α-四氟硼酸的结构、非化学计量和几何阻挫
Structure, non-stoichiometry, and geometrical frustration of alpha-tetragonal boron
摘要：
最近发现的所谓纯的α-四氟硼酸需要重新审视其结构。该系统也是有趣的元素晶体，这是在β-菱面体硼中发现的一种新类型的几何挫折。采用密度泛函理论计算方法，对纯α-四硼酸的结构和热力学性质进行了研究。与β-菱面体硼不同，在B_52中，两个4c间隙位几乎满足稳定共价键的条件（带隙和完全填充的价带）。这表明纯的α-四氟硼酸的基态是化学计量的。然而，共价条件并不完全满足，因为存在不能消除的非键合间隙状态。4c位的半占据产生宏观量的剩余熵，其与β-菱面体硼的剩余熵一样大。因此，α-四氟硼酸可以被分类为具有几何挫折的元素晶体。只有在有限的温度下才能发生偏离化学计量的现象。热力学分析表明，δ与化学计量组成B_（52+ δ）的偏差很小，且为正值。对于所报道的高压合成条件，预测δ为约0.1至0.2。纯的和含C或N的α-四氢硼之间的一个重要区别是间隙位置的占据：纯的形式倾向于占据4c位置，而含C或N的形式占据2a，8h和8i位置的混合物。本文提供了位置占用，δ值和晶格参数的关系，使我们能够识别纯的α-四氢呋喃，并将其与其他形式区分开来。
英文摘要：
Recent discoveries of supposedly pure alpha-tetragonal boron require to revisit its structure. The system is also interesting with respect to a new type of geometrical frustration in elemental crystals, which was found in beta-rhombohedral boron. Based on density functional theory calculations, the present study has resolved the structural and thermodynamic characteristics of pure alpha-tetragonal boron. Different from beta-rhombohedral boron, the conditions for stable covalent bonding (a band gap and completely filled valence bands) are almost fulfilled at a composition B_52 with two 4c interstitial sites occupied. This indicates that the ground state of pure alpha-tetragonal boron is stoichiometric. However, the covalent condition is not perfectly fulfilled because non-bonding in-gap states exist that cannot be eliminated. The half occupation of the 4c sites yields a macroscopic amount of residual entropy, which is as large as that of beta-rhombohedral boron. Therefore, alpha-tetragonal boron can be classified as an elemental crystal with geometrical frustration. Deviations from stoichiometry can occur only at finite temperatures. Thermodynamic considerations show that deviations delta from the stoichiometric composition B_(52+delta) are small and positive. For reported high-pressure syntheses conditions delta is predicted to be about 0.1 to 0.2. An important difference between pure and C- or N-containing alpha-tetragonal boron is found in the occupation of interstitial sites: the pure form prefers to occupy the 4c sites, whereas in C- or N-containing forms a mixture of 2a, 8h, and 8i sites are occupied. The present article provides relations of site occupation, delta values, and lattice parameters, which enable us to identify pure alpha-tetragonal and distinguish the pure form from other ones.
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