High damping in Fe-Ga-La alloys: Phenomenological model for magneto-mechanical hysteresis damping and experiment

doi:10.1016/j.jmst.2020.07.043

Abstract

Abstract:

Ferromagnetic high damping (FHA) alloys with a wide temperature range from -150 °C to 300 °C have unique application value in extreme environments. In the present work, the damping behaviors of Fe-21Ga-xLa (x = 0.12 wt.%, 0.24 wt.%, 0.47 wt.%, 1.18 wt.%, and 2.33 wt.%La) alloys have been studied in detail, and a new phenomenological model has been proposed. With the increase of La content, the Laves phase (LaGa₂) in the matrix increases gradually, and the resistance opposing the domain movement increases as well. Combined with the results of synchrotron radiation X-ray diffraction, neutron diffraction, and magnetic domain observation, the resistance mainly comes from three parts: the average stress related to the lattice distortion of the matrix, the average stress related to the increasing area energy of domain walls (DWs), and the average stress related to the increasing demagnetization energy induced by the Laves phase. Different from the traditional method of reducing internal stress through annealing to improve the damping capacity, the proper internal stress barriers are necessary to Barkhausen jumps to dissipate energy. Therefore, proper doping to balance resistance and mobility of DWs is a reliable way to improve damping capacity. Meanwhile, for Fe-Al and Fe-Cr based Alloys, the new model also has a good fitting effect. This study provides a theoretical and experimental reference for improving the functional properties of ferromagnetic alloys.

Key words: Magneto-mechanical hysteresis damping, Laves phase (LaGa₂), Internal stress distribution, Neutron-diffraction patterns, Domain walls

Meng Sun, Anatoly Balagurov, Ivan Bobrikov, Xianping Wang, Wen Wen, Igor S. Golovin, Qianfeng Fang. High damping in Fe-Ga-La alloys: Phenomenological model for magneto-mechanical hysteresis damping and experiment[J]. J. Mater. Sci. Technol., 2021, 72: 69-80.

Figures/Tables 11

Fig. 1. Damping properties of Fe-Ga-La samples. (a) Plots of damping vs train amplitude; (b) Plots of damping vs temperature at different frequencies of 0.2, 0.5, 1, 3, and 5 Hz for Fe-21Ga-0.47La alloy; (c) The magnetostriction behaviors for Fe-Ga-La alloys; (d) The variations of damping and magnetostriction with La content.

Fig. 2. Microstructures of Fe-Ga-La samples. (a-d) Inverse pole figure-Z direction (IPF-Z) EBSD maps for Fe-21Ga-xLa (x = 0.12 wt.%, 0.47 wt.%, 1.18 wt.%, and 2.33 wt.%) samples. The black area corresponds to the Ga + La-rich phase; (e) BSE image of Fe-21Ga-2.33La sample; (f) EDS profiles of the Ga + La-rich phase.

Fig. 3. Magnetic domain configurations of the Fe-Ga-La alloys. Low (a) and medium (b) magnification micromagnetic domain images for Fe-21Ga-0.12La alloy, and the corresponding typical flux-closure model (c); Low (d) and medium (e) magnification micromagnetic domain images for Fe-21Ga-0.47La alloy, and the corresponding typical flux-closure model (f); Low (g) and medium (h) magnification micromagnetic domain images for Fe-21Ga-1.18La alloy, and the corresponding typical flux-closure model (i).

Fig. 4. XRD profiles of WQ Fe-21Ga samples with different La addition. (a) S-GIXRD patterns of Fe-21Ga-xLa (x = 0.12 wt.%, 0.24 wt.%, 0.47 wt.%, 1.18 wt.%, 2.33 wt.%) samples; (b) Crystal structure model of the Ga + La-rich phase (LaGa2); (c) The variation curve of average lattice parameter with La content.

Fig. 5. Geometric phase analysis (GPA) comparison of the high-resolution TEM images of the Fe-21Ga-0.12La and Fe-21Ga-0.47La samples. (a) High-resolution TEM (HRTEM) image and corresponding FFT pattern of Fe-21Ga-0.12La; (b) and (c) Distortion maps along [100] and [010] directions, respectively, and the bottom corresponds the frequency map of distortion distribution; (d) HRTEM image and corresponding FFT pattern of Fe-21Ga-0.47La; (e) and (f) Distortion maps along [100] and [010] directions, respectively, and the bottom corresponds the frequency map of distortion distribution, showing the matrix is more distorted with 0.47 wt.% La addition.

Fig. 6. Comparison of theory with experimental data of Fe-21Ga-0.12La alloy.

Table 1 The fitting parameters (α,β,K, and χ2) and average microstrain (εave) with different fitting conditions in the Fe-21Ga-0.12La sample.δ

0.12 wt. % La	α (×10^-4)	β (×10^-4)	K	χ² (×10^-4)	Strain ε_ave(×10^-4)
S.B model	-	-	0.65	52.8	2.042(Mises’ criterion)
n = 1 (σ_mid = 0)	7.49	0.698	1.60	8.01	5.30
n = 2 (σ_mid = 0)	7.92	0.327	1.61	7.77	5.60

Fig. 7. (a) High-resolution neutron-diffraction patterns of Fe-21Ga-0.12La, and (b) corresponding plot of comparison of the (Δd)2 over d2 dependences for Fe-21Ga-0.12La. The bottom line shows the diffractometer resolution function.

Fig. 8. (a) Comparison of average microstrains derived from modified model with n = 2 and average microstrains derived from neutron diffraction (ND) experiments for Fe-21Ga-xLa (x = 0.12 wt.%, 0.24 wt.%, 0.47 wt.%, 1.18 wt.%, and 2.33 wt.%) samples; (b) The distribution of the contribution sources of the domain wall's restoring force in the process of the DW movement.

Fig. 9. Schematic of the high damping mechanism of Fe-21Ga alloy with proper La doping.

Fig. 10. The phenomenological model with n = 2 applied to the damping behaviors of Fe-9Al alloy (a) and Fe-12Cr-1Al alloy (b). The circles represent the corrected experimental data by Cochardt’s correction, and the fitted curves were obtained from Eq. (10).

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