Structure, nonstoichiometry, and geometrical frustration ofα-tetragonal boron

Abstract

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 B 52 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 non-bonding ingap 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 (B 52+δ ) are small and positive. For 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 and distinguish the pure form from other ones.

Thermodynamic stability and properties of boron subnitrides from first principles

“…We note that the representation of the atomic configuration of t-B 50 N 2 has still not been decisive due to a variety of ways for individual boron and nitrogen atoms to fully and/or partially occupy 13 14 15 16 at.% N different interstitial sites [70][71][72]. In the present work, the atomic configuration of t-B 50 N 2 , recently proposed by Uemura et al [72] is chosen, as it is found to be the lowest-energy configuration, among several considered possible occupations of the interstitial atoms. The configuration is represented by (1) four icosahedral clusters, centered at (a/4, a/4, c/4), (3a/4, 3a/4, c/4), (3a/4, a/4, 3c/4), and (a/4, 3a/4, 3c/4) of the tetragonal unit cell, (2) two interstitial boron atoms, partially placed either at the 8h or at the 8i sites, and (3) two interstitial nitrogen atoms, located at the 2b sites.…”

Hydrogenation, dehydrogenation of α-tetragonal boron and its transition to δ-orthorhombic boron

“…In all the cases, the kinetic cutoff energy E cutoff was 40 Ry. The convergence was well tested in our previous studies [19] and increasing E cutoff to 80 Ry changes the formation energy only by 2 to 4 meV/atom. Structural optimizations were performed with respect to atomic positions and cell parameters and no constraints on the crystal symmetry were imposed, except the tetragonal symmetry for the lattice parameters.…”

“…When they occupy two (4c) sites in different ab planes, we call it the out-of-plane configuration (see figure 2). The lowest-energy structure of pure α-T boron is B 52 in the out-of-plane configuration [10,19] and in this paper pure α-T boron is always related to this structure, unless otherwise stated.…”

“…For pure α-T boron the characteristics of interstitial sites were analyzed previously [19]. It was found that up to a composition n=52 the (4c) site is the most preferable POS, followed by (8h) and (8i).…”

“…Unfortunately, owing to the lack of accurate information about the crystal structures, it is not clear if the various reported samples represent the same phase or if they contain impurities. A recent theoretical study by Uemura et al has identified the characteristic features of pure α-T boron B 52 [19]. It was shown that the occupation of interstitial sites as well as non-stoichiometric compositions, i.e.non-integer number of atoms per primitive unit cell, are crucial for the stability of the system.…”