Abstract: In order to account explicitly for the existence of long-periodic layered structures and the strong structural relaxations in the most common binary and ternary alloys of the Bi-Sb-Te-Se system, we have developed a one-dimensional cluster expansion (CE) based on first-principles electronic structure calculations, which accounts for the Bi and Sb bilayer formation. Excellent interlayer distances are obtained with a van der Waals density functional. It is shown that a CE solely based on pair interactions is sufficient to provide an accurate description of the ground-state energies of Bi-Sb-Te-Se binary and ternary systems without making the data set of ab initio calculated structures unreasonably large. For the binary alloys A1−xQx (A=Sb, Bi; Q=Te, Se), a ternary CE yields an almost continuous series of (meta)stable structures consisting of consecutive A bilayers next to consecutive A2Q3 for 0<x<0.6. For x>0.6, the binary alloy segregates into pure Q and A2Q3. The Bi-Sb system is described by a quaternary CE and is found to be an ideal solid solution stabilized by entropic effects at T≠0 K but with an ordered structure of alternating Bi and Sb layers for x=0.5 at T=0 K. A quintuple CE is used for the ternary Bi-Sb-Te system, where stable ternary layered compounds with an arbitrary stacking of Sb2Te3, Bi2Te3, and Te-Bi-Te-Sb-Te quintuple units are found, optionally separated by mixed Bi/Sb bilayers. Electronic properties of the stable compounds were studied taking spin-orbit coupling into account.

Abstract: A long-standing challenge in physics is to understand why cementite is the predominant carbide in steel. Here we show that the prevalent formation of cementite can be explained only by considering its stability at elevated temperature. A systematic highly accurate quantum mechanical study was conducted on the stability of binary iron carbides. The calculations show that all the iron carbides are unstable relative to the elemental solids, -Fe and graphite. Apart from a cubic Fe23C6 phase, the energetically most favorable carbides exhibit hexagonal close-packed Fe sublattices. Finite-temperature analysis showed that contributions from lattice vibration and anomalous Curie-Weis magnetic ordering, rather than from the conventional lattice mismatch with the matrix, are the origin of the predominance of cementite during steel fabrication processes.