Observation of Soft Phonon Modes in Superionic Copper Selenide

Authors

Sergey Danilkin, Mohana Yethiraj and Don Kearley (ANSTO)

Introduction

Copper selenide is a mixed ionic-electronic conductor that has recently received attention from the technological and physical points of view in particular due to its high ionic conductivity. The characteristic feature of copper selenide is the presence of low-energy phonon modes similar to other Cu and Ag fast ionic conductors. These low-lying modes provide the thermal motion that lowers the activation energy of the ionic-conduction process.

Recently we have revisited a previously studied compound, the Cu_1.8Se superionic conductor, in which the structure of the superionic a-phase (normally high temperature) persists at room temperature. Our neutron inelastic scattering experiment was carried out as part of commissioning tests of the TAIPAN thermal triple axis spectrometer.

Our new data cover a wider q-range and are measured with higher accuracy than previous work.  We were able to observe that the TA1 [110], TA [100] and TA [111] phonons decrease in frequency at q/q_m > 0.5, rather than the flattening observed previously. Further, the transverse acoustic branch with wavevector in the [111] direction shows a considerably greater decrease for q/qm > 0.25 than 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).

Experimental phonon dispersion curves were compared with lattice dynamics calculations using the density functional theoretical approach to obtain the force-constant matrix from first prinicples. The most remarkable features of calculated acoustic modes are the low frequencies and the instability over a large area of reciprocal space.

This is in agreement with experiment TA [111] phonon mode which shows instability and goes to negative values at q/q_m > 0.3 - 0.4 (Figure 1). The instability of acoustic modes is directly related to the order disorder transformations observed in copper-selenide followed by a - b phase transition at a lower temperature.

The appearance of strong superstructural reflections at the edge of the Brillouin zone (BZ) (Figure 1) can cause effects similar to the folding of the BZ. Indeed, the TA phonon branch in [111] direction has clear tendency to soften and the boundary of the BZ can be considered as a new BZ centre, although phonon intensities at new (2.5, 2.5, 1.5) BZ center are weak. This effect has direct relationship to the suggestion of Wakamura that the low-energy optic modes in superionic conductors originate from the zone-edge acoustic phonons because of folding of BZ.

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.

Surface plot of the inelastic scattering intensity in Cu1.8Se determined from a series of constant-Q scans along direction [2+q, 2+q, 2-q]. Dots correspond to fitted positions on phonon peaks in individual scans. Line shows calculated dispersion curve. Surface plot of inelastic scattering intensity in Cu _1.8 Se determined from a series of constant-E scans along direction [1+q, 1+q, 1+q].