Mysterious SiB3: Identifying the Relation between α- and β-SiB3

Abstract

Binary silicon boride SiB₃ has been reported to occur in two forms, as disordered and nonstoichiometric α-SiB_3-x , which relates to the α-rhombohedral phase of boron, and as strictly ordered and stoichiometric β-SiB₃. Similar to other boron-rich icosahedral solids, these SiB₃ phases represent potentially interesting refractory materials. However, their thermal stability, formation conditions, and thermodynamic relation are poorly understood. Here, we map the formation conditions of α-SiB_3-x and β-SiB₃ and analyze their relative thermodynamic stabilities. α-SiB_3-x is metastable (with respect to β-SiB₃ and Si), and its formation is kinetically driven. Pure polycrystalline bulk samples may be obtained within hours when heating stoichiometric mixtures of elemental silicon and boron at temperatures 1200-1300 °C. At the same time, α-SiB_3-x decomposes into SiB₆ and Si, and optimum time-temperature synthesis conditions represent a trade-off between rates of formation and decomposition. The formation of stable β-SiB₃ was observed after prolonged treatment (days to weeks) of elemental mixtures with ratios Si/B = 1:1-1:4 at temperatures 1175-1200 °C. The application of high pressures greatly improves the kinetics of SiB₃ formation and allows decoupling of SiB₃ formation from decomposition. Quantitative formation of β-SiB₃ was seen at 1100 °C for samples pressurized to 5.5-8 GPa. β-SiB₃ decomposes peritectoidally at temperatures between 1250 and 1300 °C. The highly ordered nature of β-SiB₃ is reflected in its Raman spectrum, which features narrow and distinct lines. In contrast, the Raman spectrum of α-SiB_3-x is characterized by broad bands, which show a clear relation to the vibrational modes of isostructural, ordered B₆P. The detailed composition and structural properties of disordered α-SiB_3-x were ascertained by a combination of single-crystal X-ray diffraction and ²⁹Si magic angle spinning NMR experiments. Notably, the compositions of polycrystalline bulk samples (obtained at T ≤ 1200 °C) and single crystal samples (obtained from Si-rich molten Si-B mixtures at T > 1400 °C) are different, SiB_2.93(7) and SiB_2.64(2), respectively. The incorporation of Si in the polar position of B₁₂ icosahedra results in highly strained cluster units. This disorder feature was accounted for in the refined crystal structure model by splitting the polar position into three sites. The electron-precise composition of α-SiB_3-x is SiB_2.5 and corresponds to the incorporation of, on average, two Si atoms in each B₁₂ icosahedron. Accordingly, α-SiB_3-x constitutes a mixture of B₁₀Si₂ and B₁₁Si clusters. The structural and phase stability of α-SiB_3-x were explored using a first-principles cluster expansion. The most stable composition at 0 K is SiB_2.5, which however is unstable with respect to the decomposition β-SiB₃ + Si. Modeling of the configurational and vibrational entropies suggests that α-SiB_3-x only becomes more stable than β-SiB₃ at temperatures above its decomposition into SiB₆ and Si. Hence, we conclude that α-SiB_3-x is metastable at all temperatures. Density functional theory electronic structure calculations yield band gaps of similar size for electron-precise α-SiB_2.5 and β-SiB₃, whereas α-SiB₃ represents a p-type conductor.