Comparison of the Site Occupancies Determined by Combined Rietveld Refinement and Density Functional Theory Calculations: Example of the Ternary Mo–Ni–Re σ Phase

The site occupancies of the Mo–Ni–Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3⁵ = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg–Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo–Ni–Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results

χ and σ Phases in Binary Rhenium–Transition Metal Systems: a Systematic First-Principles Investigation

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

χ and σ Phases in Binary Rhenium–Transition Metal Systems: a Systematic First-Principles Investigation

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

Comparison of the Site Occupancies Determined by Combined Rietveld Refinement and Density Functional Theory Calculations: Example of the Ternary Mo–Ni–Re σ Phase

The site occupancies of the Mo–Ni–Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3⁵ = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg–Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo–Ni–Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results

Systematic First-Principles Study of Binary Metal Hydrides

First-principles calculations were systematically performed for 31 binary metal–hydrogen (<i>M</i>–H) systems on a set of 30 potential crystal structures selected on the basis of experimental data and possible interstitial sites. For each <i>M</i>–H system, the calculated enthalpies of formation were represented as functions of H composition. The zero-point energy correction was considered for the most stable hydrides via additional harmonic phonon calculations. The sequence of stable hydrides (ground-state) given by the convex hull was found in satisfactory agreement with the experimental data. In addition, new high pressure dihydrides and trihydrides were predicted, providing orientations for new materials synthesis. The overall results provide a global overview of hydride relative stabilities and relevant input data for thermodynamic modeling methods

Thermodynamic Modeling of the Ni–H System

A new thermodynamic assessment of the Ni–H system has been carried out, providing a complete description valid up to 6 × 10⁹ Pa of this system at the center of hydrogen storage issues. The study includes the hydride formation reaction and the presence of a miscibility gap in the fcc interstitial solid solution of hydrogen in nickel. In addition to a complete literature review, first-principles calculations were carried out and combined with other modeling approaches. The cluster expansion method allowed us to describe the energetic interactions between atoms leading to the miscibility gap in the fcc solid solution. Besides, the compressibility at high pressure was characterized for each phase including the condensed phases. For this purpose, a specific high-pressure model was assessed with the contribution of quasi-harmonic phonon calculations. The obtained consistent model allows us to characterize entirely the thermochemical behavior of the Ni–H system