Fe-Ga alloys (GalFeNOLs) are the focus of attention due to their enhanced magneto-elastic properties, namely, magnetostriction in low saturation magnetic fields. In the last several years, special attention has been paid to the anelastic properties of these alloys. In this review, we collected and analyzed the frequency-, amplitude-, and temperature-dependent anelasticity in Fe-Ga and Fe-Ga-based alloys in the Hertz range of forced and free-decay vibrations. Special attention is paid to anelasticity caused by phase transitions: for this purpose, in situ neutron diffraction tests with the same heating or cooling rates were carried out in parallel with temperature dependencies measurements to control ctructure and phase transitions. The main part of this review is devoted to anelastic effects in binary Fe-Ga alloys, but we also consider ternary alloys of the systems Fe-Ga-Al and Fe-Ga-RE (RE-Rare Earth elements) to discuss similarities and differences between anelastic properties in Fe-Ga and Fe-Al alloys and effect of RE elements. We report and discuss several thermally activated effects, including Zener- and Snoek-type relaxation, several transient anelastic phenomena caused by phase transitions (D03 ↔ A2, D03 → L12, L12 ↔ D019, D019 ↔ B2, Fe13Ga9 → L12+Fe6Ga5 phases), and their influence on the above-mentioned thermally activated effects. We also report amplitude-dependent damping caused by dislocations and magnetic domain walls and try to understand the paradox between the Smith-Birchak model predicting higher damping capacity for materials with higher saturation magnetostriction and existing experimental results. The main attention in this review is paid to alloys with 17-20 and 25-30%Ga as the alloys with the best functional (magnetostriction) properties. Nevertheless, we provide information on a broader range of alloys from 6 to 45%Ga. Due to the limited space, we do not discuss other mechanical and physical properties in depth but focus on anelasticity. A short introduction to the theory of anelasticity precedes the main part of this review of anelastic effects in Fe-Ga and related alloys and unsolved issues are collected in summary.
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