Equilibrium p-T Phase Diagram of Boron: Experimental Study and Thermodynamic Analysis

Abstract

Solid-state phase transformations and melting of high-purity crystalline boron have been in situ and ex situ studied at pressures to 20 GPa in the 1500–2500 K temperature range where diffusion processes become fast and lead to formation of thermodynamically stable phases. The equilibrium phase diagram of boron has been constructed based on thermodynamic analysis of experimental and literature data. The high-temperature part of the diagram contains p-T domains of thermodynamic stability of rhombohedral β-B106, orthorhombic γ-B28, pseudo-cubic (tetragonal) t'-B52, and liquid boron (L). The positions of two triple points have been experimentally estimated, i.e. β–t'–L at ~ 8.0 GPa and ~ 2490 K; and β–γ–t' at ~ 9.6 GPa and ~ 2230 K. Finally, the proposed phase diagram explains all thermodynamic aspects of boron allotropy and significantly improves our understanding of the fifth element.

Three-dimensional buckled honeycomb boron lattice with vacancies as an intermediate phase on the transition pathway from α-B to γ-B

“…When γ-B 28 is synthesized from amorphous boron, α-B 12 and β-B 106 , extreme conditions such as high pressures and high temperatures are usually adopted. [5][6][7][8][9] We examined the thermal motions of atoms in the hex-B 1/8 structure by calculating the mean squared-displacements, defined as oR…”

“…There is a general consensus that although denser α-B 12 is in a stable phase at elevated pressures, it transforms to β-B 106 as the temperature increases. [5][6][7] However, based on extrapolation of the phase boundary, α-B 12 has been claimed to be stable at normal conditions. 8 Conversely, γ-orthorhombic boron is stable at high pressures and its crystal structure is now well established based on theoretical and experimental studies.…”

“…8 Conversely, γ-orthorhombic boron is stable at high pressures and its crystal structure is now well established based on theoretical and experimental studies. 5 Various experiments have demonstrated that γ-B 28 can be synthesized from several starting materials, including amorphous boron, α-B 12 , and β-B 106 , at pressures of 7-20 GPa and temperatures of 1500-2500 K. [5][6][7][8][9] Other boron phases such as α-tetragonal (T-B 50 or T-B 52 ) and β-tetragonal boron (T-192 or β-B 192 ) also contain icosahedra but have been suggested to be intermediate phases formed during structural transformations under high-pressure high-temperature conditions according to Ostwald's step rule. 5,6,9,10 Although α-B 12 and γ-B 28 contain distorted cubic close-packed B 12 icosahedra, the structural difference is that γ-B 28 has additional B 2 dumbbells occupying all the octahedral cavities.…”

Integrated form of the Anderson-Grüneisen equation of state forp-V-Tdata fit: Application to the compounds of boron, carbon, silicon and some metals.

“…We need to explore the HPHT thermodynamics for understanding the syntheses of these new materials for new challenging applications as superhard [5,6], advanced electronic [7] and photovoltaic [8], superconductors [9] as well as clathrate thermoelectric materials [10,11]: (1) boron allotropes [12] (orthorhombic γ-B 28 [13][14][15][16], pseudo-cubic t'-B 52 [17]) and boron-rich compounds (subnitride B 13 N 2 [18,19]), (2) superhard compounds with diamond structure (nanostructured cBN [20] and c-BC 5 [21,22]); (3) covalent clathrates of new stoichiometries (Na 4-x Si 24 [8,10] & Na 24+x Si 136 [10,11]) and even (4) new unexpected semiconductors, like antifluorite Mg 2 C [23,24], dense Mg 2 C 3 [25] and pure silicon allotrope with quasi-direct bandgap, Si 24 [8]. Although a part of the lacking data can be replaced by fitted parameters of common models [26][27][28] or with ab initio calculations [24], the reliable p-V-T equations of state (EOS) data are crucial for that.…”

Thermodynamic calculation of the B-C system at pressures to 24 GPa

“…Pressure dependencies of molar volumes were represented using the Murnaghan approximation [5]. Bulk moduli, their pressure derivatives, and thermal expansion coefficients for -B 106 , graphite, diamond, and liquid phase were taken from [6,7], while the data on high-pressure phases, -B 28 [8] and t-B 52 [9], -from [10]. We also used literature data on the thermal expansion [11] and compressibility [12] of B 4 C boron carbide.…”