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A new method for M–H and λ–H determination using the magnetostrictive delay line technique
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 304 (2006) 164–167 www.elsevier.com/locate/jmmm
A new method for M–H and l–H determination using the magnetostrictive delay line technique Evangelos Hristoforou, Panagiotis Dimitropoulos Laboratory of Physical Metallurgy, National Technical University of Athens, Zografou Campus, Athens 15780, Greece Available online 15 March 2006
Abstract In this paper, a new technique for the determination of M–H loop and l–H loop is proposed, based on the magnetostrictive delay line (MDL) technique and used for long magnetostrictive ribbons, wires and rods of uniform cross-section. The principle of the M–H loop determination is based on the biasing field effect at the MDL search coil, while the principle of the l–H loop is based on the biasing and pulsed field effects at the MDL excitation point. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.Ej; 72.55.+s; 85.70.Ec Keywords: Magnetostrictive delay lines; M–H loop; l–H loop
1. Introduction Magnetostriction, the deformation of a magnetic body during its magnetization, is a fundamental sensing effect with a variety of configurations and applications [1]. The Villari effect, magneto-acoustic emission, Matteucci effect and Wiedemann effect, are some of the applications of magnetostriction [2–4]. Magnetostrictive theory and related devices cover a wide spectrum of applications of instrumentation and measurement [5]. The magnetostrictive delay line (MDL) technique has been employed for the development of a new tool for the determination of the M–H and l–H loop [6]. The motivation of such work has been the determination of these loops as well as the ability of measuring their nonuniformity function [7]. Fig. 1(a) and (b) illustrates the basic MDL set-up. The MDL is activated by transmitting pulsed current H e ðtÞ ¼ H e f ðtÞ, through the excitation coil or the pulsed current conductor. Pulsed current generates a pulsed magnetic field along the magnetostrictive element. This field generates a pulsed microstrain at the region of Corresponding author. Tel.: +30 210 7722 178; fax: +30 210 772 119.
E-mail address: [email protected] (E. Hristoforou). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.127
excitation of the magnetostrictive element lðH oe þ H e ðtÞÞ due to the magnetostriction effect. Since the magnetostrictive material is in the shape of cylinder or ribbon, it can operate as acoustic waveguide. Therefore, the pulsed microstrain propagates along the length of the magnetostrictive element as longitudinal acoustic pulse. As soon as it arrives at the region of the search coil, it is detected as pulsed voltage output, proportional to the first derivative of the propagating pulse, due to the inverse magnetostriction effect. The generation and detection of the pulsed microstrain is possible and repeatable due to the presence of biasing fields at the acoustic stress point of origin and the search area, H oe and H or , respectively, which orient the magnetic dipoles in a given direction. 2. Theory The propagating pulsed microstrain induces stresses sðlÞ in the MDL. These stresses act as effective field H s ¼ f ðsÞ in the MDL, added in the already existing biasing field along its length. Provided that the said microstrain propagates without dispersion and aftereffects, which are applicable for the front acoustic wave, the microstrain arrives at the region of the search coil, inducing such an effective field H s along the length of the MDL. Thus, the
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
165
and H e changes, V o becomes V o ¼ AacH e mðH or Þ
(a)
1
2
dl dl ¼ C3H e . dH dH
(8)
Thus V o =H e ¼ C 3 dl=dH, where C3 is a constant, mainly dependent on the material and the biasing fields at the excitation and receiving regions.
3
3. M–H loop
4
2
3
(b) Fig. 1. Two simplest magnetostrictive delay line (MDL) set-ups: (a) excitation coil — search coil and (b) excitation pulsed current conductor — search coil. (1) Excitation coil, (2) MDL, (3) search coil and (4) excitation pulsed current conductor.
flux within the magnetic region inside the search coil is FðtÞ ¼ SmðH or ÞðH or þ H s Þ,
(1)
Keeping He, Hoe constant and changing Hor, the peak magnitude of the MDL pulsed voltage output is given by Eq. (6). Normalizing Vo as well as its integral function and calibrating the MDL set-up using a standard Ni magnetostrictive wire of known M–H loop, the m–H and M–H loops at the region of the receiving coil of the MDL can be determined. Since the applied biasing field is DC, the method determines the DC m–H and M–H loops. In this paper, representative data of amorphous positive magnetostrictive ribbons and wires of the rather typical Fe78Si7B15 composition are presented. Fig. 2(a) and (b) illustrate the dependence of Vo and magnetization M loops on the biasing field H, concerning an amorphous Fe78Si7B15 magnetostrictive wire, after stress–current annealing under
dF dH s ¼ AmðH or Þ , (2) dt dt where A includes S and search coil parameters. Effective field and stress are assumed to be proportionately related:
V o ðtÞ ¼
(3)
Thus V o ðtÞ becomes dl df ðtÞ He dH dt and V o , the peak value of V o ðtÞ is given by
V o ðtÞ ¼ AamðH or Þ
(4)
dl , (5) dH where c is the maximum of df =dt. In case H e ; H oe are unchanged and H or changes, V o becomes V o ¼ AacH e mðH or Þ
V o ¼ Aacc1 H e mðH or Þ ¼ C 1 mðH or Þ,
0.8
0.3
-2000
-1500
-1000
dl dl ¼ C2 , (7) dH dH where C2 is a constant, mainly dependent on the material and the excitation field and biasing field at the excitation and receiving regions, respectively. Under these conditions dl=dH is proportional to V o . When H oe ; H or are constants
-0.2
0
500
1000
1500
2000
1000
1500
2000
-1.2 Biasing field (A/m)
0.8
(6)
where constant c1 ¼ ðdl=dHÞmax . Coefficient C1 is a constant, mainly dependent on the material and the fields at the excitation regions. Under these conditions mðH or Þ is proportional to V o . In case that H e ; H or are constant and H oe changes, V o becomes
-500
-0.7
(a)
Normalized M-H loop
H s ¼ alðH oe ; H e ðtÞÞ.
Normalized MDL voltage output
where S is the cross-section of the magnetostrictive element. Thus the voltage output Vo(t) at the search coil is
0.3
-2000
-1500
-1000
-500 -0.2 0
500
-0.7
V o ¼ AacH e mðH or Þ
(b)
-1.2 Biasing field (A/m)
Fig. 2. Permeability (a) and magnetization loops (b) concerning amorphous Fe78Si7B15 wire after stress–current annealing.
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
166
40 35 30 25 20 15 10 5
-2000
0 0
200
400
(a)
800 600 1000 Biasing field (A/m)
1200
1400
1600
1 0.8 0.6 0.4 0.2
-1500
-1000
(a)
Normalized lamda-H loop
30 25 20 15 10 5
-2000 200
400
600 800 1000 Biasing field (A/m)
1500
2000
1000
1500
2000
0.8 0.6 0.4 0.2
-1500
-1000
1200
1400
1600
Fig. 3. Permeability (a) and magnetization loops (b) concerning Fe78Si7 B15 amorphous ribbon after thermal annealing.
400 MPa and 0.5 A for 10 min. The peculiar bi-stable response of as cast Fe78Si7B15 wires has also been observed. The experimental data and detailed procedures can be found in Ref. [6]. Fig. 3(a) and (b) illustrate the same response for the case of amorphous Fe78Si7B15 ribbon after thermal annealing in 300 1C and Ar atmosphere for 1 h and consequent slow rate cooling. 4. k–H loop Keeping He and Hor constant, while the biasing field Hoe changes, the peak magnitude of the MDL pulsed voltage output Vo is given by Eq. (7), being proportional to dl(Hoe)/dH. Normalization process and calibration against a standard Ni magnetostrictive wire of known l–H loop results in the DC l–H function determination. Indicative results are also presented concerning amorphous as-cast positive Fe78Si7B15 magnetostrictive wires. Fig. 4(a) and (b) illustrate the normalized MDL response and the l dependence on Hoe, respectively. Maintaining the basing fields Hoe and Hor steady and changing the excitation field He, the peak magnitude of Vo/He is given by Eq (8). Thus, the integral of Vo/He on He is proportional to the magnetostriction l. Normalization and calibration against a standard Ni magnetostrictive wire of known l–H loop results in the l–H loop determination.
0 -500 0 500 Biasing field (A/m)
Fig. 4. Normalized MDL response on biasing field at the excitation point (a) and integration of the MDL voltage output corresponding to the DC l–H loop (b).
1.2
Normalized MDL voltage output
0
1000
1
(b)
0
(b)
0 -500 0 500 Biasing field (A/m) 1.2
-2000
1 0.8 0.6 0.4 0.2
-1500
-1000
(a)
0 -500 0 500 Pulsed field (A/m)
1000
1500
2000
1000
1500
2000
1.2 Normalized lamda-H function
MDL voltage output (mV)
45
Magnetization (a.u.)
1.2
Normalized MDL voltage output
50
-2000
(b)
1 0.8 0.6 0.4 0.2
-1500
-1000
0 -500 0 500 Pulsed field (A/m)
Fig. 5. Normalized Vo/He MDL response on the pulsed field (a) and integration of Vo/He corresponding to the AC l–H loop (b).
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
Fig. 5(a) and (b) illustrate the normalized MDL response and its integral corresponding to the l–H function for the case of as-cast amorphous Fe78Si7B15 wires. 5. Discussion Considering the sample vibrated by the propagating elastic pulse, the method is an alternative vibrating sample magnetometer (VSM) technique, the MDL–VSM technique. The main advantage with respect to the classic VSM technique is the by-design ability of measuring the nonuniformity of permeability, magnetization and flux density of the under test specimen, by moving the position of the receiving coil and the surrounding biasing coil. Apart from that there is no need to cut the sample in pieces as for the case of the VSM. The described technique can also be used to measure the M–H loop of any magnetostrictive element, by gluing it on a glass substrate [8]. Controlling the temperature of the set-up, the dependence of the m–H, M–H and l–H loops on temperature can be determined. Changing the biasing field with a frequency less than 1 kHz,
167
corresponding to the pulsed current excitation period, the dependence of m–H, M–H and l–H loops on frequency may also be determined. Temporal dependence tests of m–H, M–H and l–H loops may also be performed. Future work is under way to improve and precisely calibrate the instrument. References [1] A. Bienkowski, R. Szewczyk, R. Kolano, Mater. Sci. Eng. A 375 (2004) 1024. [2] S.N. Kane, M. Va´zquez, A. Hernando, A. Gupta, Mater. Sci. Eng. A 304 (2001) 1055. [3] A.F. Cobeno, A.P. Zhukov, E. Pina, J.M. Blanco, J. Gonzalez, J.M. Barandiaran, J. Magn. Magn. Mater. 215 (2000) 743. [4] J. Bydzˇovsky´, L. Kraus, P. Sˇvec, M. Pasquale, M. Kolla´r, Sensor Actuat. A 110 (2004) 82. [5] E. du Tremolet de Lacheisserie, Magnetostriction: Theory and Applications of Magnetoelasticity, CRC Press, Boca Raton FL, 1994. [6] E. Hristoforou, H. Chiriac, M. Neagu, Sensor Actuat. A 67 (1998) 49. [7] E. Hristoforou, R.E. Reilly, J. Appl. Phys. 69 (1991) 5008. [8] E. Hristoforou, H. Chiriac, M. Neagu, I. Darie, J. Phys. IV 8 (1998) 809.
Journal of Magnetism and Magnetic Materials 304 (2006) 164–167 www.elsevier.com/locate/jmmm
A new method for M–H and l–H determination using the magnetostrictive delay line technique Evangelos Hristoforou, Panagiotis Dimitropoulos Laboratory of Physical Metallurgy, National Technical University of Athens, Zografou Campus, Athens 15780, Greece Available online 15 March 2006
Abstract In this paper, a new technique for the determination of M–H loop and l–H loop is proposed, based on the magnetostrictive delay line (MDL) technique and used for long magnetostrictive ribbons, wires and rods of uniform cross-section. The principle of the M–H loop determination is based on the biasing field effect at the MDL search coil, while the principle of the l–H loop is based on the biasing and pulsed field effects at the MDL excitation point. r 2006 Elsevier B.V. All rights reserved. PACS: 75.60.Ej; 72.55.+s; 85.70.Ec Keywords: Magnetostrictive delay lines; M–H loop; l–H loop
1. Introduction Magnetostriction, the deformation of a magnetic body during its magnetization, is a fundamental sensing effect with a variety of configurations and applications [1]. The Villari effect, magneto-acoustic emission, Matteucci effect and Wiedemann effect, are some of the applications of magnetostriction [2–4]. Magnetostrictive theory and related devices cover a wide spectrum of applications of instrumentation and measurement [5]. The magnetostrictive delay line (MDL) technique has been employed for the development of a new tool for the determination of the M–H and l–H loop [6]. The motivation of such work has been the determination of these loops as well as the ability of measuring their nonuniformity function [7]. Fig. 1(a) and (b) illustrates the basic MDL set-up. The MDL is activated by transmitting pulsed current H e ðtÞ ¼ H e f ðtÞ, through the excitation coil or the pulsed current conductor. Pulsed current generates a pulsed magnetic field along the magnetostrictive element. This field generates a pulsed microstrain at the region of Corresponding author. Tel.: +30 210 7722 178; fax: +30 210 772 119.
E-mail address: [email protected] (E. Hristoforou). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.02.127
excitation of the magnetostrictive element lðH oe þ H e ðtÞÞ due to the magnetostriction effect. Since the magnetostrictive material is in the shape of cylinder or ribbon, it can operate as acoustic waveguide. Therefore, the pulsed microstrain propagates along the length of the magnetostrictive element as longitudinal acoustic pulse. As soon as it arrives at the region of the search coil, it is detected as pulsed voltage output, proportional to the first derivative of the propagating pulse, due to the inverse magnetostriction effect. The generation and detection of the pulsed microstrain is possible and repeatable due to the presence of biasing fields at the acoustic stress point of origin and the search area, H oe and H or , respectively, which orient the magnetic dipoles in a given direction. 2. Theory The propagating pulsed microstrain induces stresses sðlÞ in the MDL. These stresses act as effective field H s ¼ f ðsÞ in the MDL, added in the already existing biasing field along its length. Provided that the said microstrain propagates without dispersion and aftereffects, which are applicable for the front acoustic wave, the microstrain arrives at the region of the search coil, inducing such an effective field H s along the length of the MDL. Thus, the
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
165
and H e changes, V o becomes V o ¼ AacH e mðH or Þ
(a)
1
2
dl dl ¼ C3H e . dH dH
(8)
Thus V o =H e ¼ C 3 dl=dH, where C3 is a constant, mainly dependent on the material and the biasing fields at the excitation and receiving regions.
3
3. M–H loop
4
2
3
(b) Fig. 1. Two simplest magnetostrictive delay line (MDL) set-ups: (a) excitation coil — search coil and (b) excitation pulsed current conductor — search coil. (1) Excitation coil, (2) MDL, (3) search coil and (4) excitation pulsed current conductor.
flux within the magnetic region inside the search coil is FðtÞ ¼ SmðH or ÞðH or þ H s Þ,
(1)
Keeping He, Hoe constant and changing Hor, the peak magnitude of the MDL pulsed voltage output is given by Eq. (6). Normalizing Vo as well as its integral function and calibrating the MDL set-up using a standard Ni magnetostrictive wire of known M–H loop, the m–H and M–H loops at the region of the receiving coil of the MDL can be determined. Since the applied biasing field is DC, the method determines the DC m–H and M–H loops. In this paper, representative data of amorphous positive magnetostrictive ribbons and wires of the rather typical Fe78Si7B15 composition are presented. Fig. 2(a) and (b) illustrate the dependence of Vo and magnetization M loops on the biasing field H, concerning an amorphous Fe78Si7B15 magnetostrictive wire, after stress–current annealing under
dF dH s ¼ AmðH or Þ , (2) dt dt where A includes S and search coil parameters. Effective field and stress are assumed to be proportionately related:
V o ðtÞ ¼
(3)
Thus V o ðtÞ becomes dl df ðtÞ He dH dt and V o , the peak value of V o ðtÞ is given by
V o ðtÞ ¼ AamðH or Þ
(4)
dl , (5) dH where c is the maximum of df =dt. In case H e ; H oe are unchanged and H or changes, V o becomes V o ¼ AacH e mðH or Þ
V o ¼ Aacc1 H e mðH or Þ ¼ C 1 mðH or Þ,
0.8
0.3
-2000
-1500
-1000
dl dl ¼ C2 , (7) dH dH where C2 is a constant, mainly dependent on the material and the excitation field and biasing field at the excitation and receiving regions, respectively. Under these conditions dl=dH is proportional to V o . When H oe ; H or are constants
-0.2
0
500
1000
1500
2000
1000
1500
2000
-1.2 Biasing field (A/m)
0.8
(6)
where constant c1 ¼ ðdl=dHÞmax . Coefficient C1 is a constant, mainly dependent on the material and the fields at the excitation regions. Under these conditions mðH or Þ is proportional to V o . In case that H e ; H or are constant and H oe changes, V o becomes
-500
-0.7
(a)
Normalized M-H loop
H s ¼ alðH oe ; H e ðtÞÞ.
Normalized MDL voltage output
where S is the cross-section of the magnetostrictive element. Thus the voltage output Vo(t) at the search coil is
0.3
-2000
-1500
-1000
-500 -0.2 0
500
-0.7
V o ¼ AacH e mðH or Þ
(b)
-1.2 Biasing field (A/m)
Fig. 2. Permeability (a) and magnetization loops (b) concerning amorphous Fe78Si7B15 wire after stress–current annealing.
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
166
40 35 30 25 20 15 10 5
-2000
0 0
200
400
(a)
800 600 1000 Biasing field (A/m)
1200
1400
1600
1 0.8 0.6 0.4 0.2
-1500
-1000
(a)
Normalized lamda-H loop
30 25 20 15 10 5
-2000 200
400
600 800 1000 Biasing field (A/m)
1500
2000
1000
1500
2000
0.8 0.6 0.4 0.2
-1500
-1000
1200
1400
1600
Fig. 3. Permeability (a) and magnetization loops (b) concerning Fe78Si7 B15 amorphous ribbon after thermal annealing.
400 MPa and 0.5 A for 10 min. The peculiar bi-stable response of as cast Fe78Si7B15 wires has also been observed. The experimental data and detailed procedures can be found in Ref. [6]. Fig. 3(a) and (b) illustrate the same response for the case of amorphous Fe78Si7B15 ribbon after thermal annealing in 300 1C and Ar atmosphere for 1 h and consequent slow rate cooling. 4. k–H loop Keeping He and Hor constant, while the biasing field Hoe changes, the peak magnitude of the MDL pulsed voltage output Vo is given by Eq. (7), being proportional to dl(Hoe)/dH. Normalization process and calibration against a standard Ni magnetostrictive wire of known l–H loop results in the DC l–H function determination. Indicative results are also presented concerning amorphous as-cast positive Fe78Si7B15 magnetostrictive wires. Fig. 4(a) and (b) illustrate the normalized MDL response and the l dependence on Hoe, respectively. Maintaining the basing fields Hoe and Hor steady and changing the excitation field He, the peak magnitude of Vo/He is given by Eq (8). Thus, the integral of Vo/He on He is proportional to the magnetostriction l. Normalization and calibration against a standard Ni magnetostrictive wire of known l–H loop results in the l–H loop determination.
0 -500 0 500 Biasing field (A/m)
Fig. 4. Normalized MDL response on biasing field at the excitation point (a) and integration of the MDL voltage output corresponding to the DC l–H loop (b).
1.2
Normalized MDL voltage output
0
1000
1
(b)
0
(b)
0 -500 0 500 Biasing field (A/m) 1.2
-2000
1 0.8 0.6 0.4 0.2
-1500
-1000
(a)
0 -500 0 500 Pulsed field (A/m)
1000
1500
2000
1000
1500
2000
1.2 Normalized lamda-H function
MDL voltage output (mV)
45
Magnetization (a.u.)
1.2
Normalized MDL voltage output
50
-2000
(b)
1 0.8 0.6 0.4 0.2
-1500
-1000
0 -500 0 500 Pulsed field (A/m)
Fig. 5. Normalized Vo/He MDL response on the pulsed field (a) and integration of Vo/He corresponding to the AC l–H loop (b).
ARTICLE IN PRESS E. Hristoforou, P. Dimitropoulos / Journal of Magnetism and Magnetic Materials 304 (2006) 164–167
Fig. 5(a) and (b) illustrate the normalized MDL response and its integral corresponding to the l–H function for the case of as-cast amorphous Fe78Si7B15 wires. 5. Discussion Considering the sample vibrated by the propagating elastic pulse, the method is an alternative vibrating sample magnetometer (VSM) technique, the MDL–VSM technique. The main advantage with respect to the classic VSM technique is the by-design ability of measuring the nonuniformity of permeability, magnetization and flux density of the under test specimen, by moving the position of the receiving coil and the surrounding biasing coil. Apart from that there is no need to cut the sample in pieces as for the case of the VSM. The described technique can also be used to measure the M–H loop of any magnetostrictive element, by gluing it on a glass substrate [8]. Controlling the temperature of the set-up, the dependence of the m–H, M–H and l–H loops on temperature can be determined. Changing the biasing field with a frequency less than 1 kHz,
167
corresponding to the pulsed current excitation period, the dependence of m–H, M–H and l–H loops on frequency may also be determined. Temporal dependence tests of m–H, M–H and l–H loops may also be performed. Future work is under way to improve and precisely calibrate the instrument. References [1] A. Bienkowski, R. Szewczyk, R. Kolano, Mater. Sci. Eng. A 375 (2004) 1024. [2] S.N. Kane, M. Va´zquez, A. Hernando, A. Gupta, Mater. Sci. Eng. A 304 (2001) 1055. [3] A.F. Cobeno, A.P. Zhukov, E. Pina, J.M. Blanco, J. Gonzalez, J.M. Barandiaran, J. Magn. Magn. Mater. 215 (2000) 743. [4] J. Bydzˇovsky´, L. Kraus, P. Sˇvec, M. Pasquale, M. Kolla´r, Sensor Actuat. A 110 (2004) 82. [5] E. du Tremolet de Lacheisserie, Magnetostriction: Theory and Applications of Magnetoelasticity, CRC Press, Boca Raton FL, 1994. [6] E. Hristoforou, H. Chiriac, M. Neagu, Sensor Actuat. A 67 (1998) 49. [7] E. Hristoforou, R.E. Reilly, J. Appl. Phys. 69 (1991) 5008. [8] E. Hristoforou, H. Chiriac, M. Neagu, I. Darie, J. Phys. IV 8 (1998) 809.