New Ground-State Crystal Structure of Elemental Boron

Abstract

Elemental boron exhibits many polymorphs in nature based mostly on an icosahedral shell motif, involving stabilization of 13 strong multicenter intraicosahedral bonds. It is commonly accepted that the most thermodynamic stable structure of elemental boron at atmospheric pressure is the β rhombohedral boron (β-B). Surprisingly, using high-resolution transmission electron microscopy, we found that pure boron powder contains grains of two different types, the previously identified β-B containing a number of randomly spaced twins and what appears to be a fully transformed twinlike structure. This fully transformed structure, denoted here as τ-B, is based on the Cmcm orthorhombic space group. Quantum mechanics predicts that the newly identified τ-B structure is 13.8 meV=B more stable than β-B. The τ-B structure allows 6% more charge transfer from B 57 units to nearby B 12 units, making the net charge 6% closer to the ideal expected from Wade's rules. Thus, we predict the τ-B structure to be the ground state structure for elemental boron at atmospheric pressure. DOI: 10.1103/PhysRevLett.117.085501 Boron and related materials exhibit such extreme properties as low density, high hardness, high melting temperature, superconductivity, and ferromagnetism [1][2][3][4][5][6][7][8][9][10][11][12][13][14], making them candidates for such applications as high power electronics, superconductors, heat resistant alloys, coatings in nuclear reactors, body armor vests, abrasives, and cutting tool applications [7][8][9][10][11][12][13][14][15][16][17]. However, boron leads to quite complex structures arising from its unique bonding character that prefers formation of icosahedral shell complexes that stabilize 13 strong multicenter intraicosahedral bonds (requiring 26 electrons, Wade's rule). These complex structures make it difficult to interpret and understand the relationships between structure and properties. Indeed, even the ground state structure of boron has been controversial for over 30 years [6,[15][16][17].A number of crystalline structural forms for elemental boron have been discovered over the last two centuries [18][19][20]. However, only three phases correspond to pure boron: α-B 12 [18], β-B 105 [19], and γ-B 28 [20], with most of the others probably stabilized by impurities [21][22][23]. It has been long suspected that the β rhombohedral boron (β-B 105 ) structure is the most thermodynamic stable allotrope at low pressures [6,[15][16][17]. However, the quantum mechanics studies [15,16] predict that the α-B 12 structure is more stable than β-B 105 by 25.3 meV=atom, leading to a long debate of which phase is the ground state structure for elemental boron [6,[15][16][17]24]. Recent quantum mechanics studies have suggested that particular choices for the partial occupation sites in β-B 105 and including zero point motion might lead to an energy for β-B 105 that is more stable than α-B 12 structure at ambient conditions [16,25].Twinned structures have been observed in β-B 105 [26,27] and boron related materials such as ...

An et al. Reply:

“…An et al Reply: Our Letter reported high-resolution transmission electron microscopy on commercial quality boron showing that ∼2=3 of the grains exhibit smooth microstructure, leading to an x-ray diffraction pattern of well-known beta boron [1]. The other 1=3 grains exhibit a uniform zigzag pattern that extends across the entire grain and exhibits a very regular twinlike symmetry on every other lattice plane.…”

Boron oxides under pressure: Prediction of the hardest oxides

“…Well-established α, β, γ , and tetragonal T allotropes are superhard, and have been confirmed to be pure boron allotropes [1]. Recently, yet another pure bulk modification of boron, τ -B [2], and two-dimensional (2D) allotropes of boron, borophenes, were identified [3,4]. Boron oxide B 2 O 3 and suboxide B 6 O are well established, but there are also controversial compounds proposed in the literature [4][5][6][7][8][9][10][11][12][13][14][15].…”

Data-Driven Learning of Total and Local Energies in Elemental Boron

“…Among the most fundamental is determining the thermodynamically stable ground state between two competing forms: α-rhombohedral boron, which contains B 12 icosahedra exclusively [4], and β-rhombohedral boron (β-B in the following), which exhibits partial occupations and geometric frustration, most unusual for an elemental ground-state structure [5][6][7][8][9]. The energy difference between the α and β forms has been studied extensively using density-functional theory (DFT) [8][9][10][11][12][13][14][15] and recently probed by calorimetric experiments [16]; the consensus is now that β-B is indeed more stable at ambient conditions.…”