In the first experimental data obtained with the new triple-axis spectrometer Taipan at the OPAL reactor, we measured a superionic conductor.
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| In the first experimental data obtained with the new triple-axis spectrometer Taipan at the OPAL reactor, we measured a superionic conductor. |
Superionic conductors are superior in conductivity and therefore sought after in a number of technological applications. Our measurements on copper selenide contribute to the understanding of the structure and mechanism of superionic conductors.
Superionic conductors, particularly copper selenide
Superionic conductors are materials that exhibit very high conductivity. Because of this, they have a wide range of technological applications such as solid-state capacitors (which can have 2-3 orders of magnitude higher capacitance than a conventional equivalent at the same working voltage), fuel cells, batteries and more.
Their high power density or ability to store and release large amounts of energy in a short time has already led to their consideration in regenerative braking applications for hybrid vehicles, for instance. However, they are not completely understood and display very interesting physics.
Copper selenide is a mixed ionic-electronic conductor which received attention specifically due to its high ionic conductivity. In Cu2-δSe, at room temperature the superionic a-phase exists in the concentration range δ = 0.15 to 0.25 [1].
The characteristic features of copper selenide are the ordering of Cu atoms in the lowtemperature phase and a random distribution of Cu over interstitial sites in the high-temperature superionic phase. Lattice dynamics of Cu2-δSe are similar to other Cu and Ag fast ionic conductors showing the presence of low-energy excitations.
The importance of low-lying modes that make most of the contribution to thermal motion, due to high density of states and low activation energy, is widely recognised.
What measuring phonons tells us about the material
Phonons measure the characteristic way in which copper and selenium atoms move within the material - this determines, among other things,how stiff the material is and how fast sound travels in it. (Hint: stiffer materials have higher sound velocity.) Phonons were so named because they form the waves that propagate sound (from the Greek: phonos for sound). When a phonon “softens”, it means that there is something along the arrangement of atoms in that particulardirection that makes the crystal somewhat less stiff.
Acoustic modes go through E = hw = 0 at phonon wave vector q = 0, the slope is linear at low q. The slope of the dispersion curve at low-q (where it is linear) represents sound velocity for that mode of propagation.
Collectively, the property of the phonons is called “lattice dynamics” and describes how the lattice moves! The lattice sites of superionic conductors generally are not fully occupied, as is the case for copper sites in the material Cu2-δSe; the vacancies form conduits for ionic hopping behaviour, which makes the superionic characteristics possible. The structure although solid, has liquid-like characteristics where the diffusion is considered. Hence, studies of the lattice dynamics and the phonon dispersion relations in these materials should give a wealth of information about the mechanism related to superionic behaviour.
The measured data and interpretation using models
Measurements of phonon dispersion curves were performed on a single-crystal sample of Cu1.8Se which has the structure of the superionic a-phase at room temperature. The inelastic neutron scattering data were obtained with the TAIPAN thermal triple-axis spectrometer [2]. For phonon wave-vectors q/qm ≈ 0.5, all measured phonon branches had a pronounced broadening.
These data cover a wider q-range and were measured with higher accuracy, and we found that the transverse acoustic phonons TA1 [110], TA [100] and TA [111] demonstrate a decrease in frequency at q/qm ≥ 0.5 rather than the flattening seen previously [3]. The transverse acoustic [111] branch shows a considerably greater decrease for q/qm ≥ 0.25 than the other TA phonon branches (Figure 1). In contrast, the q-dependence of frequency of TA2 [110] phonons and longitudinal modes shows almost linear behaviour (Figure 2).
Much of the time, it is difficult to interpret the phonon measurements directly. Hence, it is useful to calculate some models and see whether the model fits the data reasonably well. Naturally, the “best” model resembles the data the most and then can be used to make a meaningful interpretation of the observations.
Experimental phonon dispersion curves were compared with calculations performed in the frame of density-functional theoretical approach [4]. The most remarkable features of calculated acoustic modes are the low frequencies and the instability over a large area of reciprocal space.
In agreement with experiment TA [111] phonon mode show instability and go to negative values at q/qm ≥0.3 – 0.4 (Figure 1). Similar behaviour demonstrate calculated acoustic TA [100], TA1 [110] and LA [110] modes. This indicates that the stoichiometric compound is dynamically unstable and antifluorite structure is not the true low-temperature one. The instability of acoustic modes is directly related to the order–disorder transformations observed in copper-selenide followed by a-phase transition at a lower temperature [1].
Previously, in neutron-diffraction experiments, we observed the superstructure reflections in non-stoichiometric Cu1.8Se single crystal at ambient temperature [5]. The intensity of the superstructural reflection is quite large in [111] direction (saturated area at hw = 0, q/qm = 0.5 in Figure 1) and comparable with the (222) Bragg peak at hw = 0, q/qm = 0.
The appearance of strong reflections at the edge of the Brillouin zone (BZ) can cause effects similar to the folding of the BZ. Indeed, TA phonon branch in [111] direction has clear tendency to soften (Figure 1) and the boundary of BZ can be considered as a new BZ centre, although phonon intensities at “new” (2.5 2.5 1.5) BZ center are weak. Wakamura suggested that the low-energy mode in β-AgI originates from the zone-edge acoustic phonons in γ-AgI because of folding of BZ [6].
However, the important difference in the case of the Cu1.8Se compound is that the ordering process and folding of the BZ are driven by a soft mode.
Next experiments
In the next experiments at TAIPAN we will investigate the almost stoichiometric compound Cu1.98Se just below and above their superionic phase transition. We already know that quasielastic broadening changes dramatically during the phase transitions reflecting enhancement of Cu diffusion in the superionic phase. Dispersion curves should tell us more about the interatomic correlation and the mechanism of ionic transport.
Acknowledgement
These experimental data are amongst the first to be recorded with the new instrument TAIPAN and we would like to take this opportunity to thank all those who have been involved with the building of this instrument. The authors would like to thank N.N. Bickulova from Sterlitamak University for synthesising the crystal studied in this work.
Authors
Sergey A. Danilkin, Mohana Yethiraj and Gordon J. Kearley
ANSTO
References
- N.H. Abrikosov, V.F. Bankina, M.A. Korzhuev, G.K. Demenski and O.A. Teplov, Sov. Phys. - Solid State 25 (1983) 1678.
- S. Danilkin, G. Horton, R. Moore, G. Braoudakis and M. Hagen, J. Neutron Res. 15 (2007) 55.
- S.A. Danilkin, A.N. Skomorokhov, A. Hoser, H. Fuess, V. Rajevac and N.N. Bickulova, J. Alloys Compd. 361 (2003) 57.
- G. Kresse and J. Furthmüller, Software VASP, Vienna (1999).
- S.A. Danilkin, Solid State Ionics 180 (2009) 483.
Published: 11/12/2009