Maximum Entropy Method Visualization of Disorder and Ion Migration in Thermoelectric Cu_2‐δSe

Abstract

Cu 2-δ Se is a cheap, nontoxic high performance thermoelectric material with extraordinary properties such as liquid-like phonons or a large enhancement of the thermopower at the phase transition between the low temperature β-phase and the super-ion conducting high temperature α-phase. Here, the nuclear-weighted X-ray maximum entropy method (NXMEM) is used to study disorder and ion migration in both the βand the α-phase based on the analysis of single crystal X-ray diffraction data. The NXMEM density calculated at different temperatures very convincingly shows an unbiased view of ion migration from copper-rich to copper-deficient layers eventually leading to the equal distribution in the cubic high temperature phase. This directly confirms that copper mobility and disordering is the driving force behind the peculiar phase transition. In the super-ionic phase, no density is observed in the octahedral holes even though it is the point of lowest density in the Se anion procrystal. Thus, Cu ions neither occupy this site at equilibrium nor use this site for migration. The NXMEM density suggests an ion migration pathway between 32f sites skirting around the octahedral cavity. In Cu 2 Se, the strong cation-cation repulsion leads to cooperative effects with highly complex equilibrium disorder and ion migration paths.Rationally designed improvements in the performance of functional materials are closely tied to a detailed understanding of the atomic arrangement. In an era of increasing demands for sustainable energy solutions, thermoelectric materials capable of interconverting heat and electricity have received great attention. Cu 2-δ Se is a cheap nontoxic material with a very high thermoelectric figure of merit. [1][2][3][4] Furthermore, it exhibits extraordinary physical properties. These include liquid-like phonons [2] or a highly peculiar thermopower enhancement prior to a super-ionic phase transition around 400 K. [1] The unusual transport behavior presumably is related to structural changes in the disordered low temperature β-Cu 2-δ Se crystal structure when the critical temperature is approached. Here, we use the model-independent maximum entropy method (MEM), [5] and

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

“…Cu 2Àx Se is a promising thermoelectric material as it is cheap, non-toxic and has a high thermoelectric figure of merit (zT) (Eikeland et al, 2017;Liu, Yuan et al, 2013;Lu et al, 2015;Qiu et al, 2016;Nguyen et al, 2013;Brown et al, 2016;Brown, Day, Caillat & Snyder, 2013;Brown, Day, Borup et al, 2013;Dalgaard et al, 2018;Liu et al, 2012;Miyatani, 1973;Vučić et al, 1984Vučić et al, , 1981Vucic et al, 1982;Yu et al, 2012;Chi et al, 2014;Mahan, 2015;Sirusi et al, 2015;Sun et al, 2015;Kang et al, 2016). The compound has a phase transition at 350-410 K depending on the degree of Cu deficiency (Brown, Day, Caillat & Snyder, 2013;Chi et al, 2014;Eikeland et al, 2017;Liu, Yuan et al, 2013;Vučić et al, 1984).…”

“…In 2011, Gulay et al claimed to have solved the structure of -Cu 2Àx Se from X-ray diffraction data (Gulay et al, 2011), but their model had a very low agreement with the data and was later shown to be incorrect (Eikeland et al, 2017). Even with all this effort to understand the structure of -Cu 2Àx Se, there is still wide acknowledgement that a sufficient structural model has not yet been found (Brown et al, 2016;Dalgaard et al, 2018;Eikeland et al, 2017;Frangis et al, 1991;Gulay et al, 2011;Liu, Yuan et al, 2013;Lu et al, 2015;Milat et al, 1987;Nguyen et al, 2013;Yamamoto & Kashida, 1991;Brown, Day, Caillat & Snyder, 2013;Kashida & Akai, 1988;Qiu et al, 2016;Rahlfs, 1936). Even with all this effort to understand the structure of -Cu 2Àx Se, there is still wide acknowledgement that a sufficient structural model has not yet been found (Brown et al, 2016;Dalgaard et al, 2018;Eikeland et al, 2017;Frangis et al, 1991;Gulay et al, 2011;Liu, Yuan et al, 2013;Lu et al, 2015;Milat et al, 1987;Nguyen et al, 2013;Yamamoto & Kashida, 1991;Brown, Day, Caillat & Snyder, 2013;Kashida & Akai, 1988;Qiu et al, 2016;Rahlfs, 1936).…”

“…The high-temperature -Cu 2Àx Se has the cubic anti-fluorite structure with the Cu atoms distributed in a disordered way on the corners and center of tetrahedra between the layers of the face-centeredcubic (f.c.c.) Se lattice (Dalgaard et al, 2018;Eikeland et al, 2017;Danilkin et al, 2011Danilkin et al, , 2012.…”

“…Later studies by Brown et al attempted to find the structure using pair distribution function and density functional theory (DFT) analysis (Brown, Day, Borup et al, 2013;Brown, Day, Caillat & Snyder, 2013;Brown et al, 2016). Even with all this effort to understand the structure of -Cu 2Àx Se, there is still wide acknowledgement that a sufficient structural model has not yet been found (Brown et al, 2016;Dalgaard et al, 2018;Eikeland et al, 2017;Frangis et al, 1991;Gulay et al, 2011;Liu, Yuan et al, 2013;Lu et al, 2015;Milat et al, 1987;Nguyen et al, 2013;Yamamoto & Kashida, 1991;Brown, Day, Caillat & Snyder, 2013;Kashida & Akai, 1988;Qiu et al, 2016;Rahlfs, 1936). One reason for this lack of structural information is the difficulty in synthesizing high-quality single crystals of the phase.…”

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

“…This observation is consistent with a previous postulate that compressive strain stabilizes Cu + occupancy of otherwise higher-energy octahedral sites 23,34 . When Cu + gain access to these new interstitial (octahedral 24,25 or other nearby 35 ) sites, the Cu + sub-lattice becomes mobile and the Cu-vacancy ordering is lost.

Fig. 4DFT investigation of the correlation between lattice strain and cation disorder.

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