Structural failure of layered thermoelectric In₄Se_3-δ semiconductors is dominated by shear slippage

Abstract

In₄Se_3-δ semiconductors exhibit high zT as an n-type TE material, making them promising materials for thermoelectric (TE) applications. However, their commercial applications have been limited by the degradation of their mechanical properties upon cyclic thermal loading, making it important to understand their stress response under external loadings. Thus we applied molecular dynamics (MD) simulations using a density functional theory (DFT) derived force field to investigate the stress response and failure mechanism of In₄Se_3-δ under shear loading as a function of strain rates and temperatures. We considered the most plausible slip system (001)/<100> based on the calculations. We find that shear slippage among In/Se layered structures dominates the shear failure of In₄Se_3-δ. Particularly, Se vacancies promote disorder of the In atoms in the shear band, which accelerates the shear failure. With increasing temperature, the critical failure strength of In₄Se₃ and the fracture strain of In₄Se₃ decrease gradually. In contrast, the fracture strain of In₄Se_2.75 is improved although the ultimate strength decreases as temperature increases, suggesting that the Se vacancies enhance the ductility at high temperature. In addition, the ultimate strength and the fracture strain for In₄Se_2.75 increase slightly with the strain rate. This strain rate effect is more significant at low temperature for In₄Se_2.75 because of the Se vacancies. These findings provide new perspectives of intrinsic failure of In₄Se_3-δ and theory basis for developing robust In₄Se_3-δ TE devices.

Introduction

Thermoelectric (TE) devices can directly convert the heat from automotive exhausts into electricity, which is of great significance for energy sustainability [1,2]. Many efforts have been made to improve the low efficiency of TE energy conversion, which is characterized by the figure of merit, $\mathit{zT}={\mathrm{S}}^2\sigma \mathrm{T}/\kappa$, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity [2]. The zT could be improved by optimizing the power factor ($\text{PF}={\mathrm{S}}^2\sigma$) and reducing the thermal conductivity (κ) through introducing point and planar defects (vacancies, doping, elemental substitutions and nano-engineering) in various high-performance TE materials such as Mg₂(Si, Ge, Sn) [3], [4], [5], [6], CoSb₃ [7], [8], [9], Bi₂Te₃ [10], [11], [12], PbTe [13], [14], [15], SnSe [16], [17], [18], Zintl phases [19,20], and Half-Heusler alloys [21], [22], [23]. The engineering application of TE materials requires mechanical robustness that can undergo cycling thermal stress in a temperature gradient and can resist crack opening or failure of devices from vibrations. Unfortunately, thermo-mechanical loadings can cause the degeneration of the mechanical properties, leading to the failure of TE devices [24], [25], [26], [27]. Thus, it is essential to obtain an in-depth understanding of how mechanical properties of these TE materials behave in engineering applications.

A TE device requires one p-type and one n-type leg which are equally important for engineering applications. The n-type TE material In₄Se_3-δ (self-doping by Se deficiency) was reported as a promising candidate for applications in the mid-temperature range (500 to 900 K) with a zT value of 1.48 at 705 K. This high zT value is attributed to its highly anisotropic crystal structure arising from a disordered two-dimensional crystalline sheets coupled with a charge density wave (CDW) instability arising from its distinctive electronic structure [28], [29], [30]. Many efforts have been made to improve the thermoelectric and mechanical properties of In₄Se_3-δ. Zhu et al. [31] reported that the electrical conductivity and thermal conductivity of polycrystalline In₄Se_3-δ compounds can be controlled by adjusting Se vacancies, with the zT value reaching ~1.0 for δ = 0.65 and 0.8. Li et al. successfully strengthened the flexural strength of In₄Se_2.65 TE material by 40% through introducing the uniformly distributed TiC nanoparticles into In₄Se_2.65 composites [32]. In addition, many theoretical predictions have been made on the electronic and thermal transport properties of In₄Se_3-δ. Thus, Luo et al. [33] used first-principles simulations to show that the site and concentration of Se vacancies strongly effects the thermoelectric performance of In₄Se₃. Ji et al. [28] used molecular dynamics (MD) simulations to find that phonon propagation is strongly dependent on the Se deficiency along the In/Se chain direction, which is pivotal in optimizing TE performance.

We have applied density functional theory to determine that the (001)/<100> is the easiest slip system of In₄Se₃ under shear stress among these slip systems ((001)/<100>, (100)/<010>, (010)/<001>, (110)/<100> and (−110)/<110>) [34]. Nevertheless, such DFT studies are limited to hundreds of atoms and zero temperature so that the intrinsic failure mechanism of In₄Se₃ at higher temperatures as a function of Se deficiency and strain rate remains unknown.

This work determines the deformation mechanism of the In₄Se_3-δ TE materials under shear loading along (001)/<100> slip system, including the effects of temperature and strain rate. Applying large-scale MD simulations to finite shear deformation on single crystal In₄Se_3-δ along the (001)/<100> slip system, we find shear slippage in In/Se layered structures dominates the shear fracture of In₄Se_3-δ and that Se vacancies accelerate this failure process. Increasing temperatures have a dramatic influence on the ultimate strength and the fracture strain. The strain rate has a slight effect on the mechanical properties but it is more significant at low temperature for In₄Se_2.75 because of the presence of Se vacancies.