An incommensurately modulated structure of η'-phase of Cu(3+x)Si determined by quantitative electron diffraction tomography.

The diffraction data of η'-Cu(3+x)(Si,Ge) were collected by 3D quantitative electron diffraction tomography on a submicrometer-sized sample, and the structure was solved by the charge-flipping algorithm in superspace. It is shown that the structure is trigonal, and it is incommensurately modulated with two modulation vectors q(1) = (α, α, 1/3) and q(2) = (-2α, α, 1/3), superspace group P31m(α, α, 1/3)000(-2α, α, 1/3)000. The modulation functions of some atoms are very complicated and reach amplitudes comparable with the unit cell dimensions. The modulated structure can be described as sheets of Cu clusters separated by honeycomb layers of mixed Si/Ge positions. The shape of the Cu clusters in the sheets strongly varies with the modulation phase, and the predominant form is an icosahedron. The striving of the Cu layers to form icosahedral clusters is deemed to be the main driving force of the modulation. The combination of methods used in this work can be applied to other structures that are difficult to crystallize in large crystals and opens new perspectives, especially for investigations of aperiodic or otherwise complex metallic alloys.