## 4 Results  
The experimental data generated by both methods and provided by the data handling software are summarized in Table 2.  
The first three columns of Table 2 provide the simplest means of particle size distribution wherein 10, 50, and 90 vol.% of powder consists of particles smaller than D10, D50, and D90, respectively. Hence, D50 represents the median particle diameter by volume.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Powder Designation**} & \multicolumn{8}{c}{**Laser Particle Size Analyzer**} & \multicolumn{8}{c}{**Sub-Sieve AutoSizer**} \\ \cline{2-10}  & **D10** & **D50** & **D90** & **Span** & **D[4,3]** & **D[3,2]** & **S\({}_{\text{M}}\)** & **Porosity** & **\(d_{\text{FN}}\)** & **S\({}_{\text{M}}\)** \\  & **\(\mu\)m** & **\(\mu\)m** & **\(\mu\)m** & **\(\mu\)m** & **m\({}^{2}\)/g** & **\%** & **\%** & **\(\mu\)m** & **m\({}^{2}\)/g** \\ \hline
316L-A & 16.9 & 28.0 & 39.8 & 0.82 & 28.0 & 22.1 & 0.034 & 42.1 & 24.0 & 0.031 \\ \hline
316L & 6.4 & 12.9 & 22.3 & 1.23 & 13.8 & 10.8 & 0.070 & 40.7 & 10.9 & 0.069 \\ \hline NC100.24 & 13.0 & 28.0 & 41.8 & 1.03 & 27.5 & 19.7 & 0.039 & 62.0 & 11.8 & 0.064 \\ \hline ABC100.30 & 17.6 & 30.9 & 44.3 & 0.86 & 30.8 & 26.4 & 0.029 & 55.9 & 17.0 & 0.045 \\ \hline YTF-HY2 & 2.00 & 4.10 & 7.91 & 1.44 & 4.59 & 3.54 & 0.215 & 52.5 & 3.26 & 0.234 \\ \hline Cobalite CNF & 1.95 & 6.36 & 15.14 & 2.07 & 7.54 & 4.45 & 0.165 & 72.7 & 2.24 & 0.327 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Powder properties from laser diffraction and air permeability methods.  
Figure 5: LM micrographs of cross-sectioned powder particles: NC100.24 (**a**); ABC100.30 (**b**).  
The width of the distribution is quantified by  
\[Span=(D90\!-\!D10)/D50 \tag{18}\]  
The next two columns contain the weighted mean particle diameters D[4,3] and D[3,2], where the volumes and surface areas of individual particles are used as the weights, respectively. D[4,3] is termed the mean diameter over volume or the De Broukere mean diameter. Laser light diffraction results are reported on a volume basis, and therefore, the D[4,3] is often presented as the mean particle size.  
By definition, the Sauter mean diameter D[3,2], also termed the volume/surface mean diameter, can be expressed as  
\[\mathrm{D}[3,2]=\frac{\sum_{i}\pi\mathrm{d}_{i}\mathrm{}^{2}\mathrm{d}_{i}}{ \sum_{i}\pi\mathrm{d}_{i}\mathrm{}^{2}}=\frac{6\sum_{i}\pi\mathrm{d}_{i}\mathrm{ }^{2}}{6\sum_{i}\pi\mathrm{d}_{i}\mathrm{}^{2}}=\frac{6\sum_{i}\mathrm{V}_{i} }{\sum_{i}\mathrm{S}_{i}}=\frac{6}{\mathrm{S}_{\mathrm{v}}}=\mathrm{d}_{\mathrm{ FN}} \tag{19}\]  
where \(d_{i}\), \(V_{i}\), and \(S_{i}\) are the diameter, volume, and surface area of the \(i\)-th particle, respectively.  
From Equation (19), it becomes obvious that the Fisher Number (\(d_{FN}\)) is equivalent to the Sauter mean diameter (D[3,2]) because both parameters are calculated using the specific surface area criterion.  
Based on the direct particle size measurements, the LPSA software calculates and reports the surface area per unit volume of the powder (\(S_{V}\)). For ease of comparison, the \(S_{V}\) values were converted to surface areas per unit mass (\(S_{M}\)) using a simple relationship (see Equations (15) and (16)):  
\[\mathrm{S}_{M}=\mathrm{S}_{V}/\rho \tag{20}\]  
and are presented in Table 2 along with specific surface areas measured with the SAS.