*2.5. Particle Size Distributions*

For the comparison of the three mill types and their grinding performance, the particle size distributions (PSD) were obtained after sieving the ground material according to DIN EN 15149-2 with sieve mesh size of 3.15, 2.00, 1.00, 0.71, 0.50, 0.40, 0.25, 0.16, 0.10 and 0.063 mm. The data points used for the distribution curves refer to the cumulative mass which was observed under the respective mesh size, e.g., the mass obtained at a particle size value of 0.40 mm are all the particles that fell through the sieves with mesh size 0.40 mm and under.

A representative particle size value for which 10%, 50% and 90% of the mass are accumulated (x10, x50, x90) can be calculating from: (i) the upper (Xu) and the lower (Xl) size class value (in mm) between which the respective particle size value is to be expected, (ii) the mass percentage (%) under each of the two size class (Qu and Ql) and (iii) the ratio (*R*) between (Qu − Ql) and (Xu − Xl). The following equations were used:

$$\mathbf{R} = \frac{\mathbf{Q}\_{\mathbf{u}} - \mathbf{Q}\_{\mathbf{l}}}{\chi\_{\mathbf{u}} - \chi\_{\mathbf{l}}} \tag{6}$$

$$
\lambda \mathbf{x} \theta \mathbf{0} = \lambda \mathbf{l}\_l + \frac{\theta \mathbf{0} - \mathbf{Q}\_\mathbf{u}}{\mathbf{R}} \tag{7a}
$$

$$\chi\text{50} = \chi\_{\text{l}} + \frac{50 - \text{Q}\_{\text{u}}}{\text{R}}\tag{7b}$$

$$\chi \ge 10 = \chi\_{\rm l} + \frac{10 - Q\_{\rm u}}{R} \tag{7c}$$

The difference between x90 and x10 is defined here as the width of the PSD curve and used in Section 3.4 to discuss the characteristics of the distribution curves. The full dataset, however, can be found in Table S1 of the Supplementary Materials.
