The Concept of Scaling Analysis Describing the Properties of Soft Magnets

Abstract

Modelling hysteresis curves is an important issue of research on soft magnetic materials. The paper presents the ideas of modelling the properties of soft magnets based on scaling analysis. The article describes in detail the application of the Widom scaling procedure for modelling energy losses and the coercive field of the Ni-Fe alloy and 6.5% Si-Fe steel. Finally, the results of scaling analysis and its possible advantages are discussed.

Scaling-based prediction of magnetic anisotropy in grain-oriented steels

“…In the previous studies, a scaling function was usually represented by Maclaurin series [30][31][32][33][34][35][36][37].…”

“…The scaling analysis is also used in materials science, including the study of magnetic material properties such as power loss [30][31][32][33][34], coercivity [35][36][37], magnetic viscosity [38][39][40] or hysteresis loops [41][42][43][44][45].…”

The modified procedures in coercivity scaling

“…After the scaling transformations, the following relationship of scaled coercivity was proposed: (3) where H 0 , H 1 , H 2 are amplitudes, while δ and ε are so-called scaling exponents. The aforementioned scaling transformations were described in detail in [5,6]. Taking into account the frequency dependence of the coercivity given by (1), the relationship (3) was reduced to:…”

“…Coercivity can be expressed as the frequency dependence: (1) where H 0 is the static coercivity, B and n are the coefficients depending on the microstructure, intrinsic parameters and geometry of the materials [2][3][4]. In general, the frequency dependence of coercivity (1) has the power law form, that may suggest its scaling properties [5,6]. The scaling behavior of coercivity in thin magnetic films and multilayers has been investigated e.g.…”