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Effects of tensile stress on magnetic Barkhausen emissions in amorphous FeSiB alloy
4~4 Journalof magnetism ~ 4 and magnetic J H materials
ELSEVIER
Journal of Magnetism and Magnetic Materials 153 (1996) 231-234
Effects of tensile stress on magnetic Barkhausen emissions in amorphous Fe-Si-B alloy A. Mitra
a,1,
L.B. Sipahi
a,
M.R. Govindaraju
a,
D . C . Jiles
a, *,
V.R.V. Ramanan b
a Ames Laboratory, Iowa State University Ames, Iowa 50011, USA ABB Transmission Technology Institute Raleigh, NC 27606, USA
Received 11 November 1994; revised 20 March 1995
Abstract Magnetic hysteresis and Barkhausen emissions have been measured for amorphous FeszB~oSi8 samples with positive magnetostriction of As = 27 × 10 -6 under tensile stress of up to 35 MPa. The root mean square voltage of the Barkhausen signal and the number of events per cycle increased monotonically with the applied stress. The results are explained in terms of a theory which includes a stress-dependent hysteresis model and a stochastic process model for the Barkhausen emissions.
1. Introduction Magnetic Barkhausen emissions are caused by the abrupt changes in the magnetization of a material under the action of a smoothly varying alternating magnetic field. These emissions are detected as voltage pulses in a detection coil which is placed either on the surface of the specimen (surface Barkhausen) or wrapped around the specimen (encircling Barkhausen). It has been found that as the magnetization process depends on the stress state of the material [1], the Barkhausen emissions are necessarily sensitive to stress [2,3]. The macroscopic anisotropy of the amorphous alloys is magnetoelastic in origin due to the lack of crystallinity. This means that domain wall movement and domain rotation in these alloys are predomi-
* Corresponding author. Permanent Address: Magnetism Group, National Metallurgical Laboratory, Jamshedpur 831007, India.
nantly controlled by the elastic energy [4]. In the present work, the effects of external stress on magnetic hysteresis and magnetic Barkhausen emissions have been studied. A model theory has been developed to explain the results, in which the change in the angular dependence of anisotropy energy as a function of tensile stress leads to an increase in the differential susceptibility of the hysteresis loop and thereby to an increase in the Barkhausen voltage.
2. Experimental The sample used in the present study was an amorphous Fe82B10Si8 ribbon with positive saturation magnetostriction (As= 27 × 1 0 - 6 ) . The magnetic hysteresis loop was measured using a sinusoidal applied magnetic field of maximum amplitude Hmax = 366 A m -1 ( 4 . 6 0 e ) at a frequency of 100 Hz. The Barkhausen emissions were measured using an encircling coil with the specimen subjected to 10 Hz sinusoidal magnetizing field. A detection thresh-
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 4 8 8 - 2
232
A. Mitra et al./Journal o f Magnetism and Magnetic Materials 153 (1996) 231-234 M (kG)
old voltage of 350 mV was used to eliminate lowamplitude signals (background noise). Measurements were performed under tensile stresses of O, 12, 23 and 35 MPa, applied along the ribbon axis, which was also the direction of applied field.
....... .:5-.= ~, 6 t-
I
I
I
[
d ''~
''
=, -
'
.-*"
./,/-
a
. . . .
H(Oe)
3. R e s u l t s
The Barkhausen waveforms at three different stress levels are shown in Fig. 1. The corresponding hysteresis loops are shown in Fig. 2. The differential permeability around the hysteresis loops increased with the application of tensile stress along the direction of the field. Fig. 3 shows the change of root mean square voltage (V~m~) of the Barkhausen emissions as a function of the field amplitude at four different stress levels. When no stress was applied, V~ms increased monotonically with the applied field
<:.7....."" t Fig. 2. Hysteresis loops at different tensile stresses: (a) 0 MPa; (b) 12 MPa; and (c) 35 MPa; at a maximum field amplitude of 366 Am- l (4.60e). 90
200 180
8O
160
A > 140 E
E 70
S0
100
~
go } ~: so
6o ~
¢E
4O
40 30
I
(a)
i
0
051
.
.
.
.
l
I
1.5 2 215 3 35 Applied Magnetic Field (Oe)
4
l
0
45
Fig. 3. Variation of the rms voltage (Vrms) with applied magnetic field at different tensile stresses: (11) 0 MPa, ( + ) 12 MPa, ( * ) 23 MPa, and ( O ) 35 MPa.
'
600
5OO
40O
3o0
oo 2OO
.
: __---+
10o o o.5
I10ms Fig. 1. Barkhansen signals at different tensile stresses: (a) 0 MPa; (b) 12 MPa; and (c) 35 MPa; at a maximum field amplitude of 366 A m - i (4.60e).
1
1.5 2 2.5 3 3.5 Applied Magnetic Field (Oe)
4
4.5
Fig. 4. Variation of number of counts per magnetizing cycle ( N O) with applied magnetic field at different tensile stresses: ( i ) 0 MPa, ( + ) 12 MPa, ( * ) 23 MPa, and ( O ) 35 MPa.
A. Mitra et aL/ Journal of Magnetism and MagneticMaterials153 (1996) 231-234 With the application of tensile stress, Vrm~ increased faster with the field amplitude at low fields and saturated at higher fields. The saturation value of V~ms also increased with tensile stress. The number of Barkhausen counts per magnetizing cycle (N O) varied with the amplitude of the magnetic field at different levels of tensile stress, as shown in Fig. 4. It was found that N O increased with the field amplitude and tended to saturate. The saturation value of the number of Barkhausen counts increased with the applied tensile stress. amplitude nma x.
4. Discussion
The Barkhausen effect is caused by irreversible discontinuous changes of magnetization. The voltage pulses which are generated in the detection coil are proportional to d M j J d t in the material, where Mj~ is the change in magnetization occurring as Barkhausen jumps [5,6]. As Barkhausen emission originates largely from the irreversible motion of domain walls, it is reasonable to assume that d Mjs/dt is proportional to the rate of change of irreversible magnetization. Barkhausen activity in the material, d M j J d t , can therefore be expressed as a combination of factors: d d d dH d-t Mjs = "/d-~Mi= = Y ' ~ Mi~ d r "
(1)
where H is the applied magnetic field and y is a dimensionless parameter which is a product of the number of Barkhausen events per unit irreversible change of magnetization and the average Barkhausen jump size (Mdi~c). Since d M i ~ / d H is the irreversible differential susceptibility (X[rr) which is stress dependent, it can be determined from the hysteresis loop. The Barkhausen emissions arise only from the change in magnetization M, not from the changes of the field H, and are detected via the change in magnetic induction d B / d t , which generates a voltage in the detection coil. Therefore the Barkhausen voltage Vjs is given by d d dH Vjs : - n A d t B j s = -nAp'°Y-d'-HMirr dt "
(2)
where n and A are the number of turns and the area of the coil, respectively, and /z 0 is the permeability
233
of free space. The Barkhausen voltage Vjs is therefore proportional to the differential irreversible susceptibility, dMirr/dH, of the material. The differential magnetostriction, d h / d M , is large and positive for FeB2B~0Si 8. According to the theory of hysteresis [7], an additional effective field H~ due to stress arises as a result of the magnetoelastic interaction. This field H,~ is given by 3 tr
dh
2
aM"
(3)
Therefore, for positive d h / d M and tensile stress o-, this field reinforces the applied field and the magnetic domains will tend to orientate along the direction of the applied tensile stress. This increases the differential permeability of the hysteresis loop d M / d H , which therefore causes dMi~r/dH to increase. As the Barkhausen voltage is proportional to the differential irreversible susceptibility according to Eq. (2), it is clear that it will increase with the application of tensile stress along the direction of the applied field. Previous work on materials with negative d h / d M [8] has shown that tensile stress along the field axis causes a reduction in d M / d H and a reduction in the Barkhausen activity. These previous results, when combined with the present results, are consistent with the interpretation of the changes in the Barkhausen signal in terms of the changes in the differential susceptibility, rather than as a result of other mechanisms such as changes in domain wall area or thickness.
5. Conclusions
Magnetic hysteresis and Barkhausen emissions of Fe82B~oSi 8 alloy under tensile stress have been measured. The differential permeability of the hysteresis loop increased with the application of tensile stress along the field direction. This resulted in an increase in differential susceptibility at all points along the hysteresis loop. The Barkhausen activity, represented in terms of the root mean square voltage, also increased with tensile stress. As shown in the model equations, the Barkhausen activity is expected to be proportional to differential susceptibility and to the
234
A. M itra et al. /Journal of Magnetism and Magnetic Materials 153 (1996) 231-234
rate of change of applied field. The model also predicts that differential susceptibility increases with the tensile stress along the field direction due to the positive differential magnetostriction d A/dM, and therefore that the Barkhausen voltage increases also. This is in accordance with observations.
Acknowledgements This work was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract number W-7405-ENG-82. It was also supported by the Indo-US Science and Technology Fellowship Program and the State of Iowa.
References [1] D.C. Jiles and D.L. Atherton, J. Phys. D: Appl. Phys. 17 (1984) 1265. [2] H. Kwun, J. Magn. Magn. Mater. 49 (1985) 235. [3] R. Rautioaho, P. Karjalainen and M. Moilanen, J. Magn. Magn. Mater. 68 (1987) 321. [4] F.E. Luborsky, Amorphous Metallic Alloys (Butterworths, London-Boston, 1983). [5] L.J. Swartzendruber, L.H. Bennett, H. Ettedgui and I. Aviram, J. Appi. Phys. 67 (1990) 5469. [6] D.C. Jiles, L.B. Sipahi and G. Williams, J. Appl, Phys. 73 (1993) 5830. [7] M.J. Sablik and D.C. Jiles, IEEE Trans. Magn. 29 (1993) 2113. [8] D.C. Jiles, R. Ranjan and D.R. Haugen, J. Appl. Phys. 64 (1988) 3620.
ELSEVIER
Journal of Magnetism and Magnetic Materials 153 (1996) 231-234
Effects of tensile stress on magnetic Barkhausen emissions in amorphous Fe-Si-B alloy A. Mitra
a,1,
L.B. Sipahi
a,
M.R. Govindaraju
a,
D . C . Jiles
a, *,
V.R.V. Ramanan b
a Ames Laboratory, Iowa State University Ames, Iowa 50011, USA ABB Transmission Technology Institute Raleigh, NC 27606, USA
Received 11 November 1994; revised 20 March 1995
Abstract Magnetic hysteresis and Barkhausen emissions have been measured for amorphous FeszB~oSi8 samples with positive magnetostriction of As = 27 × 10 -6 under tensile stress of up to 35 MPa. The root mean square voltage of the Barkhausen signal and the number of events per cycle increased monotonically with the applied stress. The results are explained in terms of a theory which includes a stress-dependent hysteresis model and a stochastic process model for the Barkhausen emissions.
1. Introduction Magnetic Barkhausen emissions are caused by the abrupt changes in the magnetization of a material under the action of a smoothly varying alternating magnetic field. These emissions are detected as voltage pulses in a detection coil which is placed either on the surface of the specimen (surface Barkhausen) or wrapped around the specimen (encircling Barkhausen). It has been found that as the magnetization process depends on the stress state of the material [1], the Barkhausen emissions are necessarily sensitive to stress [2,3]. The macroscopic anisotropy of the amorphous alloys is magnetoelastic in origin due to the lack of crystallinity. This means that domain wall movement and domain rotation in these alloys are predomi-
* Corresponding author. Permanent Address: Magnetism Group, National Metallurgical Laboratory, Jamshedpur 831007, India.
nantly controlled by the elastic energy [4]. In the present work, the effects of external stress on magnetic hysteresis and magnetic Barkhausen emissions have been studied. A model theory has been developed to explain the results, in which the change in the angular dependence of anisotropy energy as a function of tensile stress leads to an increase in the differential susceptibility of the hysteresis loop and thereby to an increase in the Barkhausen voltage.
2. Experimental The sample used in the present study was an amorphous Fe82B10Si8 ribbon with positive saturation magnetostriction (As= 27 × 1 0 - 6 ) . The magnetic hysteresis loop was measured using a sinusoidal applied magnetic field of maximum amplitude Hmax = 366 A m -1 ( 4 . 6 0 e ) at a frequency of 100 Hz. The Barkhausen emissions were measured using an encircling coil with the specimen subjected to 10 Hz sinusoidal magnetizing field. A detection thresh-
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 4 8 8 - 2
232
A. Mitra et al./Journal o f Magnetism and Magnetic Materials 153 (1996) 231-234 M (kG)
old voltage of 350 mV was used to eliminate lowamplitude signals (background noise). Measurements were performed under tensile stresses of O, 12, 23 and 35 MPa, applied along the ribbon axis, which was also the direction of applied field.
....... .:5-.= ~, 6 t-
I
I
I
[
d ''~
''
=, -
'
.-*"
./,/-
a
. . . .
H(Oe)
3. R e s u l t s
The Barkhausen waveforms at three different stress levels are shown in Fig. 1. The corresponding hysteresis loops are shown in Fig. 2. The differential permeability around the hysteresis loops increased with the application of tensile stress along the direction of the field. Fig. 3 shows the change of root mean square voltage (V~m~) of the Barkhausen emissions as a function of the field amplitude at four different stress levels. When no stress was applied, V~ms increased monotonically with the applied field
<:.7....."" t Fig. 2. Hysteresis loops at different tensile stresses: (a) 0 MPa; (b) 12 MPa; and (c) 35 MPa; at a maximum field amplitude of 366 Am- l (4.60e). 90
200 180
8O
160
A > 140 E
E 70
S0
100
~
go } ~: so
6o ~
¢E
4O
40 30
I
(a)
i
0
051
.
.
.
.
l
I
1.5 2 215 3 35 Applied Magnetic Field (Oe)
4
l
0
45
Fig. 3. Variation of the rms voltage (Vrms) with applied magnetic field at different tensile stresses: (11) 0 MPa, ( + ) 12 MPa, ( * ) 23 MPa, and ( O ) 35 MPa.
'
600
5OO
40O
3o0
oo 2OO
.
: __---+
10o o o.5
I10ms Fig. 1. Barkhansen signals at different tensile stresses: (a) 0 MPa; (b) 12 MPa; and (c) 35 MPa; at a maximum field amplitude of 366 A m - i (4.60e).
1
1.5 2 2.5 3 3.5 Applied Magnetic Field (Oe)
4
4.5
Fig. 4. Variation of number of counts per magnetizing cycle ( N O) with applied magnetic field at different tensile stresses: ( i ) 0 MPa, ( + ) 12 MPa, ( * ) 23 MPa, and ( O ) 35 MPa.
A. Mitra et aL/ Journal of Magnetism and MagneticMaterials153 (1996) 231-234 With the application of tensile stress, Vrm~ increased faster with the field amplitude at low fields and saturated at higher fields. The saturation value of V~ms also increased with tensile stress. The number of Barkhausen counts per magnetizing cycle (N O) varied with the amplitude of the magnetic field at different levels of tensile stress, as shown in Fig. 4. It was found that N O increased with the field amplitude and tended to saturate. The saturation value of the number of Barkhausen counts increased with the applied tensile stress. amplitude nma x.
4. Discussion
The Barkhausen effect is caused by irreversible discontinuous changes of magnetization. The voltage pulses which are generated in the detection coil are proportional to d M j J d t in the material, where Mj~ is the change in magnetization occurring as Barkhausen jumps [5,6]. As Barkhausen emission originates largely from the irreversible motion of domain walls, it is reasonable to assume that d Mjs/dt is proportional to the rate of change of irreversible magnetization. Barkhausen activity in the material, d M j J d t , can therefore be expressed as a combination of factors: d d d dH d-t Mjs = "/d-~Mi= = Y ' ~ Mi~ d r "
(1)
where H is the applied magnetic field and y is a dimensionless parameter which is a product of the number of Barkhausen events per unit irreversible change of magnetization and the average Barkhausen jump size (Mdi~c). Since d M i ~ / d H is the irreversible differential susceptibility (X[rr) which is stress dependent, it can be determined from the hysteresis loop. The Barkhausen emissions arise only from the change in magnetization M, not from the changes of the field H, and are detected via the change in magnetic induction d B / d t , which generates a voltage in the detection coil. Therefore the Barkhausen voltage Vjs is given by d d dH Vjs : - n A d t B j s = -nAp'°Y-d'-HMirr dt "
(2)
where n and A are the number of turns and the area of the coil, respectively, and /z 0 is the permeability
233
of free space. The Barkhausen voltage Vjs is therefore proportional to the differential irreversible susceptibility, dMirr/dH, of the material. The differential magnetostriction, d h / d M , is large and positive for FeB2B~0Si 8. According to the theory of hysteresis [7], an additional effective field H~ due to stress arises as a result of the magnetoelastic interaction. This field H,~ is given by 3 tr
dh
2
aM"
(3)
Therefore, for positive d h / d M and tensile stress o-, this field reinforces the applied field and the magnetic domains will tend to orientate along the direction of the applied tensile stress. This increases the differential permeability of the hysteresis loop d M / d H , which therefore causes dMi~r/dH to increase. As the Barkhausen voltage is proportional to the differential irreversible susceptibility according to Eq. (2), it is clear that it will increase with the application of tensile stress along the direction of the applied field. Previous work on materials with negative d h / d M [8] has shown that tensile stress along the field axis causes a reduction in d M / d H and a reduction in the Barkhausen activity. These previous results, when combined with the present results, are consistent with the interpretation of the changes in the Barkhausen signal in terms of the changes in the differential susceptibility, rather than as a result of other mechanisms such as changes in domain wall area or thickness.
5. Conclusions
Magnetic hysteresis and Barkhausen emissions of Fe82B~oSi 8 alloy under tensile stress have been measured. The differential permeability of the hysteresis loop increased with the application of tensile stress along the field direction. This resulted in an increase in differential susceptibility at all points along the hysteresis loop. The Barkhausen activity, represented in terms of the root mean square voltage, also increased with tensile stress. As shown in the model equations, the Barkhausen activity is expected to be proportional to differential susceptibility and to the
234
A. M itra et al. /Journal of Magnetism and Magnetic Materials 153 (1996) 231-234
rate of change of applied field. The model also predicts that differential susceptibility increases with the tensile stress along the field direction due to the positive differential magnetostriction d A/dM, and therefore that the Barkhausen voltage increases also. This is in accordance with observations.
Acknowledgements This work was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract number W-7405-ENG-82. It was also supported by the Indo-US Science and Technology Fellowship Program and the State of Iowa.
References [1] D.C. Jiles and D.L. Atherton, J. Phys. D: Appl. Phys. 17 (1984) 1265. [2] H. Kwun, J. Magn. Magn. Mater. 49 (1985) 235. [3] R. Rautioaho, P. Karjalainen and M. Moilanen, J. Magn. Magn. Mater. 68 (1987) 321. [4] F.E. Luborsky, Amorphous Metallic Alloys (Butterworths, London-Boston, 1983). [5] L.J. Swartzendruber, L.H. Bennett, H. Ettedgui and I. Aviram, J. Appi. Phys. 67 (1990) 5469. [6] D.C. Jiles, L.B. Sipahi and G. Williams, J. Appl, Phys. 73 (1993) 5830. [7] M.J. Sablik and D.C. Jiles, IEEE Trans. Magn. 29 (1993) 2113. [8] D.C. Jiles, R. Ranjan and D.R. Haugen, J. Appl. Phys. 64 (1988) 3620.