Shock waves in complex binary solids: Cubic Laves crystals, quasicrystals, and amorphous solids

Shock waves have been simulated by molecular dynamics in the cubic Laves phase C15, in related Frank-Kasper-type (AlCu)Li quasicrystals, and in an amorphous solid of the same composition and potential parameters. The goal of this study was to generate shock waves in periodic and aperiodic structures and to compare their behavior. The expectation was that new types of defects would show up in aperiodic materials. Three regimes are observed in the Laves phase: at low shock wave intensity the system reacts elastically, at high intensities it turns disordered. In the intermediate region the velocity of the elastic wave saturates and an additional plastic wave appears. Extended defects are created which form a network of walls of finite width. The crystallites in between are rotated by the shock wave. If the samples are quenched a polycrystalline phase is obtained. The size of the grains decreases with increasing shock wave intensity until complete fragmentation occurs in the third regime. The behavior of the quasicrystal models is similar, except that there is a continuous transition from a quasielastic behavior to the plastic regime. Ring processes are observed which break up into open paths when the shock wave energy grows. The transition to a complete destruction of the structure is continuous. In the amorphous solid a linear $u_s-u_p$ relation is found over the whole range of piston velocities. Two regimes are present, with unsteady plastic waves at weak shock strengths and steady waves in the range coinciding with the upper regime in the ordered structures.

Figure 1

Oblate and prolate rhombohedron. Light gray: small atoms; dark gray: large atoms. Left: the × marks the atom around which ten oblate rhombohedra fit together. The atoms marked with the + form a puckered decagon, around which the ring processes occur. Right: the atoms marked with o denote the intersection points of the ⟨100⟩ direction.

Figure 2

The rhombic dodecahedron. The atom marked with an × and its symmetry-equivalent copies are the primary sites of flips. The large light gray atoms are also very mobile. The atoms marked with + and o are secondary sites for diffusion.

Figure 3

Shear pressure $S$ of three samples representative for the three regimes.

Figure 4

Uniaxial pressure $P_{xx}$ of three samples typical for the three regimes.

Figure 5

Shock vs piston velocity. At low piston velocity (quasi)elastic behavior is observed. Between $u_p∕c_l=0.3$ and 0.6 approximately a crossover to the plastic shock wave and finally the change of slope to a materials-independent value is found. The velocities $u_p$ and $u_s$ are scaled by the velocity of sound $c_l$ valid for the different directions.

Figure 6

Orientation dependence of the shock vs piston velocities. The quasicrystal curves are identical if errors are taken into account. Therefore they are not marked individually. For the Laves crystal, the velocities along the fourfold direction differ from the other orientations which on their part are again quite similar. The velocities $u_p$ and $u_s$ are scaled by the velocity of sound $c_l$ valid for the different directions.

Figure 7

In situ displacement field of the Laves crystal at $u_p∕c_l=0.45$. The large antiparallel arrows indicate slip planes. The ring of large arrows marks a rotation axis. Pictures of the quasicrystals look similar. The numbers at the figure represent the size in nearest-neighbor distances $a$.

Figure 8

Displacement field of the Laves crystal at $u_p∕c_l=0.45$ after quenching. Shown is nearly the same part of the sample as in Fig. 7. Pictures of the quasicrystals look similar. The numbers at the figure represent the size in nearest-neighbor distances $a$.

Figure 9

Slice through the whole Laves crystal after quenching $(260\times 61a^2)$. The various textures (dotted and striped) are generated by displacements of parts of the sample with respect to each other and represent the newly created grains.

Figure 10

Sequence of shocked samples of the TI model. A third of the width and a fifth of the length has been cut out around the center of the simulation cell. The boxes are displayed to enhance the three-dimensional impression. The central squares show the starting place of the shock waves. The arrows indicate the path of the shock fronts which have left the boxes already at the recording time of the pictures. The thick black lines illustrate the local rotation axis. In the first two pictures the spheres represent the jumping atoms directly, while in the last two pictures they are overshadowed by clouds of atoms with large displacements.

Figure 11

Shock wave in the BI model. Half the width and a third of the length has been cut out of the simulation cell. The box is displayed to enhance the three-dimensional impression. The square within the box represents the starting place of the shock waves and the arrows indicate the path of the shock fronts. In the instant represented in the picture the left-moving wave is at the left end of the box, whereas the right-moving wave has already left the box. The dots indicate atoms with large displacements. In the left half of the box many points disappear when the shock front proceeds further which emphasizes the transient character of the large displacements. Only a few singular points are left over like in the region where the shock waves started. They mark the sites where atoms have jumped to alternate positions.

Figure 12

Shock vs piston velocity for the amorphous solid (dotted curve). The fcc curve (full line) is from Holian and Lomdahl (Ref. 16).