IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 4, APRIL 2014 2003404

Magnetic Properties of Fe56.7Ni10Si33.3Roland Groessinger1, Monika Antoni1, Stephan Sorta1, Martin Palm2, Julius C. Schuster3, and Karl Hiebl3

1Institute of Solid State Physics, Technical University of Vienna, Vienna A-1040, Austria2MPI Eisenforschung, Düsseldorf D-40237, Germany

3AG Neue Materialien, University of Vienna, Vienna A-1090, Austria

The magnetic properties of polycrystalline Fe56.7Ni10Si33.3 were investigated. For this purpose, frequency-dependent hysteresisloops, minor loops, and losses were determined. The coercivity and the losses measured under sinusoidal and triangular conditionsincrease strongly with the frequency, whereas under constant dB/dt conditions, they are nearly frequency independent. The minorloops as measured under constant dB/dt are also nearly frequency independent. The magnetostriction of Fe56.7Ni10Si33.3 is rathersmall, as typical for a 3d-based alloy.

Index Terms— Coercivity, Fe-Ni-Si, hysteresis, losses, magnetostriction.

I. INTRODUCTION

Fe-Ni-Si is an interesting system for possible applicationsin the area of magnetism in the context of soft magnetic

Fe–Si-based alloys, which can be ductilized by the additionof nickel to be rolled to thin transformer sheets. In a recentreinvestigation of the phase diagram, the existence of a contin-uous series of solid solutions θ (Fe1−xNix)2Si with a hexagonalcrystal structure was discovered [1]. This high temperaturephase is quenchable in a small composition region around0 > x > 0.2. Superconducting quantum interference device(SQUID) and Faraday-pendulum magnetometer measurementsindicated soft magnetic behavior [2] but were considered notto be precise enough in low fields. Therefore the physicalproperties of a polycrystalline sample of the compositionFe56.7Ni10Si33.3 are reported here.

II. EXPERIMENT

About 100 g of the composition Fe56.7Ni10Si33.3 was induc-tion melted and cast from ingots of 99.99 wt% pure Fe, Ni, andSi. From this ingot rings were cut using spark plasma erosion.The dimensions of the ring were outer diameter Da = 56 mm,inner diameter Di = 45 mm − ratio Di/Da = 0.8, height5 mm.

X-ray diffraction (XRD) analysis (CoKα1-radiation) con-firmed the hexagonal crystal structure published earlier. ForFe56.7Ni10Si33.3, the Ni2In-type, P63/mmc space group wasfound with the lattice parameters [1]:

a = 0.39621(6) nm c = 0.49196(8) nmFe (1) in 2a 0.0 0.0 0.0Fe (2) in 2d 1/3 2/3 3/4Si (1) in 2c 1/3 2/3 1/4.

The magnetic properties were studied at room temperaturemeasuring the frequency dependence of the hysteresis loop(between 5 and 800 Hz), the initial M(H) curve, and minorloops of a ring shaped sample, where a zero demagnetizingfactor can be assumed. The measurements are performed

Manuscript received August 1, 2013; revised September 30, 2013; acceptedOctober 4, 2013. Date of current version April 4, 2014. Corresponding author:R. Groessinger (e-mail: rgroess@ifp.tuwien.ac.at).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2013.2285811

Fig. 1. Frequency dependence of the hysteresis loop of polycrystallineFe56.7Ni10Si33.3 at room temperature for sinusoidal H-field.

applying a sinusoidal H (t), a triangular H (t), and a triangu-lar B(t). The details of the measurements are described in [3].

Longitudinal and transversal magnetostriction measure-ments of all samples were performed at room temperatureby a strain gauge method using an ac bridge (50 kHz bridge;HBM-type KWS 85A1) in a pulsed-field magnetometer, whichexhibits a maximum magnetic field of 4.2 × 106 A/m at a pulseduration of 50 ms.

III. RESULTS AND DISCUSSION

A. Hysteresis Loops

Fig. 1 shows the frequency behavior (5–800 Hz) of thehysteresis loop of polycrystalline Fe56.7Ni10Si33.3 at roomtemperature. The applied field H (t) was sinusoidal. The sam-ple is far from saturation.

Fig. 2 shows minor loop results as obtained under a sinu-soidal applied field at a frequency of 20 Hz. From the initialcurves as given in Fig. 1 as well as from the minor loopmeasurements, a pinning type of magnetization process isprobable. There exist also similar measurements applying atriangular external field H (t). It is interesting to investigatethe dependence of the “minor loop”-losses (obtained by inte-grating the minor loops) as a function of the external maximumfield. This dependence is plotted for a frequency f = 20 Hzin Fig. 3. For this frequency, both curves (sinusoidal andtriangular field) are nearly identical; for higher frequencies,

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2003404 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 4, APRIL 2014

Fig. 2. Minor loops as obtained for polycrystalline Fe56.7Ni10Si33.3 at roomtemperature, applying a sinusoidal field at a frequency of 20 Hz.

Fig. 3. “Minor loop” losses as function of the maximum current (Imax,which is proportional to the maximum external field), applying a sinusoidaland a triangular field at a frequency of 20 Hz.

Fig. 4. Minor loops as obtained for polycrystalline Fe56.7Ni10Si33.3 atroom temperature measured under constant dB/dt and varying the maximuminduction B and the frequency between 10 and 200 Hz.

the curve determined under sinusoidal conditions becomesmore steep.

Fig. 4 also shows minor loops, however, measured underconstant dB/dt and varying the maximum induction B . Itis worth noting that these curves measured within the fre-quency range of 10–200 Hz are practically identically. Thisbecomes better understandable if one looks at the frequencydependence of the losses—see Fig. 6—as well as on the skindepth δ.

Fig. 5 shows the frequency dependence of the coercivitymeasured under different experimental conditions: sinusoidalfield H (t), triangular external field H (t), and triangular B(t)(dB/dt = const.).

Fig. 5. Frequency dependence of the coercivity measured under a sinusoidalfield (upper black curve) up to a maximum current of 4 A, triangular field(red curve) up to a maximum current of 4 A and under a triangular B(t)applying maximal 0.3, 0.2, and 0.1 T.

Fig. 6. Frequency dependence of the losses measured under a sinusoidalfield (upper black curve), triangular field (red curve), and a triangular B(t)applying maximal 0.3, 0.2, and 0.1 T.

TABLE I

FITTING PARAMETERS: A (HC( f = 0)), B AND C (EDDY CURRENT

CONTRIBUTION) FOR HC( f )

The frequency dependence of the coercivity was analyzed.The following function is fitted to the frequency-dependentcoercivity as well as losses:

F(x) = A + B.x + C.√

x.

Let x be the frequency and F the respective quantity (eitherthe losses or the coercive field). This formula is based on theassumption that the frequency dependence of the coercivitycan be explained by a shielding due to eddy currents withinthe metallic conducting sample [4]. Table I shows the resultof this fitting process for HC( f ).

GROESSINGER et al.: MAGNETIC PROPERTIES OF Fe56.7Ni10Si33.3 2003404

TABLE II

FITTING PARAMETERS ANALYZING THE FREQUENCY

DEPENDENCE OF THE LOSSES

B. Losses

Integrating the area of the hysteresis loops (see Fig. 1) asa function of the frequency allows to estimate the losses.Within this paper, it is also tried to compare the losses asmeasured under a sinusoidal field, a triangular field, and thecondition dB/dt = constant, which is generally considered asthe correct one [5].

Fig. 6 shows the frequency dependence of the losses asdetermined under the above-described conditions.Applying now a function of the type

F(x) = A + B.x + C.√

x

which is based on the general loss separation [6], where theparameters are defined in the following two equations:

(BH) = Wtot = Wh + Wclass + Wexc

= Wh + B2. f + B1. f 0.5

Wtot = Wh + C B1.5max f 0.5 + a

A.π2.B2max

6ρ

f = Wh + C B1.5max f 0.5 + aWC f

where Wh represents here the frequency-independent hystere-sis losses, B1 (prop. excess losses) and B2 (prop. eddy currentlosses) are fitting parameters. A(m2) is the cross section of thesample, Bmax gives the maximum induction of the material,and ρ is the specific electrical resistivity; a describes a constantthat is determined by the shape of the driving field. Thisprocess allows to analyze the losses according to the differentloss contributions [6]. Table II shows the result of this fittingprocess for W ( f ). The errors given for the coefficient �A,�B, and �C can be used as a hint concerning the reliabilityof the parameter.

The losses as measured under constant dB/dt are nearlyfrequency independent. Under these conditions are the fitcoefficients B and C not reliable as visible regarding thecorresponding errors.

C. Electrical Resistivity

For dynamic applications, the specific electrical resistiv-ity of a material is important determining the eddy currentcontribution. Therefore the specific electrical resistivity wasmeasured between 4.2 K and room temperature using astandard four-probe method. Fig. 7 shows the temperaturedependence of the specific electrical resistivity of polycrys-talline Fe56.7Ni10Si33.3. The resistivity is for a metallic samplerather high but typically for a three-component alloy material.

Fig. 7. Temperature dependence of the specific electrical resistivity ρ ofpolycrystalline Fe56.7Ni10Si33.3.

Fig. 8. Field dependence of the longitudinal, transversal, and saturationmagnetostriction as obtained on polycrystalline Fe56.7Ni10Si33.3 at roomtemperature.

Taking now the specific electrical resistivity at room temper-ature (ρ = 180 μ�cm) and estimating the relative permeabil-ity μr from the hysteresis measurement (Fig. 1) to μr ≈ 20allows to calculate the skin depth δ for the frequenciesinteresting here. This delivers values for δ between 40 mm( f = 10 Hz) and 10 mm ( f = 200 Hz). These values aremuch bigger than that of the ring ((Da−Di)/2 = 5.5 mm). Thismakes now understandable why the minor loops (see Fig. 4)as well as the losses (see Fig. 6) under constant dB/dtconditions are nearly frequency independent.

D. Magnetostriction

From the XRD data, a hexagonal structure was found.Generally a hexagonal structure increases the orbitalcontribution—even for 3d-metals. For testing this idea, themeasurement of the magnetostriction is a well-suited tool.Fig. 8 shows the magnetostriction as measured at room tem-perature.

Even applying a maximum field of about 4.5 T, the lin-ear magnetostriction λparallel and λtransversal are far from anysaturation. The achieved saturation magnetostriction value(which is mainly a volume magnetostriction) is rather small(up to 2.5 ppm), which is typical for a 3d-metal. For this alloy,even a ferrimagnetic type of ordering was suggested [1], which

2003404 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 4, APRIL 2014

may also explain why the linear magnetostriction cannot besaturated. This means that this Fe-Ni-Si alloy is not interestingfor any magnetoelastic sensor application.

IV. CONCLUSION

Polycrystalline Fe56.7Ni10Si33.3 exhibits a saturation induc-tion below 0.6 T, which is too small to be interesting for asoft magnetic application. The coercivity and the losses areabove that of Fe3%Si. This is due to the fact that this alloycrystallizes in a hexagonal structure. Measurements of thefrequency dependence of the hysteresis loop show a strongdifference when they are determined applying a sinusoidalfield, a triangular field or a constant dB/dt.

The frequency dependence of the coercivity and of thelosses is steep under sinusoidal conditions. The “minor loop-losses” increase with the maximum field; however at higherfields, they saturate. Minor loop measurements performedunder constant dB/dt conditions are nearly frequency inde-pendent, which can also be understood regarding the fact thatthe skin depth for the frequencies used here is much largerthan the sample dimensions.

Analyzing the frequency dependence of the coercivity andof the losses gives as most important parameter the term thatis proportional to the square root of the frequency. This meansthat the classical eddy currents are the main contributiondescribing the dynamic effect of the coercivity.

The specific electrical resistivity ρ of this material issignificantly higher than that of a pure element but alsothan that of Fe3%Si. This is typical for a highly substitutedlattice.

The linear magnetostriction at room temperature is rathersmall and cannot be saturated in fields up to about 4.5 T.A low magnetostriction is typically for a 3d-based alloy;however, the fact of difficulties to saturate the material—whichis also visible in the shape of the hysteresis loop—may be dueto a ferrimagnetic ordering but also due to internal stressescombined with a not-cubic crystal structure.

REFERENCES

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[2] S. Ackerbauer, K. Hiebl, W. Schnelle, F. Weitzer, and J. C. Schuster,“(Fe,Ni)2Si, a new soft magnetic phase,” in Proc. Int. Conf. SCTE,vol. 170. 2011, pp. 370–377.

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