Explanation:
Crystallography. an arrangement in space of isolated points (lattice points ) in a regular pattern, showing the positions of atoms, molecules, or ions in the structure of a crystal.
If an atom experiences sufficient thermal activation, it can move to a neighboring lattice position.4 If the vibration frequency of the atom is v and the atom has Z nearest neighbors, the total number of jump attempts is vZ. However, only a small fraction of the attempts will be successful, with a probability depending on the ratio between the necessary activation energy for a single jump QD and the thermal activation kBT. The effective jump frequency ΓD is then
(5.6)
With each successful jump, the atom travels one atomic distance λ and the total traveling distance in unit time is thus ΓDλ. Substituting the jump frequency ΓD into the expression for the root mean square displacement of a random walker [equation (5.5)] and using the spatial coordinate r leads to
