We study the effect of characteristic size variation on the phonon thermal transport in crystalline GeTe for a wide range of temperatures using the first-principles density-functional method coupled with the kinetic collective model approach. The characteristic size dependence of phonon thermal transport reveals an intriguing collective phonon transport regime, located in between the ballistic and the diffusive transport regimes. Therefore, systematic investigations have been carried out to describe the signatures of phonon hydrodynamics via the competitive effects between grain size and temperature. A characteristic nonlocal length associated with phonon hydrodynamics and a heat wave propagation length has been extracted. The connections between phonon hydrodynamics and these length scales are discussed in terms of the Knudsen number. Further, the scaling relation of thermal conductivity as a function of characteristic size in the intermediate size range emerges as a crucial indicator of the strength of the hydrodynamic behavior. A ratio concerning normal and resistive scattering rates has been employed to understand these different scaling relations, which seems to control the strength and prominent visibility of the collective phonon transport in GeTe. This systematic investigation emphasizes the importance of the competitive effects between temperature and characteristic size on phonon hydrodynamics in GeTe, which can lead to a better understanding of the generic behavior and consequences of the phonon hydrodynamics and its controlling parameters in low-thermal conductivity materials.

中文翻译：

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特征尺寸对结晶GeTe中集体声子传输的影响

我们使用第一性原理密度泛函方法结合动力学集体模型方法研究了特征尺寸变化对大范围温度下晶体 GeTe 中声子热传输的影响。声子热传输的特征尺寸依赖性揭示了一个有趣的集体声子传输机制，位于弹道和扩散传输机制之间。因此，已经进行了系统研究以通过晶粒尺寸和温度之间的竞争效应来描述声子流体动力学的特征。已经提取了与声子流体动力学和热波传播长度相关的特征非局部长度。声子流体动力学和这些长度尺度之间的联系是根据克努森数讨论的。更多，作为中间尺寸范围内特征尺寸的函数的热导率的比例关系成为流体动力学行为强度的关键指标。已采用关于法向散射率和电阻散射率的比率来理解这些不同的缩放关系，这似乎控制了 GeTe 中集体声子传输的强度和显着可见性。这项系统研究强调了温度和特征尺寸之间的竞争效应对 GeTe 中声子流体动力学的重要性，这可以更好地理解声子流体动力学及其控制参数在低导热材料中的一般行为和后果。