- Email: [email protected]
Piezoimpedane and pressure sensors with NiZn ferrite device
Sensors and Actuators A 147 (2008) 504–507
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Piezoimpedane and pressure sensors with NiZn ferrite device N. Zhang ∗ , Z.L. Wang, X. Fang Magnetoelectronic Laboratory, Nanjing Normal University, Ninghai Road, Nanjing 210097, Jiangsu Province, China
a r t i c l e
i n f o
Article history: Received 15 December 2007 Received in revised form 3 June 2008 Accepted 12 June 2008 Available online 22 June 2008 PACS: 62.50.+p 75.80.+q 73.50.Dn 85.70.Ge
a b s t r a c t The hydrostatic pressure effect on the magnetism, capacitance and impedance of a NiZn ferrite device has been investigated. Giant piezomagnetism, piezocapacitance and piezoimpedane independent on skin effect have been observed simultaneously under a pressure of several MPa. With increasing the frequency of the current applied across the ferrite device, the piezoimpedane has been found to undergo a maximum at a current frequency of 500 Hz. Under a pressure of 6 MPa, the maximum of piezoimpedane can reach about 71%. And the pressure sensitivity of the impedance can be higher than 0.18 MPa−1 when the pressure is lower than 3 MPa. Analysis shows that these giant pressure effects in the ferrite device result from the variation of the inner stress in the ferrite under an external pressure. © 2008 Elsevier B.V. All rights reserved.
Keywords: Piezomagnetic effect Piezoimpedance Magnetic device Ferrite
1. Introduction When a magnetic material carrying an alternating current is subjected to an external magnetic field along the direction of the current flow, it exhibits a sharp change in its electrical impedance. This effect is known as the giant magnetoimpedance (GMI) effect [1]. The GMI effect is believed to stem from the skin effect, which results from the external field-induced change in the effective permeability (eff ) of the magnetic material [2]. On the other hand, it is well known that the permeability can also be changed by applying a stress on the magnet. Therefore, one can expect a behavior of external stress-induced change of the impedance in the GMI material. It is known as the giant stress impedance (GSI) effect [3,4]. GMI effect and the related GSI in Co-based or Fe-based amorphous ribbons or films and nanocrystalline materials have been extensively studied [5–8] and applied in fabricating highly sensitive magnetic sensors in last 10 years [9–11]. For the GSI effect mentioned above, a higher frequency alternating current is required since it depends on skin effect. The typical frequency needed for the GSI is no lower than 100 kHz. Additionally, a tensile stress is needed since the GSI occurs only in some wires or ribbons so far.
Recently, with a hydrostatic pressure and an ac current at a lower frequency than that in the case of the GSI in amorphous ribbons, we have observed another kind of GSI effect that is independent on skin effect in a magnetic device. It is, in fact, a giant piezoimpedance (GPI) effect. Pressure effect on magnetic cores has ever been investigated about 10 years ago [12], but further studies on the related piezoimpedance and other pressure effect based on the piezomagnetism have seldom seen so far. In this work, a systematic investigation of the GPI effect and other related pressure effect in ferrite device is presented. We will show that the sensitivity of the GPI effect can reach 18.4% MPa−1 in a sensitive area of pressure. 2. Piezoimpedance depending on piezomagnetic effects It is well known that most magnetic materials, especially some ferrites, can show a piezomagnetic effect. For a magnet with very high permeability , the magnetization mainly depends on the movement of the wall of magnetic domain. For such a magnet, the initial permeability in the process of reversible magnetization under an external stress is given by i =
∗ Corresponding author. Tel.: +86 13057685507. E-mail address: [email protected] (N. Zhang). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.06.012
20 Ms2 l + 1, 32 ıs
(1)
where Ms is the saturated magnetization, s the saturated magnetostrictive coefficient, l and ı are the width and thickness of the
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
wall of magnetic domains, respectively, and is the internal stress, which can be changed by external stress. Thus piezomagnetic effect in the reversible process for a magnet with a high permeability can be expressed as i − 1 =− i ≈− . i i
(2)
Eq. (2) suggests that the piezomagnetic effect can be enhanced with increasing and , but is inverse proportional to practical internal stress . For this reason, if a search coil is circled on such a magnet, one can expect to observe the piezomagnetic effect, which is presents a stress-induced change of inductance L in the coil taking the relation L = VN2 0 into account, where n (the circles in a unit length of the coil), V (the volume surrounded by the coil) and 0 (permeability in vacuum) are all constants for a given coil [13]. In other words, the piezomagnetic effect can also be written as L i = , i L0
(3)
where L0 is the inductance of the coil without pressure. Besides the inductance, a coil always has a resistance and a distributed capacitance [14]. When an ac current is applied across a coil, the measurable values of those parameters will be related one after another and related to the current frequency ω/2 closely. Generally, the equivalent circuit of an inductor suggests that the inductance and capacitance of an inductor should be parallel, and they are serial with its resistance, as shown in Fig. 1 [15]. In this model, the effective capacitance Cs and the impedance Z of the inductor can be, respectively, expressed as Cs = Cp − Z=
L Rp2 (1 − ω2 Cp L)
,
(4)
ωLRp ω2 L2 + Rp2 (1 − ω2 Cp L)
,
(5)
where Rp is the resistance of the inductor under a dc current, Cp is the capacitance independent on current frequency. Cp can usually be extrapolated from the measured Cs versus frequency without external magnetic field or stress. On the other hand, it is known that, when in an alternative electromagnetic field, the magnetic relaxation of a magnet can lead to permeability dispersion, ˜ = − i , where and are elastic and viscous permeability, respectively. Thus, the effective permeability should be eff =
2
2
+ " =
2i + (ω/ωc ) 1 + (ω/ωc )
2
2
,
(6)
where ωc is the frequency of relaxation. Eq. (6) indicates that the permeability in an alternative field is also a function of the field frequency. Considering the relation L = VN2 0 eff and Eqs. (4) and (5), one can expect to observe the effects of piezomagnetism (PM), piezocapacitance (PC) and piezoimpedance (PI) in a coil with magnetic core simultaneously. Collecting results from Eqs. (3)–(6), the
Fig. 1. Equivalent circuit of the ferrite device.
505
PM, PC and PI are, respectively, given by L =− , L0
(7)
Cs L , = 2 2 C0 2 C0 Rp (1 − ω Cp L)
(8)
Z = Z0
−ωLRp3 (1 − ω2 Cp L) Z0
[ω2 L2
2 − Rp2 (1 − ω2 Cp L) ]
3/2
,
(9)
where C0 and Z0 are the capacity and impedance without pressure. Eqs. (7)–(9) suggest that, with increasing external stress, the distribute capacitance increases, but the inductance and impedance decrease. 3. Characterization of the pressure sensor with the ferrite device Generally speaking, any one of ferromagnetic materials has the PM behavior. However, to get a sharp and repeatable PM effect, one should obtain a soft magnet with higher permeability. In this sense, NiZn and MnZn ferrites are some desirable magnets [16]. But NiZn was believed to work at higher frequencies. Commercial NiZn ferrite with nominal initial permeability at about 1000 was employed in this study. The geometrical shape of the magnetic core is also important for strong piezomagnetic effects. Magnets with closed magnetic circuit geometry are preferable. The ferrite cores used are in the shape of rings of 4 mm in height and 9 mm in diameter. A search coil of ten turns was wound and cemented with glue on to the ring. The present number of turns is not the optimal in the sensitivity, but it was found that the value measured on the turns is more stable. A cylinder containing a piston was applied as a pressure container. The inner diameter of the cylinder is five times larger than that of the ring. The ring-shaped ferrite with the search coil was placed at the center of the container filled with powder of SiO2 , as shown in Fig. 2. The average grain size of the SiO2 powder is about 1.5–2 m. Thus, a pseudo hydrostatic pressure can be applied on the ferrite ring by applying a force on the piston. By the way, since there is not a strong electric field in the present pressure experiments, the dielectricity of SiO2 powder can be ignored. 4. Experimental results and discussion An ac electric bridge has been applied to measure the inductance L and capacitance C of the device. A function generator and a voltmeter were used to measure the impedance Z of it. In the measurement of the impedance, the search coil, the function generator
Fig. 2. Schematic draft of the pressure sensor with the ferrite device.
506
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
Fig. 3. Frequency dependence of inductance and capacitance without pressure.
and the voltmeter are in parallel connection. The ac current I0 supplied by the function generator is constant. So the impedance can be obtained by the relation Z = V/I0 , where V is the voltage measured. The current frequency dependence of the inductance and capacitance of the device is shown in Fig. 3. As can be seen, the inductance versus frequency presents a curve of relaxation type, as described by Eq. (6). The capacitance can decreases nearly two orders of magnitude as the frequency increases by a factor of ten. The pressure dependence of the inductance, capacitance and impedance with different current frequency for the device are shown in Fig. 4. Firstly, it is found that the inductance is inverse proportional to pressure at all different frequency, as suggested by Eq. (7). Secondly, the impedance decreases, but the capacitance increases with increasing pressure at all frequencies. These results
Fig. 4. Pressure dependence of the inductance (upper panel), capacitance (middle panel) and impedance (lower panel) for manganite zinc ferrite device at different frequency, respectively.
Fig. 5. Frequency dependence of impedance without pressure and with a pressure of 6 MPa, respectively, as well as the corresponding piezoimpectance for the NiZn ferrite device.
are consistent with that described by Eqs. (8) and (9). According to the pressure dependent inductance (the upper panel of Fig. 4), one can obtain the differential coefficients of the inductance about pressure (dL/dP). The differential coefficient at the current frequency of 500 Hz is also shown in the upper panel of Fig. 4 for the numerical estimation later on. Fig. 5 shows the frequency dependence of the impedance of the device without pressure and with a pressure of 6 MPa, as well as the corresponding PI. Where PI is defined as Z/Z0 = (Z0 − Z)/Z0 = (Z0 I0 − ZI0 )/Z0 I0 = (V − V0 )/V0 , where V0 is voltage measured without pressure. It is found that: (1) the pressure effects on impedance can exist in the all range of the current frequency used, from 50 Hz to 200 kHz, (2) the absolute value of PI undergoes a maximum at about a frequency of 500 Hz, (3) the maximums of PI can reach about 70.3%. This effect can be considered “giant”, even “colossal”. In addition, the GPI occurs mostly in the area of pressure lower than 3 MPa, as shown in Fig. 6. This area can be called sensitive area, in which the sensitivity of PI can reach about 0.184 MPa−1 . For well understanding the results shown in Figs. 4 and 5, it is worthy of analyzing the experimental results using the formulas above. Taking the inductance versus pressure at the current frequency of 500 Hz, at which the PI reaches its maximum, as an example, the differential coefficient L/P (the upper penal of Fig. 4) at pressures of 0.5, 1 and 1.5 MPa are −0.396, −0.255 and −0.174 mH MPa−1 , respectively. From Eqs. (2) and (3), which give the characterization of piezomagnetic effect, one can have / = L/L = / ≈ P/P, where we approximately take the variation of the inner stress in the magnetic core directly proportional to the applied one (pressure), namely ∝P. Then one has the piezomagnetic coefficient / = /P = L/P/VN2 0 . For the L versus P at frequency of 500 Hz, it was found L = 0.921 mH at zero pressure, yielding VN2 0 = 9.21 × 10−4 mH. Thus we obtain piezomagnetic coefficient /P = −430, −277 and −189 MPa−1 under pressures of 0.5, 1, and 1.5 MPa, respectively.
Fig. 6. Pressure dependence of the impedance and the corresponding piezoimpectance for the NiZn ferrite device with a current frequency at 500 Hz.
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
For a magnet with internal stress, the energy per unit area wall of magnetic domain and the magnetic elastic energy can be, respectively, written as
= 2ı K1 + E =
3 s , 2
3 s cos2 , 2
507
Acknowledgment This work was supported by the National Science Foundation of China under Grant No. 10674071.
(10) References (11)
where K1 is the constant of crystalline magnetic anisotropy, and is included angle of the internal stress and the magnetization Ms . Both K1 and s are ordinary very small for a magnet with high . Thus, Eqs. (10) and (11) suggest that ␥ and E are all proportional to the stress , which includes internal and external ones. Enhancement of pressure can increase ␥ and E , then decrease the movement of the wall of magnetic domain and reduce the magnetization. Additional, it is worthwhile to notice that those pressure effects are independent on skin effect since they can occur in a wide area of current frequency and get their maximum at a frequency of 500 Hz, which is much lower than that to induce the GSI effect depending on skin effect [9–11]. The pressure sensors with the ferrite device could have even broader applications. There are evidences that these pressure effects in conjunctions with a redesigned pressure container could be used for sonic measurement in water. Additionally, all the pressure effects mentioned above can appear not only in NiZn ferrite, but also in MnZn one, which initial permeability can reach 10,000 or more. But the corresponding values of the piezomagnetic effects for MnZn ferrite are not much higher than that observed for NiZn ferrite. 5. Conclusion Under a hydrostatic pressure of several MPa, a ferrite core with a closed magnetic circuit can show a sharp piezomagnetic effect. Based on this, colossal piezocapacitance and piezoimpedance effects can be observed simultaneously from the search coil circled on the ferrite core with an alternating current in a wide frequency area. These effects can be proved to be independent on skin effect.
[1] F.L.A. Machado, C.S. Martins, S.M. Rezende, Phys. Rev. B 51 (1995) 3926–3929. [2] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189–1191. [3] L.P. Shen, T. Uchiyama, K. Mohri, E. Kita, K. Bushida, IEEE Trans. Magn. 33 (5) (1997) 3355. [4] M. Knobel, M. Vazquez, M.L. Sanchez, A. Hernando, J. Magn. Magn. Mater. 169 (1997) 89. [5] L.V. Panina, K. Mohri, K. Bushida, M. Noda, J. Appl. Phys. 76 (1994) 6198. [6] M. Tejedor, B. Hernando, M.L. Sanchez, V.M. Prida, M. Vazquez, J. Magn. Magn. Mater. 196/197 (1999) 330. [7] B. Hernando, M.L. Sanchez, V.M. Prida, M. Tejedor, J. Appl. Phys. 90 (2001) 4783. [8] M. Knobel, M.L. Sánchez, C. Gómez-Polo, P. Marín, M. Vázquez, A. Hernando, J. Appl. Phys. 79 (1996) 1646. [9] K.-H. Shin, M. Inoue, K.-I. Arai, J. Appl. Phys. 85 (1997) 5465. [10] J.M. Barandiaran, J. Gutierrez, Sens. Actuator A 59 (1997) 38. [11] A. Ludwig, M. Tewes, S. Glasmachers, M. Löhndorf, E. Quandt, J. Magn. Magn. Mater. 242–245 (2002) 1126. [12] A. Schweiger, Siemens Components No. 1 (1997) 16–l8. [13] H.G. Dill, Electron. Des. 17 (1) (1964) 52. [14] Z. Jiang, P.S. Excell, Z.M. Hejazi, IEEE Trans. Microwave Theory Tech. 45 (1) (1997) 139. [15] C.A. Romero-Talamás, P.M. Bellan, S.C. Hsu, Rev. Sci. Instrum. 75 (8) (2004) 2664. [16] D. Stoppels, J. Magn. Magn. Mater. 160 (1996) 323.
Biographies N. Zhang obtained Bachelor degree of science in 1982 from Nanjing Normal University, Nanjing, China, Master degree and Ph.D. in science from Nanjing University, Nanjing, China, in 1985 and 1997, respectively, now employed by Nanjing Normal University as a professor. His current fields of interest include Giant magnetoresistance effect in compounds and composites, magnetoelectronic effect in layered composites, and giant piezoimpedance and magnetoimpedance effects in ferrites with high permeability. Z. L. Wang obtained Bachelor degree of science in 2002 from Tangshan Normal College, Tangshan, Hebei Province, China, now is a PhD student in Nanjing Normal University, Nanjing, China. His current fields of interest include giant piezoimpedance and converse magnetoelectric effects in composites. X. Fang obtained Bachelor degree of science in 2002 from Jinan University, Jinan, Shandong Province, China, now is a PhD student in Nanjing Normal University, Nanjing, China. His current fields of interest include giant piezoimpedance and converse magnetoelectric effects in heterotypic composites.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Piezoimpedane and pressure sensors with NiZn ferrite device N. Zhang ∗ , Z.L. Wang, X. Fang Magnetoelectronic Laboratory, Nanjing Normal University, Ninghai Road, Nanjing 210097, Jiangsu Province, China
a r t i c l e
i n f o
Article history: Received 15 December 2007 Received in revised form 3 June 2008 Accepted 12 June 2008 Available online 22 June 2008 PACS: 62.50.+p 75.80.+q 73.50.Dn 85.70.Ge
a b s t r a c t The hydrostatic pressure effect on the magnetism, capacitance and impedance of a NiZn ferrite device has been investigated. Giant piezomagnetism, piezocapacitance and piezoimpedane independent on skin effect have been observed simultaneously under a pressure of several MPa. With increasing the frequency of the current applied across the ferrite device, the piezoimpedane has been found to undergo a maximum at a current frequency of 500 Hz. Under a pressure of 6 MPa, the maximum of piezoimpedane can reach about 71%. And the pressure sensitivity of the impedance can be higher than 0.18 MPa−1 when the pressure is lower than 3 MPa. Analysis shows that these giant pressure effects in the ferrite device result from the variation of the inner stress in the ferrite under an external pressure. © 2008 Elsevier B.V. All rights reserved.
Keywords: Piezomagnetic effect Piezoimpedance Magnetic device Ferrite
1. Introduction When a magnetic material carrying an alternating current is subjected to an external magnetic field along the direction of the current flow, it exhibits a sharp change in its electrical impedance. This effect is known as the giant magnetoimpedance (GMI) effect [1]. The GMI effect is believed to stem from the skin effect, which results from the external field-induced change in the effective permeability (eff ) of the magnetic material [2]. On the other hand, it is well known that the permeability can also be changed by applying a stress on the magnet. Therefore, one can expect a behavior of external stress-induced change of the impedance in the GMI material. It is known as the giant stress impedance (GSI) effect [3,4]. GMI effect and the related GSI in Co-based or Fe-based amorphous ribbons or films and nanocrystalline materials have been extensively studied [5–8] and applied in fabricating highly sensitive magnetic sensors in last 10 years [9–11]. For the GSI effect mentioned above, a higher frequency alternating current is required since it depends on skin effect. The typical frequency needed for the GSI is no lower than 100 kHz. Additionally, a tensile stress is needed since the GSI occurs only in some wires or ribbons so far.
Recently, with a hydrostatic pressure and an ac current at a lower frequency than that in the case of the GSI in amorphous ribbons, we have observed another kind of GSI effect that is independent on skin effect in a magnetic device. It is, in fact, a giant piezoimpedance (GPI) effect. Pressure effect on magnetic cores has ever been investigated about 10 years ago [12], but further studies on the related piezoimpedance and other pressure effect based on the piezomagnetism have seldom seen so far. In this work, a systematic investigation of the GPI effect and other related pressure effect in ferrite device is presented. We will show that the sensitivity of the GPI effect can reach 18.4% MPa−1 in a sensitive area of pressure. 2. Piezoimpedance depending on piezomagnetic effects It is well known that most magnetic materials, especially some ferrites, can show a piezomagnetic effect. For a magnet with very high permeability , the magnetization mainly depends on the movement of the wall of magnetic domain. For such a magnet, the initial permeability in the process of reversible magnetization under an external stress is given by i =
∗ Corresponding author. Tel.: +86 13057685507. E-mail address: [email protected] (N. Zhang). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.06.012
20 Ms2 l + 1, 32 ıs
(1)
where Ms is the saturated magnetization, s the saturated magnetostrictive coefficient, l and ı are the width and thickness of the
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
wall of magnetic domains, respectively, and is the internal stress, which can be changed by external stress. Thus piezomagnetic effect in the reversible process for a magnet with a high permeability can be expressed as i − 1 =− i ≈− . i i
(2)
Eq. (2) suggests that the piezomagnetic effect can be enhanced with increasing and , but is inverse proportional to practical internal stress . For this reason, if a search coil is circled on such a magnet, one can expect to observe the piezomagnetic effect, which is presents a stress-induced change of inductance L in the coil taking the relation L = VN2 0 into account, where n (the circles in a unit length of the coil), V (the volume surrounded by the coil) and 0 (permeability in vacuum) are all constants for a given coil [13]. In other words, the piezomagnetic effect can also be written as L i = , i L0
(3)
where L0 is the inductance of the coil without pressure. Besides the inductance, a coil always has a resistance and a distributed capacitance [14]. When an ac current is applied across a coil, the measurable values of those parameters will be related one after another and related to the current frequency ω/2 closely. Generally, the equivalent circuit of an inductor suggests that the inductance and capacitance of an inductor should be parallel, and they are serial with its resistance, as shown in Fig. 1 [15]. In this model, the effective capacitance Cs and the impedance Z of the inductor can be, respectively, expressed as Cs = Cp − Z=
L Rp2 (1 − ω2 Cp L)
,
(4)
ωLRp ω2 L2 + Rp2 (1 − ω2 Cp L)
,
(5)
where Rp is the resistance of the inductor under a dc current, Cp is the capacitance independent on current frequency. Cp can usually be extrapolated from the measured Cs versus frequency without external magnetic field or stress. On the other hand, it is known that, when in an alternative electromagnetic field, the magnetic relaxation of a magnet can lead to permeability dispersion, ˜ = − i , where and are elastic and viscous permeability, respectively. Thus, the effective permeability should be eff =
2
2
+ " =
2i + (ω/ωc ) 1 + (ω/ωc )
2
2
,
(6)
where ωc is the frequency of relaxation. Eq. (6) indicates that the permeability in an alternative field is also a function of the field frequency. Considering the relation L = VN2 0 eff and Eqs. (4) and (5), one can expect to observe the effects of piezomagnetism (PM), piezocapacitance (PC) and piezoimpedance (PI) in a coil with magnetic core simultaneously. Collecting results from Eqs. (3)–(6), the
Fig. 1. Equivalent circuit of the ferrite device.
505
PM, PC and PI are, respectively, given by L =− , L0
(7)
Cs L , = 2 2 C0 2 C0 Rp (1 − ω Cp L)
(8)
Z = Z0
−ωLRp3 (1 − ω2 Cp L) Z0
[ω2 L2
2 − Rp2 (1 − ω2 Cp L) ]
3/2
,
(9)
where C0 and Z0 are the capacity and impedance without pressure. Eqs. (7)–(9) suggest that, with increasing external stress, the distribute capacitance increases, but the inductance and impedance decrease. 3. Characterization of the pressure sensor with the ferrite device Generally speaking, any one of ferromagnetic materials has the PM behavior. However, to get a sharp and repeatable PM effect, one should obtain a soft magnet with higher permeability. In this sense, NiZn and MnZn ferrites are some desirable magnets [16]. But NiZn was believed to work at higher frequencies. Commercial NiZn ferrite with nominal initial permeability at about 1000 was employed in this study. The geometrical shape of the magnetic core is also important for strong piezomagnetic effects. Magnets with closed magnetic circuit geometry are preferable. The ferrite cores used are in the shape of rings of 4 mm in height and 9 mm in diameter. A search coil of ten turns was wound and cemented with glue on to the ring. The present number of turns is not the optimal in the sensitivity, but it was found that the value measured on the turns is more stable. A cylinder containing a piston was applied as a pressure container. The inner diameter of the cylinder is five times larger than that of the ring. The ring-shaped ferrite with the search coil was placed at the center of the container filled with powder of SiO2 , as shown in Fig. 2. The average grain size of the SiO2 powder is about 1.5–2 m. Thus, a pseudo hydrostatic pressure can be applied on the ferrite ring by applying a force on the piston. By the way, since there is not a strong electric field in the present pressure experiments, the dielectricity of SiO2 powder can be ignored. 4. Experimental results and discussion An ac electric bridge has been applied to measure the inductance L and capacitance C of the device. A function generator and a voltmeter were used to measure the impedance Z of it. In the measurement of the impedance, the search coil, the function generator
Fig. 2. Schematic draft of the pressure sensor with the ferrite device.
506
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
Fig. 3. Frequency dependence of inductance and capacitance without pressure.
and the voltmeter are in parallel connection. The ac current I0 supplied by the function generator is constant. So the impedance can be obtained by the relation Z = V/I0 , where V is the voltage measured. The current frequency dependence of the inductance and capacitance of the device is shown in Fig. 3. As can be seen, the inductance versus frequency presents a curve of relaxation type, as described by Eq. (6). The capacitance can decreases nearly two orders of magnitude as the frequency increases by a factor of ten. The pressure dependence of the inductance, capacitance and impedance with different current frequency for the device are shown in Fig. 4. Firstly, it is found that the inductance is inverse proportional to pressure at all different frequency, as suggested by Eq. (7). Secondly, the impedance decreases, but the capacitance increases with increasing pressure at all frequencies. These results
Fig. 4. Pressure dependence of the inductance (upper panel), capacitance (middle panel) and impedance (lower panel) for manganite zinc ferrite device at different frequency, respectively.
Fig. 5. Frequency dependence of impedance without pressure and with a pressure of 6 MPa, respectively, as well as the corresponding piezoimpectance for the NiZn ferrite device.
are consistent with that described by Eqs. (8) and (9). According to the pressure dependent inductance (the upper panel of Fig. 4), one can obtain the differential coefficients of the inductance about pressure (dL/dP). The differential coefficient at the current frequency of 500 Hz is also shown in the upper panel of Fig. 4 for the numerical estimation later on. Fig. 5 shows the frequency dependence of the impedance of the device without pressure and with a pressure of 6 MPa, as well as the corresponding PI. Where PI is defined as Z/Z0 = (Z0 − Z)/Z0 = (Z0 I0 − ZI0 )/Z0 I0 = (V − V0 )/V0 , where V0 is voltage measured without pressure. It is found that: (1) the pressure effects on impedance can exist in the all range of the current frequency used, from 50 Hz to 200 kHz, (2) the absolute value of PI undergoes a maximum at about a frequency of 500 Hz, (3) the maximums of PI can reach about 70.3%. This effect can be considered “giant”, even “colossal”. In addition, the GPI occurs mostly in the area of pressure lower than 3 MPa, as shown in Fig. 6. This area can be called sensitive area, in which the sensitivity of PI can reach about 0.184 MPa−1 . For well understanding the results shown in Figs. 4 and 5, it is worthy of analyzing the experimental results using the formulas above. Taking the inductance versus pressure at the current frequency of 500 Hz, at which the PI reaches its maximum, as an example, the differential coefficient L/P (the upper penal of Fig. 4) at pressures of 0.5, 1 and 1.5 MPa are −0.396, −0.255 and −0.174 mH MPa−1 , respectively. From Eqs. (2) and (3), which give the characterization of piezomagnetic effect, one can have / = L/L = / ≈ P/P, where we approximately take the variation of the inner stress in the magnetic core directly proportional to the applied one (pressure), namely ∝P. Then one has the piezomagnetic coefficient / = /P = L/P/VN2 0 . For the L versus P at frequency of 500 Hz, it was found L = 0.921 mH at zero pressure, yielding VN2 0 = 9.21 × 10−4 mH. Thus we obtain piezomagnetic coefficient /P = −430, −277 and −189 MPa−1 under pressures of 0.5, 1, and 1.5 MPa, respectively.
Fig. 6. Pressure dependence of the impedance and the corresponding piezoimpectance for the NiZn ferrite device with a current frequency at 500 Hz.
N. Zhang et al. / Sensors and Actuators A 147 (2008) 504–507
For a magnet with internal stress, the energy per unit area wall of magnetic domain and the magnetic elastic energy can be, respectively, written as
= 2ı K1 + E =
3 s , 2
3 s cos2 , 2
507
Acknowledgment This work was supported by the National Science Foundation of China under Grant No. 10674071.
(10) References (11)
where K1 is the constant of crystalline magnetic anisotropy, and is included angle of the internal stress and the magnetization Ms . Both K1 and s are ordinary very small for a magnet with high . Thus, Eqs. (10) and (11) suggest that ␥ and E are all proportional to the stress , which includes internal and external ones. Enhancement of pressure can increase ␥ and E , then decrease the movement of the wall of magnetic domain and reduce the magnetization. Additional, it is worthwhile to notice that those pressure effects are independent on skin effect since they can occur in a wide area of current frequency and get their maximum at a frequency of 500 Hz, which is much lower than that to induce the GSI effect depending on skin effect [9–11]. The pressure sensors with the ferrite device could have even broader applications. There are evidences that these pressure effects in conjunctions with a redesigned pressure container could be used for sonic measurement in water. Additionally, all the pressure effects mentioned above can appear not only in NiZn ferrite, but also in MnZn one, which initial permeability can reach 10,000 or more. But the corresponding values of the piezomagnetic effects for MnZn ferrite are not much higher than that observed for NiZn ferrite. 5. Conclusion Under a hydrostatic pressure of several MPa, a ferrite core with a closed magnetic circuit can show a sharp piezomagnetic effect. Based on this, colossal piezocapacitance and piezoimpedance effects can be observed simultaneously from the search coil circled on the ferrite core with an alternating current in a wide frequency area. These effects can be proved to be independent on skin effect.
[1] F.L.A. Machado, C.S. Martins, S.M. Rezende, Phys. Rev. B 51 (1995) 3926–3929. [2] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189–1191. [3] L.P. Shen, T. Uchiyama, K. Mohri, E. Kita, K. Bushida, IEEE Trans. Magn. 33 (5) (1997) 3355. [4] M. Knobel, M. Vazquez, M.L. Sanchez, A. Hernando, J. Magn. Magn. Mater. 169 (1997) 89. [5] L.V. Panina, K. Mohri, K. Bushida, M. Noda, J. Appl. Phys. 76 (1994) 6198. [6] M. Tejedor, B. Hernando, M.L. Sanchez, V.M. Prida, M. Vazquez, J. Magn. Magn. Mater. 196/197 (1999) 330. [7] B. Hernando, M.L. Sanchez, V.M. Prida, M. Tejedor, J. Appl. Phys. 90 (2001) 4783. [8] M. Knobel, M.L. Sánchez, C. Gómez-Polo, P. Marín, M. Vázquez, A. Hernando, J. Appl. Phys. 79 (1996) 1646. [9] K.-H. Shin, M. Inoue, K.-I. Arai, J. Appl. Phys. 85 (1997) 5465. [10] J.M. Barandiaran, J. Gutierrez, Sens. Actuator A 59 (1997) 38. [11] A. Ludwig, M. Tewes, S. Glasmachers, M. Löhndorf, E. Quandt, J. Magn. Magn. Mater. 242–245 (2002) 1126. [12] A. Schweiger, Siemens Components No. 1 (1997) 16–l8. [13] H.G. Dill, Electron. Des. 17 (1) (1964) 52. [14] Z. Jiang, P.S. Excell, Z.M. Hejazi, IEEE Trans. Microwave Theory Tech. 45 (1) (1997) 139. [15] C.A. Romero-Talamás, P.M. Bellan, S.C. Hsu, Rev. Sci. Instrum. 75 (8) (2004) 2664. [16] D. Stoppels, J. Magn. Magn. Mater. 160 (1996) 323.
Biographies N. Zhang obtained Bachelor degree of science in 1982 from Nanjing Normal University, Nanjing, China, Master degree and Ph.D. in science from Nanjing University, Nanjing, China, in 1985 and 1997, respectively, now employed by Nanjing Normal University as a professor. His current fields of interest include Giant magnetoresistance effect in compounds and composites, magnetoelectronic effect in layered composites, and giant piezoimpedance and magnetoimpedance effects in ferrites with high permeability. Z. L. Wang obtained Bachelor degree of science in 2002 from Tangshan Normal College, Tangshan, Hebei Province, China, now is a PhD student in Nanjing Normal University, Nanjing, China. His current fields of interest include giant piezoimpedance and converse magnetoelectric effects in composites. X. Fang obtained Bachelor degree of science in 2002 from Jinan University, Jinan, Shandong Province, China, now is a PhD student in Nanjing Normal University, Nanjing, China. His current fields of interest include giant piezoimpedance and converse magnetoelectric effects in heterotypic composites.