Defect migration on D4

Mode

Playback

Speed
* modes 2 and 3 assume Postulate 1. Mode 4 is static geometry.
View is orthographic, so equal lattice vectors subtend equal lengths.
Drag to rotate · scroll to zoom · right-drag to pan

State

void class σ−1 (P)
position(1,1,1)
updates0
last step
in D4?
Position in units of a/4.

Key

trapped K=4 node
shared edge, kept (1)
released, edges broken (5)
engaged, edges formed (5)
P void (σ=−1)
N void (σ=+1)
cell-corner atom
face-centre atom
K=12 shell (optional)
open edge channel (mode 4)
closed face channel (mode 4)
Lattice atoms are drawn as small site markers so the defect stays visible. Distances are exact either way. Switch on true sphere radii for close-packing contact, where the trapped node is 0.225 of a lattice sphere.
A hop keeps two bounding atoms and exchanges the other two. Five tetrahedron edges break, five form, and one is preserved. The defect moves by a/2 and the void class flips. Under the propagation rule of the paper (Postulate 1) each hop also carries one time step, so a defect at rest cannot stay in place and oscillates between two adjacent voids. Distances are exact: nearest neighbors sit at a/√2 and a hop is a/2. Mode 4 shows why the six edge channels are open and the four face channels closed: a defect crossing a face would lie within the metric wall of three atoms at once. Note that P and N are a host-void parity, not particle and antiparticle. The outlined cube is one conventional FCC cell: eight corner atoms (dark) and six face-centre atoms (light), four atoms per cell. The K=12 toggle draws the cuboctahedral coordination shell of one atom.