An Incommensurately Modulated Structure of η′-Phase of Cu_3+xSi Determined by Quantitative Electron Diffraction Tomography

Abstract

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.

Low temperature formation of copper rich silicides

“…Corrêa et al [12] measured the Cu 3þx Si polymorphs by X-ray powder diffraction using copper radiation and established six modifications in this narrow compositional range, although they found all modifications having the similar unit cell. Palatinus et al [13] using their SUPERFLIP software [14] implemented in JANA2006 [15] interpreted their data on h phases having incommensurate structure. 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 However, these long period and incommensurate structures were not confirmed as separate thermodynamic phases [4].…”

Single nano crystal analysis using automated electron diffraction tomography

“…The success of ADT has encouraged other groups to develop their own systems for tomographic acquisition of electron diffraction data (Palatinus et al 2011;Gemmi et al 2012;Fan et al 2013;Cora et al 2014). A promising alternative experimental setting was proposed with the rotation electron diffraction (RED) method, where mechanical sample tilt is supplemented by beam tilt for a finer reciprocal space sampling (Zhang et al 2010).…”

“…It is anyway possible to perform ADT without any specific acquisition software, eventually collecting data in selected area electron diffraction (SAED) and using TEM imaging for crystal tracking (see, e.g., Palatinus et al 2011;Gemmi et al 2012). This procedure normally implies a longer beam exposure and eventually a more pronounced sample degradation due to beam damage.…”

A New Method Based on Electron Diffraction for Detecting Nanoparticles in Injectable Medicines

“…24 Each data collection consisted in a sequence of 61 patterns collected by rotating the goniometer in step of 1 in the range À30 to þ30 . Data analysis and unit cell determination were carried out both by the software PETS 27 and ADT3D. 20…”