Thermal properties of a solid through of Fibonacci oscillators

We treat the study of the thermodynamics of a crystalline solid, applying algebra of Fibonacci oscillators. As is known a solid
is formed by a large number of atoms connected by cohesive forces of various types. Each atom moves only in a small neighborhood,
vibrating around its point of balance. The impurity states are located, and correspond the movement of electrons inside a
space (structure) limited, resulting in some areas or types of electronic interaction, i.e., the network is experiencing a
kind of electron rearrangement change in motion of nuclear spins, etc. In our study, we consider models Einstein and Debye.
We applied to ($q_1,q_2$)-algebra and deform the energy spectrum, we obtain a Hamiltonian ($q_1,q_2$)-deformed and
hence thermodynamic quantities. The interpretation of the results allowed the strain acting as parameters factors disorder or
impurities which alter the characteristics of a crystal structure, e.g., in the case of semiconductors.
The main results indicate that we have more flexibility in adopting values for $q_1$ and $q_2$, we can imagine the future, a new element
with ideal characteristics, or even occasionally improve an existing element. We need more studies and evidence to
substantiate such a complex case. For example, we are trying to establish a connection between this theory and experiences
through the growth of thin films, an issue that will be addressed elsewhere.