then he referred

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that the LEE mode observed in the low-temperature phase is related to a pre-transition-phenomenon to the SIC phase (high-temperature phase).

Sakuma et al. [4] have measured the neutron inelastic scat- tering of CuI at several temperatures and have analyzed the spectra by making use of a model fimction for generalized density of states. They have concluded that the value of LEE is almost independent of temperature, while the half-width of the LEE mode increases with increasing temperature. The half-width of the LEE corresponds to the imaginary part of the LEE mode.

To interpret the LEE mode we have presented the ionic plasma model [5], in which the LEE mode is explained as an ionic plasma oscillation of mobile cations. Cation SIC are composed of lattice ions (anions) and mobile ions (cations). We regard lattice ions as a uniform negative charge distri- bution and the LEE mode is interpreted as being the plasma oscillation of cations in the anion background. The model might be connected with a philosophy that the cage sublat- tice is considered by introducing a heavy ion mass, which conveniently characterizes immobile lattice ions [6]. The plasma model of mobile cations interprets consistently the experimental features ( 1 )-(4) mentioned above [5].

In the present paper we investigate the remaining characteristic of the LEE mode, i.e. its temperature dependence. In the following a superionic material ~- Ag2Te is considered as a case study. The FCC sublattice of ~-Ag2Te is divided into tetrahedra and octahedra, as shown

M Kobayashi et al. /Physica B 219&220 (1996) 460-462 461

)

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . )

Fig. 1. Antifluorite structure. Open circles show the FCC Te 2- lattice sites and the solid circles show the tetrahedral sites.

Table 1 The temperature dependence of the Ag-ion density in ~-Ag2Te determined by MD calculations [7]

Temperature (K) ZI Zo

550 0.985 0.015 650 0.949 0.051 750 0.878 0.122 850 0.841 0.159

in Fig. 1. It is known that a Ag ion moves from a tetrahedron into its neighboring octahedron through the triangular inter- face between them. For example in Fig. 1, a Ag ion inside a tetrahedron ABCD diffuses into the neighboring tetrahe- dron CDEF through an octahedron DBCFGH in the high- temperature s-phase. A molecular dynamics (MD) calcula- tions for ~-AgzTe have suggested that the Ag ion stays most of the time at the tetrahedral site and moves to its neighbor- ing tetrahedral site through the vicinity of the octahedral site [7]. The residence time of silver ions at the tetrahedral and octahedral sites have been calculated by counting the time steps of the MD method. The ratio of the time steps which have been calculated by MD are shown in Table 1. In Ta- ble 1 Zx and Zo are the ratios of time steps of how long Ag ions stay at tetrahedral and octahedral sites, respectively.

The Table 1 shows that a Ag ion stays only a very short time within an octahedron. This means that the energy level inside of an octahedron is high and does not provide a comfortable environment for a Ag ion. Then it seems that a Ag ion in an octahedron moves in the local surroundings independently. In other words, the residence time in an

octahedral site is too short to perform a cooperative motion there. It is speculated that the Ag ions in the high energy and unstable sites (octahedral sites) diffuse through the strong local electric field which is made by Te ions to get the low energy and more stable sites (tetrahedral sites). For the case of superionic conductor ~-AgI, this process has been shown more realistically by calculating the real-space pseudo- potential which reflects the valence electron distribution [8].

On the other hand, a Ag ion in a tetrahedron stays there for a long time. Ag ions in different tetrahedra interact each other through the long-range electrostatic force. Then, it is expected that the Ag ions in tetrahedral sites can interact cooperatively and perform a collective motion.

If this speculation is right, the carrier concentration n in the cation plasma frequency, which is given [5] by

(4~rtZ2e2 "~ 1/2

~" = \ ~-TM ) '

might be considered as that of mobile ions in tetrahedra. The square root of the Ag concentration normalized by x / ~ is shown in the Table 2. Here no is the Ag concentration in tetrahedra at T = 550 K.

Table 2 shows clearly that the mobile ion plasma fre- quency decreases with increasing temperature. This depen- dence agrees with the results of neutron scattering experi- ments [ 1 ]. In this way, the ionic plasma model explains all the characteristic features of the LEE modes observed ex- perimentally.

A comment must be made here. Almost all the experi- ments conceming LEE modes have been done in the low temperature/3-phase. On the other hand, the above discus- sions are done by using MD results for the high temperature c~-phase. This fact may lead to a numerical disagreement when a direct comparison with experiments is made. How- ever, since the rate of concentration of Frenkel defects in the/~-phase is expected to be similar to that in the ~ phase in tendency, our conclusion is in essence unaffected.

A similar excitation to that discussed here is also known in amorphous solids. There the excitation is called boson peak. It is discussed that the boson-peak frequency is correlated with the position of the first sharp diffraction peak (FSDP) in the structure factor which reflects the medium-range order (MRO) of amorphous solids. Immobile ions in SIC form the

Table 2 Concentration of Ag ions

Temperature (K) x/n/x/~

550 1 650 0.982 750 0.944 850 0.924

462 M. Kobayashi et al. /Physica B 219&220 (1996) 460-462

Table 3 Low energy excitations

Superionic conductor Amorphous solid

Order LRO (immobile ions) MRO Randomness Yes (mobile ions) Yes (in total) FSDP No Yes Material Ionic-covalent material Metal, semiconductor Observation Neutron scattering Raman and neutron scattering

Specific heat Specific heat, thermal conductivity, ultrasound

lattice and have the long-range order (LRO). The properties concemed with the LEE of SIC and amorphous solids are shown in Table 3. The LEE mode in SIC is connected with mobile ions and the boson peak in the amorphous solids is correlated with the MRO. Although a more careful study is required, a simple comparison leads us to conclude that the origin of these two excitation modes is different.

References

[1] See, for example, S.M. Shapiro and M.B. Salamon, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North-Holland, Amsterdam, 1979) p. 237.

[2] J.P. Rino, Y.M.M. Hornos, G.A. Antonio, I. Ebbsj6, R.K. Kalia ~.nd P. Vashishta, J. Chem. Phys. 89 (1988) 7542.

[3] S. Hoshino, Solid State Ionies 48 (1991) 179. [4] T. Sakuma and K. Shibata, J. Phys. Soc. Japan 58 (1989)

3061; T. Sakuma, K. Shibata and S. Hoshino, Solid State Ionics 53-56 (1992) 1278.

[5] M. Kobayashi, T. Tomoyose and M. Aniya, J. Phys. Soc. Japan. 60 (1991) 3742.

[6] M. Aniya, M. Kobayashi and H. Okazaki, J. Phys. Soc. Japan. 59 (1990) 4029.

[7] M. Kobayashi, T. Tomari, F. Yachibana and H. Okazaki, Phys. Rev. B 40 (1989) 9552.

[8] M. Aniya, in: Solid State Ionic Materials, eds. B.V.R. Chowdari et al. (World Scientific, Singapore, 1994) p. 223.