# _Ab Initio_ Study of the Mechanism of Proton Migration in Perovskite LaScO\({}_{3}\)
## 4 Discussion  
The proton conduction is an Arrhenius-type thermal activated process, phenomenologically reminiscent of a polaron-type electronic conductivity. The proton jump times can be accurately represented by the proton polaron model [16]. Conceptually, a proton satisfies the definition of a polaron, since it can be represented as a trapped charge in an elastic crystal field. The polaron nature of proton conductivity was potentially proposed in [23]. However, such a concept as a \"proton polaron\" has not yet become widespread in the study of the conductivity in perovskites, including the structures of the ABO\({}_{3}\) type. The mechanism for the appearance of a polaron in an ionic crystal with an implanted proton is obvious. Longitudinal optical oscillations in such a system occur when positive and negative ions move in opposite directions. As a result of such oscillations, regions of excess (relative to the equilibrium value) charge of different signs alternating in space arise in the crystal. In the area where the proton is located, an excess of negative charge will most likely appear. It is clear that in such a system, there must be an interaction between the proton and longitudinal optical phonons. Here, the notion of a \"polarization cloud\" that moves along with the proton becomes appropriate. This is how a new quasi-particle, the polaron, appears. Consequently, the problem of the polaron, and not the \"bare\" proton, comes to the fore. Moreover, the residual interaction between the polaron and phonons is weak. A polaron drags a region of lattice distortion behind it, so its effective mass is greater than the mass of a \"bare\" proton, and the energy, on the contrary, is less than that  
Figure 13: Angular distributions of the nearest geometrical neighbors of the proton, obtained during its migration in the LaScO\({}_{3}\) crystal lattice in the presence of an electric field of strength \(E=4.9\times 10^{10}\) V/m (series 7–9) at different temperatures; the initial position of the proton corresponds to position 3 (as classified in Table 1) and its initial velocity is 0; the captions within of the figure reflect the temperature and the type of neighbors (in brackets). of a \"bare\" proton. If a proton creates a deformation, which linear dimensions exceed the lattice constant, one can speak of a large-radius polaron. Otherwise, we are dealing with a small-radius polaron. In this paper, we consider the proton-phonon interaction in the structure of the ABO\({}_{3}\) perovskite in the form of a polaron. In addition to the aforementioned facts, we analyze the problem arising with the control of the proton conductivity in the LaScO\({}_{3}\) perovskite using an external electric field. The path of the proton migration in the perovskite structure is determined not by the direction of the field strength, but by the elastic deformations of the crystal lattice of this compound. The mass of the La atom is 3.1 times the mass of the Sc atom. Therefore, the La-O valence phonon mode has a lower energy compared to the Sc-O mode. Consequently, in the LaScO\({}_{3}\) perovskite, the thermally activated La-O mode acts as the main driving force for the interaction of the low-energy phonon mode and the diffusion mode of protons. Polarons appear due to the deformation of the crystal lattice. Polaron states are characterized by distinct absorption peaks in the visible (VIS) and near-IR (NIR) ranges of the optical absorption spectrum. Dielectric spectroscopy is an important tool in the study of polaron states. In particular, the electrical transition between polaron states largely determines the temperature-dependence of the relaxation frequency for the DC electrical conductivity. When the crystal lattice contracts, the protons slow down. As the temperature rises, protons resist pressure more and more and retain a higher diffusion coefficient. With the increasing pressure on the sample, the activation barrier for proton diffusion increases.