**Acknowledgements**

The authors thank Mario Enrique Rodríguez-Garcia of the Center of Applied Physics and Advanced Technology (CFATA, UNAM) for the support received for carrying out the experiments, the program Cátedras-CONACYT, and the National Council for Science and Technology (CONACyT) for funding through project 256923.

*Modern Spectroscopic Techniques and Applications*

**4. Conclusions**

behavior did not show large changes as in the amplitude signal. The highest PTR phase signal corresponded to the SHT sample, while the lowest PTR phase signal corresponded at 700°C. This means that the PTR amplitude signal was more sensitive than the PTR phase signal, to observe the effect of the PHT temperature on α

The finite element method (FEM) offers an option for the solution of complex problems in engineering with a multiphysical profile and equations difficult to solve analytically. The model presented in this chapter, and developed on the COMSOL

brass thermal, structural, and Vickers microhardness properties.

**70**

**Figure 10.**

*brass samples.*

*Comparison among (a) Vickers microhardness and (b) amplitude and (c) phase signals of PTR applied to* 

*Modern Spectroscopic Techniques and Applications*
