A refinement of the parameters of α-manganese

Gazzara, Charles P.; Middleton, R.; Weiss, R. J.; Hall, E. O.

doi:10.1107/s0365110x67001689

Cited by 55 publications

(21 citation statements)

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“…We found no evidence of a stable tetragonally distorted lattice, unlike Hobbs et al [48,49], although their calculations only show a very marginal effect. The energy difference between the nm and afm states of α-Mn, that we measure to be 28 meV/atom, does, interestingly, agree well with Hobbs et al The internal coordinates show a high degree of consistency both with the nm state from this work and with other theoretical [48,49] and experimental [47,50,55,59] work, although this is, perhaps, not surprising given their relative invariance as a function of temperature above and below the magnetic transition [55]. For the magnetic structure we find large moments on MnI and MnII atoms, that agree qualitatively with the (near-)collinear moments found in other work [49,55], and smaller moments on MnIII and MnIV atoms, consistent with the majority of previous studies (see Hobbs et al [49] and references therein).…”

Section: Appendix A: Elemental Data and Ground-state Crystal Structursupporting

confidence: 90%

“…With these assumptions there are still 16 distinct relative orientations of moments between the different atomic types for the tetragonal structure. Calculations were initialized in all of these distinct magnetic states with either cubic [59] or tetragonal [49,55] lattice parameters. Despite many distinct magnetic states being initially stable only one stable afm structure was found after full relaxation (see Table VI).…”

Section: Appendix A: Elemental Data and Ground-state Crystal Structurmentioning

confidence: 99%

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Transition metal solute interactions with point defects in fcc iron from first principles

2015

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We present a comprehensive set of first-principles electronic structure calculations of the properties of substitutional transition metal solutes and point defects in austenite (face-centered cubic, paramagnetic Fe). Clear trends were observed in these quantities across the transition metal series, with solute-defect interactions strongly related to atomic size, and only weakly related to more subtle details of magnetic or electronic structure. Oversized solutes act as strong traps for both vacancy and self-interstitial defects and as nucleation sites for the development of protovoids and small self-interstitial loops. The consequent reduction in defect mobility and net defect concentrations in the matrix explains the observation of reduced swelling and radiation-induced segregation. Our analysis of vacancy-mediated solute diffusion demonstrates that below about 400 K Ni and Co will be dragged by vacancies and their concentrations should be enhanced at defect sinks. Cr and Cu show opposite behavior and are depleted at defect sinks. The stable configuration of some oversized solutes is neither interstitial nor substitutional; rather they occupy two adjacent lattice sites. The diffusion of these solutes proceeds by a novel mechanism, which has important implications for the nucleation and growth of complex oxide nanoparticles contained in oxide dispersion strengthened steels. Interstitial-mediated solute diffusion is negligible for all except the magnetic solutes (Cr, Mn, Co, and Ni). Our results are consistent across several antiferromagnetic states and surprising qualitative similarities with ferromagnetic (body-centered cubic) Fe were observed; this implies that our conclusions will be valid for paramagnetic iron.

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Section: Appendix A: Elemental Data and Ground-state Crystal Structursupporting

confidence: 90%

Section: Appendix A: Elemental Data and Ground-state Crystal Structurmentioning

confidence: 99%

Transition metal solute interactions with point defects in fcc iron from first principles

2015

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“…It should also be mentioned that Bijvoet differences in such structures had been suggested for electron diffraction (Parthasarathy, 1961), through arguments based on the dynamical theory.…”

Section: F(hkl)+= S (F + Af" + Iaf") (Aj+ Ibj)mentioning

confidence: 98%

“…These proposals seem opportune now, since accurate refinements of such structures have recently been carried out: e-manganese (Gazzara, Middleton, Weiss & Hall, 1967) and hexagonal selenium (Cherin & Unger, 1966). It should also be mentioned that Bijvoet differences in such structures had been suggested for electron diffraction (Parthasarathy, 1961), through arguments based on the dynamical theory.…”

Section: F(hkl)+= S (F + Af" + Iaf") (Aj+ Ibj)mentioning

confidence: 99%

Possibility of `Bijvoet differences' in the non-centrosymmetric structures of the elements

Chandrasekaran¹

1968

Acta Cryst Sect A

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SHORT COMMUNICATIONSThis furnishes a2 ab cos y ac cos fl (a.bxe) 2=V 2= abcosy b 2 bccosct ac cos P bc cos ct c2 = a2bEc211 q-2 cos ~ cos fl cos y-cos 2 --COS 2 #--COS 2 y].More details are contained in a text by Buerger (1942, pp. 349-351). The corresponding expression for V .2 may be obtained in the same way. Application of (7) to the evaluation of (a. b x c) (a*. b* x c*) yields 1 0 0 0 1 0 0 0 1 and leads at once to the identity V V* = 1.An expression for V that contains both direct and reciprocal lattice quantities may be obtained by starting with a= Ib* x c*I/V* =b'c* sin ~*/V*.When b* and c* are expressed by direct lattice quantities this becomes a = (c a sin B/V) (a b sin y/V) (sin ~t*/V*).Solving for V, and using V V* = 1 leads to the final result,V=a b c sin ~t* sin B sin y.which remains valid when the star is switched to other angles, as in V=a b c sin ~ sinB* sin y.Therefore also, (sin ~/sin c~*) = (sin B/sin P*) = (sin y/sin y*),which is the equivalent of the sine law of spherical trigonometry:sin r/sin R = sin s/sin S= sin t/sin T.Relationships reciprocal to (11) and (12), of the form V*=a* b* c* sin ~ sin/~* sin y* (15) are, of course, correct also. Another expression for V follows from solving a*= b c sin ~/V for V:V= b c sin o~/a*.Cyclic variation yields two additional formulas, and analogous expressions exist for V*. Combining (12) and (16) yields a a* sin fl* sin 9,= 1,which invites comparison with a. a*= 1, that is, a a* cos (a, a*)= 1 .(18) It follows that cos (a, a*) = sin ~* sin y = sin B sin y*,where (13) has also been used. The argument of the cosine is the angle between the zone direction [100] and the normal to the (100) plane. An expression for cos (a, a*) containing direct lattice quantities only follows from solving equation (12) Expressions analogous to (19), (20), and (21) It is proposed that it would be interesting to look for and measure Bijvoet differences in the noncentrosymmetric structures of the elements like ~t-manganese and the hexagonal, isomorphous tellurium and selenium. This would check directly the validity of some of the usual assumptions regarding temperature factors in X-ray diffraction.The purpose of this communication is to point out the possibility of directly checking the usual assumptions on the temperature factors in X-ray diffraction in cases where the anomalous scattering is appreciable, through experiments on the non-centrosymmetric structures of some elements.Considering such a structure with n atoms in the unit cell, the structure factors of the pair of reflexions, hkl and hk[, would be n F(hkl)+= .S (f + Af" + iAf") (Aj+ iBj)i (temperature factor)j, (1)

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“…The MgCu 2 [2] structure type is found in 807 compounds. In descending order of frequency are then the Cr 3 Si [3] (260 compounds), Th 6 Mn 23 [4] (204 compounds), NaZn 13 [5] (91 compounds), Be 5 Au [6] (75 compounds), a-Mn [7] (73 compounds), Ti 2 Ni [8] (62 compounds), b-Mn [9] (41 compounds), Cu 5 Zn 8 [10] (39 compounds), Sm 11 Cd 45 [11] (19 compounds), and YCd 6 [12] (19 compounds) structures.…”

Section: Introductionmentioning

confidence: 99%

Laves Phases, γ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal

Berger

Johnson

Nebgen

et al. 2008

Chemistry A European J

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Of the most common cubic intermetallic structure types, several (MgCu(2), Cu(5)Zn(8), Ti(2)Ni, and alpha-Mn) have superstructures with unusual symmetry properties. These superstructures (Be(5)Au, Li(21)Si(5), Sm(11)Cd(45), and Mg(44)Ir(7)) have the unusual property of pairs of perpendicular pseudo fivefold axes, most apparent in their X-ray diffraction patterns. The current work shows that an 8D to 3D projection method cleanly describes most (and in one case, all) of the atomic positions in the four superstructures mentioned above. This type of projection, which maps the E(8) lattice (a mathematically simple 8D crystal) into 3D space, combines the desired higher dimensional point group's perpendicular fivefold rotations with 3D translational symmetry-exactly what we see in the experimental crystal structures. The projection method successfully accounts for all heavy atom positions in the four superstructures, and at least 60-70 % of the light atom positions. The results suggest that all of these structures, previously known to be connected only by qualitative similarities in their atomic "clusters", are approximants of a single, as-yet unknown, class of quasicrystal.

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A refinement of the parameters of α-manganese

Cited by 55 publications

References 4 publications

Transition metal solute interactions with point defects in fcc iron from first principles

Transition metal solute interactions with point defects in fcc iron from first principles

Possibility of `Bijvoet differences' in the non-centrosymmetric structures of the elements

Laves Phases, γ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal

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