Identifying faceted crystal shape from three-dimensional tomography data

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.