Site occupation in the Cr-Ru and Cr-Osσphases

Abstract

The site occupation in the Cr-Ru and Cr-Os phases is computed as a function of temperature. Generally, in phases the larger atoms occupy the sites with larger coordinations numbers, as can be explained on the basis of atomic-size and electronic structure. However, for Cr 2 Ru and Cr 2 Os the atomic-size argument predicts that Ru and Os occupy the sites with larger coordination numbers, whereas the reasoning based on the approximate degeneracies of electronic levels predicts that Cr occupies those sites. By comparing these predictions with the theoretically computed and the experimentally measured site occupations, the atomic-size and electronic arguments can be judged on their predictive merits.

Non-Stoichiometry and Calphad Modeling of Frank-Kasper Phases

“…Prototype σ Cr-Fe has been by far the most investigated system by many different first-principles calculations. 10 years after the first CWM-CVM study [28], Korzhavyi et al [38] were able to better reproduce the experimental data by adopting the BWA in the CEF formalism with the 2 5 = 32 end-members calculation in the Korringa-Kohn-Rostoker (KKR) method (see Figure 6). The influence of magnetism on the stability was investigated with disordered local moments, based on the Coherent Potential Approximation (CPA) of the spin orientation.…”

“…Figure 6. Fe site fraction in σ Cr-Fe, obtained by CWM-CVM at 500K (left) [28], and obtained by BWA at 1,000 K (right) [38]. Experimental points from [45].…”

“…The first significant work done on the σ phase has been performed on the two systems Cr-Fe [28] and Re-W [29]. The energies associated to the change of local atomic configurations have been parameterized by a set of Effective Cluster Interactions (ECI).…”

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

“…Recently the site occupation in the σ-phase has been widely studied by such methods [5][6][7][8][9][10][11][12][13]. However, most of these methods were based on a formalism, which is quite computationally demanding.…”

Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

“…In the 1950s Frank and Kasper (3,4) recognized complex tetrahedral atomic-and molecular-packing geometries that bridge the familiar close-packed crystals [e.g., face-centered cubic (FCC), hexagonally close-packed (HCP), and body-centered cubic (BCC) structures] characterized by periodic order, and quasiperiodic crystals (QCs) that extend crystallography beyond the 230 space groups relevant to periodic crystals (5,6). The scientific literature is replete with examples of Frank-Kasper phases in hard materials, particularly in the area of intermetallics (7)(8)(9), but also in a few complex elemental crystals, including manganese (10,11) and uranium (12). Recently, this class of crystalline order has cropped up in a host of soft materials, including dendrimers (13), surfactant solutions (14), and block polymers (15,16), often in close proximity to QC phases (17)(18)(19).…”