Mysterious SiB 3 : Identifying the Relation between α- and β-SiB 3

Abstract

Binary silicon boride SiB 3 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-SiB 3 . Similar to other boron-rich icosahedral solids, these SiB 3 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-SiB 3 and analyze their relative thermodynamic stabilities. α-SiB 3–x is metastable (with respect to β-SiB 3 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-SiB 3 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 SiB 3 formation and allows decoupling of SiB 3 formation from decomposition. Quantitative formation of β-SiB 3 was seen at 1100 °C for samples pressurized to 5.5–8 GPa. β-SiB 3 decomposes peritectoidally at temperatures between 1250 and 1300 °C. The highly ordered nature of β-SiB 3 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 B 6 P. The detailed composition and structural properties of disordered α-SiB 3–x were ascertained by a combination of single-crystal X-ray diffraction and 29 Si 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 B 12 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 B 12 icosahedron. Accordingly, α-SiB 3–x constitutes a mixture of B 10 Si 2 and B 11 Si 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-SiB 3 + Si. Modeling of the configurational and vibrational entropies suggests that α-SiB 3–x only becomes more stable than β-SiB 3 at temperatures above its decomposition into SiB 6 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-SiB 3 , whereas α-SiB 3 represents a p-type conductor.