Figure 1

(Color online) Angular distribution functions; these are frequency distributions of angle cosines among the immediate neighbors of a given particle. They were constructed by randomly moving each particle away from a perfect lattice site within a sphere of radius equal to 0.1 interparticle separations, from its mean “ideal crystal” position. Using the square of the radius saves time calculating roots,[21] while the cosine of the angle is calculated by a simple dot product. The area under each graph is normalized to $N_0(N_0-1)∕2$, but since the number of measured nearest neighbors will not always be the same for large displacements the $y$ axis is left dimensionless. (top) bcc shown as the solid line, fcc shown as the dotted line, and hcp shown as the dashed line. Triangles show positions of optimized boundaries between ${\chi }_i$ regions which are used for analysis as described in Table . (Bottom) a comparison of crystal and amorphous tetrahedral structures, with $r_{ij}<1.8r_0$ to include around 16 neighbors: dots represent the cubic diamond structure, dashes represent the hexagonal diamond, and the solid line is a standard “bc8” model for amorphous silicon (Ref. 22). $\chi$ regions in the lower panel are indicative only, and have not been precisely optimized.Reuse & Permissions

Figure 2

(Color online) (a) A slice through a snapshot of molecular dynamics of simulated bcc iron (blue squares) with a vacancy in one corner of the cell free boundary conditions. The boundary (surface) atoms are largely unidentified (open circles), although occasionally the 12-fold coordination leads to a misidentification as fcc (green triangles). (b) Rotated view of (a) applying a halo from periodic boundary conditions enables all atoms to be correctly assigned, and the vacancy (and its periodic images) indicated by its unassigned neighbors.Reuse & Permissions

Figure 3

(Color online) Snapshot from molecular dynamics on simulated bcc zirconium—showing the changing mosaic of fcc (green triangles) and hcp (red hexagons) structures—the data are a cluster cut from the simulation, so surfaces of the data cannot typically be assigned. The zirconium slices show an ever changing pattern of equal amounts of fcc and three different hcp orientations (see also Fig. 5).Reuse & Permissions

Figure 4

(Color online) The orientation of hcp “crystallites” in zirconium MD. (a) A snapshot from the MD simulation similar to Fig. 4 (b) Orientation plot: lines show the $c$ axis indicating a multiply microtwinned structure, with fcc occurring where we presume that the orientation of the hcp does not permit a low energy interface. Recall that these crystallites are short lived, and the long-range crystal structure in this simulation (determined by simulated x-ray scattering) is bcc. The discrepancy between long- and short-range crystal structure arises from the dynamic instability of the bcc Zr structure.Reuse & Permissions

Figure 5

(Color online) Crystal formed by hard spheres in which the coordinates have been read in using confocal microscopy. Most atoms are assigned fcc (green triangles) or hcp (red hexagons). (a) The view of the crystal down the $c$ axis and images of two close-packed layers. Regions of two hcp, two fcc, and one of each can be seen. (b) The view perpendicular to the $c$ axis, showing stacking sequence.Reuse & Permissions