Dynamic fracture of icosahedral model quasicrystals: A molecular dynamics study

Ebert et al. [Phys. Rev. Lett. 77, 3827 (1996)] have fractured icosahedral $\mathrm{Al}-\mathrm{Mn}-\mathrm{Pd}$ single crystals in ultrahigh vacuum and have investigated the cleavage planes in situ by scanning tunneling microscopy (STM). Globular patterns in the STM images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large-scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode-I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high-symmetry axes. From detailed analyses of the fractured samples we conclude that both the plane structure and the clusters strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.

Figure 1

Tiles of the icosahedral binary model decorated with two types of atoms and the Bergman-type cluster. Top: prolate rhombohedron (left) and oblate rhombohedron (right). Bottom: rhombic dodecahedron (left) and the 45 atoms building the Bergman-type cluster (right) inherent in the model quasicrystal. Small gray and large black spheres denote $A$ and $B$ atoms, respectively.

Figure 2

Surface energy of cleavage planes perpendicular to twofold and fivefold axes.

Figure 3

Kinetic energy density. Sound waves emitted by the propagating crack and the elliptical region without damping are clearly visible. See online movie (Ref. 35).

Figure 4

Snapshot of a simulation with some $4\times {10}^6$ atoms. Only atoms with low coordination number are displayed. See online movie (Ref. 36).

Figure 5

Bergman-type cluster cut by a flat surface.

Figure 6

Visualization of the clusters cut by the dynamic crack. Midpoints of clusters are indicated as black dots; the clusters are idealized as spheres. The crack propagated from the left to the right. The upper and lower fracture surfaces are projected onto an $x\text{−}z$ plane.

Figure 7

Average crack velocities for different loads and orientations.

Figure 8

Height profiles of sections of the simulated fracture surfaces. Load: $k=1.3$, orientation $2_2$ (top), $5_2$ (middle), $5_{\mathrm{p}2}$ (bottom). The height increases from black $(⩽-2r_0)$ to white $(⩾+2r_0)$. The scanning sphere has the same size as an atom of type $B$.

Figure 9

Clusters cut by the fracture surfaces. The visualization technique is described in Sec. 3C and Fig. 6. Load: $k=1.3$. Orientation: $5_2$.

Figure 10

Surface energy and density of cluster centers for the orientation $2_2$. The corresponding fracture surface is shown in Fig. 8, top.

Figure 11

Surface energy and density of cluster centers for the orientation $5_2$. The corresponding fracture surface is shown in Fig. 8, middle.

Figure 12

Fracture surfaces perpendicular to twofold axes. In the left picture (simulation) the atomically sharp seed crack can be seen on the top, whereas below this area the simulated fracture surface appears. The orientation of the sample is $2_2$; the load was $k=1.3$. The surface was geometrically scanned with an atom of type $B$. Thus atomic resolution is achieved. The right picture [experiment, adopted from Ebert et al. (Ref. 43)] shows an STM image of icosahedral $\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$ cleaved in ultrahigh vacuum. As $20r_0$ is approximately $5\mathrm{nm}$ the surfaces are displayed at the same length scale.