Using algorithms developed by Crocker and Grier38 and code
developed by Professor Eric Weeks,39 micrometer-scale particle
locations are found with an accuracy of 40 nm in the x-y plane and
80 nm in the z direction. From these particle locations, the radial
distribution function, g(r), and coverage density, F, and distributions
of the number of nearest neighbor, #NN, and local bond order, ψ6,
are used to describe the distribution and arrangement of the particles.
#NN is calculated by counting the number of particles around a
particle of interest within a distance of less than the second nearest
neighbor distance of hexagonal close-packed crystals, 3D, where
Dis a particle diameter. #NN for hexagonal close-packed and square
close-packed crystals equals 6 to 8, respectively. Moreover, #NN
for a particle neighboring a point defect and next to a line defect
equals 5 and 7, respectively. ψ6 is a parameter that describes the
orientation of a single particle in a crystal domain. It is calculated
by using all angle θ information between particles of interest i and
its nearest neighbors j with respect to a horizontal line. Prior to the
computation, vectors r of i and j are determined for all nearest
neighbors N as shown by .