Abstract
Boron Carbide exhibits a broad composition range, implying a degree of intrinsic substitutional disorder. While the observed phase has rhombohedral symmetry (space group R3¯m), the enthalpy minimizing structure has lower, monoclinic, symmetry (space group Cm). The crystallographic primitive cell consists of a 12-atom icosahedron placed at the vertex of a rhombohedral lattice, together with a 3-atom chain along the 3-fold axis. In the limit of high carbon content, approaching 20% carbon, the icosahedra are usually of type B11 Cp, where the p indicates the carbon resides on a polar site, while the chains are of type C–B–C. We establish an atomic interaction model for this composition limit, fit to density functional theory total energies, that allows us to investigate the substitutional disorder using Monte Carlo simulations augmented by multiple histogram analysis. We find that the low temperature monoclinic Cm structure disorders through a pair of phase transitions, first via a 3-state Potts-like transition to space group R3m, then via an Ising-like transition to the experimentally observed R3¯m symmetry. The R3m and Cm phases are electrically polarized, while the high temperature R3¯m phase is nonpolar.
Highlights
The phase diagram of boron carbide is not precisely known, with both qualitative and quantitative discrepancies among the different research groups [1, 2, 3, 4, 5, 6, 7]
At 20% carbon a proposed B4C structure featured pure boron icosahedra B12 with a C-C-C chain [14]. This structure exhibits R3m symmetry, later experimental work [13, 15] suggested that the icosahedron should be B11C instead of B12 and the chain should be C-B-C instead of C-C-C
We construct an artificial model inspired by boron carbide by placing an orientational degree of freedom at the vertices of a rhombohedral lattice, mimicking the distribution of carbon sites among polar vertices of B11Cp icosahedra
Summary
The phase diagram of boron carbide is not precisely known, with both qualitative and quantitative discrepancies among the different research groups [1, 2, 3, 4, 5, 6, 7]. As determined crystallographically [11, 12, 13], boron carbide has a 15-atom primitive cell, consisting of an icosahedron and 3-atom chain, in a rhombohedral lattice with symmetry R3m. At 20% carbon a proposed B4C structure featured pure boron icosahedra B12 with a C-C-C chain [14]. This structure exhibits R3m symmetry, later experimental work [13, 15] suggested that the icosahedron should be B11C instead of B12 and the chain should be C-B-C instead of C-C-C. Icosahedra are connected along edges of the rhombohedral lattice, which pass through the polar sites
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