Automated Growth Rate Measurement of the Facet Surfaces of Single Crystals of the β‑Form of l‑Glutamic Acid Using Machine Learning Image Processing

Precision measurement of the growth rate of individual single crystal facets (hkl) represents an important component in the design of industrial crystallization processes. Current approaches for crystal growth measurement using optical microscopy are labor intensive and prone to error. An automated process using state-of-the-art computer vision and machine learning to segment and measure the crystal images is presented. The accuracies and efficiencies of the new crystal sizing approach are evaluated against existing manual and semi-automatic methods, demonstrating equivalent accuracy but over a much shorter time, thereby enabling a more complete kinematic analysis of the overall crystallization process. This is applied to measure in situ the crystal growth rates and through this determining the associated kinetic mechanisms for the crystallization of β-form l-glutamic acid from the solution phase. Growth on the {101} capping faces is consistent with a Birth and Spread mechanism, in agreement with the literature, while the growth rate of the {021} prismatic faces, previously not available in the literature, is consistent with a Burton–Cabrera–Frank screw dislocation mechanism. At a typical supersaturation of σ = 0.78, the growth rate of the {101} capping faces (3.2 × 10–8 m s–1) is found to be 17 times that of the {021} prismatic faces (1.9 × 10–9 m s–1). Both capping and prismatic faces are found to have dead zones in their growth kinetic profiles, with the capping faces (σ c = 0.23) being about half that of the prismatic faces (σ c = 0.46). The importance of this overall approach as an integral component of the digital design of industrial crystallization processes is highlighted.