Germanene-like defects in amorphous germanium revealed by three-dimensional visualization of high-resolution pair-distribution functions

The structural description of even the most basic monatomic amorphous materials is under considerable debate. In this work, an intuitive computational technique has been developed to construct three-dimensional statistical density maps to directly visualize local atomic structure of amorphous germanium (a-Ge), enabling the interpretation of recent state-of-the-art experiments and simulations. The continuous random network (CRN) model is compared to our experimental model refined through a Reverse Monte Carlo routine. In this refinement a-Ge has two dominant structures: a fourfold coordinated tetrahedron and a buckled threefold coordinated local structure similar to silicene and germanene. These structures account for 95.7% of the total atoms in a 5:2 ratio respectively. Our method shows well defined structural ordering in the second shell of a-Ge. This novel visualization tool enables the interpretation of complex disordered materials and reveals the bimodal structures of a-Ge.

Figure 1

Normalized pair correlation functions of a-Ge. Experimental data [14] is compared to the CRN model [18] and the RMC refined data from the CRN seed [19]. The inset highlights the second coordination shell features. The refined model fits excellently with the experimental PCF, matching all the features that do not exist in the CRN model.

Figure 2

Subcoordinate set of the CRN model (top) and the refined model (bottom). Approximately 25% of the coordinate set is being displayed. The RMC model created a fairly uniform distribution showing no long-range inhomogeneity such as cracks or voids. Due to the large numbers it is difficult to find structural differences between the two models.

Figure 3

Normalized bond angle distribution for the CRN model (dashed) and the refined model (black). The CRN model is very symmetric while the refined model is broader and asymmetric with no clear underlying cause.

Figure 4

Gaussian-smoothed 3D atomic density contour plot of the 17 atom LAMs for the CRN model (top) and the refined model (bottom). Each LAM is presented as a cross-eyed stereogram for 3D visualization. Sharper contours correspond to higher densities. Animated rotations of each contour plot are shown in supplemental videos 1 and 2 respectively of the Supplemental Material [23].

Figure 5

Gaussian-smoothed 3D atomic density contour plot of 17 atom LAMs for the refined model. The top LAM shows only threefold coordinated clusters where atom 4's distance from the origin is greater than 2.7 $\AA$ and the bottom LAM shows only fourfold coordinated clusters where atom 4's distance from the origin is within 2.7 Å. Both images are presented as cross-eyed stereograms. Animated rotations of each contour plot are shown in videos 3 and 4 respectively of the Supplemental Material [23].