(668c) Morphological Measurements of Faceted Crystals Using Image Analysis

Crystal shape or morphology is usually described by the orientation of faces and their normal distances, h, (called h-vector) from the crystal center. Although every theoretical model on crystal morphology uses such description of crystal shape, measurement of these quantities is regarded as extremely difficult. In this work we demonstrate a methodology to measure the shape distribution of a population of faceted crystals using image analysis.

In this method, the h-vector of a crystal is extracted from readily measurable quantities. For flat or plate like crystals, optical micrograph of a population of crystals is taken and preprocessed to obtain the binary images of each individual crystal. A set of Ferret's diameters is then measured along the direction of each face in addition to the area and perimeter of the crystal. Additional measurements like location of boundary pixels or vertex can also be made whenever necessary. This information can then be translated into h-vector with respect to a suitably chosen origin.

Confocal microscopy is used to measure the shape of a 3D crystal by analyzing stacks of cross-sectional images of a crystal taken at different heights. Cross-sectional images are pre-processed in a similar way and converted to binary images. The binary image in a given stack can be considered as a flat crystal and treated in the fashion discussed above to obtain the detailed geometric description (h-vector). The h-vectors obtained for all stacks along with the information of height are then translated mathematically to get the h-vector for the 3D crystal.

Experimentally measured h-vector must be supplemented with information about the miller indices of the faces. Fixed interplanar angular relationship between different crystal faces is used in this method to obtain such miller indices. The neighboring faces of any crystal face follow a fixed pattern of interplanar angles. It has been shown that miller index of a crystal face can be uniquely obtained by recognizing pattern of such interplanar angles. However, this technique alone is not sufficient for some rare situations of highly symmetric crystals for which a face specific dye should be used to identify the miller index of a specific face.

To benchmark our code, we first test this procedure for images of a population of flat crystals generated using MATLAB code with known h-distribution. Our result shows a close match between the supplied distribution and measured distribution with a relative error of order 10^-3. We also verify the methodology for the shape measurements for 3D crystal by comparing it with single crystal x-ray diffraction method which measures the h-vector of a crystal accurately. The methodology is then successfully used to measure the morphology distribution of acetaminophen crystals.

In the current methodology, however a certain degree of manual intervention is needed in mounting crystals to the microscope. To minimize such intervention and to make this procedure attractive for industrial use we suggest building of a specialized machine which can measure morphology of a large number of crystals automatically.