Identifying Faceted Crystal Shape from Three-Dimensional Tomography Data

Abstract

Experimental accessibility of crystal shape is still limited today. We present a new method for extracting three-dimensional (3D) crystal shape from measurement data. The algorithm is demonstrated on data obtained by microcomputed tomography (μCT) for potash alum, although the approach is applicable to any 3D imaging technique and any faceted crystal. First, the crystal face normals are identified using a 3D Hough transform. In a second step, the relationship between the identified and all potentially arising crystal face normals is matched to obtain the relative orientation between the measurement data and the crystal model. The final shape parameters guarantee maintainance of the symmetry of the geometric crystal model and, hence, are compatible with common approaches to model the growth of multifaceted crystals. The procedure can be automated, which opens the possibility of evaluating full particle size-and-shape distributions, within the discussed limitations concerning crystal quality and sample size.

Impact of agglomeration on crystalline product quality within the crystallization process chain

“…Concave points were used in the past e.g. for the model‐based segmentation of nuclei , the splitting of touching cells , and for dividing agglomerates into single crystals . They can be computed by using MATLAB (MathWorks, Version R2010b).…”

Disorientation angle distribution of primary particles in potash alum aggregates

“…The presented algorithms were implemented in MATLAB 2015b, with MAT-LAB 2014a used for visualization [33]. They use our previous framework regarding convex geometry [25,34], image processing of µCT data [16,20] the cdd library [35] and the Marching Cubes rendering algorithm [36]. We considered octahedral potash alum crystals with 8 faces, as opposed to the previously used 26 faces [16,20] .…”

“…Classification techniques such as discriminant factorial analysis or support vector machine can be combined with twodimensional (2D) image-based shape factor analysis to measure the degree of agglomeration [11,12,13], or to track the aggregate volume [14]. Threedimensional (3D) and stereo imaging techniques enable a full description of the particle shape [15,16,17,18,19]. They can be used to obtain the size, shape, and orientation of each primary particle in an aggregate [20].…”

Simulations of crystal aggregation and growth: Towards correct crystal area

“…This work follows the crystal representations used in prior publications of the Briesen group and therein developed MATLAB code. In the “geometrically complex” method, each primary particle is described by a set of unit face normals a i , as well as their distances h i from the coordinate system origin (H‐Representation).…”

“…Crystals may change the set of visible faces through growth and dissolution, as well as undergo breakage or form aggregates of several crystals. While two‐dimensional (2D), as well as three‐dimensional (3D) imaging methods have recently been established for characterizing complex particle shapes, simplifications are typically undertaken in order to model these processes. In this contribution, we focus on growth and aggregation while neglecting breakage.…”