Two Milling Time Regimes in the Evolution of Magnetic Anisotropy of Mechanically Alloyed Soft Magnetic Powders

Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 1 Two milling time regimes in the evolution of magnetic anisotropy of mechanically alloyed soft magnetic powders J. J. Ipus1,2, J. S. Blázquez1, V. Franco1, C. F. Conde1, A. Conde1,* 1 Departamento de Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080, Sevilla, Spain. 2 Materials Science and Engineering Departament, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Abstract The milling time evolution of magnetic anisotropy of ball milled powders can be described considering two regimes. First, for short milling times, the main factor affecting the magnetic behavior of the alloy is the accumulation of internal stresses. Second, for long milling times, magnetic anisotropy can be explained using three contributions: long-range magnetoelastic, averaged short-range magnetoelastic and averaged magnetocrystalline anisotropies. *Corresponding author details: Prof. A. Conde: Tel: (34) 95 455 28 85 / Fax: (34) 95 461 20 97 e-mail: [email protected]s Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 2 1. Introduction Soft magnetic nanocrystalline alloys have been extensively studied since the discovery of Finemet alloys in 1988 [ 1 ]. In these alloys, the peculiar two-phase microstructure is responsible for their excellent soft magnetic properties. This microstructure consists of ferromagnetic -Fe type crystallites (5-20 nm in size) embedded in a residual amorphous phase, also ferromagnetic but with a lower Curie temperature, which enables the magnetic exchange coupling between nanocrystals and averages out the magnetocrystalline anisotropy [ 2 ]. Nanocrystalline alloys are metastable systems that require non conventional casting techniques to be produced. Generally, controlled devitrification of a precursor amorphous alloy previously produced by ultrafast quenching techniques (e.g. meltspinning) is used as the production route. However, nanocrystalline microstructures could be easily obtained by mechanical alloying [ 3 ]. Nevertheless, these systems exhibit coercivities some orders of magnitude higher than those of similar alloys obtained by rapid quenching methods [ 4 , 5 , 6 ]. The interest in mechanical alloying technique is due to its versatility and suitability to produce nanocrystalline alloys in a much wider compositional range than that achievable by rapid quenching techniques, limited to compositional regions in the vicinity of deep eutectics. Moreover, the subsequent compaction and consolidation of the obtained powder could lead to overcome the shape problem of nanocrystalline alloys obtained by rapid quenching techniques, generally thin ribbons and coatings in order to achieve very high cooling rates. In recent years, soft magnetism in mechanically alloyed nanocrystalline materials has been studied by Shen et al. [4], concluding that the main contribution to Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 3 the coercivity in mechanically alloyed powders comes from the long-range fluctuations in the residual stress. In this work this idea has been applied to analyze the coercivity of Fe85Nb5B10 and Fe75Nb10B15 compositions prepared by ball milling of elemental powders. 2. Experimental The two studied compositions were prepared by ball milling in a planetary mill Fritsch Pulverisette 4 Vario from elemental powders (>99% purity) using hardened steel balls and vials. The initial powder mass was 30 g and the ball to powder ratio was 10:1. Two different rotational speeds of the main disk () were used: 150 and 350 rpm. The power released from the milling media to the powders was found to follow a 3 law [ 7 ], which allows us to define an equivalent milling time teq=(/0)3, being 0=150 rpm. The ratio between the rotational speeds of the vials and the main disk was -2. Manipulation of the powders was done under argon atmosphere in a Saffron glove box. Hysteresis loops were recorded at room temperature using a Lakeshore 7407 vibrating sample magnetometer (VSM) with a maximum applied magnetic field H =1.5 T. Saturation magnetization, MS, was obtained from the extrapolation of high field M(H) curve to zero field. As powder particles after milling are small (25-250 microns [ 8 ]), they can be aligned in an external field by rotation of the whole particle. In order to avoid this effect, which yields an undesirable not good reproducibility of the measurements, powder particles were glued together and encapsulated in an Al foil. Figure 1 shows the differences between hysteresis loops registered for free powder and glued powder. For free powder, low field susceptibility is higher and coercivity is lower than for glued Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 4 powder, which is in agreement with the presence of an extra mechanism in free powder (rotation of the whole powder particle) to align the magnetic moments with the external field. 3. Results and discussion Figure 2 shows the XRD patterns of the studied alloys as a function of the equivalent milling time. A bcc Fe(Nb) supersaturated solution is produced for both alloys but, for the alloy with 10 at. % of Nb, an amorphous phase is also developed at long milling times. Evolution of the microstructure of studied samples with milling time has been detailed elsewhere [8]. Transmission electron microscopy studies have also shown that highly pure boron inclusions remains till the end of the milling time studied [ 9 ]. These inclusions are not detected by conventional XRD experiments. Figure 3 shows the magnetization and coercivity values obtained from the hysteresis loops for both alloys. Saturation magnetization initially decreases due to the presence of impurities in the neighborhood of Fe atoms, which reduces its magnetic moment, in agreement with the evolution of the hyperfine magnetic field observed by Mössbauer spectrometry [8]. For longer milling times, MS remains almost constant for the alloy with 5 at. % of Nb, whereas for the alloy with 10 at. % of Nb, it continuously decreases due to the formation of a paramagnetic amorphous phase (Curie temperature 250 K [ 10 ]). An initial increase in HC is observed but, after teq40 h, coercivity decreases continuously. From HC and MS values, an effective anisotropy can be obtained as C SC eff p MH K with pC=0.64 for cubic shape particles [ 11 ]. If this parameter is Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 5 represented as a function of the estimated maximum microstrain of the supersaturated solid solution, obtained from XRD [8], a good linear correlation is obtained for short milling times, as shown in figure 4. This linear correlation is lost as milling time increases: microstrain becomes saturated and other effects must be taken into account. As microstrain is proportional to the square root of the dislocation density, a linear dependence of Keff with microstrain is in agreement with previous results [4]. However, the extrapolation to zero microstrain does not lead to zero magnetic anisotropy, unlike found in ref. [4]. This could be ascribed to the presence of boron inclusions in the studied samples, which might contribute to the magnetic hardening of the system. Following Shen et al [4], the total anisotropy in a nanocrystalline powder sample, Keff, is the addition of three main contributions: long-range magnetoelastic, K  ,ma, averaged short-range magnetoelastic, <K  ,mi>, and averaged magnetocrystalline anisotropies, <K1>: 2 1 2 , 2,KKKK mimaeff   (1) and an implicit equation for Keff can be obtained as: 2/3 2/33 2 1 22 2 3 2 3 A KD KK eff miSmaSeff                        (2) where  S is the magnetostriction (-7 ppm for -Fe [ 12 ]);  ma and  mi the macro and microstrain, respectively; K1 is the magnetocrystalline anisotropy (~2·104 J/m3 for -Fe); D is the average crystal size and A the exchange stiffness constant (~10-11 J/m). For long milling times, strains are saturated. Therefore, in this regime, we can plot Keff2 versus D3Keff3/2 as shown in figure 5. A good linear correlation is obtained for milling times above 50 h (samples with small crystal size and low coercivity) but the Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 6 behavior is far from linear for samples milled less time (see the inset in figure 5). From the extrapolation to D = 0, similar long-range magnetoelastic anisotropies, about 2-3 kJ/m3 are obtained for both alloys. They are of the same order of magnitude than those found for other Fe based alloys [4]. Taking into account that both magnetostriction and magnetocrystalline anisotropy of the crystalline phase must be similar, the exchange stiffness constant might be obtained from the slope of the regression lines in Fig. 4. Resulting values are ~5 times larger for the alloy with 5 at. % of Nb than for the alloy with 10 at. % of Nb and this could be ascribed to the less efficiency of the paramagnetic amorphous matrix for transmitting the magnetic coupling between ferromagnetic nanocrystals, as predicted by Hernando et al. [2] in their extended theory of magnetic coupling in two phase nanocrystalline systems. Assuming a value of A=10-11 J/m for the alloy with 5 at. % of Nb, and magnetostriction constant, Young modulus and magnetocrystalline anisotropy of bcc Fe, yields Kmi~5·104 J/m3 and a microstrain of 3 %, which is of the order of that obtained from XRD [8]. 4. Conclusions In conclusion, the evolution of the magnetic anisotropy of ball milled powder can be described using two milling time regimes. At low milling times, the progressive increase in the microstrain is responsible for an initial magnetic hardening of the system. After microstrain becomes saturated, the evolution of the magnetic anisotropy is governed by three contributions: long-range magnetoelastic, averaged short-range magnetoelastic and averaged magnetocrystalline anisotropies. The values of the parameters obtained in this study are in agreement with those obtained from other independent techniques. Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 7 Acknowledgements This work was supported by the Ministry of Science and Innovation (MICINN) and EU FEDER (project. No. MAT2007-65227) and the PAI of the Regional Government of Andalucía. J.J.I. acknowledges a Postdoctoral Research Associate position from Carnegie Mellon University. Figure captions Figure 1. Low field region of hysteresis loops for free and glued powder samples. The inset shows the first quadrant to appreciate the differences at larger fields. Figure 2. XRD patterns of the two studied samples as a function of the milling time. Figure 3. Room temperature saturation magnetization (above) and coercivity (below) of the two studied alloys as a function of the equivalent milling time. Figure 4. Effective anisotropy vs. maximum microstrain. Figure 5. Linear region of the square of effective anisotropy vs. D3Keff3/2. The inset shows the full range to appreciate the deviation from the linear behaviour for short milling times (large crystal size). Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 8 Figure 1 0 2 4 0 50 -60 -40 -20 0 20 40 60 -10 -5 0 5 10 15 M [emu/g] H [kOe] glued powder free powder HC [Oe] M [emu/g] Journal of Alloys and Compounds 509 (2011) 1407-1410 http://dx.doi.org/10.1016/j.jallcom.2010.10.207 9 Figure 2