Carbon-rich icosahedral boron carbides beyondB4Cand their thermodynamic stabilities at high temperature and pressure from first principles

Abstract

We investigate the thermodynamic stability of carbon-rich icosahedral boron carbide at different compositions, ranging from B 4 C to B 2 C, using first-principles calculations. Apart from B 4 C, generally addressed in the literature, B 2.5 C, represented by B 10 C p 2 (C-C), where C p and (C-C) denote a carbon atom occupying the polar site of the icosahedral cluster and a diatomic carbon chain, respectively, is predicted to be thermodynamically stable under high pressures with respect to B 4 C as well as pure boron and carbon phases. The thermodynamic stability of B 2.5 C is determined by the Gibbs free energy G as a function of pressure p and temperature T , in which the contributions from the lattice vibrations and the configurational disorder are obtained within the quasiharmonic and the mean-field approximations, respectively. The stability range of B 2.5 C is then illustrated through the p-T phase diagrams. Depending on the temperatures, the stability range of B 2.5 C is predicted to be within the range between 40 and 67 GPa. At T 500 K, the icosahedral C p atoms in B 2.5 C configurationally disorder at the polar sites. By investigating the properties of B 2.5 C, e.g., elastic constants and phonon and electronic density of states, we demonstrate that B 2.5 C is both mechanically and dynamically stable at zero pressure, and is an electrical semiconductor. Furthermore, based on the sketched phase diagrams, a possible route for experimental synthesis of B 2.5 C as well as a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested.

Effect of temperature and configurational disorder on the electronic band gap of boron carbide from first principles

“…To examine the impact of temperature and configurational disorder of B and C atoms induced by high concentrations of low-energy B/C substitutional defects on the band gap of the material, we consider in the present work two atomic configurations of B 4 C. Those are (1) ordered B 4 C, where the C p atoms are well oriented, occupying the same polar position for every icosahedron, and (2) disordered B 4 C, where the C p atoms configurationally disorder at the polar sites without the formation of inter-and intraicosahedral bonds between the C p atoms. The former has been demonstrated by several independent first-principles calculations to exhibit the lowestenergy configuration at T = 0 K [17,19,[40][41][42], and it thus has presumably been believed to be the ground state for B 4 C, while the latter has been predicted to be favored with respect to the ordered one at elevated temperature [19,43,45]. As demonstrated in our previous work [45], the energy difference between the ordered and disordered B 4 C at T = 0 K, taking into account the influence of the zero-point motion, is 72 meV per unit cell, accordingly resulting in the mean-field-estimated order-disorder transition temperature of 730 K. It is worth noting that the same configurational transition from the ordered to the disordered states of B 4 C has been independently predicted by Yao et al [43] to take place at T 717 K, in line with our prediction [45].…”

“…The former has been demonstrated by several independent first-principles calculations to exhibit the lowestenergy configuration at T = 0 K [17,19,[40][41][42], and it thus has presumably been believed to be the ground state for B 4 C, while the latter has been predicted to be favored with respect to the ordered one at elevated temperature [19,43,45]. As demonstrated in our previous work [45], the energy difference between the ordered and disordered B 4 C at T = 0 K, taking into account the influence of the zero-point motion, is 72 meV per unit cell, accordingly resulting in the mean-field-estimated order-disorder transition temperature of 730 K. It is worth noting that the same configurational transition from the ordered to the disordered states of B 4 C has been independently predicted by Yao et al [43] to take place at T 717 K, in line with our prediction [45]. In the present work, we use simulation boxes containing 120 atoms, arranged in a supercell of 2 × 2 × 2 primitive rhombohedral unit cells, for both ordered and disordered B 4 C.…”

Structural models of increasing complexity for icosahedral boron carbide with compositions throughout the single-phase region from first principles

“…Furthermore, the SQS approach in principle breaks the point-group symmetry. To deal with these issues, we employ the projection technique, suggested by Moakher et al [48], to derive the rhombohedrally averaged elastic con-stantsC ij , following the procedure described in our previous works on boron carbide [16,32]. Thus twelve independent elastic constants, i.e., 56 , and C 66 , must be calculated to obtain the six averaged elastic constants, given bȳ…”

“…This is owing to its structural complexity as well as the similarities of B and C atoms in terms of the atomic form factors for x-ray diffraction [13] and of the nuclear scattering cross sections ( 11 B and 12 C) for neutron diffraction [11,14]. It should be * annop.ektarawong@liu.se noted that the issues, regarding the solubility range [15][16][17] and atomic configuration [18][19][20][21] of boron carbide, have still been inconclusively debated.…”

The Effects of Carbon Content on the Anisotropic Deformation Mechanism of Boron Carbide

“…Similar to other ceramic materials, the mechanical properties and deformation mechanisms of boron carbide strongly depend on its chemical compositions, microstructure, and fabrication processes [ 1 , 2 , 10 , 11 , 12 , 13 , 14 , 15 ]. In particular, depending on the synthesis conditions, boron carbide has a relatively broad composition range, from 8 to 20 at % C, with varying distributions of carbon (C) and boron (B) atoms into icosahedra and chains to form thermodynamically stable solid solutions, resulting in a complex phase diagram [ 2 , 16 ].…”