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arXiv 1709.01876cond-mat.mtrl-sci
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非金属固体的峰值本征热导率和氩实验数据的新解释

Peak intrinsic thermal conductivity in non-metallic solids and new interpretation of experimental data for argon

Ahmed Hamed, Anter El-Azab

摘要:

在微扰理论和线性化玻尔兹曼输运方程的框架下研究了三声子过程的非弹性性质。通过考虑这种类型的相互作用在统计平均意义上的能量守恒规则,不同形式的正则化能量守恒狄拉克δ函数的3声子散射率的影响进行了评估。引人注目的是,采用洛伦兹分布,根据声子正常模式的本征能量展宽的形状,由于晶体非谐性的领先项,被发现在低温下激活umklapp过程中起着关键作用,导致本征晶格热导率峰在有限的温度完美的晶体。这种独特的行为,独特的洛伦兹,奠定了基础,发展可调参数的计算模型,在低温下的有限晶格电导率的可靠预测,即使在没有外来散射过程。采用Boltzmann输运方程的迭代解法计算了固体氩在整个温度范围内(2-80 K)的本征热导率。首次成功地恢复了实验观察到的$T^2$在低温($T$)极限和峰值温度(~ 8 K)的行为,以及通过单独使用3-声子过程在20 K以上的经典高温$T^{-1}$行为。良好的协议与实验表明,声子-声子相互作用占主导地位,在整个温度范围内,在氩气中,与以前的假设,声子缺陷散射占主导地位的亚峰制度。观察到声子聚焦引起的单晶体低温热导率的各向异性。此外,在单模弛豫时间近似下,氩的电导率被低估了一个数量级。

英文摘要:

The inelastic nature of 3-phonon processes is investigated within the framework of perturbation theory and linearized Boltzmann Transport Equation. By considering the energy conservation rule governing this type of interactions in a statistical average sense, the impact of different forms of the regularized energy-conserving Dirac delta function on 3-phonon scattering rates was evaluated. Strikingly, adopting Lorentz distribution, in accordance with the shape of eigenenergy broadening of phonon normal modes due to the leading term of crystal anharmonicity, was found to play a critical role in activating umklapp processes at low temperature, leading to intrinsic lattice thermal conductivity peak at finite temperature for perfect crystal. This characteristic behavior, unique to the Lorentzian, lays foundation for developing adjustable-parameter-free computational models for reliable prediction of the finite lattice conductivity at low temperature, even in the absence of extrinsic scattering processes. An iterative solution scheme for Boltzmann Transport Equation was used to compute the intrinsic thermal conductivity of solid argon over the entire temperature range (2-80 K). For the first time, the experimentally observed $T^2$ behavior in the low temperature, $T$, limit and the peak temperature (~ 8 K) were successfully recovered, in addition to the classical high temperature $T^{-1}$ behavior above 20 K by the sole use of 3-phonon processes. The good agreement with experiment indicates that phonon-phonon interactions dominate over the entire temperature range in argon, contrary to previous hypotheses that phonon-defect scattering dominates the sub-peak regime. Anisotropy in thermal conductivity of single crystal at low temperature due to phonon focusing was observed. In addition, argon conductivity is underestimated by an order of magnitude in Single Mode Relaxation Time approximation.

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