(a) Configuration of the corundum lattice, with white circles representing oxygen atoms and solid ones representing aluminum atoms. (b) An idealized view of the basal plane with three sublattice layers, where the oxygen atoms (white circles) at the vertices of white triangles belong to anion sublattice and the other oxygen atoms belong to anion sublattice . The aluminum atoms (solid circles) belonging to sublattice are located in the middle of two anion sublattice planes.
The schematics of the simulation setup. A reinforced alumina projectile impacts on an alumina single crystal’s (0001) surface at . The simulation embodies atoms in total. The inner planes and are two major planes where deformations are visualized.
Shock wave front position in the direction and penetration depth as functions of time. For the wave front position curve, the portion with a negative slope for corresponds to the rarefaction wave.
The pressure snapshots of the substrate under the basal surface where the impact was initiated. From (a) to (b), the symmetry of the shock wave front undergoes a gradual change from threefold to sixfold. This is due to the anisotropies of alumina lattice.
Schematic of the symmetry transition of wave front’s cross section on basal planes. Point source lying in plane generates wave (solid curves) that travels at different speeds along crystalline orientations. The cross sections of the wave front on planes are sketched at and . Dashed lines denote the wave front in a previous moment.
Simulation on bulk alumina to verify the wave propagation symmetry. A small core in the center produces wave by oscillating in the  direction. All four pictures shown here are pressure profiles on basal planes, where pressure gradients are visualized using grayscale. (a) The pressure snapshot on the basal plane in which the core initially lies at . (b) The pressure snapshot on the basal plane above (in the direction) the oscillating core at . (c) The pressure snapshot on the basal plane below (in the direction) the oscillating core at . (d) The pressure snapshot on the same plane as in (c) at .
Substrate pressure at viewed normal to the impact velocity, with its center exposed through a quarter cut. Planes and correspond to inner surfaces and in Fig. 2. Four sample cubes P1–P4 of size are chosen with local density, temperature, and pressure measurements. For each of the four regions, local pair distribution function and bond angle distribution are compared to those of the uniform alumina samples prepared with the same densities and temperatures through either slow heating from crystal or fast quenching from molten state.
The pair correlation function and bond angle distribution of, from top to bottom, respectively, P4, replicated P4 sample through slow heating , and replicated P4 sample through fast quenching . All three samples share common features.
The pair correlation function and bond angle distribution of, from top to bottom, respectively, P3, replicated P3 sample through slow heating , and replicated P3 sample through fast quenching . There are similarities between P3 and but neither resembles .
Plots of pair correlation function and bond angle distribution of P1 and P2. The well-isolated peaks imply that they are both in crystalline form.
The prism plane (plane in Fig. 2) view of the and Burgers vectors of pyramidal dislocations. Here the large spheres represent oxygen atoms and the small ones are aluminum atoms. The dashed line denotes the lattice plane that has cation holes only, along which the activation energy of pyramidal dislocation motion is lower.
Snapshots of pyramidal slips under high shear stress induced by penetration and expansion of the projectile. (a) Basal plane cross section of the whole substrate at and . Atoms are color coded using coordination numbers. Streaks of pyramidal slips form a hexagramlike pattern. (b) A close-up of the boxed region color coded by atomic species ( means coordination number). Two of the pyramidal slips are circled in cyan and their orientations labeled. Mismatch of atomic layers across these slips arises from the relative sliding between the slip surfaces.
(a) Coordination number snapshot of center plane (plane in Fig. 2) at , where blue atoms have normal coordination number. Pyramidal slips along run parallel with a spacing of . (b) An up-close view of the circled region in (a) using ball-and-stick representation, rotated to align with the prism plane. The circled green stripe in (a) turns out to be a thin stripe of amorphized material along , which intersects the prism plane along . These are atoms with abnormal coordinates resulting from the slip.
direction view of the corundum lattice’s prism plane. (a) The perfect corundum lattice. (b) A case where severe stacking problem happens when the upper half is sheared by relative to the bottom, where SP refers to slip plane. (c) The case when the upper half is sheared by relative to the bottom and there is no stacking problem caused by the alumina atom pairs. (d) The relaxed crystal structure of (c) which creates a SF and local twinning region between the two planes.
The generalized SF energy along alumina’s basal plane, where results of vertically relaxed system are compared with no relaxation.
The coordination number snapshot on the center prism plane (plane in Fig. 2) at . Basal slip is triggered by horizontal expansion of the projectile and bending of basal layers, causing shear along basal planes. Basal twin is also present in this view, appearing on consecutive crystalline layers.
(a) Results of the ring analysis in a basal slice in front of the projectile tip at . One of the twins along (white arrows), s1, is on the outer boundary of a severely deformed region. It is also shown in (b), the center plane (plane in Fig. 2) snapshot where atoms are color coded by their coordination numbers. Here the projectile atoms are colored in white. (c) A close-up image of (b) showing details of s1, with the twin planes highlighted using yellow lines, and the twin in between is contrasted against normal lattice using thick white line segments. The positions of the dislocations are determined by the misalignment of lattice planes, and extra half planes are singled out with thin white lines. For clarity only aluminum atoms are visualized here. (d) The twin length (left) and the number of defect atoms and twin atoms (right) in a planar twin segment as a function of time. It shows the correlation between twin size and the number of defects.
(a) Prism plane (plane in Fig. 2) view of one rhombohedral twin using ball-and-stick representation. The red spheres are oxygen atoms and blue ones aluminum atoms. Two mirror planes are highlighted using yellow lines, and twinned lattice planes using white lines. (b) A thin slice of the prism plane (plane in Fig. 2) showing the twinning region. The atoms are color coded by deviation in the number of six-member rings from a perfect crystal, and only deviant atoms are shown. The streaks on the right are twins along planes, the same orientation as the one in (a). Those on the left running perpendicular are rhombohedral twins along and planes, which intersect the prism plane along . However, their Burgers vector is not along .
Basal snapshots showing symmetry of rhombohedral twin, which are effectively identified using ring analysis. (a) A full-size basal plane cut in front of the impact initiation site at . Atoms are color coded by deviation in the number of six-member rings from perfect crystalline atoms (blue) using the gradient bar above. (b) The same plane color coded by deviation in coordination number from perfect crystalline atoms (blue). The three fold structure of rhombohedral twins (parallel streaks of white line segments) in (a) is invisible here.
Basal plane view of the entire substrate in front of the impact point (a) and prism plane (plane in Fig. 2) view (b) of some structural change regions by visualizing the deviation in coordination number at when stresses shear the center of the substrate in the direction due to the unloading. All the aluminum atoms in that region transform from six coordinated to five coordinated. Two-thirds of the oxygen atoms transform from four coordinated to three coordinated.
Ball-and-stick presentations of atoms around the arrow head in Fig. 20(b) at different time frames, viewed perpendicular to the same prism plane (plane in Fig. 2). Here the red spheres represent oxygen atoms and the blue ones aluminum atoms. The structural change appears due to shear in the prism plane and fully recovers when the shear stresses are relieved .
(a) Prism plane (plane in Fig. 2) view using coordination numbers at , showing the major cracks at the early stage of unloading. The white vertical line on the left denotes the centerline of the substrate with part of plane shown on the other side. The long crack next to it initiates from the amorphized stripe where rhombohedral twins intersect. The parallel streaks on the right side are twins along . (b) A blownup of the boxed region in (a). It demonstrates that cracks initiate around the region where twins along cross slip to through basal deformations.
(a) Center prism plane (plane in Fig. 2) view on the same height with the projectile center at . Fractures are observed on the boundaries between amorphous regions and structural change regions. (b) Basal plane view a few nanometers in front of the cracks in (a). Cracks form on the boundary of structural change regions and normal lattice, which relieves the stress and reverses the structural change.
The final configuration of the system at , color coded by pressure. The system fractures along the surface of two frustums connected at the neck. In the top half the substrate fractures along the surface of the amorphous region. In the bottom half it fractures along the twin deformations.
Result of cylindrical tensile loading on a bulk alumina sample measuring on the basal surface when cracks form in the sample. Atoms are color coded by their coordination number, where colors other than blue refer to the change in coordination numbers. It is clearly demonstrated that the weak planes in the system under basal tensile loading are the prism planes.
Cohesive energy, bulk modulus, and elastic constants calculated from the interactive potential compared to experimental data. These data along with detailed parameters of the interaction potential, and structural and dynamical properties of crystalline -alumina, amorphous, and molten alumina are given by Vashishta et al. (Ref. 35)
The local pressure, temperature, and density values at P1–P4.
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