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. 3.6, p. 296
Section 3.6.2.6.8. Antiphase domain boundaries^{a}Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy 
In the diffraction pattern of an ordered alloy, a dissimilar broadening can often be observed for structure and superstructure peaks (with the former being present in both the ordered and disordered states). The superstructure peaks, in fact, bear microstructural information on the interface between the ordered regions in the material: broadening occurs when domains meet out of phase, creating an antiphase domain boundary (APB or APDB). A general formula for APDBrelated broadening does not exist: for a given ordered structure, the Fourier coefficients correspond to the normalized value of , where F(0) is the structure factor of a cell positioned at L = 0 and is the complex conjugate of the structure factor of a cell at a distance L along the direction [hkl]. Being the result of a combination of probabilities, the peak is always expected to be Lorentzian.
Explicit formulae have been derived for the Cu_{3}Au ordered alloy (L1_{2} phase; Wilson, 1943; Wilson & Zsoldos, 1966; Scardi & Leoni, 2005). Several types of boundaries can form, depending on the way that the domains meet: the broadening depends both on the boundary plane and on the local arrangement of Au atoms leading to conservative (no Au atoms in contact) or nonconservative (Au atoms in contact) boundaries. By arranging the indices in such a way that h ≥ k ≥ l and that l is always the unpaired index, the broadening of the superstructure reflections can be described as (Scardi & Leoni, 2005)In this formula, δ = γ_{APDB}/a_{0} is the probability of occurrence of an APDB, a_{0} is the unitcell parameter and f(h, k, l) is a function of hkl defined in Table 3.6.2, obtained from the results of Wilson (1943) and Wilson & Zsoldos (1966).

The average distance between two APDBs is given by 1/δ. For a random distribution of faults, the broadening is Lorentzian and A^{APDB} = exp(−4Lδ/3).
References
Scardi, P. & Leoni, M. (2005). Diffraction wholepattern modelling study of antiphase domains in Cu_{3}Au. Acta Mater. 53, 5229–5239.Google ScholarWilson, A. J. C. (1943). The reflexion of Xrays from the `antiphase nuclei' of AuCu_{3}. Proc. R. Soc. Lond. Ser. A, 181, 360–368.Google Scholar
Wilson, A. J. C. & Zsoldos, L. (1966). The reflexion of Xrays from the `antiphase nuclei' of AuCu_{3}. II. Proc. R. Soc. Lond. Ser. A, 290, 508–514.Google Scholar