# PARTICLE SHAPE APPLICATION EXAMPLE: Diamond Abrasives

### The challenge

Finely-cut diamond abrasive is used to make industrial drills, grinding wheels and discs, dental tools and lapidary equipment. Grinding tools are used to shape steels, alloys, ceramics, glass, granite and other materials. Two sizes, or grits, of abrasive were studied. Below is a typical raw image of particles from each of the two samples.

Here are two collections of particle thumbnails from the two samples:

The first sample contains very fine sizes. There are also a few spherical bubbles present. They are between about 30 and 40 microns in diameter. | The second sample has considerably larger grains, with straight-faceted sides. Some of the sides are convex and some are concave. |

Size distribution is of primary interest; but since the abrasive grains are not round, a single size measure is inadequate. Length and width are
needed. Particle shape also has a large effect on abrasive performance. A polygon shape with sharp angles performs best.

For size measurement, the elliptical model will work best. The particles are not ellipses; however a fitted ellipse can provide a good measure of
width, length and aspect ratio. We will use the least bounding ellipse. For shape we use the polygon model since most particles appear polygonal
with straight sides. Polygon order is the
number of sides of the fitted polygon, and polygon angles are the interior angles of the polygon. Convexity tells us whether a particle has
a generally convex shape, that is, how well it matches the fitted polygon. A particle with indented sides would have a lower convexity than one
that fills most of the polygon.

## Applicable measures |
Measure
Bounding Ellipse Width Bounding Ellipse Length Ellipse Aspect Ratio Polygon Order Polygon Angles Convexity Smoothness |
Range of acceptance
3 - 500 microns 10 - 500 microns 0 to 1.0 0 to 25 0 to 180 0 to 1.0 0 to 1.0 |

Image analysis settings included minimum pixel area: 5; maximum pixel area: 50000; binary threshold: 80%; focus rejection parameter: 50; pump speed: 40%, and the option to correct size for diffraction effects is was enabled.