ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2016, Vol. 80, No. 9, pp. 1097–1100. © Allerton Press, Inc., 2016. Original Russian Text © A.V. Kalgin, S.A. Gridnev, E.S. Grigorjev, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Seriya Fizicheskaya, 2016, Vol. 80, No. 9, pp. 1200–1203.
Internal Friction and Magnetoelectric Response in Two-layer Composites Tb0.12Dy0.2Fe0.68–PbZr0.53Ti0.47O3 A. V. Kalgina, *, S. A. Gridneva, and E. S. Grigorjevb aVoronezh
State Technical University, Voronezh, 394026 Russia Air Force Academy, Voronezh, 394064 Russia *e-mail:
[email protected]
bZhukovsky–Gagarin
Abstract⎯The inverse magnetoelectric effect and internal friction in two-layer composites based on ferromagnetic Tb0.12Dy0.2Fe0.68 and piezoelectric PbZr0.53Ti0.47O3 are studied in an ac electrical field in the frequency range of 52–213 kHz at temperatures of 293 to 400 K. A correlation is found between the internal friction and the efficiency of the inverse magnetoelectric transformation at resonant frequencies. DOI: 10.3103/S1062873816090203
INTRODUCTION Today’s rapidly developing electronic technologies require the creation and investigation of materials with unusual physical properties. Such materials particularly include magnetoelectric ferromagnetic–piezoelectric composites, which are capable of changing their polarization under the action of a magnetic field (the direct magnetoelectric effect) and electric fieldinduced magnetization (the inverse magnetoelectric effect) [1, 2]. The magnetoelectric (ME) effect in composites occurs due to interaction between electric and magnetic fields through magnetostrictive and piezoelectric strains in the corresponding components [3]; it is therefore sensitive to structural changes in the composite’s components. The internal friction method, which is characterized by high structural sensitivity that unattainable for all other methods, provides information about the structural features of materials [4‒6]. There could therefore be a correlation between the ME effect and the internal friction in composites, so studying the internal friction inside ferromagnetic– piezoelectric composites is an important problem for physicists. The internal friction in ME composites has mainly been studied in samples using longitudinal oscillation modes with frequencies of hundreds of kHz [4–6] and twist oscillation modes with frequencies of tens of Hz [7–9] in the temperature range of phase transitions. We could find no data in the literature about correlations between the internal friction in composites and the efficiency of ME transformation. The aim of this work was to study internal friction by means of resonance and matching it with the magnetoelectric response in two-layer composites
Tb0.12Dy0.2Fe0.68–PbZr0.53Ti0.47O3 (TDF–PZT) with layers of TDF (Tb0.12Dy0.2Fe0.68) of different thicknesses in the 293–400 K temperature range. EXPERIMENTAL Samples of two-layer TDF–PZT composites were produced via the deposition of ferromagnetic TDF layers of carefully mixed granulated terfenol and epoxide compound on piezoceramic PZT plates 8 × 6 × 0.3 mm3 in size that were preliminarily polarized according to thickness under industral conditions. The terfenol granules were ~50 μm in size, and their mass fraction was 0.82. The TDF layers were glued together with the PZT layers, polymerized at room temperature for 24 h, and then brought to sizes of 6 × 6 × a mm3 (a = 0.3, 0.6, 0.9, 1.2, and 1.5 mm) using an abrasive sheet of grade K 1000. The geometry of the two-layer TDF– PZT composite samples is shown in Fig. 1. Internal friction Q–1 was determined from the resonant curves of coefficient of inverse ME transformation αB as a function of ac electrical field frequency f. Resonant frequency fr of a composite sample and res-
1097
TDF Epoxy adhesive
H=
Silver electrodes
1 M
2 3
P
PZT
U
Um
Fig. 1. Schematic view of a TDF–PZT composite sample and the orientation of vectors of magnetization M and polarization P inside it.
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αB, 10–3 G cm V–1 12
0.055
10
0.050
αB, 10–3 G cm V–1 12
Q–1
10 8
8
0.045 6
1
6
fp
0.040
2 3
4
4
2
4 2
0.035 5 0
0 50
100
150
200 f, kHz
Fig. 2. Dependences αB(f) for composite 0.9 TDF–0.3 PZT in electric field E = 133.3 V cm–1 and a constant magnetic field of varying strength H= = (1) 0; (2) 1; (3) 1.5; (4) 2, and (5) 2.5 kOe.
−1
=
Δ f 0.7 . 3 fr
(1)
The αB(f) dependences were derived in studying the inverse ME effect in TDF–PZT composites [11], while the ME effect was studied by measuring the change in magnetization M of the composites in an ac electrical field. The electrical field that arose upon applying ac voltage U to the PZT layer’s electrodes deformed the PZT layer due to the inverse piezoeffect; the deformations were transferred to the TDF layer because of the mechanical bond between the PZT and TDF layers and changed the composite magnetization under the magnetoelastic effect. The change in magnetization was detected from the variation in the amplitude of induced voltage Um on an inductance coil made of copper wire 5 mm long, produced by coiling 200 turns of copper wire 0.08 mm I diameter on a composite sample. Using measured voltage Um, coefficient αB was calculated using the equation αB = Bm/E = Um/(2πfENS) [G cm
V–1],
1.0 1.5 H=, kOe
2.0
2.5
0
Fig. 3. Dependences Q–1(H=) and αB(H=) at frequency fr and room temperature for composite 0.9 TDF–0.3 PZT, plotted using the experimental data in Fig. 2.
Below, the composites are designated as (a)TDF– (b)PZT, where a is the thickness of the TDF layer, mm.
onant curve width ∆f0.7 corresponding to 0.7 of the height of the resonant peak of αB(f), were first found from the αB(f) curve. The internal friction was then calculated using the equation [10]
Q
0.5
(2)
where Bm is the amplitude of magnetic induction in the TDF layer, G; E = U/b is the electrical field strength, V cm–1; b is the thickness of the PZT layer, mm; N is the number of induction coil turns; and S is the area of the TDF layer’s cross section, cm2.
RESULTS AND DISCUSSION Resonant curves αB(f) for composite 0.9 TDF– 0.3 PZT measured at different magnitudes of shifting magnetic field H= and room temperature are shown in Fig. 2. It can be seen that coefficient αB, being a function of f, passes through the peak at resonant frequency fr of the first harmonic of longitudinal oscillations along the sample’s length. This is because the inverse ME effect originates in the composites due to interaction between the ferromagnetic and piezoelectric subsystems via elastic deformations, and the deformations are greatly enhanced at the resonant frequencies. In addition, coefficient αB first grows sharply in fields 0 < H= < 1.5 kOe and then rises slightly in fields 1.5 < H= < 2.5 kOe. This explained by the domains in the TDF layers actively changing direction in the magnetic field in the range of 0–1.5 kOe; this raises the composite’s magnetization, the induction coil voltage, and thus coefficient αB. In the range of 1.5–2.5 kOe, there are virtually no magnetic domains capable of changing direction; the magnetic field thus raises the composite’s magnetization slightly, and thus αB as well. The inverse ME effect in composites is caused by the action of mechanical stresses on the magnetic domain structure, and a constant magnetic field drastically changes the number of domains; the contribution from the domain dynamics to the internal frictions in the composites should therefore diminish as the field grows, so Q–1 should also fall with an increase in H= (Fig. 3).
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INTERNAL FRICTION AND MAGNETOELECTRIC RESPONSE
αB, 10–3 G cm V–1 11
Q–1 0.055
10 9
0.050
αB, G cm V–1 1
0.005
2 3
0.004
8 7
0.045
0.003 4
6 5
0.040
4
1099 fr, kHz 130 120 110 100 90 80 70 60 280 300 320 340 360 380 400 T, K
5
0.002 0.001
3
0.035 0
0.5
1.0 a, mm
2 2.0
1.5
The internal friction obviously correlates with the efficiency of the inverse ME transformation at the resonant frequency. Curves similar to those in Figs. 2 and 3 were also derived for composites 0.3 TDF–0.3 PZT, 0.6 TDF– 0.3 PZT, 1.2 TDF–0.3 PZT, and 1.5 TDF–0.3 PZT. If resonant curves αB(f) are used for all composites at different H=, the same correlation can be observed from a comparison of the Q–1(a) and αB(a) dependences at fr, H= = 2.5 kOe, and at room temperature for different composites (Fig. 4). The peak on the αB(a) curve at fr can be explained using the model in [12], according to which coefficient αB depends on the volume of ferromagnetic mV and piezoelectric pV components of the composite; elastic constants ms11 and ps11of the ferromagnetic and piezoelectric, respectively; their densities mρ and pρ; the composite sample length L; angular frequency ω of the ac electrical field; and piezomagnetic q11 and piezoelectric d31 coefficients:
2V (1 − V ) m q11 pd31 tan(kL 2) kL[V m s11 + (1 − V ) p s11]
(3)
,
where V = pV ( pV + mV ) is the volume fraction of the piezoelectric component in the composite, −1
⎡ ⎤ k = ω [ ρ V + ρ(1 − V )] ⎢ pV + 1m− V ⎥ , s11 ⎦ ⎣ s11 and ω = 2πf. Parameters s, ρ, L (taken as equal to the PZT layer length), ω, q11, and d31 change negligibly, and equation p
m
40
80
120
160
200 f, kHz
Fig. 5. Dependences αB(f) for composite 0.9 TDF–0.3 PZT at H= = 1 kOe, E~ = 133.3 V cm–1, and temperatures of (1) 293, (2) 325, (3) 350, (4) 375, and (5) 400 K. Dependence fr(T) is shown in the insert.
Fig. 4. Q–1 and αB as functions of magnetic layer thickness а at the resonant frequency at H= = 2.5 kOe and room temperature.
αB =
0
V(1 – V) has a maximum; i.e., a peak should be observed on the αB(a) curve. The minimum on the Q–1(a) curve is probably due to competition between two factors. On the one hand, a PZT layer of one thickness weakly deforms the thicker TDF layer and thus affects the mobility of the domains in the TDF layer, thereby raising Q–1 in the composite at in same magnetic field. On the other hand, the number of domains that participate in remagnetization in the same magnetic field grows with the thickness of the TDF layer, as is evident from the magnetization curve for a thicker TDF sample reaching saturation in stronger fields. This is equivalent to a rise in Q–1. The correlation between Q–1 and αB can be observed by comparing the Q–1(T) and αB(T) dependences at fr, which were plotted for the composites in this work using dependences αB(f) in the fr range at different temperatures. As examples, Figs. 5 and 6 show dependences αB(f), Q–1(T), and αB(T) for composite 0.9 TDF–0.3 PZT. Figure 5 shows that the resonant peak shrinks, broadens, and shifts toward low frequencies as the temperature increases. The reduction in αB is explained by αB ~ q11(H=) = ∂λ11/∂H= and λ11 ~ M 12. According to our experiment, the M(H=) slope for TDF falls as the temperature rises. Slope λ(H=) therefore also falls, along with ∂λ11/∂H= and αB. The drop in frequency fr as the temperature rises (see the insert in Fig. 5) is due to an increase in the product of effective density 〈ρ〉 and the effective compliance of the composite 〈s11〉 according to the equa-
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αB, 10–3 G cm V–1 5.5
Q–1 0.5
5.0
0.4
4.5 4.0
0.3
3.5 3.0
0.2
in the 9–32 kHz range as the temperature rises from 293 to 400 K for composite 0.9 TDF–0.3 PZT at H= = 1 kOe (Fig. 5). Our study of the relations between Q–1 and αB in the region of resonant frequencies of the first harmonic of longitudinal oscillations along a sample’s length at different H=, a, and T for TDF–PZT composites show an inverse correlation between Q–1 and αB, allowing Q–1 to be used as an indicator of the high efficiency of ME interaction.
2.5 0.1 2.0 0 280
300
320
340 360 T, K
380
400
1.5
ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation, project no. 14-12-00583. REFERENCES
Fig. 6. Temperature dependences and αB(T) at fr for composite 0.9 TDF–0.3 PZT, plotted using the experimental data in Fig. 5. Q–1(T)
tion for the resonant frequencies of longitudinal oscillations along a sample’s length:
fr = n 2L
1 , ρ s11
(4)
where n is the number of nodes along the sample’s length that corresponds to the oscillation harmonic number, and L is the sample’s length. CONCLUSIONS The inverse ME effect in composites is due to the action of mechanical stresses on the magnetic domain structure. The latter becomes more labile and movable with an increase in the temperature, so a rise in temperature results in additional magnetic loss and an increase in Q–1 in a composite in general (Fig. 6). According to Eq. (1), an increase in Q–1 is possible especially when ∆f0.7 grows; i.e., when the αB(f) peak broadens. The width of resonant curve Δf0.7 thus grows
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Translated by O. Ponomareva
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