**Author details**

Schrodinger equations) were obtained and solved. The characteristic frequencies (energy levels) and shape were found and estimated (see **Figure 6**). For the ground

*Local modes of the order parameter at TB [9]. Dash dot line shows the local potential which has local energy levels 0, 1, and 2 (dash). Solid lines show corresponding local oscillations' shape dependence on normalized*

*Solid State Physics - Metastable, Spintronics Materials and Mechanics of Deformable…*

cosh <sup>2</sup>*<sup>z</sup>* <sup>∗</sup> ; *<sup>z</sup>* <sup>∗</sup> <sup>¼</sup> *<sup>z</sup>*

where *A*<sup>0</sup> is an amplitude. For the local vibration ground state (51) and for the isosurface deformation parameter *q* Eq. (39), both shapes coincide qualitatively. In the limit *q* < < 1, both coincide completely. The local vibration of the order parameter describes a correlated motion of the atomic layers in twin boundary. Meanwhile, the quantum and thermal treatments give probabilistic descriptions of the atomic motion. The results (the found smooth arising of the atomic motion amplitude in TB) give evidence that different probabilistic (quantum and thermal) and dynamic methods lead to qualitatively identical features of the atomic basic state

This research is supported by the FFI National Academy of Sciences of Ukraine,

grant 4/18-H, Ministry of Science and Education of Ukraine under the Projects

*lT*

*:* (51)

state in TB, the local vibration shape can be written as

inside TB.

**44**

**Figure 6.**

*coordinate z* <sup>∗</sup> *.*

**Acknowledgements**

M05486 (0118U002048).

*<sup>η</sup>*<sup>0</sup> *<sup>z</sup>* <sup>∗</sup> ð Þ¼ *<sup>A</sup>*<sup>0</sup>

Victor A. Lykah<sup>1</sup> \* and Eugen S. Syrkin<sup>2</sup>

1 Educational-scientific Institute of Physical Engineering National Technical University "Kharkiv Polytechnic Institute", Kharkiv, Ukraine

2 B.I. Verkin Institute for Low Temperature Physics of National Academy of Sciences of Ukraine, Kharkiv, Ukraine

\*Address all correspondence to: lykahva@yahoo.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
