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By Martin J. Buerger

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8) but in directions normal to the body diagonal. The magnetic structure of the tetragonal fluoride MnF2 , in its low-temperature antiferromagnetic phase, was another study in early times (Erickson 1953). In this case the conclusion that atomic moments are aligned parallel and antiparallel to the fourfold axis stands unchallenged to the present day. Neutron powder diffraction was also used to determine magnetic structures involving ferromagnetic and ferrimagnetic ordering (Shull et al. 1951b). Ferromagnetic ordering (atomic magnetic moments in parallel alignment) in elements such as Fe and Co does not result in increased repeat distances, so the magnetic diffraction coincides with the nuclear diffraction peaks.

Fe3Al), many such solid solutions become fully ordered into new crystal structures. The peaks in the correlation function sharpen up and the uncertainty in the chemical occupancy is removed. The changes are (a) (b) c a c b a b Fig. 10 The two β-brass (CuZn) structures; (a) with Cu and Zn disordered over both the origin and unit cell body centre position (bcc) and (b) with Cu and Zn fully ordered. 30 Theory – the bare essentials illustrated in Fig. 10(b). The new crystal structure has a new diffraction pattern related to, though easily distinguished from that due to the parent phase.

But the Miller indices also define the relative spacing between the planes. That is, the spacing of (nh nk nl) is 1/n times the spacing of (hkl). We will later call this the d-spacing of (hkl) and define a reciprocal lattice made from points separated by d along directions defined by the plane normals. As with lattice directions, some planes with different Miller indices are actually identical under the symmetry operations of the lattice. This is indicated by grouping in parentheses ¯ in a cubic crystal are all equivalent { }.

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