Correction to Quantitative metrics for assessing positional and orientational order in colloidal crystals

Quantifying disorder in colloidal films spin-coated onto patterned substrates

“…Real-space methods such as those discussed here can also be used in tandem with new developments in coherent x-ray diffractive imaging [34]. In this work, we show that information about orientational order in spin-coated colloidal deposits, obtained by using orientationalorder based Minkowski structure metric [31,35,36], can be complemented by an examination of structural heterogeneity via persistent homology using the first Betti number [37].…”

“…Also, the discrete nature of N N (a) is not a continuous function of the particle coordinates which is responsible for the lack of robustness of ψ s as structure metric. As a result, the Minkowski structure metric (msm) ψ msm s is introduced to overcome these issues [31,35,36,42]. In the msm, the contribution of each nearest neighbor to the structure metric is weighted by a relative length factor l(λ)/L, where l(λ) is the length between two neighboring vertices of the Voronoi cell of particle a that corresponds to a given bond λ (or edge of the structure), and L = λ ∈B(a) l(λ ) is the total perimeter length of the Voronoi cell of particle a, as can be seen in Fig.…”

“…Although there exist several methods for characterizing colloidal structures in real space [27][28][29][30], these translational-and orientational-order-based methods are more suited to homogeneous structures of reasonably high crystallinity. For example, a recent comparison of various * ayethiraj@mun.ca † wens@unav.es different methods for making colloidal crystals [30,31] uses bond-orientational order parameters that can sensitively distinguish crystals for which 0.8 < 6 < 1.…”

Controlling disorder in self-assembled colloidal monolayers via evaporative processes

“…This formalism is functionally identical to the Minkowski structure metric used elsewhere. 47,91,93 Images of assembled particles can be analyzed to find regions that demonstrate predominantly 4-, 5-, or 6-fold symmetry, distinguishing between regions of hexagonally close packed crystallinity and defects. 95 The local crystalline phase, θ n , can also be analyzed to identify grains.…”