Acta Crystallographica Section A

Foundations of Crystallography

Volume 69, Part 5 (September 2013)

research papers

Acta Cryst. (2013). A69, 475-482    [ doi:10.1107/S0108767313018138 ]

Diffuse scattering intensity near the Bragg reflection in a (para)magnetic bulk face-centred cubic Ni3Fe-type permalloy

S. M. Bokoch, V. A. Tatarenko and I. V. Vernyhora

Abstract: Within the scope of the self-consistent-field (SCF) and mean-SCF approximations, the Matsubara-Kanzaki-Krivoglaz lattice-statics method as well as the Krivoglaz-Clapp-Moss approach, the kinematic diffuse scattering intensities near the Bragg reflection caused by the atomic short-range order (taking into account the long-range magnetic order) in a (para)magnetic bulk face-centred cubic Ni-Fe alloy are investigated in detail. The reciprocal-space symmetry analysis of both the `direct' `electrochemical' and short-range `exchange' interactions as well as the long-range `indirect' `strain-induced' contribution to the Fourier components of interatomic `mixing' energies and the diffuse scattering intensity contributions near the `fundamental' [Gamma](000)-point is carried out. In the [Gamma]-point vicinity, the rigorous symmetry regularities for all the energy and diffuse scattering intensity contributions are formulated. As revealed, the short-range order (SRO) diffuse scattering intensity behaves conditionally as I_{{\rm SRO}}({\bf k}) \propto k^{2} for {\bf k} \rightarrow {\bf 0} from all the reciprocal-space directions, which is in contrast to the conventional Huang diffuse scattering intensity conditionally definable as I_{{\rm Huang}}({\bf k}) \propto k^{-2} for {\bf k} \rightarrow {\bf 0}. Special attention is paid to the analytic (i.e. azimuthal) and nonanalytic (i.e. first-kind-jump-discontinuous `radial') behaviours of the Fourier components of interatomic `mixing' energies or the SRO intensities near and at the [Gamma](000)-point.

Keywords: interatomic interactions; magnetic impurity interactions; short-range order; diffuse scattering; statistical thermodynamics.

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