## 3 Results and Discussion
### Chemical Composition
#### 3.2.2 Crystalline Structure  
The crystalline structures of the samples were analysed by means of X-ray powder diffraction (XRD). The XRD patterns of the different samples are compared with that of HA and \(\beta\)-TCP in Figures 6 and 7. This comparison reveals that even though HA was the major component of the resultant powders, there was a small amount of \(\beta\)-tricalcium phosphate (\(\beta\)-Ca3(PO4)2: \(\beta\)-TCP) in all of them. Furthermore, the presence of \(\beta\)-TCP was observed with higher frequency for the powders calcined at 950 \({}^{\circ}\)C, which explains the decrease in the Ca/P ratio by increasing the calcination temperature, as obtained from ICP-OES analysis. Many authors have observed that this change of phase, from HA to \(\beta\)-TCP, takes place at calcination temperatures between 600 \({}^{\circ}\)C and 950 \({}^{\circ}\)C [20]. Figure 5: Fourier transform infrared spectra of fish bone samples thermally treated at 950 \({}^{\circ}\)C.  
Figure 6: X-ray powder diffraction (XRD) patterns of material thermally treated at 750 \({}^{\circ}\)C compared with stoichiometric HA and TCP. This biphasic calcium phosphate is a very suitable material for bone substitute applications, because while the HA provides a scaffold for new bone formation via osteoconduction, the reabsorption of \(\beta\)-TCP oversaturates the local environment with calcium and phosphate ions, accelerating the new bone formation [37]. The main peaks identified in the XRD patterns of the samples are slightly shifted with respect to synthetic HA, which indicates a change in the unit cell parameters. This change in lattice is due to the substitutions of Ca ions by Na, Mg, Sr, or K ions observed in the composition analysis. The lattice parameters and the unit cell volume can be calculated from XRD patterns by combining Bragg's Law equation and the following equation [38]:  
\[\frac{1}{d^{2}}=\frac{4}{3}\left(\frac{h^{2}+k^{2}+hk}{a^{2}}\right)+\frac{l^{ 2}}{c^{2}} \tag{1}\]  
\[v=a^{2}c\ sin\ sin\ 60o \tag{2}\]  
where '\(d\)' is the interplanar distance, (\(h\ k\ l\)) are the lattice planes, '\(a\)' and '\(c\)' are the lattice parameters, and '\(v\)' is the unit cell volume. Crystallite size was calculated by using [PERSON]'s equation [39]:  
\[t=\frac{k\lambda}{\beta cos\theta} \tag{3}\]  
where '\(t\)' is the average dimension of crystallites in a direction normal to the diffracting plane, \(\beta\) is the full width of the peak at half maximum intensity (in radians) located at 20, \(\lambda\) is the wavelength of X-ray radiation (1.5418 A), and k is the Scherrer constant that is usually assumed to be 1. The cell parameters of the different samples after thermal treatment are compared with those of synthetic HA in Table 5.  
Figure 7: XRD patterns of material thermally treated at 950 \({}^{\circ}\)C compared with stoichiometric HA and TCP. Additionally, the cell parameter ratio c/a can be used to estimate the carbonate content in B-type HA (Table 5), according to a quantitative method [40] that relates the _c/a_ ratio with the stoichiometric coefficient \(x\) that can be replaced in the B-type HA formula. \[x=6(30.383\;c/a-22.208)^{3/4} \tag{4}\]  
\[Ca_{10-\frac{x}{2}}(PO_{4})_{6-x}(CO_{3})_{x}(OH)_{2} \tag{5}\]  
The crystallite size of the samples calcined at 750 \({}^{\circ}\)C, measured from the (211) reflection, was around 50 nm (except for Salmo), which is very similar to the average crystallite size in mature bone [41]. However, the increase in calcination temperature to 950 \({}^{\circ}\)C lead to an increase in crystallinity and the growth of the crystallites to values around 60 nm.