To the question of the dependence of the change in the speed of ultrasound and the natural frequency of vibration of atoms in monatomic planes during a polymorphic transition in iron

Iron is one of the most used metals in industry and construction. Machines and mechanisms made of iron operate over a wide range of temperatures and voltages. Checking their performance during operation is carried out using non-destructive testing. One of the methods of non-destructive testing is the method of molecular acoustics, which links the internal structure and physical and mechanical characteristics with the values of the longitudinal and transverse ultrasound velocity. The change in the speed of sound upon deformation of the material is characterized by a change in the number of defects in the crystal lattice or by the rotation of mesoscopic volumes. However, a change in the speed of ultrasound also occurs during polymorphic transformation, which is associated with a change in the geometric dimensions of the cell of the crystal lattice and can be both under the influence of temperature and under pressure. Therefore, when analyzing a material by the method of molecular acoustics, it is necessary to understand what exactly happened in the material - a polymorphic transition or an accumulation of defects. This is possible only with an accurate determination of two parameters - the natural frequency of atomic vibration, which changes during the polymorphic transition, and a change in the ultrasonic wave velocity due to a change in the interatomic interaction of atomic shells. Therefore, the main goal of this work is to derive a theoretical equation relating the change in the natural vibration frequency of atoms during the polymorphic transition of iron from aFe to yFe, with a change in the specific area per atom in the atomic plane.