BeF $_2$线性热膨胀系数的第一性原理研究：巨热膨胀
A first-principles investigation of the linear thermal expansion coefficients of BeF$_2$: Giant thermal expansion
摘要：
我们提出的线性热膨胀系数（TEC）的BeF $_2$的理论研究的结果，在一个直接Gruneisen形式主义，其中采用保密变形。所需的物理量，如优化的晶体结构，弹性常数，模式Gruneisen参数，声子态密度计算从第一性原理。BeF $_2$在低压下表现出广泛的多态性，除了实验观察到的$α$ -石英相之外，还考虑了最低能量相[ $α$-空间群为（SG）P的方英石$4_1 2_1 2$及其与SG P $4_3 2_1 2$的相似相]。为了基准测试的目的，类似的计算进行金红石相的$_2$，其中体积TEC（$α_v$），从计算的线性TEC沿$a$（$α_a$）和$c$（$α_c$）方向，是非常好的协议与实验数据和以前的理论结果。对于所考虑的相位的BeF $_2$，我们没有发现任何负热膨胀（NTE）。然而，我们观察到不同的热性能的不同阶段。线性TEC非常大，特别是$α$ -方石英相及其类似相的$α_c$，导致巨大的$α_v$（300 K时为$\sim 175 \times 10^{-6} {\rm K}^{-1}$）。巨大的$α_v$来自于低频声子模的大Gruneisen参数，以及$α$ -方石英相的C13弹性常数是负符号和大幅度的。弹性常数，高频介电常数，玻恩有效电荷张量，和上述阶段的BeF $_2$的热性能的第一次报告，因此作为预测。
英文摘要：
We present the results of a theoretical investigation of the linear thermal expansion coefficients (TECs) of BeF$_2$, within a direct Gruneisen formalism where symmetry-preserving deformations are employed. The required physical quantities such as the optimized crystal structures, elastic constants, mode Gruneisen parameters, and phonon density of states are calculated from first-principles. BeF$_2$ shows an extensive polymorphism at low pressures, and the lowest energy phases [$α$-cristobalite with space group (SG) P$4_1 2_1 2$ and its similar phase with SG P$4_3 2_1 2$] are considered in addition to the experimentally observed $α$-quartz phase. For benchmarking purposes, similar calculations are performed for the rutile phase of ZnF$_2$, where the volumetric TEC ($α_v$), derived from the calculated linear TECs along the $a$ ($α_a$) and $c$ ($α_c$) directions, is in very good agreement with experimental data and previous theoretical results. For the considered phases of BeF$_2$, we do not find any negative thermal expansion (NTE). However we observe diverse thermal properties for the distinct phases. The linear TECs are very large, especially $α_c$ of the $α$-cristobalite phase and its similar phase, leading to giant $α_v$ ($\sim 175 \times 10^{-6} {\rm K}^{-1}$ at 300 K). The giant $α_v$ arises from large Gruneisen parameters of low-frequency phonon modes, and the C13 elastic constant that is negatively signed and large in magnitude for the $α$-cristobalite phase. The elastic constants, high-frequency dielectric constants, Born effective charge tensors, and thermal properties of the above phases of BeF$_2$ are reported for the first time and hence serve as predictions.
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