Today’s featured paper is a PRB by Lorenz-M. Stadler et al. on coherent x-ray imaging of antiphase domain boundaries in FeAl alloy.
The basic idea of antiphase boundary is simple, and illustrated for a binary 2D alloy on the diagram to the left. In the checkerboard pattern of two kinds of atoms the antiphase domain is created when the black-white-black-white-black order is skipped by a “phase shift” of pi, resulting in “white-black-black-white-…” after which regular order is restored again.
In three dimensions the antiphase domain can be a little more complicated to visualize, but the basic idea is precisely the same.
The figure on the right attempts to show what the antiphase domain boundary (a 2D boundary across which the A-B-A-B order undergoes a phase “skip” to create antiphase domain) in three dimensions. This domain is as if one shifted a certain region by (1/2, 1/2, 1/2) vector. The tricky thing in studying these type of antiphase domains is that nothing out of ordinary happens in terms of crystalline structure – if the two types of atoms have no contrast, the crystal looks ideal, with no grain boundary or other type of defect to speak of.
X-rays often allow to create some contrast between different types of atomic species, but individual domain walls are still very difficult to detect. Microscopy methods using microfocused x-ray beams are not terribly sensitive to the presence of the antiphase domain walls, since both domains have similar scattering contributions.
One way to go around it is to make use of the fact that if the beam straddles the domain wall 50-50, and the x-ray beam is coherent, the contributions from two domains will be out of phase and cancel each other out. This is a similar approach to the one used by Paul Fenter in a recent Nature Physics paper (more on this later).
In many cases, the antiphase boundaries are bunched pretty close together (meaning the typical size of anti-phase domain is smaller than the beam size). However, if the x-ray beam is coherent, the domains will contribute to the Bragg peak with phases of 0 or pi, depending on whether the domain is in “phase” or “antiphase” with respect to some arbitrary checkerboard pattern in 3D. The result is a “speckle”, with the number of first-order speckles roughly equal to the number of domains.
Speckle images in reciprocal space can be reconstructed using phase-retrieval methods to get information on the precise location of antiphase boundaries and their shapes in such binary alloys – in this case FeAl.
The power of this technique is that one gets information about antiphase domain boundaries deep within the sample, and in principle one could get a full 3D information as well. Electron microscopy is a key competitor to x-ray based techniques, but because of stronger electron-matter interactions, typically near-surface region dominates the signal, making detection of sub-surface phase defects very difficult. The contrast between different types of atoms – in this case Fe and Al – is very tiny as well. And techniques like TEM require sectioning of the sample, which is likely to completely modify the topology of the surface, introducing defects that did not exist in the “bulk” of as-formed material.
Simply outstanding work, as usual, here is some background references that provide more information on the work done by the same first author:
Detrending analysis of XPCS data, Lorenz-M. Stadler et al., Phys. Rev. E 74, 041107 (2006)
Dynamics of antiphase domains in CoGa alloys, Lorenz-M. Stadler, Phys. Rev. B 69, 224301 (2004)
Lorenz-M. Stadler, PhD Thesis, Universitat Wien (2005) (Chapter 7 contains the work described here)