Large barocaloric effects in thermoelectric superionic materials

We predict the existence of large barocaloric effects above room temperature in the thermoelectric fast-ion conductor ${\mathrm{Cu}}_2\mathrm{Se}$ by using classical molecular dynamics simulations and first-principles computational methods. A hydrostatic pressure of 1 GPa induces large isothermal entropy changes of $\left|\mathrm{\Delta }S\right|\sim 15–45\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and adiabatic temperature shifts of $\left|\mathrm{\Delta }T\right|\sim 10\mathrm{K}$ in the temperature interval $400\le T\le 700\mathrm{K}$. Structural phase transitions are absent in the analyzed thermodynamic range. The causes of such large barocaloric effects are significant $P$-induced variations on the ionic conductivity of ${\mathrm{Cu}}_2\mathrm{Se}$ and the inherently high anharmonicity of the material. Uniaxial stresses of the same magnitude, either compressive or tensile, produce comparatively much smaller caloric effects, namely, $\left|\mathrm{\Delta }S\right|\sim 1\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and $\left|\mathrm{\Delta }T\right|\sim 0.1\mathrm{K}$, due to practically null influence on the ionic diffusivity of the material. Our simulation work shows that thermoelectric compounds presenting high ionic disorder, like copper and silver-based chalcogenides, may render large mechanocaloric effects and thus are promising materials for engineering solid-state cooling applications that do not require the application of electric fields.

Figure 1

General description of ${\mathrm{Cu}}_2\mathrm{Se}$. (a) Ball-stick representation of the high-$T$ cubic structure known as fluorite (space group $Fm\overline{3}m$); for clarity purposes, the Cu ions are represented orderly in a simple cubic lattice. (b) Tetrahedra formed by Se ions on the vertices; the center of the tetrahedra are described by the pseudocubic Wyckoff position $8c\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)$. (c) Octahedra formed by Cu ions on the vertices; the center of the octahedra are described by the pseudocubic Wyckoff position $4b\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$. (d) Ionic diffusion coefficients estimated at different temperatures from neutron spectroscopy experiments [41], first-principles calculations based on density functional theory (AIMD-DFT), and molecular dynamics simulations performed with the Morse potential reported in Ref. [29] considering null ionic charges (MD-FF).

Figure 2

Barocaloric effects in bulk ${\mathrm{Cu}}_{2-\delta }\mathrm{Se}$ at temperatures $400\le T\le 700\mathrm{K}$. (a) Ionic diffusion coefficients calculated at zero pressure and (b) $P=1$ GPa. (c) Isothermal entropy changes induced by a maximum hydrostatic pressure of 1 GPa. (d) Adiabatic temperature changes induced by a maximum hydrostatic pressure of 1 GPa.

Figure 3

Thermodynamic properties of ${\mathrm{Cu}}_{2-\delta }\mathrm{Se}$ at temperatures $400\le T\le 700\mathrm{K}$. (a) $T$ derivative of the volume calculated at zero pressure and (b) $P=1$ GPa. Thermal expansion coefficients defined as ${\alpha }_T=\frac{1}{V}{\left(\frac{dV}{dT}\right)}_P$ are shown in the insets. (c) Heat capacity calculated at zero pressure and (d) $P=1$ GPa.

Figure 4

Elastocaloric effects in bulk ${\mathrm{Cu}}_{2-\delta }\mathrm{Se}$ at temperatures $400\le T\le 700\mathrm{K}$. (a) Ionic diffusion coefficients calculated at zero uniaxial tensile stress and (b) $\sigma =1$ GPa. (c) Isothermal entropy changes induced by a maximum uniaxial tensile stress of 1 GPa. (d) Adiabatic temperature changes induced by a maximum uniaxial tensile stress of 1 GPa.