Structure, nonstoichiometry, and geometrical frustration of α -tetragonal boron

Recent discoveries of supposedly pure α-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 β-rhombohedral boron. Based on density functional theory calculations, the present study has resolved the structural and thermodynamic characteristics of pure α-tetragonal boron. Different from β-rhombohedral boron, the conditions for stable covalent bonding (a band gap and completely filled valence bands) are almost fulfilled at a composition B52 with two 4c interstitial sites occupied. This indicates that the ground state of pure α-tetragonal boron is stoichiometric. However, the covalent condition is not perfectly fulfilled because nonbonding 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 β-rhombohedral boron. Therefore α-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 δ from the stoichiometric composition (B52+δ) are small and positive. For the reported high-pressure syntheses conditions δ is predicted to be about 0.1 to 0.2. An important difference between pure and C- or N-containing α-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, δ values, and lattice parameters, which enable us to identify pure α-tetragonal boron and distinguish the pure form from other ones.

Duke Scholars

Author Hagen Eckert Thomas Lord Department of Mechanical Engineering and Materia ...

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