*3.2.1.2 Illustration of theoretical model*

We will study in this paragraph the variations of the photothermal signal as a function of the square root of the frequency in the case of a bulk sample. **Figure 2** represents the theoretical variations normalized amplitude and phase of the photothermal signal as a function of the square root of the frequency for three values of the thermal conductivity (k = 0.1, 2.0 and 4.0 W/m K) of a bulk sample.

#### **Figure 2.**

*Theoretical variation of the normalized amplitude (a) and phase (b) of the photothermal signal with the square root of modulation frequency for three numerical values of thermal conductivity.*

*Improvement of the Thermal Properties of Sorel Cements DOI: http://dx.doi.org/10.5772/intechopen.91774*

We see that the normalized amplitude and the phase of the PTD signal are insensitive to variations of k (the three curves are coincident), which means that in this case we cannot determine the thermal conductivity of the sample.

**Figure 3** represents the theoretical variations normalized amplitude and phase curves for different values of thermal diffusivity D. These curves show a remarkable sensitivity of the PTD signal to variations in thermal diffusivity, which allows determining thermal diffusivity with great precision.

#### *3.2.2 Sample composed (layer deposed on a substrate)*
