Electron diffraction, and its use to study the nanoscale crystallography of materials, has had something of a renaissance in recent years. The ease with which electron diffraction patterns can now be acquired with modern instrumentation, coupled with developments in electron optical techniques, faster detectors and sensitive cameras have all contributed to microscopists looking again at what novel information electron diffraction can provide. In this presentation, we will focus on scanning electron diffraction (SED), whereby electron diffraction patterns are acquired at each real space pixel, so that following a raster scan across a region of interest, a rich 4D data set is obtained that contains a wealth of information about the phases present, their orientation, defective regions and strain. Automation of pattern acquisition and sensitive recording devices also enable very fast data collection and open new avenues for recording unique crystallographic data from highly beam-sensitive materials [1]. SED can also be applied whilst precessing the beam [2] and this combination, known, in general, as scanning precession electron diffraction (SPED), which may lead to more accurate measurements of local crystallography through access to higher order reflections and greater sensitivity to in-plane rotations, strain, etc.

Figure 1 shows an example of SED analysis, with and without precession, considering the effects of strain brought about by the addition of Sb in a GaAs nanowire, whose wire axis is parallel to the axis in the zinc blende structure ([0001] in wurtzite). Fig 1 (a) shows a series of ‘virtual dark field’ (VDF) images created by plotting the intensities of particular reflections, from an unprecessed pattern series, as a function of real space position. The contrast seen in the VDF resembles the contrast seen in conventional DF images showing changes in intensity brought about through planar bending in the doped region. In Fig 1(b) the strain components are plotted, derived from measuring the distortions of precessed diffraction patterns relative to a reference (undistorted) region well away from the Sb region. The magnitude and direction of the strain is as expected from finite element modelling.

In reality, any 2D crystallographic map such as those shown in Figure 1, is really a projection of a 3D structure. As such, in order to be sensitive to changes in strain and orientation in 3 orthogonal directions, it becomes necessary to tilt the sample and ultimately to record a full tilt series of crystallographic information so that, using tomographic methods, a complete 3D reconstruction of the local crystallography is made possible [3]. Recently, we have combined SPED and tomography to reconstruct both real space morphology and orientation maps in three dimensions, to interrogate the local crystallography of sub-volumes of material and to determine, for example in the case of a Ni-base superalloy, a novel 3D orientation relationship between a matrix phase and an embedded carbide particle, see Figure 2. To extend this to map strain, as illustrated in Fig 1 (b), into 3D is considerably more challenging as such ‘tensor tomography’ demands a new approach to recover, in general, six strain components at every voxel. We will discuss progress in this regard and show how a model-fitting approach may be the best route forward [4].

[1] E.F. Rauch and L. Dupuy, Arch. Metall. Mater. 50, 87–99 (2005).

[2] P.A. Midgley and R. Vincent, Ultramicroscopy, 53, 271–282 (1994).

[3] A.S. Eggeman, R. Krakow and P.A. Midgley, Nature Commun. 6, 7267 (2015).

[4] The authors acknowledge the many people who have contributed to this work including R. Leary. R. Krakow, J. Barnard, J.M. Thomas, A. van Helvoort, Z. Saghi, M. Benning. C. Schoenlieb, J. Ma, O. Messe, C. Rae, A. Knowles, H. Stone, A. Ferrari, S. Hodge, U. Sassi, D. de Fazio. 

The authors acknowledge funding from the Royal Society and from the ERC grant 291522-3DIMAGE. DJ acknowledges an an Associateship from the Cambridge NanoDTC.

Figures:

Figure 1. Left: (a) schematic of a GaAs nanowire, the blue region represents zinc blende GaAs, white Sb-doped zinc blende GaAs, pink wurtzite GaAs ; (b) a 111 / 0001 VDF image; (c) 224 VDF image and (d) a VDF image formed from diffuse scattering between reflections. The central region is strained through the addition of Sb. Right: Strain component and rotation maps indicating deformation near the Sb-doped region.

Figure 2. Left: 3D reconstruction of a region of a Ni -base superalloy showing matrix phase, eta phase and a cubic Nb-rich carbide. Right: Pole figures showing the correlation between planes in the matrix and carbide phases consistent with the carbide/matrix interface being parallel to the (111) plane of the carbide and the (531) plane of the matrix [3].

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