International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 2.3, p. 70
Section 2.3.2.6. Structure factors^{a}School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia |
The locations of the Bragg peaks for neutrons are calculated as they are for X-rays^{7} (Section 1.1.2 ), and the intensities of these peaks are determined by a structure factor, which in the nuclear case is [cf. Chapter 1.1, equation (1.1.56) ]where b_{i} here denotes the coherent scattering length, T_{i} has been introduced to represent the effect of atomic displacements (thermal or otherwise, see Section 2.4.1 in Kisi & Howard, 2008), h is the scattering vector for the hkl reflection, and the vectors u_{i} represent the positions of the m atoms in the unit cell.
For coherent magnetic scattering, the structure factor readswhere p_{i} is the magnetic scattering length. The vector q_{i} is the `magnetic interaction vector' and is defined by a triple vector product (Section 2.3.4 in Kisi & Howard, 2008), and has modulus sin α as already mentioned. In this case the sum needs to be taken over the magnetic atoms only.
As expected by analogy with the X-ray case, the intensity of purely nuclear scattering is proportional to the square of the modulus of the structure factor . In the simplest case of a collinear magnetic structure and an unpolarized incident neutron beam, the intensity contributed by the magnetic scattering is proportional to , and the nuclear and magnetic contributions are additive.
References
Kisi, E. H. & Howard, C. J. (2008). Applications of Neutron Powder Diffraction. Oxford University Press.Google Scholar