Stability of theωstructure of transition elements

Abstract

Properties of the ω structure are investigated for 27 transition elements from the viewpoints of thermodynamical and mechanical stability based on first-principles calculations. The thermodynamical stability of the ω structure is compared with those for the body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures. Similarly to the case of those popular crystal structures, the occupation number for d orbitals is found to roughly determine relative energy and volume of the nonmagnetic (NM) ω structure. For the group 4 elements (Ti, Zr, and Hf), the ω structure is almost the lowest in energy among the investigated crystal structures and is also mechanically stable. The ω structure of the group 7 elements (Mn, Tc, and Re) is also mechanically stable. The ω Fe is found to exhibit a complicated magnetic state that is different from the ferromagnetic (FM) and NM ones. This magnetic state is the most favorable among the investigated magnetic states. The ω Fe in this magnetic state is also mechanically stable. Energies of binary alloys composed of the elements in the group 4 and those in the groups 5 and 6 are estimated by linear interpolation, and most of the alloys show concentration ranges where the ω structure is the lowest in energy among the investigated crystal structures.

The α → ω Transformation in Titanium-Cobalt Alloys under High-Pressure Torsion

“…The formation of ω-phase in Ti, Zr, and Hf, and their alloys have attracted much theoretical work and computer simulations [3,7,10,[55][56][57][58][59][60][61][62][63][64][65][66][67][68]. Already in 2001, Greef et al performed the first-principles electronic structure calculations and constructed the equilibrium free energies for the α-and ω-phases in Ti [55].…”

“…On the language of the algebraic geometry the transformation is effected as the transformation of the 11-atomic fragment of the {3, 4, 3} polytope into the 11-atomic fragment of the {3, 3, 5} polytope [66]. The relative stability of ω-phase in comparison with body-centered-cubic, face-centered-cubic, and hexagonal-close-packed structures has been studied in reference [67] for 27 transition elements from the viewpoint of thermodynamical and dynamical stability based on first-principles calculations. For the group 4 elements (Ti, Zr, and Hf), the ω structure is almost the lowest in energy among the investigated crystal structures and is also dynamically stable.…”

Microstructural Evolution and Carbides in Quenched Ultra-low Carbon (Fe–C) Alloys

“…The theoretical calculation results have suggested that the ω-Fe occurs as the lowest energy barrier in the γ-Fe → α-Fe pathway, however, the ω-Fe is dynamically unstable. 24,[31][32][33][34][35] When carbon atoms join in the ω-Fe structure, the ω-Fe(C) particles can be stabilized at the twinning boundaries and observed at room temperature after quenching.…”

“…Our previous experimental observations also confirmed that the metastable ω-Fe phase formed at the twining boundaries, [24][25][26] and theoretical calculation results suggested that the carbon atoms can stabilize the ω-Fe phase, thus, the metastable ω-Fe phase can be written as the ω-Fe(C) phase in carbon steels. 24,[31][32][33][34][35] A complete γ →α solid-solid transformation pathway in iron has been explained in detail in a previous publication. 33) At the beginning of the transformation, metastable ω-Fe particles will form in order to provide enough space for carbon atoms; meanwhile, the γ →α transformation happens as shown in Fig.…”

A Simple Method for Observing <i>ω</i>-Fe Electron Diffraction Spots from <112>_<i>α</i>-Fe Directions of Quenched Fe–C Twinned Martensite

“…[6][7][8][9][10] The nature of these spots at 1/3{112} and 2/3{112} have been recently explained based on a new metastable hexagonal ω -Fe phase (AB2-type, space group: p6/mmm, 3 atoms in one unit cell), which is distributed at the twin boundaries and has the crystallographic relationship with α-Fe: [18][19][20][21] Theoretical calculation results have also predicted the existence of the metastable ω -Fe phase and its relationship with the twin boundary (the twin boundary structure and the ω -Fe phase can stabilize each other energetically). [21][22][23][24][25] The ω -Fe phase has a particle-like morphology, the size is about 1-3 nm and the size distribution is very narrow. 20) In this paper, a detailed analysis of electron diffraction patterns during TEM observations has been carried out on the <110 > α-Fe zone axes of the twinned martensite formed in Fe-C binary alloys.…”