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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 8, AUGUST 2013
Design Parameters for Nanostructured Soft Magnetic Alloys Javier A. Moya , Soledad Gamarra Caramella , Leonardo J. Marta , and Carlos Berejnoi Grupo Interdisciplinario en Materiales-IESIING, Universidad Católica de Salta, INTECIN UBA-CONICET, Salta, Argentina Universidad Nacional de Salta, Facultad de Ingeniería, Salta, Argentina Magnetic properties of some nanocrystalline soft magnetic alloys are evaluated by means of a model obtained from literature. The influence of alloy elements in grain diameter, crystalline fraction and anisotropies are investigated in order to obtain information for the design of nanocrystalline soft magnetic materials. The study concerns materials with nanocrystalline composition of Fe, Fe-Si, Fe-Si-Al, and Fe-Ge, and is complemented with alloys containing nanocrystals of Fe and Fe-Co from literature. Results indicate that the reduction of grain diameter in Fe-based nanocrystal alloys is the main challenge to enhance the soft magnetic properties, when induced anisotropies are suppressed. For Fe-(Si,Al,Ge)-based nanocrystals, it is necessary to obtain a good balance of the magnetoelastic anisotropies. This can be achieved by modifying the amount of crystallized fraction via changes in the chemical composition of the nanocrystals and/or the matrix. In the case of Fe-Co, magnetic softness is attained by decreasing the Co content or with the addition of elements like Si or Al. Index Terms—Coercive force, magnetic anisotropy, nanostructured materials, soft magnetic materials.
I. INTRODUCTION
P
ARAMETERS that define soft magnetic materials are high magnetization polarization, , high permeability, , (especially at high frequencies) and low coercive force, . will depend mainly on the content of ferromagnetic The elements of the alloy, principally Fe and Co, whereas depends strongly on total magnetic anisotropy, : (1) where is a constant equal to 0.2 for our materials [1]. Among the anisotropies, the most common in nanocrystalline , and the soft magnetic materials are the magnetocrystalline, magnetoelastic and field induced uniaxial anisotropies, and , respectively. is averaged out according In nanocrystalline materials, to the random anisotropy model (RAM) [1] (this model is limited to cases where the local exchange stiffness constant of the amorphous phase is not much smaller than that of the crystalline one, as the cases reported here. Otherwise, it can be employed the model in [2]). The RAM states that, if the natural exchange ferromagnetic length is greater than the structural correlation length (grain size, ), is averaged over the the magnetocrystalline anisotropy and nanograins in the exchange coupled volume results (2) where is the exchange stiffness, is a proportionality factor is the volume fracestimated in 1.5 for cubic anisotropies, tion of crystalline phase and , a constant that takes into account the symmetry of the random anisotropy axis; for cubic
Manuscript received February 17, 2013; revised March 26, 2013; accepted April 11, 2013. Date of current version July 23, 2013. Corresponding author: J. A. Moya (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2013.2259149
anisotropies, it was estimated in 0.5. The correlation length . is renormalized as Magnetoelastic anisotropy deals with the magnetostriction and the internal (or external) stresses , with the constant form (3) In nanocrystalline biphasic materials, the total magnetostriction constant can be expressed as , and are the magnetoelastic constants for cryswhere talline and amorphous phases, respectively. is due to the directional The field induced anisotropy atomic order produced during annealing process under an applied magnetic field. can be calculated as The average of all anisotropies (4) and is redefined as . Equation (4) becomes self-consistent and can be solved by iteration. Soor lutions for the limiting cases where are given in bibliography [1]. versus using In this paper, we study the behavior of (4) in (1) and we obtain parameters that involve a proper design of soft nanocrystalline magnetic materials. II. MATERIALS AND METHODS The materials to be analyzed correspond to three different groups. FINEMET alloys were the first soft magnetic nanocrystalline materials developed [3]. The typical alloy composition , (FS in our studies). The is (%at.) nanocrystalline material is formed by -Fe(Si) nanograins with grain sizes generally of 10–16 nm at the end of the nanocrystallization process and a ferromagnetic amorphous matrix with [4]. The solution of Si composition near and modifies in the -Fe lattice provokes a decrease in but also reduces and of the material. NANOPERM, Fe-rich nanocrystalline alloys [5], were developed with the aim of obtaining higher . They are the simplest ferromagnetic nanocrystalline systems (in number of constituent elements), composed by Fe-B-(M) or Fe-B-(M)+Cu
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MOYA et al.: DESIGN PARAMETERS FOR NANOSTRUCTURED SOFT MAGNETIC ALLOYS
( , Zr, or ). In this case, nanograins consist of almost pure -Fe (in some cases is reported a small % B in solution [6]) in a Fe-rich amorphous matrix. HITPERM alloys [7] were developed based on the NANOPERM alloy where Fe is partially replaced by Co. of nanocrysThese alloys provide up to now the highest . talline soft magnetic materials (1.6–2.1 T) with a The material with typical composition is formed by [8], with a [9]. In previous works, nanocrystalline alloys were obtained from their precursor amorphous in compositions: (FS) [10], (FSA) [10], (FG) [4], (F) (unpublished), and (FSMo) [11]. We complement our study with two alloys from [12] and [8]. literature: Using (4) in (1), we performed the theoretical behavior of fixing the parameters , , , , and for each studied alloy, although they may vary as the crystallization progresses. In the case of the crystalline parameters, we use the chemical composition of the nanocrystals obtained in our experand from bibimental optimal annealing [10], [11] to get liography and and from direct measurements. With respect to the amorphous phase, Fe-rich amorphous alloys have always a positive magnetostriction and some studies shown a linear dewith [13]. Taking into account our rependence of for our calsults reported in [4] we estimate culus. Volume fraction of the alloys was determined by means of the Mössbauer spectroscopy, according to our model [4].
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Fig. 1. Effective magnetocrystalline anisotropy as function of grain di, ameter for different Fe-Si composition alloys. , and were computed for Fe nanocrystals in an amorphous , , and for matrix. nanocrystals in an amorphous matrix, whereas intermediate values were used for intermediate alloys.
tution of Si for Al in FS alloy was an increase in but also a shift of the minimum of the curve towards higher , as is displayed in Fig. 2(a), produced by the enlargewith respect to that of the FS alloy. These result in ment of of the FSA alloy with respect to FS one. a reduction of the In accord with our previous works, the most efficient alloying is Ge. The FG alloy has a element in increasing and consists of 76% of -Fe(Ge) nanocrystals with . This decrease in 18.2% Ge and a calculated moves the theoretical minimum towards lower values of the ( 0.40), far away from its actual value. As a consequence, a higher coercive force is obtained. B. NANOPERM-Like Alloys
III. RESULTS In Fig. 1, we analyze by means of (2) the dependence , from , the of , with different values of value for pure iron, to for . It is (in Fig. 1 is 5 ) because useful to set a lower limit at at those small values other kind of anisotropies, like magnetoelastic anisotropies, overshadow the magnetocrystalline one [14]. From Fig. 1, we can see that, for crystals with , reach it lower limit when , and further decreasing in will not have a clear effect in . In the , like phase, case of crystals with this limit of results in 20 nm. A. FINEMET-Like Alloys Sample FS presents a ,a with a chemical composition of 19% Si, so and . The theoretical behavior of with according to the RAM is shown in Fig. 2(a). The curve has at , as our FS alloy has its minimum value of (marked with an arrow), indeed the minimum is a can be increased by changing the chemnot reached. The ical composition of the alloy. In the FSA alloy, we substitute . This alloy 2% of Si by Al resulting in a presents -Fe(Si,Al) nanocrystals with an estimated composi(obtained using combined information tion of of DRX and as was done in [4] for Fe-Si-Ge nanocrystals). Data for magnetostriction in Fe-Al-Si ternary system is scarce. for our crystals by extrapoWe obtain a value of lating data from literature [15]. The consequence of the substi-
The nanograins of these alloys, of almost pure -Fe, present and . Our ver(F) with sion of NANOPERM alloy is , and . The data shown in Fig. 2(b), reveal a minimum at about with a value nearly 4 times lower than the actual one. This difference is ascribed to the presence of a self-field . The term self-field induced refers to induced anisotropy the fact that the local spontaneous magnetization-present in the nanograins during the crystallization annealing-produces the of Fe nanograins directional atomic order (this is possible as is higher than the annealing temperature). in the summation of (4) Introducing the term with (i.e., we obtain , in well agreement with data in [16]) and also behavior as is shown in Fig. 2(b). It is possible a new effect by flash annealing or by an to partially remove the appropriate annealing in a rotating field. Ito et al. [12] employed alloy and a rotating magnetic field in annealing a lower than the obtained obtained without field annealing (conventional annealing). In Fig. 2(b) curves for the alloy we plot the theoretical to compare with our data. C. HITPERM-Like Alloys For this nanocrystals composition we have and a positive [17]. Considering that the still is positive (it will turn into negative ) the curve will not at approximately
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Fig. 2. Theoretical behavior of coercive force, Hc, with crystalline volume , obtained using (4) and (1) for different kinds of soft magnetic fraction, materials: (a) FINEMET-like alloys; (b) NANOPERM-like alloys; and (c) HITPERM-like alloy. The singles open symbols inserted in the graphics correspond obtained value of the studied alloys. to the
present a minimum but always will increase monotonically as is shown in Fig. 2(c). Like in NANOPERM alloys, with nanocrystallization process in HITPERM take place in the self-induced field annealing of the -FeCo phase with high resulting in a due to magnetic atoms pair ordering increases with the square of the Co content [6]. This for in the master alloy, so in Fig. 2(c), we also plot ( in well a nanocrystalline accordance with [6]). The in conventional annealing material presents a by [18] and can be significantly reduced by suppressing annealing the material under a rotating magnetic field [19]. IV. DISCUSSION The softest magnetic properties in FINEMET-like nanocrystalline alloys are achieved principally by a good balance of the curve always magnetoelastic anisotropy energy. The presents a minimum value as a consequence of this balance of energy of nanocrystalline (negative) and amorphous matrix (positive) phases. In order to achieve this minimum, we must work with the parameters presented in (4). In crystalline often presents a non-monotonic variation with materials, solute concentration, and can take positive or negative values. will be always Instead, in Fe-rich amorphous metals, positive and we can expect a monotonically variation with . The depends on many factors, as annealing time and temperature, and chemical composition of the alloy. In respect of
IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 8, AUGUST 2013
the annealing conditions, we have to consider that the relief of in (3), is obtained at higher internal stresses, that affect the temperatures and longer time treatments. The dependence of with alloy composition is a complex issue, and in some cases it mainly depends on the Fe content and solutes in -Fe crystal: the nanocrystallization process stops as Fe is exhaust from the matrix [20]. Our examples of introducing Al or Ge in replace of Si in FINEMET alloy show two ways of moving the values. Nevertheless, minimum to lower (Ge) or higher (Al) and both elements provoke an increase in the theoretical only the alloy with Al could reach more efficiently the minimum. In a previous work [11], we present the results of partially replacing Mo by Nb in a FINEMET-like alloy. Mo is less efficient in reducing grain size than Nb and seems to be not soluble in the -Fe(s) crystals in this stage of crystallization ) but modify the nanocrystallization (i.e., does not affect the . For the alloy (FSMo) we obtain process by increasing , (a larger diameter compared with the indicating other FINEMET-like alloys) and is nearer from the minimum of the curve than that in the case of the alloy without Mo. In NANOPERM-like alloys we are limited to reducing in . This can be done by incrementing the Zr order to diminish produces an or Nb content of the alloy. The presence of a but also, when annealing under transverse or increment in is used to obtain a desirable longitudinal magnetic field, hysteresis loop shape (e.g., rectangular or flat), with different can be suppermeabilities for diverse applications. The pressed by annealing in a rotating magnetic field; however, the use of the material under high temperature service can revert this is attributed to a small %B in solution. The origin of these solution into the -Fe. Nevertheless, newest Fe-rich materials are nowadays been developed with composition Fe(Si)BPCu ( 1.8 T) and low co[21], [22], or FeBCCu [23] with high ercivity ( 7 A/m) without reporting the influence of self-field induced anisotropies becoming a very promising candidate for soft magnetic applications. of the studied alloys. HITPERM alloys have the largest but, Similar to NANOPERMs, these also experience the usually, in an order of magnitude greater and also can be suppressed by the rotating magnetic field annealing or notable reduced by longitudinal field annealing. But the most important value of the limitation consists of the large (and positive) -Fe(Co) phase (for ) that eliminates the minimum of . The curves, that increases monotonically with can be reduced by introducing Si or Al in the alloy and obtaining as well as in the and of the alloy. HITa decrease in PERM alloys were developed for high temperature uses and, in this sense, the materials are competitive with commercial high temperature alloys. V. CONCLUSION We have employed an average anisotropy model for the study of the coercive field in different kinds of soft magnetic nanocrystalline alloys. With this analysis, we have been able to show the importance of parameters in the design of soft magnetic materials. In FINEMET-like alloys with – , the most important parameter is the crystalline volume fraction on which depends the minimum of the magnetoelastic anisotropy of the material. In those cases, grain
MOYA et al.: DESIGN PARAMETERS FOR NANOSTRUCTURED SOFT MAGNETIC ALLOYS
refinement will not provide a reduction in the . For Fe-rich nanocrystals, reducing up to 10 nm will produce an effecif self-field induced uniaxial anisotropies tive decrease in can be suppressed (case of NANOPERM alloys) or do not exist (case of Fe(Si)-B-P-Cu or Fe-B-C-Cu alloys). Fe-Co-based larger than previous menalloys will always present a tioned materials due to positive magnetostriction constants in nanocrystals and in amorphous matrix and it will increase with . plays an important role in With this analysis, it is clear that achieving the soft magnetic properties in this kind of materials. can be the key for Understanding how elements can affect developing softer nanostructured materials. REFERENCES [1] G. Herzer, “The random anisotropy model,” in Properties and Applications of Nanocrystalline Alloys From Amorphous Precursors, B. Idzikowski, P. Švec, and M. Miglierini, Eds. Berlin, Germany: Springer-Verlag, 2005, vol. 184, pp. 15–34. [2] K. Suzuki and J. Cadogan, “Random magnetocrystalline anisotropy in two-phase nanocrystalline systems,” Phys. Rev. B, vol. 58, no. 5, pp. 2730–2739, 1998. [3] Y. Yoshizawa, S. Oguma, and K. Yamauchi, “New Fe-based soft magnetic alloys composed of ultrafine grain structure,” J. Appl. Phys., vol. 64, no. 10, p. 6044, 1988. [4] J. A. Moya, “Nanocrystals and amorphous matrix phase studies of Finemet-like alloys containing Ge,” J. Magn. Magn. Mater., vol. 322, no. 13, pp. 1784–1792, 2010. [5] K. Suzuki, N. Katauka, A. Inoue, A. Makino, and T. Masumoto, “High saturation magnetization and soft magnetic properties of bcc Fe-Zr-B alloys with ultrafine grain structure,” Mater. Trans. JIM, vol. 31, no. 8, pp. 743–746, 1990. [6] K. Suzuki and G. Herzer, “Magnetic-field-induced anisotropies and exchange softening in Fe-rich nanocrystalline soft magnetic alloys,” Scripta Mater., vol. 67, no. 6, pp. 548–553, 2012. [7] M. A. Willard, D. E. Laughlin, M. E. McHenry, D. Thoma, K. Sickafus, J. O. Cross, and V. G. Harris, “Structure and magnetic properties of (Fe0.5Co0.5)88Zr7B4Cu1 nanocrystalline alloys,” J. Appl. Phys, vol. 84, no. 12, p. 6773, 1998. [8] M. A. Willard, D. E. Laughlin, and M. E. McHenry, “Recent advances in the development of (Fe,Co)88M7B4Cu1 magnets (invited),” J. Appl. Phys, vol. 87, no. 9, p. 7091, 2000. [9] C. F. Conde, J. S. Blázquez, and A. Conde, “Nanocrystallization process of the hitperm Fe-Co-Nb-B alloys,” in Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors, B. Idzikowski, P. Švec, and M. Miglierini, Eds. Berlin, Germany: Springer-Verlag, 2005, vol. 184, pp. 111–121.
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