Table 1.

Shape descriptors and characterization methods to evaluate particle shape or morphology.

Shape descriptor	Order rank	Equation	Determination method	Ref.
Elongation ratio (ER)	First	$\mathrm{ER}=\frac{L}{w}$	Optical microscopy or scanning electron microscopy (SEM)	28, 69
Flatness ratio (FR)	First	$\mathrm{FR}=\frac{L}{w}$	Optical microscopy	7
Roundness (RO)	—	$\mathrm{RO}=\frac{p^2}{4\times \pi \times A}$	Optical microscopy	31
Shape factor (Fshape)	Second	$F_{\mathrm{shape}}=\frac{4\times \pi \times A}{p}$	Optical microscopy	70
Angularity	Second	$\mathrm{A}\mathrm{n}\mathrm{gularity}=\frac{p_{\mathrm{convex}}}{p_{\mathrm{ellipse}}}$	Optical microscopy	16
Surface factor (Fsurface)	Third	$F_{\mathrm{surface}}=F_{\mathrm{shape}}\times \frac{{(1+\mathrm{ER})}^2}{\pi \times \mathrm{ER}}$	Optical microscopy	7

A, the estimated area of the particle;

Angularity, a parameter to quantify particle shape;

L, length, the maximum Feret diameter;

p, Perimeter, the estimated perimeter of particle with compensation for corners;

P_convex, perimeter of the minimum convex boundary circumscribing the particle;

P_elipse, perimeter of fictitious equivalent ellipse which has the same area and the aspect ratio of aggregate particle;

w, width, the minimum Feret diameter;

—, there has been no rank order designated for RO.