${\mathrm{Cu}}_2\mathrm{S}$ in its high-temperature phases is a promising candidate for thermoelectric materials with the combination of a solid S lattice and liquidlike Cu atoms in the context of the so-called phonon-liquid electron-crystal (PLEC) mechanism. The atomic dynamics associated with the high Cu mobility is a critical component in our understanding of the low thermal conductivity in these materials. Among various possible PLEC compounds that have been studied experimentally, hexagonal $\beta -{\mathrm{Cu}}_2\mathrm{S}$ is a unique case that exhibits anisotropic diffusion channels for Cu atoms in the presence of crystalline S layers. To unveil the diffusion mechanism for such liquidlike Cu atoms, we present first-principles molecular dynamics simulations over 50 ps for hexagonal ${\mathrm{Cu}}_2\mathrm{S}$ at 450 K. Quantitative analysis of the atomic radial distributions, mean-square displacements, velocity autocorrelations, and atomic trajectories is reported and confirms the liquid-solid hybrid features. Our simulations reveal the preference of threefold triangular sites by Cu atoms in the S lattice. The triangular sites in the interlayer region do not bind Cu atoms strongly, allowing them to diffuse in the horizontal direction between S layers like a mobile liquid with a calculated diffusion coefficient $\sim 5\times {10}^{-6}{\mathrm{cm}}^2$/s. The corresponding atomic trajectories have a wide spread and cannot be described by the Chudley-Elliott jump diffusion model. In contrast, Cu atoms are more strongly confined at the triangular sites within the S planes, and Cu diffusion takes place only when the atom hops out of the S layer and enters the interlayer region. This yields a 50% smaller diffusion coefficient in the vertical direction. The anisotropic diffusion channels for liquidlike Cu atoms in hexagonal $\beta -{\mathrm{Cu}}_2\mathrm{S}$ may provide an additional degree of freedom in designing promising systems for future energy applications.

中文翻译：

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六方β-Cu2S中液态Cu原子各向异性扩散的机理

${铜}_2\mathrm{秒}$在所谓的声子 - 液体电子晶体（PLEC）机制的背景下，在其高温相中，具有固体 S 晶格和类液体 Cu 原子组合的热电材料是一种很有前景的候选材料。与高 Cu 迁移率相关的原子动力学是我们理解这些材料的低热导率的关键组成部分。在已通过实验研究的各种可能的 PLEC 化合物中，六边形$\beta -{铜}_2\mathrm{秒}$是一种独特的情况，在存在结晶 S 层的情况下表现出 Cu 原子的各向异性扩散通道。为了揭示这种类似液体的 Cu 原子的扩散机制，我们提出了超过 50 ps 的六边形分子动力学模拟${铜}_2\mathrm{秒}$在 450 K。 报告了原子径向分布、均方位移、速度自相关和原子轨迹的定量分析，并确认了液固混合特征。我们的模拟揭示了 S 晶格中 Cu 原子对三重三角形位点的偏好。层间区域的三角形位点不会强烈地结合 Cu 原子，允许它们像具有计算扩散系数的流动液体一样在 S 层之间沿水平方向扩散$～5\times {10}^{-6}{\mathrm{厘米}}^2$/秒。相应的原子轨迹分布广泛，无法用 Chudley-Elliott 跳跃扩散模型来描述。相比之下，Cu 原子更强烈地限制在 S 平面内的三角形位置，只有当原子跳出 S 层并进入层间区域时才会发生 Cu 扩散。这会在垂直方向上产生一个小 50% 的扩散系数。六方体中液态Cu原子的各向异性扩散通道$\beta -{铜}_2\mathrm{秒}$ 可以为未来能源应用设计有前途的系统提供额外的自由度。