Ab Initio Study of Lattice Site Occupancies in Binary Sigma Phases Using a Single-Site Mean Field Model

Thermodynamic analysis of the topologically close packed σ phase in the Co-Cr system

Density functional theory (DFT) calculations show that it is essential to consider the magnetic contribution to the total energy for the end-members of the σ phase. A more straightforward method to use the DFT results in a CALPHAD (Calculation of phase diagrams) description has been applied in the present work. It was found that only the results from DFT calculations considering spin-polarization are necessary to obtain a reliable description of the σ phase. The benefits of this method are: the DFT calculation work can be reduced and the CALPHAD description of the magnetic contribution is more reliable. A revised thermodynamic description of the Co-Cr system is presented which gives improved agreement with experimental phase boundary data for the σ phase.

Influence of σ Phase on the Allotropic Transformation of the Matrix in Co-Re-Cr-Based Alloys with Ni Addition

Co-Re-Cr alloys are being developed for high-temperature application in gas turbines. In these alloys, the Cr2Re3-based σ phase is stable when the Cr content is higher than 20 atomic %. The addition of Ni is being studied to partially substitute Cr, which aims to suppress σ formation without sacrificing the benefit of Cr in the oxidation resistance of the alloy. The microstructure of the alloys with varying Cr (18–23%) and Ni (8–25%) was investigated by electron microscopy in the present study, primarily to look into the stability of the σ phase and its influence on the Co matrix phase transformation. The σ phase is mainly found in two morphologies in these alloys, where at high temperature only blocky σ phase is present at grain boundaries but cellular σ is formed through a discontinuous precipitation within the grains at lower heat treatment temperatures. The presence of fine cellular σ phase influences the alloy hardness. Moreover, the σ precipitation, which depletes the matrix in Re, also influences the allotropic transformation of the Co matrix.

Effect of mixed partial occupation of metal sites on the phase stability of γ-Cr23-xFe x C6 (x = 0-3) carbides

The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr_23−xFe_xC₆ (x = 0–3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M₂₃C₆ structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M^(4a) M₁₂^(48h)) and negatively charged cubo-octahedron (M₈^(32f) C₆^(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M₂₃C₆ carbides may facilitate further development of high-chromium heat-resistant steels.

Structure formation in soft nanocolloids: liquid-drop model

Using a model where soft nanocolloids such as spherical polymer brushes and star polymers are viewed as compressible liquid drops, we theoretically explore contact interactions between such particles. By numerically minimizing the phenomenological free energy consisting of bulk and surface terms, we find that at small deformations the drop-drop interaction is pairwise additive and described by a power law. We also propose a theory to describe the small-deformation regime, and the agreement is very good at all drop compressibilities. The large-deformation regime, which is dominated by many-body interactions, is marked by a rich phase diagram which includes the face- and body-centered-cubic, σ, A15, and simple hexagonal lattice as well as isostructural and re-entrant transitions. Most of these features are directly related to the non-convex deformation free energy emerging from many-body effects in the partial-faceting regime. The phase diagram, which depends on just two model parameters, contains many of the condensed phases observed in experiments. We also provide statistical-mechanical arguments that relate the two model parameters to the molecular architecture of the polymeric nanocolloids, chain rigidity, and solvent quality. The model represents a generic framework for the overarching features of the phase behavior of polymeric nanocolloids at high compressions.