Site ordering in some σ-phase structures

Abstract

Since the first determination in 1951 of the atomic positions in the a-phase structure, many investigations have shown that the atomic sites are not randomly occupied. In particular, Bergman & Shoemaker (1954) with (Fe-Cr)a and (Fe-Mo)a, Decker, Waterstrat & Kasper (1954) with (Mn-Mo)a, and Dickins, Douglas & Taylor (1956) with (Co-Cr)a found indications that this was so. Later, neutron diffraction, applied by Kasper & Waterstrat (1956) to a study of (Fe-V)a, (Ni-V)a, and (Mn-Cr)a phases, clearly revealed the type of ordering in these particular alloys.The a-phase structure is tetragonal with 30 atoms per cell, distributed amongst one group of twofold (A), one fourfold (B) and three eightfold sites (C, D, E). If the atoms of Group VA and VIA metals making up the structure are called type X, and the 'long period' elements type Y, then it is found that type X atoms show a preference for the B sites, while type Y atoms prefer sites A and D. Sites C and E show mixed occupancy depending on the limitations set by the composition of the alloy. This scheme has recently been extended and reviewed by Spooner & Wilson (1964).In an attempt to examine further ordering in these more complex structures an X-ray and neutron-diffraction investigation was undertaken on four more of these compounds: (Mn-V), (Mn-Cr), (Co-Cr), and (Fe-Cr) a phases. Of these the first had not been investigated previously, while the (Fe-Cr) and (Co-Cr) systems had only received X-ray examination and the results could be considered of low accuracy. The (Mn-Cr) system was included as a check.All alloys were argon-arc melted, high purity materials being used. The first three alloys were crushed and, apart from slight oxidation evident in (Mn-Cr), were all single phase and used without further heat treatment. The (Fe-Cr)a alloy was annealed in vacuo at 650 °C to induce the ~--a transformation. Some ~ phase remained in the neutron diffraction sample, but this did not greatly interfere with measurements.X-ray intensities for powder samples were determined by means of a horizontal diffractometer, proportional counter and linear amplifier, while the neutron-diffraction runs were carried out at the Australian Atomic Energy Commission's Research Establishment at Lucas Heights.For each reflexion B~=0, so that the structure factors become: Fnk~ = Aafa + ABfB + Acfc + ADfD + AEfE and the problem resolves into determining the values of 25 for the five sites. Two methods were tried with the X-ray data. The first, a trial-and-error method, involved calculating all the intensities for many different values of 25, subject to the proviso that the values tried should fit the composition of the ahoy. An IBM 1620 computer was * Present Addres: School of Metallurgy, The University of New South Wales, Kensington, N.S.W., Australia.June 1965) programmed to do this, restricting itself to ten different values of 25 for each site, and printing answers only when reasonable correlation was achieved. The second method involved forming five ratios with respect to the 411 line, t...

Influence of composition and annealing conditions on the site-occupation in the σ-phase of Fe–Cr and Fe–V systems

“…populated by both kinds of alloy constituting elements. This finding agrees, at least quantitatively, with those of Yakel [6] and Algie and Hall [5], but disagrees with that of Bergman and Shoemaker [4]. The distribution of Fe and Cr atoms over the sites is neither random nor fully ordered.…”

“…According to a generalized scheme of ordering proposed by Hall and Algie [1], Fe atoms occupy only sites A and D, Cr atoms only site B while on sites C and E both kinds of atoms can be present. This disagrees with the neutron diffraction data of these authors [5], according to which all five sites are "mixed", i.e. they all host both kinds of atoms.…”

“…[6], but significantly larger than those given in Ref. [5]. According to Yakel [6], nonuniform distribution of Fe and Cr atoms follows the trend that Group VIII elements (here Fe) in binary -phases prefer lowcoordination-number sites (A and D), while Group VIb elements (here Cr) prefer high-coordination-number sites (B, C and E).…”

Site occupancy and lattice parameters in sigma-phase Co–Cr alloys

“…both Co and Cr atoms occupy them. On the other hand, following Algie & Hall (1966) all five sites are populated by both types of atoms, and the most populated sites by Co atoms are A and D. The latter agrees qualitatively with the results found for this phase in Fe-Cr and Fe-V alloy systems, where all five sites have mixed occupancies . In light of the above-described situation, studying the issue of atom distribution in the Co-Cr alloy system again was justified.…”

Ab initioanalysis of energetics of σ-phase formation in Cr-based systems

“…Using this approach, we are able to express the Gibbs energy of pure constituents in the phase, but this Gibbs energy has to be adjusted to phase equlibrium data and, therefore, its physical reliability is questionable. Further, it is known from x-ray studies 16 that the mixing of the constituents takes place at all sublattices. The CALPHAD model proposed in Ref.…”