Electron, phonon and thermoelectric properties of Cu7PS6 crystal calculated at DFT level

B Andriyevsky,A I Kashuba,M Piasecki,I P Studenyak,I E Barchiy

doi:10.1038/s41598-021-98515-6

Abstract

The promising class of the environment-friendly thermoelectrics is the copper-based argyrodite-type ion-conducting crystals exhibiting just extraordinary low thermal conductivity below the glass limit associated with the molten copper sublattice leading to a softening of phonon modes. To explain why the argyrodite structure containing copper ions favors the low thermal conductivity, we have utilized the ab initio calculations of the electron, phonon, and thermoelectric properties of Cu7PS6 crystal in the framework of the density functional and Boltzmann transport theories. To obtain the reliable thermoelectric properties of Cu7PS6, we take into account the dependence of the electron effective mass m* on the redundant carrier concentration n. We propose to use the Burstein–Moss effect for the calculation of the electron effective mass m* of a semiconductor. We have found the strong nonlinear character of copper atom vibrations in Cu7PS6 which exceeds substantially the similar values for phosphorous and sulfur atoms. The large vibration nonlinearity of the copper atoms found in Cu7PS6 explains the diffusion-like heat transfer and the relatively low coefficient of the lattice thermal conductivity (κ = 0.7 W/(m K)), which is favorable to achieve the large thermoelectric figure of merit.

Highlights

The promising class of the environment-friendly thermoelectrics is the copper-based argyrodite-type ion-conducting crystals exhibiting just extraordinary low thermal conductivity below the glass limit associated with the molten copper sublattice leading to a softening of phonon modes
The Burstein–Moss effect is shown to be successfully utilized for the calculation of the electron effective mass dependence on the electric carrier concentration of the extrinsic type in Cu7PS6 crystal
An increase of the absolute value of the electron effective mass in C u7PS6 with an increase of the electrons and holes concentration in the range n > 3 × 1020 cm−3 has been detected, which should be taken into account in the calculation of the thermoelectric properties depending on the electric carriers mobility

Summary

Introduction

The promising class of the environment-friendly thermoelectrics is the copper-based argyrodite-type ion-conducting crystals exhibiting just extraordinary low thermal conductivity below the glass limit associated with the molten copper sublattice leading to a softening of phonon modes. To explain why the argyrodite structure containing copper ions favors the low thermal conductivity, we have utilized the ab initio calculations of the electron, phonon, and thermoelectric properties of Cu7PS6 crystal in the framework of the density functional and Boltzmann transport theories. The isovalent substitution Se2− by S 2− in C u7P(Se1−xSx)[6] allows the stabilization of the polymorph (γ-modification) with the most promising properties This conclusion agrees with the results of the previous study of the conductivity of solid solution. The face-centered symmetry F43m , realized in C u7PS6 and C u7PSe6 crystals and their solid solution, is associated with the temperature-dependent copper ion diffusion, which introduces the structural disorder

Methods

Results

Conclusion