Fractal Properties of the Nd100 – xFex Alloys Surface in the Fractal Thermodynamics Model

Abstract

The study of the fractal properties of the surface of Nd_{100 – x}Fe_x alloys in a wide range of concentrations х (х = 20–90) was carried out in the framework of the fractal thermodynamics model. To this end, we performed an analysis of scanning electron microscopy images of the surfaces of a series of Nd_{100 – x}Fe_x alloys synthesized by induction melting. A high degree of proximity of the surface structure of all the studied samples, both before and after etching, to fractals is shown. The values of the parameter δ characterizing the relative deviation of the studied samples from the fractal are in the range of 0.017–0.029. Three-dimensional diagrams of the fractal parameters S_f, T_f, E_f, and x and two-dimensional diagrams of the same parameters S_f, T_f, E_f, and x reflecting the nature of the state of the surfaces of Nd_{100 – x}Fe_x alloy samples before and after etching are constructed. For all investigated alloy samples, the values of the parameters of the fractal equations of state are calculated. The correlation of the maximum value of the coercive force H_c = 4.8 kE with the values of fractal entropy S_f = 39.86, fractal temperature T_f = 529, and fractal dimension D = 2.6530 of the Nd_{100 – x}Fe_x alloys at x = 20 has been established.