χ
and σ Phases in Binary Rhenium–Transition Metal Systems:
a Systematic First-Principles Investigation
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Abstract
The
Frank–Kasper phases, known as topologically close-packed (tcp)
phases, are interesting examples of intermetallic compounds able to
accommodate large homogeneity ranges by atom mixing on different sites.
Among them, the χ and σ phases present two competing complex
crystallographic structures, the stability of which is driven by both
geometric and electronic factors. Rhenium (Re) is the element forming
the largest number of binary χ and σ phases. Its central
position among the transition metals in the periodic table plays an
important role in the element ordering in tcp phases. Indeed, it has
been shown that Re shows an opposite site preference depending on
which elements it is alloyed with. In the present work, χ- and
σ-phase stability in binary Re–<i>X</i> systems
is systematically studied by a first-principles investigation. The
heats of formation of the complete set of ordered configurations (16
for χ and 32 for σ) have been calculated in 16 well-chosen
systems to identify stability criteria. They include not only the
systems in which χ-Re–<i>X</i> (<i>X</i> = Ti, Mn, Zr, Nb, Mo, Hf, Ta, W) or σ-Re–<i>X</i> (<i>X</i> = V, Cr, Mn, Fe, Nb, Mo, Ta, W) exist but also
the systems in which both phases are not stable, including systems
in which <i>X</i> is a 3<i>d</i> element from
Ti to Ni, a 4<i>d</i> element from Zr to Ru, and a 5<i>d</i> element from Hf to Os. Careful analysis is done of the
energetic tendencies as a function of recomposition, size effect,
and electron concentration. Moreover, the site preference and other
crystallographic properties are discussed. Conclusions are drawn concerning
the relative stability of the two phases in comparison with the available
experimental knowledge on the systems