The crystal structure of the Co–Cr σ phase

Dickins, G. J.; Douglas, A. M. B.; Taylor, W. H.

doi:10.1107/s0365110x56000826

Cited by 69 publications

(31 citation statements)

References 2 publications

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“…0.51-0.54 and c ~ 4.5-5.2/k. Early suggestions that the symmetry center might be absent were shown to be improbable for alloy a phases (Dickens, Douglas & Taylor, 1956;Forsyth & d'Alte da Veiga, 1963), but uncertainty still exists for the only known elemental a-phase, fl-uranium (Tucker & Senio, 1953;Thewlis & Steeple, 1954;Steeple & Ashworth, 1966;Donohue & Einspahr, 1971).…”

Section: (B) Structure Of a Phasesmentioning

confidence: 99%

“…Composition ranges are often broad and not centered on simple stoichiometries, so that complete atomic ordering on the sites described above is unlikely. Single-crystal and powder X-ray, and powder neutron diffraction experiments on binary alloy phases with favorable atomic scattering factor differences have shown that partial ordering does occur (Kasper & Waterstraat, 1956;Dickens, Douglas & Taylor, 1956;Forsyth & d'Alte da Veiga, 1963;Spooner & Wilson, 1964). Electron-deficient (usually larger) Group Vb or VIb atoms tend to occupy the 15-coordination sites, and electron-rich (usually smaller) Group VIIb or VIII atoms tend to occupy the 12-coordinated sites.…”

Section: (B) Structure Of a Phasesmentioning

confidence: 99%

“…It is thus an extension of the experiments in which Dickens, Douglas & Taylor (1956) used suitably chosen characteristic X-ray energies to study order in a (Cr,Co) a phase.…”

Section: Introduction (A) Scope Of Experimentsmentioning

confidence: 99%

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Atom distributions in sigma phases. I. Fe and Cr atom distributions in a binary sigma phase equilibrated at 1063, 1013 and 923 K

Yakel¹

1983

Acta Crystallogr B Struct Sci

120

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same five-dimensional space group because the electron diffraction patterns are similar to those of the 7a structure except for the difference in the wavevectors and N/M varies continuously with the chemical composition (Hirabayashi et al., 1970). This suggests that the five-dimensional space groups of these two structures are the same and a series of incommensurate structures with 3/7 < N/M < 4/9 have the same space group. These are expected to have similar structures.In order to confirm this, we calculated the Fourier amplitude of the 9a structure given by Hirabayashi et al. (1970) and confirmed that the distribution of Au atoms is well approximated by (2). This shows that their five-dimensional structures are isomorphic with each other. The Fourier amplitudes P0 and P~ of this structure are listed in Table 1. Summary and concluding remarksWe carried out a five-dimensional analysis of the 7a structure based on the theory of modulated structure analysis and obtained essentially the same result as in the more sophisticated analysis based on the usual three-dimensional symmetry. It was shown that the 9a structure has the same five-dimensional space group as the 7a structure and has a similar five-dimensional structure. The present paper demonstrates that the refinement can be carried out by using only observed reflections and parameters mainly contributing to these reflections. This saves much computing time and reduces effort in analyses of commensurate structures without accompanying higher-order harmonics. absence of a center of symmetry was found in any data set, or in any of the results obtained by least-squares refinements of parameters assuming space group P42/mnm. Average site-occupation parameters of limited precision (+5-10%) were derived for the five independent sites occupied in the a structure during the refinement based on each data set. The crystal from the alloy equilibrated at 1013 K was also studied using synchrotron-radiation (SR) Bragg diffraction at photon energies just below the Fe and Cr K absorption edges, where relative differences (Alfl/Ifl)

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Section: (B) Structure Of a Phasesmentioning

confidence: 99%

Section: (B) Structure Of a Phasesmentioning

confidence: 99%

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Atom distributions in sigma phases. I. Fe and Cr atom distributions in a binary sigma phase equilibrated at 1063, 1013 and 923 K

Yakel¹

1983

Acta Crystallogr B Struct Sci

120

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“…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.…”

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confidence: 99%

Site ordering in some σ-phase structures

Algie¹,

Hall²

1966

Acta Cryst

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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...

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“…In aCo2Mo3, the parameter z4 which is 0.2520 in Nb2A1 was found to be 0-2500, as in aCoCr (Dickins, Douglas & Taylor, 1956). Calculated interatomic distances with an artificial z4=0.2520 show that the distances from J atoms to others are not significantly different from those listed in Table 3, as the differences are of the same order as the standard deviations, nor can any trend in the average coordination distances be detected, even within the standard deviation, when z4 is thus varied.…”

Section: Discussionmentioning

confidence: 99%