Atomic scale dynamics of ultrasmall germanium clusters

Abstract

Starting from the gas phase, small clusters can be produced and deposited with huge flexibility with regard to composition, materials choice and cluster size. Despite many advances in experimental characterization, a detailed morphology of such clusters is still lacking. Here we present an atomic scale observation as well as the dynamical behaviour of ultrasmall germanium clusters. Using quantitative scanning transmission electron microscopy in combination with ab initio calculations, we are able to characterize the transition between different equilibrium geometries of a germanium cluster consisting of less than 25 atoms. Seven-membered rings, trigonal prisms and some smaller subunits are identified as possible building blocks that stabilize the structure.

Figure 1. Sequence of HAADF-STEM images of a Ge cluster.

(a–h) Each subsequent image is acquired with a frame time of 0.1 s. It can be seen that a 2D-like configuration transforms into a 3D configuration. The scale bar corresponds to 0.5 nm.

Figure 2. 3D models derived from 2D experimental images.

(a–c) Parametric models refined on the basis of the experimental Fig. 1a,d,h. (d–f) Counting results in which green, red and blue dots correspond to 1, 2 and 3 atoms, respectively. (g–l) Outcome of the ab initio calculations shown along two different viewing directions.

Figure 3. Two examples of slightly varying starting configurations resulting in significantly altered relaxed structures.

(a,b) The left panels represent the top view of a model that corresponds to the experimental picture. The panels in the middle give two different configurations that are indistinguishable if viewed from the top. After relaxation with density functional theory (panels on the right), only one of the two possibilities is still compatible with the experimental image, as can be seen in Figure 2.

Figure 4. Quantitative analysis of a more elongated prolate configuration.

(a) Refined parametric model, peaked at the estimated atomic positions. Green and red dots correspond to 1 atom and 2 atoms, respectively. (b) Outcome of the ab initio calculation. It can be seen that a seven-membered ring is present. In addition, smaller fragments, consisting of 3–4 atoms are found to correspond well to the predicted ground states of trimers and tetramers.

Figure 5. Size distribution of the clusters.

(a) Time-of-flight mass abundance spectrum of Ge cluster cations. Of interest are the strong size-dependent features reflecting enhanced stability for a number of sizes in the 6 to 20 atoms range. (b) Histogram illustrating the size distribution of the investigated clusters as deduced from the TEM images. It must be noted that, although this histogram contains only clusters with a diameter <2 nm, larger clusters (with sizes up to 10 nm) also have been observed.

Figure 6. Histogram of the totally scattered intensities.

These intensities are determined from the estimated Gaussian peaks in Fig. 2a–c. The solid curve shows the estimated mixture model; the individual components are shown as dashed curves.