Hysteretic dipolar and quadrupolar properties of the spin-1 Blume–Emery–Griffiths model under pair approximation

As a continuation of previously published work [A. Erdinç and M. Keskin, Int. J. Mod. Phys. B 18, 1603 (2004), doi:10.1142/S0217979204024823] the hysteretic properties of magnetization ([Formula: see text]) and quadrupolar moment ([Formula: see text] have been investigated for the spin-1 Blume–Emery–Griffiths model using pair approximation. The magnetic field ([Formula: see text]) dependence of [Formula: see text] is produced for different values of the lattice coordination number ([Formula: see text]), biquadratic interaction ([Formula: see text]) and single-ion anisotropy ([Formula: see text]). The ([Formula: see text]) loops show different and novelty properties when [Formula: see text]. We also observed the hysteresis cycles in the ([Formula: see text], ([Formula: see text] and ([Formula: see text]) planes. These curves strongly depend on biquadratic interaction [Formula: see text]. Our results are found to be in good agreement with the other theoretical findings.

A thermodynamic approach to rate-type models in deformable ferroelectrics

The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

Structure of Alloys for (Sm,Zr)(Co,Cu,Fe)Z Permanent Magnets: First Level of Heterogeneity

An original vision for the structural formation of (Sm,Zr)(Co,Cu,Fe)Z alloys, the compositions of which show promise for manufacturing high-coercivity permanent magnets, is reported. Foundations arising from the quantitative analysis of alloy microstructures as the first, coarse, level of heterogeneity are considered. The structure of the alloys, in optical resolutions, is shown to be characterized by three structural phase components, which are denoted as A, B, and C and based on the 1:5, 2:17, and 2:7 phases, respectively. As the chemical composition of alloys changes monotonically, the quantitative relationships of the components A, B, and C vary over wide ranges. In this case, the hysteretic properties of the (Sm,Zr)(Co,Cu,Fe)Z alloys in the high-coercivity state are strictly controlled by the volume fractions of the A and B structural components. Based on quantitative relationships of the A, B, and C structural components for the (R,Zr)(Co,Cu,Fe)Z alloys with R = Gd or Sm, sketches of quasi-ternary sections of the (Co,Cu,Fe)-R-Zr phase diagrams at temperatures of 1160–1190 °C and isopleths for the 2:17–2:7 phase composition range of the (Co,Cu,Fe)–Sm–Zr system were constructed.

Efficiency of hysteretic damper in oscillating systems

This paper is dedicated to comparative analysis of nonlinear damping in the oscillating systems. More specifically, we present the particular results for linear and nonlinear viscous dampers, fractional damper, as well as for the hysteretic damper in linear and nonlinear (Duffing-like) oscillating systems. We consider a constructive mathematical model of the damper with hysteretic properties on the basis of the Ishlinskii-Prandtl model. Numerical results for the observable characteristics, such as the force transmission function and the “force-displacement” transmission function are obtained and analyzed for both cases of the periodic affection, as well as for the impulse affection (in the form of δ-function). A comparison of an efficiency (in terms of the corresponding transmission functions) of the nonlinear viscous damper and the hysteretic damper is also presented and discussed.