Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.
Dipartimento di Chimica, Università di Torino, Via Giuria 5, 10125 Torino, Italy.
J Chem Phys. 2019 Nov 14;151(18):184109. doi: 10.1063/1.5126931.
Cubic cuprous oxide, CuO, is characterized by a peculiar structural response to temperature: it shows a relatively large negative thermal expansion below 250 K, then followed by a positive thermal expansion at higher temperatures. The two branches of its thermal expansion (negative and positive) are almost perfectly symmetric at low temperatures, with the minimum of its lattice parameter at about 250 K and with the lattice parameter at 500 K almost coinciding with that at 0 K. We perform lattice-dynamical quantum-mechanical calculations to investigate the thermal expansion of CuO. Phonon mode-specific Grüneisen parameters are computed, which allows us to identify different spectral regions of atomic vibrations responsible for the two distinct regimes of thermal expansion. Two different computational approaches are explored, their results compared, and their numerical aspects critically assessed: a well-established method based on the quasiharmonic approximation, where harmonic frequencies are computed at different lattice volumes, and an alternative approach, where quadratic and cubic interatomic force-constants are computed at a single volume. The latter scheme has only recently become computationally feasible in the context of lattice thermal conductivity simulations. When proper numerical parameters are used (phonon sampling, tolerances, etc.), the two approaches are here shown to provide a very consistent description, yet at a rather different computational cost. All of the experimentally observed features of the complex thermal expansion of CuO are correctly reproduced up to 500 K, with a slight overall underestimation of the volume contraction.
立方氧化亚铜（CuO）的结构对温度具有特殊的响应特性：在 250 K 以下表现出较大的负热膨胀，然后在较高温度下呈现正热膨胀。其热膨胀的两个分支（负和正）在低温下几乎完全对称，晶格参数的最小值约为 250 K，而 500 K 时的晶格参数几乎与 0 K 时的晶格参数重合。我们进行晶格动力学量子力学计算以研究 CuO 的热膨胀。计算了声子模式特定的格林艾森参数，这使我们能够识别原子振动的不同光谱区域，这些区域负责热膨胀的两个不同状态。探索了两种不同的计算方法，比较了它们的结果，并对其数值方面进行了严格评估：一种基于准谐近似的成熟方法，其中在不同晶格体积上计算了谐频，以及另一种方法，其中在单个体积上计算了二次和三次原子间力常数。后一种方案仅在最近才在晶格热导率模拟的背景下在计算上变得可行。当使用适当的数值参数（声子采样、公差等）时，这两种方法都显示出非常一致的描述，但计算成本却大不相同。在 500 K 以下，CuO 复杂热膨胀的所有实验观察到的特征都得到了正确再现，仅对体积收缩略有低估。
