Magnetostrictive and magnetic effects in Fe-27%Co laminations

The present paper deals with the characterization of the magnetostriction of the Fe-27%Co alloy. When this alloy is annealed in the ferritic domain (between 700 ◦ C and 940 ◦ C) and submitted to a slow cooling, it exhibits a low and isotropic magnetostriction over a wide induction range ( ± 1.5T). One reason that can explain this phenomenon is a high temperature selection of magnetic bi-domains preferentially oriented in the rolling plane. As soon as this material is annealed in the austenitic domain or quenched from the ferritic domain, the low and isotropic magnetostriction disappears giving way to a classical quadratic magnetostrictive behavior.

The present paper deals with the characterization of the magnetostriction of the Fe-27%Co alloy. When this alloy is annealed in the ferritic domain (between 700 • C and 940 • C) and submitted to a slow cooling, it exhibits a low and isotropic magnetostriction over a wide induction range (±1.5T). One reason that can explain this phenomenon is a high temperature selection of magnetic bi-domains preferentially oriented in the rolling plane. As soon as this material is annealed in the austenitic domain or quenched from the ferritic domain, the low and isotropic magnetostriction disappears giving way to a classical quadratic magnetostrictive behavior.

I. INTRODUCTION
Soft ferromagnetic materials are often used to generate and transform electrical energy.
Grain-Oriented iron-silicon is widely used in high power transformers because of its very good magnetic properties along the rolling direction (RD). The laminations are usually stacked together and assembled. However, such structures are well known to emit vibrations and noise 1 . This phenomenon has two possible origins: usual magnetic forces and associated elastic deformations (that induces the so-called form effect 2 ), and magnetostriction strain strongly correlated to the crystallographic texture and orientation of the magnetic field with respect to RD. Magnetostriction in a crystalline material is a spontaneous change of material shape depending of the local magnetic state 3 . This deformation operates under a magnetic field from the initial magnetic configuration (demagnetized state) to the magnetic saturation in a range of 10 −6 to 10 −4 for usual commercial soft magnetic materials 4 .
Fe-27%Co alloy is a good candidate for on board power transformers core because of its very high magnetization saturation level and the size reduction of transformers that it can offer. This alloy exhibits unfortunately high magnitude magnetostriction constants leading to an unacceptable level of acoustic noise in operation when classical annealing operations are employed during the forming process 5 . When this alloy is annealed in the ferritic domain after a severe cold rolling deformation (between 700 • C and 940 • C), it exhibits a surprising low and isotropic magnetostriction over a wide induction range (±1.5T). The paper aims at presenting some new experimental results obtained for this material and propose some explanations of the phenomena presented.

II. LOW MAGNETOSTRICTION IN SOFT MAGNETIC MATERIALS
The magnetostriction is linked to the presence of a magnetic domain structure 6 which tends to minimize the total local free energy (1). At the domain scale, the magnetic equilibrium results from the competition between the different energetic terms: W E agrees to the exchange energy, this term is linked to the ferromagnetic coupling between nearby atoms and leads to a consistent magnetization inside a magnetic domain.
W K refers to the magnetocrystalline anisotropy energy and aims to align the magnetization along the easy axis (crystallographic axis < 100 > in case of cubic symmetry and positive magnetocrystalline constant K 1 ). W H corresponds to the magnetostatic energy which tends to align the magnetization in direction to the applied field. Finally, W S refers to the magnetoelastic energy linked to the interaction between magnetization and elastic deformations of the crystal lattice. A magnetic domain α is then characterized by its magnetization vector M α magnetized at the saturation (| M α |= M s ) and an inherent deformation corresponding to the local magnetostriction deformation µ α (2) -defined for cubic symmetry and isochoric condition in the crystallographic frame (CF).
λ 100 and λ 111 refer to the magnetostriction constants (respectively spontaneous deformation along the < 100 > and the < 111 > magnetization axis) and γ i are the direction cosines of the magnetization vector ( M α = M s γ i . e i ). When a magnetic field is applied, the magnetic equilibrium is disturbed by the domain walls displacement and the rotation of the magnetization. This leads to a macroscopic magnetostriction deformation µ = α µ α dα depending on the material constants and on the magnetic configuration 3 .
In grain-oriented (GO) electrical steels 7 , grains are strongly textured and mainly composed of magnetic domains separated by 180 • domain walls and oriented along the rolling direction (RD). The magnetic loading up to saturation along RD leads to an unchanged magnetostriction strain tensor ( µ = µ α ). It results in a very low magnetostriction. On the contrary, high magnetostriction occurs when the material is magnetized along the transverse direction (TD) due to the nucleation of transversal magnetic domains along the most favorable easy magnetic axes. In non-oriented (NO) electrical steels 8 with K 1 > 0, easy < 100 > axes are theoretically equally distributed in the space and divide each grain in six possible domain families. Magnetic domains are separated by 180 • et 90 • domain walls. The applied magnetic field tends to shift the magnetic domains towards the magnetic field direction, that leads to a change of magnetostriction strain tensor from the beginning of magnetization ( µ = µ α ). As illustrated, high or low magnetostriction can be obtained for materials of same composition. In order to get low apparent magnetostriction during magnetization process, several solutions or research axis can consequently be followed: • Reducing the true magnetostriction constants up to the lowest magnitudes: λ 100 and λ 111 are mainly dependent from chemical content in polycrystalline materials (FeCuNb-SiB nanocrystalline and cobalt based amorphous with very low magnetostriction are not considered here 9 ) and very few materials can bring such advantages, such as 80%Ni permalloys or Fe-6.5%Si 4 .
• Performed a material whose microstructure is highly textured. This allows to bring low apparent magnetostriction in specific direction (RD for example), as emphasized in the case of Fe-3%Si G.O steel. 4,7 . It could be interesting to develop the cube texture ({100} < 001 >) due to the low apparent magnetostriction along RD and TD. But, it requires that metallurgists succeed in hardly texturing every potentially interesting material.
• Introducing an induced anisotropy by annealing under the action of a magnetic field, in order to increase the domains separated by 180 • domain walls along the direction of the magnetic field, and preventing 90 • domain wall displacement 3 .

III. MATERIAL AND TECHNIQUES USED
The ferromagnetic lamination studied here (Fe-27%Co) is a magnetic material which presents the highest saturation magnetization (M s = 2.38T) of all commercial soft magnetic alloys, a high magnetocrystalline anisotropy constant (K 1 = 38 KJ/m 3 ) and magnetostriction constants λ 100 = 80ppm and λ 111 =5-10ppm in the disordered state, λ 100 = 50-60 ppm and λ 111 =0 to -5 ppm in the ordered state (data from Hall 10 ). The material is a commercial based alloy AFK1 TM from APERAM, supplied in the hot rolled state. The following steps are then applied: • Annealing at the hot rolled thickness -2.5mm -at 900 • C during 5 minutes, under The magnetostrictive behavior has been analyzed on magneto-mechanical benchmark developed at the LMT at the room temperature. The magnetic loading used is an anhysteretic magnetic loading (allowing the reversible behavior to be reached). More explanation about the device used and measuring procedure can be found in 8,11 . The experimental data (magnetostriction measurements) have been collected by strain gauges stuck on each face of strip samples whose experimental result is averaged. These strain gauges allow to characterize the magnetostriction along the direction of the applied magnetic field and transversally of the applied magnetic field (denoted Longitudinal and Transversal respectively).
The microstructure and local texture were analyzed by Electron Backscatter Diffraction   We define ∆λ that refers to the maximal difference (over the magnetization directions) of This value gives a global parameter to evaluate the magnetostriction magnitude. If we consider a set of annealing temperature, below and above the phase transition from ferritic to austenitic phase, it is clearly confirmed in figure 3 that the magnetostriction deformation is connected to the annealing condition: a ferritic annealing leads to a low and isotropic magnetostriction while austenitic annealing leads to a high and isotropic magnetostriction.

V. DISCUSSION
The behavior observed for the material annealed in the austenitic domain is in accordance with the usual estimations for this material. Theoretical saturation magnetostriction λ s can be for example calculated using homogeneous stress assumption 13   is strongly enhanced for the samples annealed in the ferritic domain. This behavior is usually associated with a strong reduction of 90 • domains (stress annealed materials for example) 4 .
• An annealing of a sample submitted to a small tranversal magnetic field removes the low magnetostriction effect (results not shown). This result confirms the low magnitude of the driving force for the bi-domain selection.
• Austenitic annealed samples submitted to a 18MPa uniaxial tensile stress exhibit a magnetostriction behavior very close to the magnetostriction behavior of ferritic annealed samples (results not shown). This result demonstrates that a moderate magneto-elastic energy is strong enough to generate the bi-domain selection.
Finally, a third batch of samples has been prepared: samples cut along RD and TD were annealed in the ferritic domain (T 3=900 • C) and quenched from T 3 to the room temperature.
Magnetostriction measurements have been performed on these samples. Results are plotted in figure 6 exhibiting an intermediate behavior between the two former behaviors. IPF-ND data plotted on the right side confirm that the microstructure is unchanged comparing to the previous ferritic annealed samples. Residual stresses after quenching could explain the discrepancies between the two ferritic annealed samples 13 . X-ray spectra reported in figure 7 shows however that the {211} peaks of the two materials are very close to each other (Bragg angle and mid-height width) irrespective of the position of the samples in the goniometer. Even if the hypothesis of a residual stress effect cannot be totally ruled out (sensitivity of the method remains small), the bi-domain selection mechanism previously supposed to explain the behavior of ferritic annealed samples seems incomplete. More precisely, the new results seem to demonstrate that the cooling step may have a significant role in the selection of the magnetic microstructure and / or its mobility. Moreover, there may be a link with the ordering mechanism that occurs in these material. This point remains an open issue at this step of the work.

VI. CONCLUSION
In this paper, a surprising low and isotropic magnetostriction has been observed in Fe-27%Co strips annealed in the ferritic domain. This results looks in discrepancy with microstructural observations which show an absence of preferential orientation. Some assump- tions have been proposed to explain this behavior not observed for samples annealed in the austenitic domain. Assumptions consist in a double mechanism of: i) bi-domain selection in each grain; ii) concentration of the bi-domain orientation in the rolling plane due to strong demagnetizing surface effect. When the recrystallization is performed in the austenitic domain, the low magnetostrictive behavior disappears according to a recrystallization and grain growth of ferritic grains submitted to strong local demagnetizing effects due to the surrounding paramagnetic matrix. Experiments show on the other hand that a high cooling rate strongly disturbs this mechanism. The role of the cooling rate is not explained at present. It may probably lead to additional conditions in the bi-domain selection and/or dynamic behavior.