Crystal structure of Cu2Se

Abstract

The crystal structures of the low-temperature (space group C2/c, Pearson symbol mS144, a = 7.1379(4) Å, b = 12.3823(7) Å, с = 27.3904(9) Å, β = 94.308º, R I = 0.0765) and high-temperature (space group Fm-3m, Pearson symbol cF12, a = 5.859(1) Å, R1 = 0.0391) modifications of Cu 2 Se were determined by means of X-ray powder and single crystal diffraction. The basic features of the two modifications are similar. The Se atoms are stacked in a close-packed arrangement with the layers in the sequence ABC. The Cu atoms are distributed over all tetrahedral interstices. The positions of Cu are completely ordered in the lowtemperature modification, whereas they are disordered in the high-temperature modification.

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

“…The disordered stacking gives rise to an average structure with higher symmetry. Several of the previously suggested structures in the literature, which have been noted to have very small differences in enthalpy, in fact have the correct twodimensional layer structure, but they all assume various periodic stacking sequences (Gulay et al, 2011;Liu, Yuan et al, 2013;Lu et al, 2015;Qiu et al, 2016). The stacking disorder found in the real structure is caused by the almost identical enthalpy of the different stacking types together with a higher entropy term from the disorder.…”

“…Here we have studied the thermoelectric material -Cu 2Àx Se for which the structure has been discussed since 1936 without any structural models being able to explain the measured scattering data satisfactorily (Eikeland et al, 2017;Frangis et al, 1991;Gulay et al, 2011;Kashida & Akai, 1988;Liu, Yuan et al, 2013;Lu et al, 2015;Milat et al, 1987;Nguyen et al, 2013;Qiu et al, 2016;Rahlfs, 1936;Yamamoto & Kashida, 1991). The reasons for this failure have been that all previous structural models have assumed three-dimensional periodicity and it has been difficult to synthesize high-quality single crystals.…”

The order–disorder transition in Cu2Se and medium-range ordering in the high-temperature phase

“…structure of Se atoms but within which more 8c sites and fewer 32f sites were occupied by Cu atoms (Machado et al, 2004). There are other studies (Yamamoto & Kashida, 1991;Gulay et al, 2011;Qiu et al, 2016) on the high-temperature structures of Cu 2 Se, all of which confirmed an f.c.c. Se sublattice while the small Cu atoms randomly distribute in different ways without any observation of ordering.…”

Apparent critical phenomena in the superionic phase transition of Cu2-xSe

“…Contradictory interpretations in the literature can be partly attributed to the incomplete understanding of the α phase crystal structure (e.g. the structural model for the α phase [20] does not agree with the measured pair distribution function [8]) and also the large diffuse background signal [18,38], which limits quantitative analysis of the diffraction patterns.…”

“…The α phase is a superstructure of the β phase where the cations are ordered. Some monoclinic [19,20] or triclinic [21] models have been proposed, but a complete model has not yet been determined. This uncertainty remains as a difficulty in understanding experimental results.…”