6. Thermal properties

explained as an effect mostly due to a higher levels of calcium and oxygen (in the OH sites)

Figure 9. Tauc plots of (a) CDHA\_A, (b) CDHA\_B, (c) CDHA\_C, and (d) CDHA\_D samples. The red line shows the

<sup>a</sup> (eV) E<sup>g</sup>

CDHA\_A 5.26 5.1 3.14 CDHA\_B 5.31 5.18 2.51 CDHA\_C 5.33 5.29 0.76 CDHA\_D 5.21 5.12 1.76

is possible that the oxygen vacancies occur at the phosphate sites as well at the OH sites. In such case, the DFT calculations predict the existence of energy levels inside the forbidden

band, which explains why the band gap energy decreases for the CDHA\_D sample.

1

. For a higher drip rate (i.e., 17 μl∙s

<sup>b</sup> (eV) ΔE<sup>g</sup> (%)

1 ), it

vacancies, as the drip rate increases from 5 to 10 μl∙s

Table 5. Optical band gap values determined from UV–Vis and PAS measurements.

extrapolation of the linear region.

Sample E<sup>g</sup>

a

b From PAS.

From UV-Vis.

90 Powder Technology

For the determination of the thermal response of the samples, a homemade photoacoustic detection (PA) measurement system was employed, for a modulation frequency ranging 400 Hz ≤ f ≤ 4 kHz. The experimental setup is similar to the PAS measurement system but replacing the Hg arc lamp and the monochromator by a 405 nm laser diode (controlled by a TTL signal), as is shown in Figure 10.

The excitation beam wavelength was chosen to avoid the contribution of the photogenerated charge carriers to the PA signal. To perform the PA measurements in the transmission configuration [21, 22], pills of powdered samples were obtained by compacting 100 mg of powdered sample. Considering the samples as optically opaque and thermally thick, the PA signal will depend on the modulation frequency as indicated by Eq. (3):

$$S = A\_0 \cdot \frac{\exp\left(-\sqrt{f/f\_c}\right)}{f}; \qquad f\_c \equiv \frac{a\_s}{\pi \cdot l\_s^2} \tag{3}$$

In Eq. (3), A<sup>0</sup> is an instrumental constant, f<sup>c</sup> is the so-called characteristic frequency of the sample, and α<sup>s</sup> and l<sup>s</sup> are the thermal diffusivity and thickness of the sample, respectively. For modulation frequencies where Eq. (3) is applicable, α<sup>s</sup> can be calculated from the slope of the linear region in the semi-logarithmic f 1/2 vs. f∙S plot (Figure 11). The results obtained have been summarized in Table 6.

Although the values of the thermal diffusivities agree with the reported values for hydroxyapatite [7, 23, 24], there is no clear correlation with the synthesis drip rate nor the stoichiometry of the samples. This is because the different levels of compaction of the sample's pills affect the effective thermal properties. The nonlinear behavior at low modulation frequencies is

Figure 10. PA measurement system. Here, S and Δϕ are the amplitude and the phase shift of the PA signal, respectively.

17 μl∙s 1

, the structural, morphological, and textural characterizations show that the pore

Sol-Gel Synthesis of Calcium-Deficient Hydroxyapatite: Influence of the pH Behavior…

to the crystallite size, which decreases for all samples as the drip rate increases. The chemical characterizations demonstrate that increasing the drip rate promotes the presence of calcium and oxygen vacancies in the hydroxyapatite structure. From the diffuse reflectance and absorbance spectra, the energy band gap of the samples increases as the drip rate does, with the

1

presence of oxygen vacancies on the phosphate sites and calcium vacancies. The results of the thermal characterization allowed determining the effective thermal diffusivity of the samples, obtaining values that agree well with those reported in the literature. However, it was not possible to establish a clear correlation between the effective thermal properties and the values of the drip rate used during the synthesis. Finally, the drip rate in the hydroxyapatite sol-gel synthesis clearly governs the pH during synthesis and, therefore, has a major impact in the

Authors acknowledge the Instituto Politécnico Nacional from Mexico, for financial support through 1855 SIP multidisciplinary and 20170229 SIP projects. The authors wish to thank the National Energy Conversion and Storage Laboratory, CICATA U. Legaria of the Instituto Politécnico Nacional of Mexico, and the PhD student René Cabrera for helping with the acquisition and analysis of XRD data. The authors thank also the PhD student Guadalupe

Romero Ortiz for helping in the acquisition of hydrogen adsorption data.

The authors of this work declare no conflicts of interest of any kind.

\*, Yolanda Jiménez-Flores<sup>1</sup>

1 Instituto Politécnico Nacional, Centro de Investigación en Ciencia Aplicada y Tecnología

2 Cátedras CONACYT, Departamento de Química, ECOCATAL, Universidad Autónoma

3 Cátedras CONACYT, Instituto Politécnico Nacional, Centro de Investigación en Ciencia

, Víctor Suárez<sup>2</sup>

, Moseratt Suárez-Quezada<sup>1</sup>

1

, possible due to a combination of a larger

http://dx.doi.org/10.5772/intechopen.76531

, contrary

93

radius size and the total pore volume tend to decrease for a drip rate up to 5 μl∙s

exception of the sample synthesized at 17 μl∙s

physical-chemical properties of the hydroxyapatite.

Acknowledgements

Conflict of interest

Author details

and Uriel Nogal<sup>3</sup>

José Bruno Rojas Trigos<sup>1</sup>

\*Address all correspondence to: jrojast@ipn.mx

Avanzada, Unidad Legaria, Ciudad de México, Mexico

Metropolitana-Iztapalapa, Ciudad de México, Mexico

Aplicada y Tecnología Avanzada, Ciudad de México, Mexico

Figure 11. f 1/2 vs. f∙S plot of (a) CDHA\_A, (b) CDHA\_B, (c) CDHA\_C, and (d) CDHA\_D. The red line shows the best fit.


Table 6. Thermal diffusivity of the samples.

indicative of a transition between thermal regimes. For larger modulations frequencies, the signal-to-noise ratio becomes too small (especially for CDHA\_D sample) to obtain reliable data. The previous results must be corroborated by other photothermal techniques, such as IR photothermal radiometry or lock-in thermography [25, 26].

#### 7. Conclusions

The sol–gel synthesis of calcium-deficient hydroxyapatite was successfully achieved, for four different drip rates during synthesis procedures, describing the distinctive features of the pH evolution, for each case. For the samples synthesized at drip rate values of 5, 8, 10, and 17 μl∙s 1 , the structural, morphological, and textural characterizations show that the pore radius size and the total pore volume tend to decrease for a drip rate up to 5 μl∙s 1 , contrary to the crystallite size, which decreases for all samples as the drip rate increases. The chemical characterizations demonstrate that increasing the drip rate promotes the presence of calcium and oxygen vacancies in the hydroxyapatite structure. From the diffuse reflectance and absorbance spectra, the energy band gap of the samples increases as the drip rate does, with the exception of the sample synthesized at 17 μl∙s 1 , possible due to a combination of a larger presence of oxygen vacancies on the phosphate sites and calcium vacancies. The results of the thermal characterization allowed determining the effective thermal diffusivity of the samples, obtaining values that agree well with those reported in the literature. However, it was not possible to establish a clear correlation between the effective thermal properties and the values of the drip rate used during the synthesis. Finally, the drip rate in the hydroxyapatite sol-gel synthesis clearly governs the pH during synthesis and, therefore, has a major impact in the physical-chemical properties of the hydroxyapatite.
