- Email: [email protected]
Dynamic losses in FeSi filled polymer bonded soft magnetic composites
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551 www.elsevier.com/locate/jmmm
Dynamic losses in FeSi filled polymer bonded soft magnetic composites M. Anhalt, B. Weidenfeller Faculty of Natural and Materials Sciences, Clausthal University of Technology, Robert-Koch-StraX e 42, 38678 Clausthal-Zellerfeld, Germany Available online 20 March 2006
Abstract The dynamic magnetization behavior of polypropylene filled with iron silicon particles in various proportions ð20:5240:1 vol%Þ in the frequency range from 0:1 Hzpf p100 Hz was measured with a computer controlled hysteresis recorder. The frequency dependence of the anomaly factor Z and the effective number of active domain walls neff in relation to the excess field were estimated. The anomaly factor follows the relation Z ¼ Z0 f x with 1:20pxp 1:41, whereas x changes with the amount of FeSi in the composite. The effective number of active domain walls is relatively low at excess fields below 20 A/m and increases rapidly for higher excess fields. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.d; 81.05.Qk Keywords: Soft magnetic composites; Dynamic losses; Anomaly factor; Excess field
1. Introduction Polymer bonded soft magnetic composites (PBSM) are materials of soft magnetic fillers in a polymeric matrix. They attract an increasing interest in electrical applications due to the ease of manufacturing processes. The benefits of such PBSMs in contrast to laminated sheets are the high isotropic electrical resistivity as well as the possibility to produce inductivities of complex shapes and for reasonable prices [1]. A disadvantage of the composite materials is the lower permeability in contrast to laminated sheets which implies that they cannot be used as a direct replacement without abatement in performance [2].
magnetic filler material gas atomized FeSi powder with 6:8% silicon content of spherical shape with a wide particle size distribution from 0 to 300 mm and a mean particle size of d¯ ¼ 106 and 90 mm, respectively, provided by Ho¨gana¨s AB, Sweden, was used. To enhance the processing properties while extruding and injection molding different additives (waxes, lubricants, stabilizers) were added to the polymer. Details of materials, sample preparation and sample homogeneity are described elsewhere [3]. The frequency-dependent power losses were measured in a frequency range from 0.1 to 100 Hz at a polarization of 0.07 T with the use of a hysteresis measurement system which is already described in Refs. [4,5]. 3. Results and discussion
2. Experimental PBSMs with different filler fractions (Table 1) in cylindrical shape have been produced. Filler particles are mixed with a polymer in a twin-screw extruder. Afterwards samples in cylindrical shape with dimensions of 120 mm length and 10 mm diameter were injection molded. As matrix material polypropylene was chosen and as soft Corresponding author.
E-mail address: [email protected] (M. Anhalt). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.152
The frequency dependence of the anomaly factor Z [6] Z¼
Pdyn , Pcl
(1)
with dynamic losses Pdyn and classical losses Pcl is shown in Fig. 1. Dynamic losses were calculated by subtracting static losses Ph from total losses Ptot (Fig. 2), whereas static losses were estimated by extrapolation of total losses to frequency f ¼ 0 Hz. Different to metallic magnetic materials classical losses of PBSM contain micro eddy currents Pmicro which cl
ARTICLE IN PRESS M. Anhalt, B. Weidenfeller / Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551
e550
Table 1 Content and mean particle size d¯ of filler material
¼ Pmacro cl
Sample
wt%
vol%
d¯ (mm)
FeSi70 FeSi80 Fesi85
70 80 85
20.5 29.6 40.1
106 90 106
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
anomaly factor η
1E-11
1E-10
1E-9 xPP + 20.5vol% FeSi = -1.41 xPP + 29.6vol% FeSi = -1.36 1E-8
xPP + 40.1vol% FeSi = -1.20 10 frequency [Hz]
100
Fig. 1. Frequency f versus anomaly factor Z with exponential factor x at a polarization of J max ¼ 0:07 T.
40 35
Ptot [J/m3]
30 25 20 15
5 0
20
40 60 frequency [Hz]
80
100
Fig. 2. Frequency versus total loss Ptot at a polarization of J max ¼ 0:07 T.
are losses in the particles and macro eddy currents Pmacro cl which are losses correlated to the body of the PBSM since the FeSi particles are not perfectly isolated from each other. Formulas were found by solving Maxwell’s equation for spherical particles and the cylindrical magnetic specimen. Pmicro ¼ cl
d¼d max X d¼d min
ðqB=qtÞ2 d 5FeSi p Nðd FeSi Þ, 240rFeSi
(3)
qB=qt is the change of magnetic induction with time, d FeSi the diameter of FeSi-particles, rFeSi the specific resistance of FeSi, Nðd FeSi Þ the particle size distribution, rPBSM the specific resistance of the injection molded cylinder and Acylinder the cross section of the cylinder. The very high values of the loss factor (Fig. 1) can be explained with the extreme low classical losses which are one of the advantages of PBSM. It can also be seen that the anomaly factor Z decreases with increasing magnetizing frequency f following the relation Z ¼ Z0 f x . The exponential factor x decreases with the amount of iron–silicon particles in the polymer from x ¼ 1:41 (20:5 vol% FeSi) and x ¼ 1:36 (29:6 vol% FeSi) to x ¼ 1:20 (40:1 vol% FeSi). An exponential factor of 0:5 can be expected for rigid domain wall movement [6] or higher values of x ¼ 0:655 for domain wall bowing [7–9]. The estimated values are unexpectedly high but comparable to the values x ¼ 0:9 and 1:8 found for nano crystalline Fe73:5 Si13:5 Cu1 Nb3 B9 [10]. One possible explanation for the drastic decrease of the anomaly factor with increasing magnetizing frequency can be the activation of domain walls at high frequencies which are pinned at crystal imperfections or impurities at low frequencies. At a given frequency, the domain walls are activated and participate in the magnetizing process. A micrography of the iron–silicon particles with grain boundaries and silicon precipitations can be seen in Fig. 3. Regarding that not only complete domain walls but also parts of domain walls can participate in the magnetizing process, an effective number of movable domain walls neff can be defined by the excess field H exc and the field H w depending on the geometry of the specimen which is necessary for the magnetization process only by one domain wall following Williams et al. [11]. H exc ðf Þ ¼ H d ðf Þ H c ,
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
10
ðqB=qtÞ2 Acylinder , 128rPBSM
(2) Fig. 3. Micrography of gas atomized FeSi6.8 particles.
(4)
ARTICLE IN PRESS M. Anhalt, B. Weidenfeller / Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551
700 600
domain walls show a drastic increase at an excess field around 20–50 A/m depending on the fraction of magnetic material in the composite. The higher the FeSi fraction in the PBSM, the lower is the excess field at which the number of active domain walls is suddenly increased.
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
500 neff
e551
400
4. Summary
300 200 100 0 11
0
100
Hexc [A/m] Fig. 4. Excess field H exc versus effective number of domain walls neff .
neff ¼
H w ðtÞ . H exc ðf Þ
(5)
In Eq. (4) H d is the dynamic coercive force at frequency f and H c the static coercive force which was determined by extrapolation of measured dynamic coercive forces to zero frequency. Because the measured dynamic coercive force is the sum of coercive forces of all FeSi particles in the PBSM, the field H w [12] is the sum of all fields which are necessary for the magnetization process by one domain wall in a singe particle. In Fig. 4 the effective number of active domain walls dependent on the excess field is shown. Concerning the large number of particles in the PBSM at low excess fields H exc o20 A=m only a relative low number neff of domain walls are active in the magnetizing process. This number of
The anomaly factor of polypropylene filled with FeSi particles in various fractions follows a Z ¼ Z0 f x relation with frequency. The value of x varies with the amount of FeSi particles and lies between 1:20pxp 1:41 for 20.5–40:1 vol% FeSi. The effective number of active domains is very low and increases suddenly at excess fields larger than 20 A/m depending on the amount of FeSi. The higher the FeSi fraction the lower the excess field at which the drastic increase of active domain walls appear. References [1] I.P. Gilbert, J. Mater. Sci. 39 (2004) 457. [2] M. de Wulf, L. Anestiev, L. Froyen, J. Melkebeek, J. Appl. Phys. 91 (2002) 7845. [3] B. Weidenfeller, M. Ho¨fer, F. Schilling, Composites A 33 (2002) 1041. [4] M. Pott-Langemeyer, W. Riehemann, W. Heye, An. Fis. B 86 (1990) 232. [5] D. Ramin, W. Riehemann, tm—Tech. Mess. 3 (2001) 116. [6] R.H. Pry, C.P. Bean, J. Appl. Phys. 29 (1958) 532. [7] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [8] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1036. [9] J.E.L. Bishop, J. Magn. Magn. Mater. 12 (1979) 102. [10] C. Wittwer, Ph.D. Thesis, 1994, Clausthal-Zellerfeld, Germany. [11] H.J. Williams, W. Shockley, C. Kittel, Phys. Rev. 80 (1950) 1090. [12] B. Weidenfeller, W. Riehemann, J. Magn. Magn. Mater. 160 (1996) 136.
Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551 www.elsevier.com/locate/jmmm
Dynamic losses in FeSi filled polymer bonded soft magnetic composites M. Anhalt, B. Weidenfeller Faculty of Natural and Materials Sciences, Clausthal University of Technology, Robert-Koch-StraX e 42, 38678 Clausthal-Zellerfeld, Germany Available online 20 March 2006
Abstract The dynamic magnetization behavior of polypropylene filled with iron silicon particles in various proportions ð20:5240:1 vol%Þ in the frequency range from 0:1 Hzpf p100 Hz was measured with a computer controlled hysteresis recorder. The frequency dependence of the anomaly factor Z and the effective number of active domain walls neff in relation to the excess field were estimated. The anomaly factor follows the relation Z ¼ Z0 f x with 1:20pxp 1:41, whereas x changes with the amount of FeSi in the composite. The effective number of active domain walls is relatively low at excess fields below 20 A/m and increases rapidly for higher excess fields. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.d; 81.05.Qk Keywords: Soft magnetic composites; Dynamic losses; Anomaly factor; Excess field
1. Introduction Polymer bonded soft magnetic composites (PBSM) are materials of soft magnetic fillers in a polymeric matrix. They attract an increasing interest in electrical applications due to the ease of manufacturing processes. The benefits of such PBSMs in contrast to laminated sheets are the high isotropic electrical resistivity as well as the possibility to produce inductivities of complex shapes and for reasonable prices [1]. A disadvantage of the composite materials is the lower permeability in contrast to laminated sheets which implies that they cannot be used as a direct replacement without abatement in performance [2].
magnetic filler material gas atomized FeSi powder with 6:8% silicon content of spherical shape with a wide particle size distribution from 0 to 300 mm and a mean particle size of d¯ ¼ 106 and 90 mm, respectively, provided by Ho¨gana¨s AB, Sweden, was used. To enhance the processing properties while extruding and injection molding different additives (waxes, lubricants, stabilizers) were added to the polymer. Details of materials, sample preparation and sample homogeneity are described elsewhere [3]. The frequency-dependent power losses were measured in a frequency range from 0.1 to 100 Hz at a polarization of 0.07 T with the use of a hysteresis measurement system which is already described in Refs. [4,5]. 3. Results and discussion
2. Experimental PBSMs with different filler fractions (Table 1) in cylindrical shape have been produced. Filler particles are mixed with a polymer in a twin-screw extruder. Afterwards samples in cylindrical shape with dimensions of 120 mm length and 10 mm diameter were injection molded. As matrix material polypropylene was chosen and as soft Corresponding author.
E-mail address: [email protected] (M. Anhalt). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.152
The frequency dependence of the anomaly factor Z [6] Z¼
Pdyn , Pcl
(1)
with dynamic losses Pdyn and classical losses Pcl is shown in Fig. 1. Dynamic losses were calculated by subtracting static losses Ph from total losses Ptot (Fig. 2), whereas static losses were estimated by extrapolation of total losses to frequency f ¼ 0 Hz. Different to metallic magnetic materials classical losses of PBSM contain micro eddy currents Pmicro which cl
ARTICLE IN PRESS M. Anhalt, B. Weidenfeller / Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551
e550
Table 1 Content and mean particle size d¯ of filler material
¼ Pmacro cl
Sample
wt%
vol%
d¯ (mm)
FeSi70 FeSi80 Fesi85
70 80 85
20.5 29.6 40.1
106 90 106
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
anomaly factor η
1E-11
1E-10
1E-9 xPP + 20.5vol% FeSi = -1.41 xPP + 29.6vol% FeSi = -1.36 1E-8
xPP + 40.1vol% FeSi = -1.20 10 frequency [Hz]
100
Fig. 1. Frequency f versus anomaly factor Z with exponential factor x at a polarization of J max ¼ 0:07 T.
40 35
Ptot [J/m3]
30 25 20 15
5 0
20
40 60 frequency [Hz]
80
100
Fig. 2. Frequency versus total loss Ptot at a polarization of J max ¼ 0:07 T.
are losses in the particles and macro eddy currents Pmacro cl which are losses correlated to the body of the PBSM since the FeSi particles are not perfectly isolated from each other. Formulas were found by solving Maxwell’s equation for spherical particles and the cylindrical magnetic specimen. Pmicro ¼ cl
d¼d max X d¼d min
ðqB=qtÞ2 d 5FeSi p Nðd FeSi Þ, 240rFeSi
(3)
qB=qt is the change of magnetic induction with time, d FeSi the diameter of FeSi-particles, rFeSi the specific resistance of FeSi, Nðd FeSi Þ the particle size distribution, rPBSM the specific resistance of the injection molded cylinder and Acylinder the cross section of the cylinder. The very high values of the loss factor (Fig. 1) can be explained with the extreme low classical losses which are one of the advantages of PBSM. It can also be seen that the anomaly factor Z decreases with increasing magnetizing frequency f following the relation Z ¼ Z0 f x . The exponential factor x decreases with the amount of iron–silicon particles in the polymer from x ¼ 1:41 (20:5 vol% FeSi) and x ¼ 1:36 (29:6 vol% FeSi) to x ¼ 1:20 (40:1 vol% FeSi). An exponential factor of 0:5 can be expected for rigid domain wall movement [6] or higher values of x ¼ 0:655 for domain wall bowing [7–9]. The estimated values are unexpectedly high but comparable to the values x ¼ 0:9 and 1:8 found for nano crystalline Fe73:5 Si13:5 Cu1 Nb3 B9 [10]. One possible explanation for the drastic decrease of the anomaly factor with increasing magnetizing frequency can be the activation of domain walls at high frequencies which are pinned at crystal imperfections or impurities at low frequencies. At a given frequency, the domain walls are activated and participate in the magnetizing process. A micrography of the iron–silicon particles with grain boundaries and silicon precipitations can be seen in Fig. 3. Regarding that not only complete domain walls but also parts of domain walls can participate in the magnetizing process, an effective number of movable domain walls neff can be defined by the excess field H exc and the field H w depending on the geometry of the specimen which is necessary for the magnetization process only by one domain wall following Williams et al. [11]. H exc ðf Þ ¼ H d ðf Þ H c ,
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
10
ðqB=qtÞ2 Acylinder , 128rPBSM
(2) Fig. 3. Micrography of gas atomized FeSi6.8 particles.
(4)
ARTICLE IN PRESS M. Anhalt, B. Weidenfeller / Journal of Magnetism and Magnetic Materials 304 (2006) e549–e551
700 600
domain walls show a drastic increase at an excess field around 20–50 A/m depending on the fraction of magnetic material in the composite. The higher the FeSi fraction in the PBSM, the lower is the excess field at which the number of active domain walls is suddenly increased.
PP + 20.5vol% FeSi PP + 29.6vol% FeSi PP + 40.1vol% FeSi
500 neff
e551
400
4. Summary
300 200 100 0 11
0
100
Hexc [A/m] Fig. 4. Excess field H exc versus effective number of domain walls neff .
neff ¼
H w ðtÞ . H exc ðf Þ
(5)
In Eq. (4) H d is the dynamic coercive force at frequency f and H c the static coercive force which was determined by extrapolation of measured dynamic coercive forces to zero frequency. Because the measured dynamic coercive force is the sum of coercive forces of all FeSi particles in the PBSM, the field H w [12] is the sum of all fields which are necessary for the magnetization process by one domain wall in a singe particle. In Fig. 4 the effective number of active domain walls dependent on the excess field is shown. Concerning the large number of particles in the PBSM at low excess fields H exc o20 A=m only a relative low number neff of domain walls are active in the magnetizing process. This number of
The anomaly factor of polypropylene filled with FeSi particles in various fractions follows a Z ¼ Z0 f x relation with frequency. The value of x varies with the amount of FeSi particles and lies between 1:20pxp 1:41 for 20.5–40:1 vol% FeSi. The effective number of active domains is very low and increases suddenly at excess fields larger than 20 A/m depending on the amount of FeSi. The higher the FeSi fraction the lower the excess field at which the drastic increase of active domain walls appear. References [1] I.P. Gilbert, J. Mater. Sci. 39 (2004) 457. [2] M. de Wulf, L. Anestiev, L. Froyen, J. Melkebeek, J. Appl. Phys. 91 (2002) 7845. [3] B. Weidenfeller, M. Ho¨fer, F. Schilling, Composites A 33 (2002) 1041. [4] M. Pott-Langemeyer, W. Riehemann, W. Heye, An. Fis. B 86 (1990) 232. [5] D. Ramin, W. Riehemann, tm—Tech. Mess. 3 (2001) 116. [6] R.H. Pry, C.P. Bean, J. Appl. Phys. 29 (1958) 532. [7] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [8] T.R. Haller, J.J. Kramer, J. Appl. Phys. 41 (1970) 1036. [9] J.E.L. Bishop, J. Magn. Magn. Mater. 12 (1979) 102. [10] C. Wittwer, Ph.D. Thesis, 1994, Clausthal-Zellerfeld, Germany. [11] H.J. Williams, W. Shockley, C. Kittel, Phys. Rev. 80 (1950) 1090. [12] B. Weidenfeller, W. Riehemann, J. Magn. Magn. Mater. 160 (1996) 136.