# Nanostructured Strontium-Doped Calcium Phosphate Cements: A Multifactorial Design
## 3 Results  
### Powder Thermal Treatment  
According to the face-centered composite design, the results of the Powder Thermal Treatment scheme are reported in Tables S1 and S2 and Figure 1.  
Considering only the significant coefficients (\(p\)-value, \(p\) < 0.05), the following regression equations can be obtained:  
\[\alpha=87.53+24.63~{}\mathrm{T}-16.11~{}\mathrm{T}^{2}-5.57~{}\mathrm{Sr}+4.91~ {}\mathrm{Sr}\cdot\mathrm{T} \tag{1}\]  
\[\alpha\mathrm{Ds}=440.54-89.21~{}\mathrm{T}^{2}-87.20~{}\mathrm{Sr}+84.00~{} \mathrm{T}-78.75~{}\mathrm{Sr}\cdot\mathrm{T} \tag{2}\]  
\[\mathrm{tin}=26.22+14.40~{}\mathrm{Sr}-13.20~{}\mathrm{T} \tag{3}\]  
\[\mathrm{HA}=29.35+13.10~{}\mathrm{T}-11.70~{}\mathrm{Sr} \tag{4}\]  
As reported in Equation (1), higher temperatures of the solid-state reaction (T) favored the formation of \(\alpha\)-TCP, while the incorporation of strontium into the TCP lattice induced the stabilization of \(\beta\)-TCP polymorph and the formation of smaller \(\alpha\)-TCP crystal domains, as previously reported [42; 54], especially at lower temperatures (Figure 2a). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Coded Levels**} & \multirow{2}{*}{**Output**} & \multirow{2}{*}{**Output**} & **Output** \\ \cline{3-3} \cline{5-8}  & & & \(-\)**1** & & & & & **Symbol** \\ \hline Powder & Sr/(Ca + Sr) (mol\%) & Sr & 0 & 2 & 4 & \(\bullet\) & \(\alpha\)-TCP (wt\%) & \(\alpha\) \\ Thermal & Temperature (\({}^{\circ}\)C) & T & 1200 & 1400 & 1600 & \(\bullet\) & \(\bullet\) & \(\alpha\)-TCP domain size (mm) & \(\alpha\mathrm{Ds}\) \\ Treatment & Dwell time (min) & Dt & 20 & 60 & 180 & \(\bullet\) & Initial setting time (min) \(\ast\) & \(\mathrm{t_{in}}\) \\  & & & & & & & CDHA after 24 h at 37 \({}^{\circ}\)C (wt\%) \(\ast\) & HA \\ \hline Powder & Sr/(Ca + Sr) (mol\%) & Sr & 0 & 2 & 4 & \(\bullet\) & Average particle size (\(\mu\)m) & \(\mathrm{Ds}_{0}\) \\ Milling & Milling Time (min) & MT & 10 & 50 & 90 & \(\bullet\) & Initial setting time (min) \(\ast\) & \(\mathrm{t_{in}}\) \\  & Milling Balls Diameter (mm) & MBD & 1 & 2 & 5 & \(\bullet\) & Final setting time (min) \(\ast\) & \(\mathrm{t_{fin}}\) \\ \hline Setting & Na\({}_{2}\)HPO\({}_{4}\) (wt\%) & SP & 0 & 2.5 & 5 & \(\bullet\) & Initial setting time (min) \(\lambda\) & \(\mathrm{t_{in}}\) \\ Solution & Sodium & Alginate (wt\%) & SA & 0 & 1 & 2 & \(\bullet\) & CDHA after 24 h at 37 \({}^{\circ}\)C (wt\%) \(\lambda\) & HA \\  & Liquid-to-Powder ratio (-) & LP & 0.50 & 0.55 & 0.60 & \(\bullet\) & Viscosity (P=\(\alpha\)) \(\lambda\) & \(\eta\) \\ \hline \hline \end{tabular}  
* *: Cements prepared with powders milled for 15 min with 5 mm diameter balls, and solutions containing 5 wt% Na\({}_{2}\)HPO\({}_{4}\), no sodium alginate (L/P = 0.55); **: Cements prepared with powders synthesized at 1400 \({}^{\circ}\)C for 60 min, and solutions containing 5 wt% Na\({}_{2}\)HPO\({}_{4}\), no sodium alginate (L/P = 0.55); \(\lambda\): Cements prepared with Sr2 powders synthesized at 1400 \({}^{\circ}\)C for 60 min, milled for 50 min with 2 mm diameter balls.  
\end{table} 
Table 1: Input factors and correspondent coded levels. Upon mixing with the solution, the strontium substitution was the main factor delaying the setting times of the cements, while a quicker transformation of \(\alpha\)-TCP into CDHA was observed after 24 h for the powders obtained at higher temperatures. After 7 days, the complete transformation of \(\alpha\)-TCP into CDHA occurred, with no substantial changes in the amount of \(\beta\)-TCP among the formulations (Figure 2b). The microstructure of cements with different amounts of strontium (Sr0 and Sr4) and high-temperature of synthesis (1200 \({}^{\circ}\)C and 1600 \({}^{\circ}\)C) was investigated and compared at 24 h after setting and immersion at 37 \({}^{\circ}\)C, considering two different dwell times of high-temperature powder synthesis before quenching, 15 (Figure 3) and 180 min (Figure 4).