Thermodynamic Stability of Boron:  The Role of Defects and Zero Point Motion

Abstract

Its low weight, high melting point, and large degree of hardness make elemental boron a technologically interesting material. The large number of allotropes, mostly containing over a hundred atoms in the unit cell, and their difficult characterization challenge both experimentalists and theoreticians. Even the ground state of this element is still under discussion. For over 30 years, scientists have attempted to determine the relative stability of alpha- and beta-rhombohedral boron. We use density functional calculations in the generalized gradient approximation to study a broad range of possible beta-rhombohedral structures containing interstitial atoms and partially occupied sites within a 105 atoms framework. The two most stable structures are practically degenerate in energy and semiconducting. One contains the experimental 320 atoms in the hexagonal unit cell, and the other contains 106 atoms in the triclinic unit cell. When populated with the experimental 320 electrons, the 106 atom structure exhibits a band gap of 1.4 eV and an in-gap hole trap at 0.35 eV above the valence band, consistent with known experiments. The total energy of these two structures is 23 meV/B lower than the original 105 atom framework, but it is still 1 meV/B above the alpha phase. Adding zero point energies finally makes the beta phase the ground state of elemental boron by 3 meV/B. At finite temperatures, the difference becomes even larger.

New Ground-State Crystal Structure of Elemental Boron

“…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].…”

“…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 B 4 C [28]. Although the growth conditions to form these twinned structures are not clear [27,29], the twinned structure might dramatically change material properties such as charge capacitance [30].…”

“…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].…”

“…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].…”

“…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).…”