Measurement of strain in nanoporous gold using nano‐beam electron diffraction
Authors: Mahr Christoph , Müller‐Caspary Knut , Grieb Tim , Krause Florian F. , Schowalter Marco , Lackmann Anastasia , Wittstock Arne , Rosenauer Andreas 
Published: December 2016

Nanoporous gold (npAu) has attracted a lot of attention during the last decade as it has interesting applications particularly in the field of catalysis [1]. It is prepared by corrosion of a suitable gold master alloy, e.g. gold/silver. The remaining material forms a sponge‐like structure built of ligaments and pores still preserving a crystalline structure over several tens of nanometres. A high surface to volume ratio, open porosity making it permeable for gases and liquids and a strongly curved ligament surface providing surface atoms of different coordination are only some properties which qualify npAu as catalytic material with well adjustable and reproducible structure.
One important structural property that is expected to have strong influence on the catalytic activity is lattice strain, because strain affects the electronic states [2]. Here we present measurements of strain in npAu. A measurement of lattice strain by means of high‐resolution TEM for example by the analysis of lattice plane distances is possible only in a very small field of view for npAu. As the positions of intensity maxima in the images depend on several experimental parameters, such as defocus, orientation, composition, lens aberrations and especially specimen thickness, maxima detection in TEM micrographs succeeds only in small parts of the sample, because thickness is varying strongly. This can be seen in Fig. 1. Close to the surface intensity maxima can be detected and thus strain can be measured, in this case tensile strain up to 5% has been found. But as the ligament gets thicker and defects become visible, contrast changes and strain analysis fails.
A method that overcomes these problems is strain analysis using nano‐beam electron diffraction (NBED) [3]. Here a focussed electron probe is scanned across the sample and at each position of the scanning beam the corresponding diffraction pattern is recorded. As distances between the non‐overlapping diffraction discs depend basically on the local lattice parameter according to Bragg's law, strain can be measured by comparing distances between diffraction discs at different positions of the scanning beam. By an analysis of distances between diffraction discs in two linearly independent directions strain as well as shear‐strain and rotation can be measured.
A further advantage of strain analysis by NBED is its large field of view, because at first sight it is limited only by the size of the scanned part of the sample. Hence strain and rotation of neighbouring ligaments in npAu can be measured. On the other hand a large field of view requires the acquisition of a large number of diffraction patterns in a short time to avoid effects of sample drift, beam induced sample damage and contamination. Here we present strain and rotation maps of npAu measured using a delay‐line detector for the acquisition of the diffraction patterns. With this detector strain maps at a scanning raster of e.g. 100x100 pixels can be recorded, allowing measurements in a field of view of several hundreds of nanometers (Fig. 2) still preserving a sampling limited spatial resolution of about 1.6 nm [4].
Furthermore we show by evaluation of simulations that two important aspects concerning the precision of the measurement have to be taken into account. As the precision of the measurement suffers from noise in the diffraction pattern, the precision degrades for shorter image integration times. On the other hand the precision can be increased using a precessing [5, 6] electron beam, as the diffraction discs are illuminated more homogeneously and hence their positions can be detected more precisely. In this way a compromise between precision and speed / size of the measurement has to be found.