Maximum Entropy Method Visualization of Disorder and Ion Migration in Thermoelectric Cu2-δSe

Dynamic correlations and possible diffusion pathway in the superionic conductor Cu2-xSe

The superionic conductor Cu_2-xSe has regained interest as a thermoelectric material owing to its low thermal conductivity, suggested to arise from a liquid-like Cu substructure, and the material has been coined a phonon-liquid electron-crystal. Using high-quality three-dimensional X-ray scattering data measured up to large scattering vectors, accurate analysis of both the average crystal structure as well as the local correlations is carried out to shed light on the Cu movements. The Cu ions show large vibrations with extreme anharmonicity and mainly move within a tetrahedron-shaped volume in the structure. From the analysis of weak features in the observed electron density, the possible diffusion pathway of Cu is identified, and it is clear from its low density that jumps between sites are infrequent compared with the time the Cu ions spend vibrating around each site. These findings support the conclusions drawn from recent quasi-elastic neutron scattering data, casting doubt on the phonon-liquid picture. Although there is diffusion of Cu ions in the structure, making it a superionic conductor, the jumps are infrequent and probably not the origin of the low thermal conductivity. From three-dimensional difference pair distribution function analysis of the diffuse scattering data, strongly correlated movements are identified, showing atomic motions which conserve interatomic distances at the cost of large changes in angles.

Solving the disordered structure of β-Cu2-xSe using the three-dimensional difference pair distribution function

High-performing thermoelectric materials such as Zn₄Sb₃ and clathrates have atomic disorder as the root to their favorable properties. This makes it extremely difficult to understand and model their properties at a quantitative level, and thus effective structure-property relations are challenging to obtain. Cu_2-xSe is an intensely studied, cheap and non-toxic high performance thermoelectric, which exhibits highly peculiar transport properties, especially near the β-to-α phase transition around 400 K, which must be related to the detailed nature of the crystal structure. Attempts to solve the crystal structure of the low-temperature phase, β-Cu_2-xSe, have been unsuccessful since 1936. So far, all studies have assumed that β-Cu_2-xSe has a three-dimensional periodic structure, but here we show that the structure is ordered only in two dimensions while it is disordered in the third dimension. Using the three-dimensional difference pair distribution function (3D-ΔPDF) analysis method for diffuse single-crystal X-ray scattering, the structure of the ordered layer is solved and it is shown that there are two modes of stacking disorder present which give rise to an average structure with higher symmetry. The present approach allows for a direct solution of structures with disorder in some dimensions and order in others, and can be thought of as a generalization of the crystallographic Patterson method. The local and extended structure of a solid determines its properties and Cu_2-xSe represents an example of a high-performing thermoelectric material where the local atomic structure differs significantly from the average periodic structure observed from Bragg crystallography.

In-situ electron microscopy mapping of an order-disorder transition in a superionic conductor

Solid-solid phase transitions are processes ripe for the discovery of correlated atomic motion in crystals. Here, we monitor an order-disorder transition in real-time in nanoparticles of the super-ionic solid, Cu_2-xSe. The use of in-situ high-resolution transmission electron microscopy allows the spatiotemporal evolution of the phase transition within a single nanoparticle to be monitored at the atomic level. The high spatial resolution reveals that cation disorder is nucleated at low co-ordination, high energy sites of the nanoparticle where cationic vacancy layers intersect with surface facets. Time-dependent evolution of the reciprocal lattice of individual nanoparticles shows that the initiation of cation disorder is accompanied by a ~3% compression of the anionic lattice, establishing a correlation between these two structural features of the lattice. The spatiotemporal insights gained here advance understanding of order-disorder transitions, ionic structure and transport, and the role of nanoparticle surfaces in phase transitions.