## 3 Results and Discussion
### Microstructural Analysis of the Directionally Solidified Rods  
Starting from the ceramic bars, directionally solidified rods by the laser floating zone technique were grown. In order to analyze the influence of the solidification rate in the microstructure of the samples, different growth speeds were used. The samples named M50, M100, and M300 correspond to rods grown at 50, 100, and 300 mm/h, respectively. As the axial temperature gradient (G) at the solid-liquid interface were of the order of \(5\times 10^{5}\) K/m in the solid, the cooling rates (CR) were 7, 14, and 41.5 K/s for pulling rates (R) of 50, 100, and 300 mm/h, respectively (CR = G x R). Figure 3 corresponds to a SEM picture of a transversal cross section of a sample grown at 50 mm/h. Three different phases can be observed: the black one corresponds to magnesium oxide (MgO) (1), \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **O** & **Mg** & **Si** & **P** & **Ca** & **Phase** \\ \hline General & 59.17 & 21.63 & 7.02 & 5.21 & 6.27 & - \\
1 & 1.0 & 1 & - & - & - & MgO \\
2 & 62.9 & 2 & - & 16.9 & 20.3 & Whitlockite (Ca\({}_{18}\)Mg\({}_{2}\)H\({}_{2}\)(PO\({}_{4}\))\({}_{14}\)) \\
3 & 3.8 & 1.8 & 1 & - & - & Forsterite (Mg\({}_{2}\)SiO\({}_{4}\)) \\
4 & 2.0 & - & 1 & - & - & SiO\({}_{2}\) \\
5 & 3.74 & - & - & 1 & 1.17 & Tricalcium Phosphate (Ca\({}_{3}\)(PO\({}_{4}\))\({}_{2}\)) \\ \hline \end{tabular}
\end{table} 
Table 2: Elemental composition (atom %) of the main present phases in the sintered ceramic rods. Figure 2: SEM (scanning electron microscope) image of the cross section of a sintered ceramic rod used as a precursor in the sample growth by the LFZ technique. the dark gray corresponds to monticellite (CaMgSiO\({}_{4}\)) (2), and the lighter gray is compatible with a solid solution of dicalcium magnesium silicate (Ca\({}_{2-x}\)Mg\({}_{x}\)SiO\({}_{4}\)) (3) with phosphorus. The identification of the phases and atomic percentages are shown in Table 3. In Phase 3, the Mg ion replaced the position of the Ca ion, and this formed a solid solution. As more than 15% of Ca was substituted by Mg, it is expected that the crystallinity of this phase cannot be retained, which forms a vitreous network where phosphorus can be incorporated. Figure 4 shows a SEM cross-section view of the sample grown at 100 mm/h. In this micrograph, four phases can be observed: the dark one corresponds to magnesium oxide (MgO) primary phase (1), and the others correspond to monticellite (CaMgSiO\({}_{4}\)), akermanite (3) (Ca\({}_{2}\)MgSi\({}_{2}\)O\({}_{7}\)), and TCP (4). Part of the TCP formed a eutectic constituent with monticellite (2), and the akermanite phase contained phosphorus that was dissolved in its structure. The atomic percentages of the phases are shown in Table 4.  
Figure 3: SEM image of a directionally solidified rod grown at 50 mm/h. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Spectrum** & **O** & **Mg** & **Si** & **P** & **Ca** & **Phase** \\ \hline General & 57.89 & 16.29 & 10.52 & 1.95 & 13.35 & \\
1 & 50.67 & 49.33 & - & - & - & MgO \\
2 & 57.71 & 13.96 & 14.84 & 0.52 & 12.98 & Monticellite (CaMgSiO\({}_{4}\)) \\
3 & 59.04 & 3.98 & 12.28 & 3.12 & 21.57 & Ca\({}_{2-x}\)Mg\({}_{x}\)SiO\({}_{4}\) + P \\ \hline \end{tabular}
\end{table} 
Table 3: EDS analysis (atom %) for directionally solidified rods at 50 mm/h. It is possible to detect small phases surrounding the akermanite, and these phases can be assigned to TCP based on a comparison with the sample grown at 100 mm/h. In fact, both microstructures are similar except for the smaller size of the phases in the case of the sample grown at a faster rate, as expected. At a faster growing rate (300 mm/h), the general composition is more similar to the starting one than that of samples grown at slower rates (100 and 50 mm/h). This fact might be due to the loss by evaporation of the most volatile elements, mainly P, and this loss is higher at lower growth speeds. The loss of phosphorus by evaporation could explain the impossibility of TCP formation in samples grown at lower speeds.