Fractal properties of the Nd_100–xFe_x alloys surface in the fractal thermodynamics model

Abstract

The study of the fractal properties of the surface of Nd100–xFex 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 images obtained by (scanning electron?) microscopy of the surfaces of a series of Nd100–xFex 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 Sf , Tf , Ef , x and two-dimensional diagrams of the same parameters: Sf , Tf , Ef , x, reflecting the nature of the state of the surfaces of Nd100–xFex alloy samples before and after etching, are constructed. For all investigated samples of alloys, the values of the parameters of the fractal equations of state arecalculated. The correlation of the maximum value of the coercive force Hc = 4.8 kE with the values of fractal entropy Sf = 39.86, fractal temperature Tf = 529, and fractal dimension D = 2.6530 of the Nd100–xFex alloys at x = 20 has been established.