论文标题
来自原子位移协方差的晶体固体的振动熵
Vibrational entropy of crystalline solids from covariance of atomic displacements
论文作者
论文摘要
从信息理论的角度研究了有限温度下固体的振动熵。从头算分子动力学（AIMD）模拟在有限温度下生成原子配置的合奏，我们从中获得了原子位移的$ n $体积分布，$ρ_n$。我们从$ \ ln {ρ_n} $的期望值中计算出信息理论熵。在近似的第一级，独立处理单个原子位移，可以使用Debye-Waller B因子应用我们的方法，从而允许衍射实验获得热力学熵的上限。在下一个近似级别，我们通过包括位移协方差纠正高估。我们将这种方法应用于元素以身体为中心的立方钠和面部中心的立方铝，显示出与金属的Debye温度高于Debye的实验值的良好一致性。在Debye温度下方，我们从协方差矩阵的特征值中提取了状态的有效振动密度，然后机械地评估熵量子，再次与实验至低温达到了良好的一致性。正如我们为高熵合金演示的那样，我们的方法很容易将其推广到复杂的固体。此外，我们的方法适用于准时近似失败的情况，正如我们通过计算Ti中的HCP/BCC过渡所证明的那样。
The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the $N$-body distribution of atomic displacements, $ρ_N$. We calculate the information-theoretic entropy from the expectation value of $\ln{ρ_N}$. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye-Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.
