- Email: [email protected]
Barkhausen noise as a microstructure characterization tool
Physica B 435 (2014) 109–112
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Barkhausen noise as a microstructure characterization tool Aphrodite Ktena a,n, Evangelos Hristoforou b, Gunther J.L. Gerhardt c, Frank P. Missell c, Fernando J.G. Landgraf d, Daniel L. Rodrigues Jr.d, M. Alberteris-Campos d a
Department of Electrical Engineering, TEI of Sterea Ellada, Psachna, Evia 34400, Greece Laboratory of Metallurgy, National Technical University of Athens, Greece c Centro de Ciências Exatas e Tecnologia, Universidade de Caxias do Sul, Brazil d Escola Politécnica, Universidade de São Paulo, São Paulo, Brazil b
art ic l e i nf o
a b s t r a c t
Available online 23 September 2013
Magnetic Barkhausen noise (mBN) is known to be related to magnetization reversal mechanisms and the underlying microstructure in magnetic materials. However, the quantitative evaluation of the material properties is hindered by the stochastic nature of the method combined with the lack of standardization. In this paper, the results of interlaboratory tests on the same series of samples are presented. Electrical steel samples have been prepared with controlled grain size (11–148 μm) and strain (0–29%) and have been characterized using the mBN technique as developed in three different laboratories. In spite of the different methodologies used, mBN is found to increase with strain and decrease with decreasing grain size, in all cases. Of special interest is the variation of the double-peaked BN envelope with the grain size, with one peak occurring in positive and the other in negative fields. The significance of the methodology used in the correct interpretation of the results for a given material is discussed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Barkhausen noise Grain size Residual stress RMS voltage envelopes
1. Introduction Magnetic Barkhausen noise (mBN) is the result of discrete magnetization jumps during the magnetization process of a material and a measure of the energy necessary to nucleate or annihilate magnetic domains and overcome obstacles in magnetic domain wall propagation, such as crystal defects, grain misorientation, grain boundaries, impurities and dislocations. Therefore, mBN is linked to a material's composition, phases, anisotropy, impurities, residual stresses, dislocation density and grain size [1–8]. In spite of its potential as a characterization or magnetic NDT (mNDT) tool, its application is limited by the still unresolved issue of decoding the mBN signature of a material with respect to these microstructural features in a standardized manner. Furthermore, the mBN community has not yet found a consensus concerning the method and the process of mBN evaluation. The basic idea is common: it involves a time-varying excitation magnetic field and the sensing of the voltage pulses induced in a pickup coil. But the realizations vary: the excitation and sensing coils are wound around the material or an yoke is used to magnetize the material in plane while the sensing coil is placed perpendicular to it; the excitation current can be triangular or sinusoidal; the frequency of excitation can be anywhere between
n Corresponding author. Tel.: þ 30 2228099606, þ30 2228099605, þ 30 6977056273; fax: þ 30 2103424977. E-mail addresses: [email protected], [email protected] (A. Ktena).
0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.09.027
0.5 and 10 Hz or even higher [9]. Because mBN is a stochastic process, the frequency content of the output is rich in information and therefore, the data acquisition and post-processing methods, e.g. sampling time and filtering, can seriously affect the output. Finally, mBN metrics used vary between laboratories and new ones are suggested [10]: mBN power, PmBN, spectra analysis [7], RMS mBN pffiffiffiffiffiffiffiffiffiffiffi voltage V mBN ¼ P mBN mBN voltage envelopes, peak heights and locations as well as the area under the mBN voltage curve are often reported [1,5,6,8–12]. In this work, the same sample sets have been characterized by three different laboratories using different mBN setups in order to study the effect of the mBN method used on the parameter (s) recorded and their ensuing evaluation, for the same underlying microstructure, i.e. grain size and true strain.
2. Materials and methods The three laboratories participating in the study are denoted as Lab1 (NTUA-National Technical University of Athens), Lab2 (UCSUniversidade de Caxias do Sul) and Lab3 (USP-Universidade de São Paulo). Three series of cold-rolled silicon steel samples have been prepared at Lab3 by cutting strips of 300 30 mm2: (1) TS-series has variable thickness, with the true strain varying from 0% to 29%; (2) RX-series also has variable thickness and is annealed at 760 1C for 2 h to obtain grain sizes 27–148 μm through recrystallization; (3) GG-series, of 540 μm thickness, is annealed at different
110
A. Ktena et al. / Physica B 435 (2014) 109–112
decrease of mBN with increasing grain size is consistent with stress release, due to annealing, and less pinning because of fewer grain boundaries. Though this is a common finding among several laboratories, contradictory results have also been reported for small grain sizes, below 30 μm, and models have been proposed to explain the non-monotonic dependence (see [12] and references therein). The grain sizes studied in this work started from 11 μm but such non-monotonicity was not observed in any of our data. The double peaked profile appears in all measurements by both laboratories (Lab2 and Lab3) with the two peaks appearing in the positive and negative high induction regions, respectively. The results are in qualitative agreement in spite of the different coil configuration and excitation. The effect of thickness manifests itself in the RX-series measurements, where the peak locations vary more with grain size. The multi-peaked profile has been attributed to a variety of factors [3–6] such as composition, tempering and dislocations. The peaks are related to domain nucleation and annihilation, when they occur in the high
temperatures and time-spans to achieve grain growth. Grain size was measured on a mid-thickness plane parallel to the sheet surface, using the intercept method, counting at least 300 intersections per sample [13]. Their properties and annealing times are summarized in Table 1. The three laboratories all measured the same samples, each one using their own mBN apparatus. The experimental set up used by Lab2 uses a 35 cm long solenoid to generate a sinusoidal excitation field at 0.5 Hz, producing a maximum applied field of 9700 A/m. The pickup coil is tightly wound around the sample. mBN voltage pulses were recorded, at a sampling rate of 500,000/s. For each sample, 12 data sets were collected. The RMS envelopes of the mBN bursts (Fig. 1) were calculated with a moving average window of 1000 points moved successively by 10 points. Lab3 magnetized the sample in plane using a yoke with the pickup coil perpendicular to the sample and 10 Hz sinusoidal excitation. mBN RMS envelopes were recorded at a sampling rate of 200 kHz [14]. Lab1 used a commercial device (MEB-2c) using an yoke to magnetize the sample in plane and a pick-up coil perpendicular to it with a triangular excitation field of 7 V, at a frequency of 10 Hz. The mBN parameters recorded are the counts of mBN peaks above a given threshold and the RMS mBN voltage obtained over 100 cycles. Several measurements were taken at various points along the center line of the samples on both sides. Next, the average number of counts, N, and RMS mBN voltage, VB, were calculated for each sample (Figs. 2 and 4).
VB [mV]
300
RX GG Power (RX) Power (GG)
200
y = 465.36x-0.24 R² = 0.9236
3. Results and discussion 3.1. The effect of grain size
100
The average values of the 12 data sets collected on each sample by Lab2 for the RX- and GG-series are shown in Fig. 1. The applied field is decreasing from a high positive value. The monotonic
y = 561.77x-0.301 R² = 0.87 0
50
100
150
GS [µm] Fig. 2. mBN voltage VB vs. grain size for the RX- and GG-series.
Table 1 Properties of samples measured. Sample TS-series True strain (%) Thickness (μm)
TS1 29 510
TS2 24 540
TS3 19 560
TS4 12 600
TS5
RX-series
RX1
RX2
RX3
RX4
RX5
Grain size (μm) Thickness (μm)
148 511
119 501
82 488
67 475
TS6
10 620
7 640 RX6
54 451
31 400
GG-series
GG1
GG2
GG3
GG4
GG5
GG6
Grain size (μm) Thickness (μm) Annealing (1C/h)
11 540 600/2
17 540 680/2
57 540 850/4
62 540 850/8
66 540 850/12
27 540 680/2
Fig. 1. mBN voltage envelopes for (a) RX-series and (b) GG-series.
TS7 3 660 RX7 27 343
TS8 2 670
TS9 0 680
A. Ktena et al. / Physica B 435 (2014) 109–112
111
Fig. 3. (a) RMS mBN voltage envelopes for samples RX7 and GG6 and (b) RMS mBN voltage for RX7 and corresponding hysteresis loop.
couns N
6000 4000
RX GG
2000 0
0
0.1
0.2
0.3
0.4
(GS)-1/2 [ m-1/2] Fig. 4. (a) Area under the RMS mBN voltage envelope, by Lab2 and (b) mBN counts vs the inverse of the square root of grain size for both RX- and GG-series, by Lab1.
induction region, or domain wall movement, around coercivity. Their locations and heights are related to the magnetization reversal mechanisms favored by each material, the composition and existing phases [3–5,7,10,12]. In case of defect-free electrical steel, the case presented here, the peaks are most likely related to domain nucleation and annihilation. Fig. 2 shows the results obtained by Lab1 for the RMS mBN voltage, VB, for the two series of samples with variable grain size. Again, mBN decreases with grain size GS asymptotically towards some minimum value: voltage VB varies approximately as GS 1/4 and the associated number of mBN counts N varies as GS 1/2. Fig. 3a depicts the comparison between two samples of the same grain size, 27 μm, and different thickness: RX7 and GG6, as measured by Lab2. The recrystallized but thinner sample yields higher mBN peaks occurring at lower fields (Fig. 3) which is consistent with smaller demagnetizing fields. In order to compare the data collected by Lab1 and Lab2, the mBN counts N and the area under the curve for the mBN voltage profiles shown in Fig. 1 are plotted against on GS 1/2 (Fig. 4). The area under the curve is a measure of the sum of all Barkhausen jumps and should be proportional to the total magnetization change over the hysteresis curve. The results compare well qualitatively despite the different methods and metrics used.
1
0.8
0.6 N VB
0.4
0.2
0
10
20
30
strain (%) Fig. 5. Normalized mBN voltage VB and counts N vs. strain.
the data collected by Lab2 [15], the mBN voltage profile initially shows two peaks progressively collapsing into one as true strain increases. This is consistent with the pinning of domain walls against dislocations becoming the prevailing magnetization reversal mechanism with increasing strain.
3.2. The effect of stress Results on the strained samples of the TS-series are similar between the laboratories involved and corroborate previous findings [5,13–15]. Fig. 5 shows mBN counts N and voltage VB vs. true strain, normalized to the highest value. mBN increases with strain reaching a plateau when the material is in the plastic region. Notice that the transition into the yielding region is observed in both curves, N and VB. Initially, dislocations increase fast and lead to higher mBN, but as the material enters the plastic region, the dislocation tangles inhibit additional magnetic configuration changes until energy is released with fracture. Furthermore, in
4. Conclusion Despite the differences in experimental methodology, mBN is a powerful tool for the non destructive evaluation of magnetic materials. The interlaboratory comparison of the mBN dependence on grain size and strain showed that mBN decreases with increasing grain size and increases with strain, consistently, in spite of the different methodology and metrics used. The mBN area under the RMS voltage curve correlates with mBN counts. The emergence of multi-peak profiles has been observed in the
112
A. Ktena et al. / Physica B 435 (2014) 109–112
material studied. Further work is needed to correlate mBN profile peak locations and heights with structural parameters and related magnetization processes. Acknowledgments This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund. Work at UCS was partially supported by CNPq and FAPERGS. FPM and FJGL are partially supported by CNPq. References [1] L. Mierczak, D.C. Jiles, G. Fantoni, IEEE Trans. Magn. 47 (2) (2011) 459. [2] H. Sakamoto, M. Okada, M. Homma, IEEE Trans. Magn. 23 (1987) 2236.
[3] D.G. Hwang, H.C. Kim, J. Phys. D: Appl. Phys. 21 (1988) 1807. [4] S.M. Thompson, B.K. Tanner, J. Magn Magn. Mater. 132 (1–3) (1994) 71. [5] C. Gatelier-Rothea, J. Chicois, R. Fougeres, P. Fleischmann, Acta Mater. 46 (14) (1998) 4873. [6] V. Moorthy, S. Vaidyanathan, T. Jayakumar, Baldev Raj, B.P. Kashyap, Acta Mater. 47 (6) (1999) 1869. [7] S. Yamaura, Y. Furuya, T. Watanabe, Acta Mater. 49 (15) (2001) 3019. [8] D.H.L. Ng, K.S. Cho, M.L. Wong, S.L.I. Chan, X.-Y. Ma, C.C.H. Lo, Mater. Sci. Eng. A358 (1–2) (2003) 186. [9] Nkwachukwu Chukwuchekwa, Anthony Moses, Phil Anderson, J. Electron. Eng. 61 (2010) 69. [10] O. Stupakov, T. Takagi, T. Uchimoto, NDT&E Int. 43 (2010) 671. [11] M. Blaow, J.T. Evans, B.A. Shaw, J. Mater. Sci. 40 (2005) 5517. [12] Jozef Pala, Jan Bydzovsky, Measurement 46 (2013) 866. [13] F.J.G. Landgraf, J.R.F. Silveira, D. Rodrigues-Jr, J. Magn. Magn. Mater. 323 (2011) 2335. [14] M. Alberteris Campos, J. Capo-Sanchez, J. Perez Benıtez, L.R. Padovese, NDT&E Int. 41 (2008) 656. [15] D.L. Rodrigues Jr., J.R.F. Silveira, G.J.L. Gerhardt, F.P. Missell, F.J.G. Landgraf, R. Machado, M.F. de Campos, IEEE Trans. Magn. 48 (2012) 1425.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Barkhausen noise as a microstructure characterization tool Aphrodite Ktena a,n, Evangelos Hristoforou b, Gunther J.L. Gerhardt c, Frank P. Missell c, Fernando J.G. Landgraf d, Daniel L. Rodrigues Jr.d, M. Alberteris-Campos d a
Department of Electrical Engineering, TEI of Sterea Ellada, Psachna, Evia 34400, Greece Laboratory of Metallurgy, National Technical University of Athens, Greece c Centro de Ciências Exatas e Tecnologia, Universidade de Caxias do Sul, Brazil d Escola Politécnica, Universidade de São Paulo, São Paulo, Brazil b
art ic l e i nf o
a b s t r a c t
Available online 23 September 2013
Magnetic Barkhausen noise (mBN) is known to be related to magnetization reversal mechanisms and the underlying microstructure in magnetic materials. However, the quantitative evaluation of the material properties is hindered by the stochastic nature of the method combined with the lack of standardization. In this paper, the results of interlaboratory tests on the same series of samples are presented. Electrical steel samples have been prepared with controlled grain size (11–148 μm) and strain (0–29%) and have been characterized using the mBN technique as developed in three different laboratories. In spite of the different methodologies used, mBN is found to increase with strain and decrease with decreasing grain size, in all cases. Of special interest is the variation of the double-peaked BN envelope with the grain size, with one peak occurring in positive and the other in negative fields. The significance of the methodology used in the correct interpretation of the results for a given material is discussed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Barkhausen noise Grain size Residual stress RMS voltage envelopes
1. Introduction Magnetic Barkhausen noise (mBN) is the result of discrete magnetization jumps during the magnetization process of a material and a measure of the energy necessary to nucleate or annihilate magnetic domains and overcome obstacles in magnetic domain wall propagation, such as crystal defects, grain misorientation, grain boundaries, impurities and dislocations. Therefore, mBN is linked to a material's composition, phases, anisotropy, impurities, residual stresses, dislocation density and grain size [1–8]. In spite of its potential as a characterization or magnetic NDT (mNDT) tool, its application is limited by the still unresolved issue of decoding the mBN signature of a material with respect to these microstructural features in a standardized manner. Furthermore, the mBN community has not yet found a consensus concerning the method and the process of mBN evaluation. The basic idea is common: it involves a time-varying excitation magnetic field and the sensing of the voltage pulses induced in a pickup coil. But the realizations vary: the excitation and sensing coils are wound around the material or an yoke is used to magnetize the material in plane while the sensing coil is placed perpendicular to it; the excitation current can be triangular or sinusoidal; the frequency of excitation can be anywhere between
n Corresponding author. Tel.: þ 30 2228099606, þ30 2228099605, þ 30 6977056273; fax: þ 30 2103424977. E-mail addresses: [email protected], [email protected] (A. Ktena).
0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.09.027
0.5 and 10 Hz or even higher [9]. Because mBN is a stochastic process, the frequency content of the output is rich in information and therefore, the data acquisition and post-processing methods, e.g. sampling time and filtering, can seriously affect the output. Finally, mBN metrics used vary between laboratories and new ones are suggested [10]: mBN power, PmBN, spectra analysis [7], RMS mBN pffiffiffiffiffiffiffiffiffiffiffi voltage V mBN ¼ P mBN mBN voltage envelopes, peak heights and locations as well as the area under the mBN voltage curve are often reported [1,5,6,8–12]. In this work, the same sample sets have been characterized by three different laboratories using different mBN setups in order to study the effect of the mBN method used on the parameter (s) recorded and their ensuing evaluation, for the same underlying microstructure, i.e. grain size and true strain.
2. Materials and methods The three laboratories participating in the study are denoted as Lab1 (NTUA-National Technical University of Athens), Lab2 (UCSUniversidade de Caxias do Sul) and Lab3 (USP-Universidade de São Paulo). Three series of cold-rolled silicon steel samples have been prepared at Lab3 by cutting strips of 300 30 mm2: (1) TS-series has variable thickness, with the true strain varying from 0% to 29%; (2) RX-series also has variable thickness and is annealed at 760 1C for 2 h to obtain grain sizes 27–148 μm through recrystallization; (3) GG-series, of 540 μm thickness, is annealed at different
110
A. Ktena et al. / Physica B 435 (2014) 109–112
decrease of mBN with increasing grain size is consistent with stress release, due to annealing, and less pinning because of fewer grain boundaries. Though this is a common finding among several laboratories, contradictory results have also been reported for small grain sizes, below 30 μm, and models have been proposed to explain the non-monotonic dependence (see [12] and references therein). The grain sizes studied in this work started from 11 μm but such non-monotonicity was not observed in any of our data. The double peaked profile appears in all measurements by both laboratories (Lab2 and Lab3) with the two peaks appearing in the positive and negative high induction regions, respectively. The results are in qualitative agreement in spite of the different coil configuration and excitation. The effect of thickness manifests itself in the RX-series measurements, where the peak locations vary more with grain size. The multi-peaked profile has been attributed to a variety of factors [3–6] such as composition, tempering and dislocations. The peaks are related to domain nucleation and annihilation, when they occur in the high
temperatures and time-spans to achieve grain growth. Grain size was measured on a mid-thickness plane parallel to the sheet surface, using the intercept method, counting at least 300 intersections per sample [13]. Their properties and annealing times are summarized in Table 1. The three laboratories all measured the same samples, each one using their own mBN apparatus. The experimental set up used by Lab2 uses a 35 cm long solenoid to generate a sinusoidal excitation field at 0.5 Hz, producing a maximum applied field of 9700 A/m. The pickup coil is tightly wound around the sample. mBN voltage pulses were recorded, at a sampling rate of 500,000/s. For each sample, 12 data sets were collected. The RMS envelopes of the mBN bursts (Fig. 1) were calculated with a moving average window of 1000 points moved successively by 10 points. Lab3 magnetized the sample in plane using a yoke with the pickup coil perpendicular to the sample and 10 Hz sinusoidal excitation. mBN RMS envelopes were recorded at a sampling rate of 200 kHz [14]. Lab1 used a commercial device (MEB-2c) using an yoke to magnetize the sample in plane and a pick-up coil perpendicular to it with a triangular excitation field of 7 V, at a frequency of 10 Hz. The mBN parameters recorded are the counts of mBN peaks above a given threshold and the RMS mBN voltage obtained over 100 cycles. Several measurements were taken at various points along the center line of the samples on both sides. Next, the average number of counts, N, and RMS mBN voltage, VB, were calculated for each sample (Figs. 2 and 4).
VB [mV]
300
RX GG Power (RX) Power (GG)
200
y = 465.36x-0.24 R² = 0.9236
3. Results and discussion 3.1. The effect of grain size
100
The average values of the 12 data sets collected on each sample by Lab2 for the RX- and GG-series are shown in Fig. 1. The applied field is decreasing from a high positive value. The monotonic
y = 561.77x-0.301 R² = 0.87 0
50
100
150
GS [µm] Fig. 2. mBN voltage VB vs. grain size for the RX- and GG-series.
Table 1 Properties of samples measured. Sample TS-series True strain (%) Thickness (μm)
TS1 29 510
TS2 24 540
TS3 19 560
TS4 12 600
TS5
RX-series
RX1
RX2
RX3
RX4
RX5
Grain size (μm) Thickness (μm)
148 511
119 501
82 488
67 475
TS6
10 620
7 640 RX6
54 451
31 400
GG-series
GG1
GG2
GG3
GG4
GG5
GG6
Grain size (μm) Thickness (μm) Annealing (1C/h)
11 540 600/2
17 540 680/2
57 540 850/4
62 540 850/8
66 540 850/12
27 540 680/2
Fig. 1. mBN voltage envelopes for (a) RX-series and (b) GG-series.
TS7 3 660 RX7 27 343
TS8 2 670
TS9 0 680
A. Ktena et al. / Physica B 435 (2014) 109–112
111
Fig. 3. (a) RMS mBN voltage envelopes for samples RX7 and GG6 and (b) RMS mBN voltage for RX7 and corresponding hysteresis loop.
couns N
6000 4000
RX GG
2000 0
0
0.1
0.2
0.3
0.4
(GS)-1/2 [ m-1/2] Fig. 4. (a) Area under the RMS mBN voltage envelope, by Lab2 and (b) mBN counts vs the inverse of the square root of grain size for both RX- and GG-series, by Lab1.
induction region, or domain wall movement, around coercivity. Their locations and heights are related to the magnetization reversal mechanisms favored by each material, the composition and existing phases [3–5,7,10,12]. In case of defect-free electrical steel, the case presented here, the peaks are most likely related to domain nucleation and annihilation. Fig. 2 shows the results obtained by Lab1 for the RMS mBN voltage, VB, for the two series of samples with variable grain size. Again, mBN decreases with grain size GS asymptotically towards some minimum value: voltage VB varies approximately as GS 1/4 and the associated number of mBN counts N varies as GS 1/2. Fig. 3a depicts the comparison between two samples of the same grain size, 27 μm, and different thickness: RX7 and GG6, as measured by Lab2. The recrystallized but thinner sample yields higher mBN peaks occurring at lower fields (Fig. 3) which is consistent with smaller demagnetizing fields. In order to compare the data collected by Lab1 and Lab2, the mBN counts N and the area under the curve for the mBN voltage profiles shown in Fig. 1 are plotted against on GS 1/2 (Fig. 4). The area under the curve is a measure of the sum of all Barkhausen jumps and should be proportional to the total magnetization change over the hysteresis curve. The results compare well qualitatively despite the different methods and metrics used.
1
0.8
0.6 N VB
0.4
0.2
0
10
20
30
strain (%) Fig. 5. Normalized mBN voltage VB and counts N vs. strain.
the data collected by Lab2 [15], the mBN voltage profile initially shows two peaks progressively collapsing into one as true strain increases. This is consistent with the pinning of domain walls against dislocations becoming the prevailing magnetization reversal mechanism with increasing strain.
3.2. The effect of stress Results on the strained samples of the TS-series are similar between the laboratories involved and corroborate previous findings [5,13–15]. Fig. 5 shows mBN counts N and voltage VB vs. true strain, normalized to the highest value. mBN increases with strain reaching a plateau when the material is in the plastic region. Notice that the transition into the yielding region is observed in both curves, N and VB. Initially, dislocations increase fast and lead to higher mBN, but as the material enters the plastic region, the dislocation tangles inhibit additional magnetic configuration changes until energy is released with fracture. Furthermore, in
4. Conclusion Despite the differences in experimental methodology, mBN is a powerful tool for the non destructive evaluation of magnetic materials. The interlaboratory comparison of the mBN dependence on grain size and strain showed that mBN decreases with increasing grain size and increases with strain, consistently, in spite of the different methodology and metrics used. The mBN area under the RMS voltage curve correlates with mBN counts. The emergence of multi-peak profiles has been observed in the
112
A. Ktena et al. / Physica B 435 (2014) 109–112
material studied. Further work is needed to correlate mBN profile peak locations and heights with structural parameters and related magnetization processes. Acknowledgments This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund. Work at UCS was partially supported by CNPq and FAPERGS. FPM and FJGL are partially supported by CNPq. References [1] L. Mierczak, D.C. Jiles, G. Fantoni, IEEE Trans. Magn. 47 (2) (2011) 459. [2] H. Sakamoto, M. Okada, M. Homma, IEEE Trans. Magn. 23 (1987) 2236.
[3] D.G. Hwang, H.C. Kim, J. Phys. D: Appl. Phys. 21 (1988) 1807. [4] S.M. Thompson, B.K. Tanner, J. Magn Magn. Mater. 132 (1–3) (1994) 71. [5] C. Gatelier-Rothea, J. Chicois, R. Fougeres, P. Fleischmann, Acta Mater. 46 (14) (1998) 4873. [6] V. Moorthy, S. Vaidyanathan, T. Jayakumar, Baldev Raj, B.P. Kashyap, Acta Mater. 47 (6) (1999) 1869. [7] S. Yamaura, Y. Furuya, T. Watanabe, Acta Mater. 49 (15) (2001) 3019. [8] D.H.L. Ng, K.S. Cho, M.L. Wong, S.L.I. Chan, X.-Y. Ma, C.C.H. Lo, Mater. Sci. Eng. A358 (1–2) (2003) 186. [9] Nkwachukwu Chukwuchekwa, Anthony Moses, Phil Anderson, J. Electron. Eng. 61 (2010) 69. [10] O. Stupakov, T. Takagi, T. Uchimoto, NDT&E Int. 43 (2010) 671. [11] M. Blaow, J.T. Evans, B.A. Shaw, J. Mater. Sci. 40 (2005) 5517. [12] Jozef Pala, Jan Bydzovsky, Measurement 46 (2013) 866. [13] F.J.G. Landgraf, J.R.F. Silveira, D. Rodrigues-Jr, J. Magn. Magn. Mater. 323 (2011) 2335. [14] M. Alberteris Campos, J. Capo-Sanchez, J. Perez Benıtez, L.R. Padovese, NDT&E Int. 41 (2008) 656. [15] D.L. Rodrigues Jr., J.R.F. Silveira, G.J.L. Gerhardt, F.P. Missell, F.J.G. Landgraf, R. Machado, M.F. de Campos, IEEE Trans. Magn. 48 (2012) 1425.