Abstract
Electron magnetic resonance (EMR) spectra of gadolinium-doped barium titanate (BaTiO3) have been studied at room temperature for gadolinium concentrations between 0.20 and 2.00 mol%. The results suggest that the Gd3+ ions occupy substitutional sites, replacing the Ba2+ ion, that the electron magnetic resonance linewidth increases with increasing gadolinium concentration, and that the range of the exchange interaction between Gd3+ ions is about 0.98 nm, of the same order as that of the same ion in other host lattices, such as strontium titanate (SrTiO3), strontia (SrO), quicklime (CaO), magnesia (MgO) and zircon (ZrSiO4). The fact that the electron magnetic resonance linewidth of the Gd3+ ion increases, regularly and predictably, with Gd concentration, shows that the Gd3+ ion can be used as a probe to study, rapidly and non-destructively, the crystallinity and degradation of BaTiO3.
ceramics; electron magnetic resonance; barium titanate; gadolinium
1 Introduction
Barium titanate (BaTiO3) is a traditional piezoelectric material that has been proposed for use in the microelectronics industry after studies revealed that its properties can be changed by controlling grain size11 Huan Y, Wang X, Fang J and Li L. Grain size effect on piezoelectric and ferroelectric properties of BaTiO ceramics. 3Journal of the European Ceramic Society. 2014; 34(5):1445-1448. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.11.030.
http://dx.doi.org/10.1016/j.jeurceramsoc...
,22 Gong H, Wang X, Zhang S, Wen H and Li L. Grain size effect on electrical and reliability characteristics of modified fine-grained BaTiO ceramics for MLCCs. 3Journal of the European Ceramic Society. 2014; 34(7):1733-1739. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.12.028.
http://dx.doi.org/10.1016/j.jeurceramsoc...
and by doping with rare earth ions33 Glinchuk MD, Bykov IP, Kornienko SM, Laguta VV, Slipenyuk AM, Bilous AG, V’yunov OI and Yanchevskii OZ. Influence of impurities on the properties of rare-earth-doped barium-titanate ceramics. Journal of Materials Chemistry. 2000; 10:941. http://dx.doi.org/10.1039/a909647g.
http://dx.doi.org/10.1039/a909647g...
. EMR spectroscopy is a convenient method for studying these impurities within the BaTiO3 structure. In this work, we study the effect of gadolinium concentration on the EMR spectrum of Gd3+ in polycrystalline BaTiO3.The importance of this investigation is twofold. First, once the effects of gadolinium concentration on the spectrum are known, it becomes possible to use EMR results to study, rapidly and non-destructively, the crystallinity and degradation of BaTiO3. Second, knowledge of the range of the exchange interaction between Gd3+ ions is essential for a better understanding of the magnetic properties of gadolinium-doped barium titanate.
1.1 Crystal structure of strontium titanate
At room temperature, barium titanate (BaTiO3) crystallizes in the perovskite structure44 Kwei GH, Lawson AC, Billinge SJL and Cheong SW. Structures of the ferroelectric phases of barium titanate. Journal of Physical Chemistry. 1993; 97(10):2368-2377. http://dx.doi.org/10.1021/j100112a043.
http://dx.doi.org/10.1021/j100112a043...
conforming to the space group P4mm(99). There are two distinct cation sites, one with twelve nearest neighbor oxygen ions, occupied by Ba atoms, and one with six nearest neighbor oxygen atoms, occupied by Ti atoms.
1.2 EMR of barium doped barium titanate
Analysis of the EMR spectrum of single-crystal gadolinium doped barium titanate55 Rimai L and deMars GA. Electron paramagnetic resonance of trivalent gadolinium ions in strontium and barium titanates. Physical Review. 1962; 127(3):702-710. http://dx.doi.org/10.1103/PhysRev.127.702.
http://dx.doi.org/10.1103/PhysRev.127.70...
shows that trivalent gadolinium ions substitutionally replace strontium ions in the lattice. The spectrum can be fitted to the Hamiltonian
with g = 1.995, b 2,0 = −293,6 × 10−4cm−1 and b 4,0 = 4.0 × 10−4 cm–1.
1.3 EMR of dilute solid solutions
The theory of dipolar broadening in diluted solid solutions was developed in Kittel & Abrahams66 Kittel C and Abrahams E. Dipolar broadening of magnetic resonance lines in magnetically diluted crystals. Physical Review. 1953; 90(2):238-239. http://dx.doi.org/10.1103/PhysRev.90.238.
http://dx.doi.org/10.1103/PhysRev.90.238...
and extended in de Biasi & Fernandes77 de Biasi RS and Fernandes AAR. The ESR linewidth of dilute solid solutions. Journal of Physics C: Solid State Physiscs. 1983; 16(28):5481-5489. http://dx.doi.org/10.1088/0022-3719/16/28/015.
http://dx.doi.org/10.1088/0022-3719/16/2...
to take exchange interactions into account. The main results of the theory can be summarized as follows:
(I) the lineshape is a truncated Lorentzian;
(II) the peak-to-peak first derivative linewidth may be expressed as
where ΔH 0 is the intrinsic linewidth, ΔHd is the dipolar broadening, C 1 is a constant and fe is the concentration of substitutional ions of the paramagnetic impurity not coupled by the exchange interaction, which can be expressed as
where f is the impurity concentration, z(rc ) the number of cation sites included in a sphere of radius rc , and rc the effective range of the exchange interaction.
(III) the intensity of the absorption line is
where C 2 is a constant.
The analysis above is based on the assumption of two ion populations, one with no exchange, which is responsible for the normal paramagnetic line, and another which, due to exchange, is either EPR silent (if the coupling is antiferromagnetic) or gives rise to a much broader line (if the coupling is ferromagnetic).
2 Experimental Procedure and Results
2.1 Sample preparation
The gadolinium doped samples used in this study were prepared from high purity BaTiO3(Aldrich, 99,9%) and Gd2O3(Reacton, 99.99%) powders by grinding them together and then firing the mixture for 24 h at 1200 °C in air. The gadolinium concentrations and reagent masses are shown in Table 1. Actual Gd concentrations were determined using the Inductively Coupled Plasma (ICP) technique. Room temperature X-ray diffraction patterns (Figure 1) of the samples matched, within experimental error, the pattern88 Kwei GH, Lawson AC and Billinge SJL. Structures of the Ferroelectric Phases of Barium Titanate. Journal of Physical Chemistry. 1993; 97(10):2368-2377. http://dx.doi.org/10.1021/j100112a043.
http://dx.doi.org/10.1021/j100112a043...
of BaTiO3. No other phases were detected.
X-ray diffraction pattern of a BaTiO3 sample doped with 0.2 mol% Gd. The indices were taken from JCPDS no. 81-2203.
2.2 Magnetic resonance measurements
All magnetic resonance measurements were performed at room temperature and 9.50 GHz using a Varian E-12 spectrometer with 100 kHz field modulation. The microwave power was 10mW and the modulation amplitude was 1 mT. The magnetic field was calibrated with an NMR gaussmeter.
The spectrum of a sample of BaTiO3 doped with 0.6 mol% Gd is shown in Figure 2. It closely matches the spectrum reported by Takeda & Watanabe99 Takeda T and Watanabe A. Two sets of E. S. R. of Gd in BaTiO ceramic semiconductor. 3+
3Journal of the Physical Society of Japan. 1964; 19(9):1742. http://dx.doi.org/10.1143/JPSJ.19.1742.
http://dx.doi.org/10.1143/JPSJ.19.1742...
for powdered Gd-doped BaTiO3. In principle, linewidth data can be extracted from any of the lines in the powder spectrum. We chose the line indicated by an arrow in Figure 2. The results are shown in Table 2 for several gadolinium concentrations.
3 Discussion
The theoretical concentration dependence of the peak-to-peak linewidth ΔH
pp, given by Equation 2, is shown in Figure 3 for ΔH
0 = 3.3 mT and eight different ranges of the exchange interaction. The values of rc
and z(rc
) for the first eight coordinate spheres are listed in Table 3, where n is the number of the order of each coordinate sphere (n = 1 includes no neighboring sites, and so on). The values of z(rc
) are those appropriate to the lattice of BaTiO3; the values of rc
were calculated from the lattice constants at room temperature as measured by X-ray diffraction88 Kwei GH, Lawson AC and Billinge SJL. Structures of the Ferroelectric Phases of Barium Titanate. Journal of Physical Chemistry. 1993; 97(10):2368-2377. http://dx.doi.org/10.1021/j100112a043.
http://dx.doi.org/10.1021/j100112a043...
, a = 0.3990 nm, c = 0.4035 nm. The experimental data are also shown in Figure 3. The experimental results fit the theoretical curve for n = 7, which corresponds, according to Table 3, to a range rc
= 0.98 nm for the exchange interaction.
Concentration dependence of the peak-to-peak linewidth, ΔH pp, in Gd-doped BaTiO3. The circles are experimental points; the curves represent results of calculations for eight different ranges of the exchange interaction.
In Table 4 we show the pertinent parameters for the dipolar broadening ΔHd
of the Gd3+ FMR spectrum in BaTiO3 and in other host lattices. One can see that there is a large range of values for the rate of increase of the dipolar broadening with concentration, expressed by the parameter C
1, from 4.5 for MgO to 750 for BaTiO3. In order to investigate the question further, we plot in Figure 4 the coefficient C
1 of Equation 2 as a function of the difference Δr = r
Gd−r
h, where r
Gd the ionic radius of Gd3+ and r
h is the ionic radius of the host lattice cation (the ionic radii were taken from Shannon1515 Shannon RD. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography. 1976; 32(5):751-767. http://dx.doi.org/10.1107/S0567739476001551.
http://dx.doi.org/10.1107/S0567739476001...
) for the Gd-doped compounds shown in Table 4. The results suggest that C
1 changes, in a systematic way, with the ionic radius misfit Δr.
Dependence of the coefficient C 1 on the ionic radius misfit Δr = r Gd – r h. Gd:ZrSiO4 data are from de Biasi & Grillo1010 de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the EMR spectrum of Gd in zircon. 3+Physica B: Condensed Matter. 2009; 404(20):3368-3370. http://dx.doi.org/10.1016/j.physb.2009.05.016.
http://dx.doi.org/10.1016/j.physb.2009.0... ; Gd:SrTiO3 data are from de Biasi & Grillo1111 de Biasi RS and Grillo MLN. Electron magnetic resonance of diluted solid solutions of Gd in SrTiO. 3+ 3Materials Chemistry and Physics. 2011; 130(1-2):409-412. http://dx.doi.org/10.1016/j.matchemphys.2011.07.002.
http://dx.doi.org/10.1016/j.matchemphys.... ; Gd:SrO data are from de Biasi & Grillo1212 de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in SrO. 3+Journal of Alloys and Compounds. 2002; 337(1-2):30-32. http://dx.doi.org/10.1016/S0925-8388(01)01941-7.
http://dx.doi.org/10.1016/S0925-8388(01)... ; :CaO data are from de Biasi & Grillo1313 de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in CaO. 3+Solid State Communications. 2002; 124(4):131-133. http://dx.doi.org/10.1016/S0038-1098(02)00479-9.
http://dx.doi.org/10.1016/S0038-1098(02)... ; Gd:MgO data are from de Biasi & Grillo1414 d de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in MgO. 3+Journal of Physics and Chemistry of Solids. 2004; 64(6):1207-1209. http://dx.doi.org/10.1016/j.jpcs.2003.12.003.
http://dx.doi.org/10.1016/j.jpcs.2003.12... .
4 Conclusions
The study of the EMR spectrum of Gd3+ in BaTiO3 shows that the peak-to-peak linewidth increases with Gd concentration. This increase is attributed to dipolar broadening and is consistent with a model based on the exchange interaction and on the misfit between the ionic radii of the doping impurity and the host cation.
The fact that the linewidth increases in a predictable way with Gd concentration suggests that gadolinium can be used as a probe to study the crystallinity and degradation of barium titanate.
Acknowledgements
The authors thank CNPq for financial support.
References
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1Huan Y, Wang X, Fang J and Li L. Grain size effect on piezoelectric and ferroelectric properties of BaTiO ceramics. 3Journal of the European Ceramic Society. 2014; 34(5):1445-1448. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.11.030
» http://dx.doi.org/10.1016/j.jeurceramsoc.2013.11.030 -
2Gong H, Wang X, Zhang S, Wen H and Li L. Grain size effect on electrical and reliability characteristics of modified fine-grained BaTiO ceramics for MLCCs. 3Journal of the European Ceramic Society. 2014; 34(7):1733-1739. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.12.028
» http://dx.doi.org/10.1016/j.jeurceramsoc.2013.12.028 -
3Glinchuk MD, Bykov IP, Kornienko SM, Laguta VV, Slipenyuk AM, Bilous AG, V’yunov OI and Yanchevskii OZ. Influence of impurities on the properties of rare-earth-doped barium-titanate ceramics. Journal of Materials Chemistry. 2000; 10:941. http://dx.doi.org/10.1039/a909647g
» http://dx.doi.org/10.1039/a909647g -
4Kwei GH, Lawson AC, Billinge SJL and Cheong SW. Structures of the ferroelectric phases of barium titanate. Journal of Physical Chemistry. 1993; 97(10):2368-2377. http://dx.doi.org/10.1021/j100112a043
» http://dx.doi.org/10.1021/j100112a043 -
5Rimai L and deMars GA. Electron paramagnetic resonance of trivalent gadolinium ions in strontium and barium titanates. Physical Review. 1962; 127(3):702-710. http://dx.doi.org/10.1103/PhysRev.127.702
» http://dx.doi.org/10.1103/PhysRev.127.702 -
6Kittel C and Abrahams E. Dipolar broadening of magnetic resonance lines in magnetically diluted crystals. Physical Review. 1953; 90(2):238-239. http://dx.doi.org/10.1103/PhysRev.90.238
» http://dx.doi.org/10.1103/PhysRev.90.238 -
7de Biasi RS and Fernandes AAR. The ESR linewidth of dilute solid solutions. Journal of Physics C: Solid State Physiscs. 1983; 16(28):5481-5489. http://dx.doi.org/10.1088/0022-3719/16/28/015
» http://dx.doi.org/10.1088/0022-3719/16/28/015 -
8Kwei GH, Lawson AC and Billinge SJL. Structures of the Ferroelectric Phases of Barium Titanate. Journal of Physical Chemistry. 1993; 97(10):2368-2377. http://dx.doi.org/10.1021/j100112a043
» http://dx.doi.org/10.1021/j100112a043 -
9Takeda T and Watanabe A. Two sets of E. S. R. of Gd in BaTiO ceramic semiconductor. 3+ 3Journal of the Physical Society of Japan. 1964; 19(9):1742. http://dx.doi.org/10.1143/JPSJ.19.1742
» http://dx.doi.org/10.1143/JPSJ.19.1742 -
10de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the EMR spectrum of Gd in zircon. 3+Physica B: Condensed Matter. 2009; 404(20):3368-3370. http://dx.doi.org/10.1016/j.physb.2009.05.016
» http://dx.doi.org/10.1016/j.physb.2009.05.016 -
11de Biasi RS and Grillo MLN. Electron magnetic resonance of diluted solid solutions of Gd in SrTiO. 3+ 3Materials Chemistry and Physics. 2011; 130(1-2):409-412. http://dx.doi.org/10.1016/j.matchemphys.2011.07.002
» http://dx.doi.org/10.1016/j.matchemphys.2011.07.002 -
12de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in SrO. 3+Journal of Alloys and Compounds. 2002; 337(1-2):30-32. http://dx.doi.org/10.1016/S0925-8388(01)01941-7
» http://dx.doi.org/10.1016/S0925-8388(01)01941-7 -
13de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in CaO. 3+Solid State Communications. 2002; 124(4):131-133. http://dx.doi.org/10.1016/S0038-1098(02)00479-9
» http://dx.doi.org/10.1016/S0038-1098(02)00479-9 -
14d de Biasi RS and Grillo MLN. Influence of gadolinium concentration on the ESR spectrum of Gd in MgO. 3+Journal of Physics and Chemistry of Solids. 2004; 64(6):1207-1209. http://dx.doi.org/10.1016/j.jpcs.2003.12.003
» http://dx.doi.org/10.1016/j.jpcs.2003.12.003 -
15Shannon RD. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography. 1976; 32(5):751-767. http://dx.doi.org/10.1107/S0567739476001551
» http://dx.doi.org/10.1107/S0567739476001551
Publication Dates
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Publication in this collection
Mar-Apr 2015
History
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Received
26 May 2014 -
Reviewed
20 Feb 2015