Disorder-insensitivity of room-temperature giant permittivity in Ca 4 − x Cu x Ti 4 O 12 (x = 3, 2 and 1)
polycrystalline ceramics
Cite as: J. Appl. Phys.126, 224102 (2019);doi: 10.1063/1.5126348
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Submitted: 3 September 2019 · Accepted: 29 November 2019 · Published Online: 12 December 2019
Lin Huang,1,a)Yongqiang Li,2,a) Fanqi Meng,3,a)Lei Guo,4Yanping Liang,4Le Zhang,1Xiaoyan Chen,1Bo Feng,1 Kai Chen,1,b) Qinghua Zhang,3,b)Lin Gu,3,5,6,b)Junming Liu,2 and Jinsong Zhu2
AFFILIATIONS
1School of Science, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China
2National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China
3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
4School of Physics, Southeast University, Nanjing 211189, People’s Republic of China
5Collaborative Innovation Center of Quantum Matter, Beijing 100190, People’s Republic of China
6School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
a)Contributions:L. Huang, Y. Li, and F. Meng contributed equally to this work.
b)Authors to whom correspondence should be addressed:[email protected],[email protected], and[email protected]
ABSTRACT
When the stoichiometric proportion of Cu in Ca4−xCuxTi4O12 polycrystalline ceramics is decreased from 3 to 2 and then to 1, the room-temperature permittivity is reduced by one order of magnitude during each step. Ca/Cu atomic disorder is observed only in some grains of Ca3CuTi4O12single-phase polycrystalline ceramics, and the disorder is not the origin of the giant permittivity in CaCu3Ti4O12. Quantitatively, the permittivity magnitude is related to the mole ratio of polaronlike 3d electrons from Cu ions.
Published under license by AIP Publishing.https://doi.org/10.1063/1.5126348
I. INTRODUCTION
Calcium copper titanate (CaCu3Ti4O12) has been studied in science and technology,1–23 partly due to the almost frequency- independent giant permittivity with four orders of magnitude at room temperature.
The relationship between the microstructure and the giant permittivity is not conclusive. Two representative arcs of the electri- cal heterogeneity manifested in impedance complex planes of poly- crystalline ceramics suggest that, as one possibility, semiconducting grains and insulating grain boundaries are responsible for the unusual giant permittivity based on the surface and internal barrier layer capacitance (IBLC) mechanism.5No grain boundaries are in single crystals; however, the electrical heterogeneity is still observed, and the dielectric properties are similar to those of polycrystalline ceramics.3 In hydrofluoric-acid-etching polycrystalline ceramics, grain boundaries themselves are experimentally proved more
conducting than grains are, although both are insulators.6–8Grain boundaries show the insulating anisotropy,8and it is the Schottky barriers that depress the current across much more than along them. Therefore, the key effect of grain boundaries on the permit- tivity is excluded, and the giant permittivity should be, at least, based on the microstructure common to polycrystalline ceramics and single crystals. CaTiO3 inclusions and twin boundaries in some grains of polycrystalline ceramics and single crystals5,9,10are a possible alternative for the IBLC mechanism. However, they are not observed infine single crystals or polycrystalline ceramics.11,12 Twin boundaries are found to increase dielectric losses in defective single crystals13or polycrystalline ceramics.10Then, Ca/Cu atomic disorder is observed as nanoclustered defects12,14,15 and suggested as another alternative to serve as internal barrier layer capacitors in a semiconducting matrix14or induce the metalliclike polarizability in the surrounding insulating regions.15 In these disorder-defect
single crystals, the disorder content is less than 10% of the bulk.12,14Defect types and densities in single crystals and polycrys- talline ceramics are very different.11However, all of them exhibit the same dielectric characters, and the origin of the giant permittiv- ity is hardly related to defects. Interestingly, the exact atomic
configuration of CaCu3Ti4O12was determined via neutron powder diffraction as early as in 1979.16From a crystallographic perspec- tive, it is the ordered arrays of Ca and Cu atoms at A and A0sites that result in a body-centered cubic structure with the space group Im3, and a relatively larger lattice parameter (about 7.39 Å) than
FIG. 1. XRD patterns (left column) and SEM images (right column) of three ceramics.
those of other simple-perovskite titanates. Such an ordered crystal structure has been directly observed via the high angle annular dark-field (HAADF) imaging when the scanning trans- mission electron microscopy (STEM) with a spherical aberration (Cs) corrector is utilized. The chemical identification of each atomic column has been further verified via the electron energy loss spectroscopy.17,18
Another important microstructure has been observed in poly- crystalline ceramics. The off-center displacement of one B-site single titanium (Ti) ion along the〈001〉directions is about 0.04 Å and correlated with the ones of other Ti ions within the 5–10 crystalline unit cells.19,20The sum of the off-center displacements is about 0.40–0.80 Å and larger than the off-center displacement of one single titanium (about 0.10 Å) in classic ferroelectric BaTiO3
(which shows a permittivity with three orders of magnitude). The off-center-displaced titanium ions were modeled as one-dimensional, antiparallel, mutually independent, andfinite-length dipole chains.19 The parallel-dipole-orientation branch can be triggered by an exter- nal AC electrical field,21 and as a result, the inversion symmetry restriction of ionic polarization is externally broken. The dielectric properties below 200 K are quantitatively well described by using the
Hamiltonian in the Ising model analysis of dielectric polarization (afinite chain).20Notably, the negative magnetodielectric effect, in which the permittivity is reduced by a large static magnetic field, reveals that polaronlike 3d electrons from B-site copper (Cu) ions are involved in low-frequency dielectric properties above 200 K.20 The comprehensive model has been proposed that the dipole chains and the polaronlike 3d electrons coexist in the bulks, thus providing an underlying, coherent, and self-consistent physic mechanism for dielectric, antiferromagnetic, optical, and photo-related properties.20 For example, the electrical heterogeneity occurs due to two dielectric processes of the dipole chains and the electrons, which are thermally activated at different temperatures. The Schottky barriers across grain boundaries and at electrode-interfaces result from the electro- static potentialfield of the electrons pinned at the grain surfaces.20 The polaron-relaxation conductivity is attributed to the thermal acti- vation of polaronlike 3d electrons in the copper-titanium sublattice, while the variable-range hopping of charge carriers is due to short- and long-range motions of these electrons.22The strong correlation effect in the angle-resolved23and inverse photoemission processes24 originates from the phonon coupling of photon-activated polaronlike 3d electrons.
FIG. 2.(a) Schematic illustration of the CaCu3Ti4O12crystal structure. (b) TEM-HAADF imaging along [001] from CaCu3Ti4O12. Frequency dependence of (c)ε0and (d) the loss tangent in CaCu3Ti4O12.
At present, the effect of Ca/Cu atomic disorder on the giant permittivity is supported by the IBLC mechanism, which is beyond the range of the comprehensive model. Thus, it is imperative to examine the ordered state of Ca and Cu atoms and then clarify the relation between such disorders and the giant permittivity. In science, the clarification may be developed into a consistent model and shed light on the mechanism of other giant permittivity mate- rials. In technology, a precise determination of Ca/Cu-ordered states by the atomic-scale direct probing is a crucial step toward modulating the dielectric properties. The study is focused on the ordered-state change by decreasing the stoichiometric proportion of Cu, the characterization of atomic orders by the direct HAAD imaging, and the comparison of permittivity magnitudes in Ca4−xCuxTiO12(x = 3, 2, and 1) polycrystalline ceramics.
II. EXPERIMENTAL
Ca4−xCuxTi4O12 (x = 3, 2, and 1) polycrystalline ceramics were prepared by a solid-state reaction method, as described in our previous work.6,20The crystalline phases of ceramics were charac- terized using a Rigaku X-ray diffractometer (D/MAX-RB) with Cu Kα radiation. The 2θ angle ranged from 20° to 90° with an increment of 0.02°. Grain sizes and uniformities were investigated using thefield-emission scanning electron microscopy (SEM Inspect F50, FEI Co., USA). All polycrystalline ceramics were polished to a thickness of 0.4 mm, and Ag electrodes were sputtered onto their surfaces. Dielectric measurements were performed at 300 K using a Hewlett-Packard impedance/gain-phase analyzer (model 4294A, Agilent Co., USA). An applied voltage of 50 mV was used in the fre- quency range from 100 Hz to1 MHz. To clearly observe the ordered states of Ca and Cu atoms, the measured pellets were polished to remove electrodes, ground into powders, andfinally dispersed onto holey carbon-coated copper grids. The HAADF imaging was per- formed at 200 keV using the transmission electron microscopy (TEM ARM-200CF, JEOL Ltd., Tokyo Japan) equipped with double spherical aberration correctors. The collection angle ranged from 90 to 370 mrad. The attainable resolution of the probe was defined by the objective prefield as 78 pm.
III. RESULTS AND DISCUSSION
Figure 1shows XRD patterns and SEM images of CaCu3Ti4O12, Ca2Cu2Ti4O12, and Ca3CuTi4O12. The XRD patterns indicate that the polycrystalline ceramics of CaCu3Ti4O12 and Ca3CuTi4O12 are single phase, while those of Ca2Cu2Ti4O12 are the composite of CaCu3Ti4O12and CaTiO3.25The SEM images show clear grains and grain boundaries with similar microstructures. No CaTiO3inclusion and twin boundaries are observed.
Figure 2(a) shows a schematic and representative crystal structure of CaCu3Ti4O12, including tilting TiO6 octahedra, and off-center displacements of Ti ions along the〈001〉directions. The left panel of Fig. 2(b) shows the TEM-HAADF imaging along [001] from CaCu3Ti4O12. Qualitatively, the intensities of atomic columns in the image are proportional to the atomic number Zn, where n is close to 2, because the intensity is highly sensitive to the Z-number (Z-contrast).26,27In the image, the intensity contrasts of spots vary. Because Cu has the highest atomic number (29), the brightest spot inFig. 2(b)indicates the Cu atomic column. Along
[001], the A site Ca atom and the A0site Cu atom alternate in one atomic column. This results in an average atomic number of 24.5 for this column and shows the spot with the moderate brightness, as shown in the right panel ofFig. 2(b). Another atomic column consists of B-site Ti atoms. Ti has the smallest atomic number (22), and the atomic column exhibits the dimmest spot. Thus, spots with various levels of brightness are matched with their respective atomic columns, as shown in the left panel ofFig. 2(b). In one row, Ca/Cu-ordered atomic columns alternate with Ti atomic columns.
In the other row, Cu atomic columns alternate with Ti atomic columns. Clearly, Ca/Cu-disorder defects are absent.
FIG. 3. (a) TEM-HAADF imaging along [001] from Ca2Cu2Ti4O12. (b) Frequency dependence ofε0and the loss tangent in Ca2Cu2Ti4O12.
The dielectric measurement was performed before the TEM-HAADF imaging, as shown inFigs. 2(c)and 2(d). The real part of the relative complex dielectric valueε0(the scientific form of the permittivity) shows a magnitude of 104in the frequency range from 100 Hz to 100 kHz at 300 K, and the loss tangent is as small as about 0.09, which are consistent with our published work.6,20 The dielectric results are highly reproducible. Therefore, Ca/Cu-disorder defects do not result in the giant permittivity, although the defects may affect the permittivity and the loss tangent.
Figure 3(a) shows the TEM-HAADF imaging along [001]
from Ca2Cu2Ti4O12. There are Ca, Cu, and Ti atomic columns, while the Ca/Cu-disorder defects are absent. With the decrease in the stoichiometric proportion of Cu from 3 to 2, the magnitude of ε0is decreased from 104to 103, but the frequency plateau becomes broader, and the loss tangent is lowered to about 0.08, as shown in Figs. 3(c)and3(d), respectively.
In Ca3CuTi4O12, the TEM-HAADF imaging indicates the coexistence of the Ca/Cu atomic ordered state and the disorder.
As shown in Fig. 4(a), the spots in the image indicate three different intensity contrasts. These represent Ca/Cu, Ti, and Ca atomic columns, respectively. Ca and Cu atoms are located at A and A0 sites, respectively, and at least, the ordered state exists in many grains of the ceramic. Interestingly, some spots show a fourth type of intensity contrast. These spots exhibit a periodic arrange- ment and constitute a group of small crystalline unit cells at A and A0sites, as shown inFig. 4(b). Because of their brightness and loca- tions, these spots indicate Ca/Cu-disorder atomic columns in which 75% of all atoms are Ca atoms, and the rest are Cu atoms. In these columns, Ca atoms arrange randomly rather than alternate with Cu atoms. Therefore, there are the Ca/Cu-disorder defects in some grains. As shown inFigs. 4(c)and4(d), the magnitude ofε0 is further decreased to 102, and the loss tangent is decreased as small as about 0.04.
Atomic-scale Cu/Ca disorder defects might result in the for- mation of nanosized local dipoles and contribute to dielectric prop- erties. However, the present experiments reveal that the disorder
FIG. 4. TEM-HAADF imaging of (a) the Ca/Cu-ordered state and (b) the disorder along [001] from Ca3CuTi4O12. Frequency dependence of (c)ε0and (d) the loss tangent in Ca3CuTi4O12.
defects do not result in the giant permittivity. With the decrease in the stoichiometric proportion of Cu (x) from 3 to 2 and then to 1, the magnitude ofε0is decreased by one order of magnitude during each step. The relationship has not been determined quantitatively so far, and the IBLC mechanism is invalid for the case. In the com- prehensive model, the polaronlike 3d electrons dominate the value ofε0at room temperature. The Hamiltonian for these electrons is different from those constructed in the polaron theory, and the
“polaronlike” character is used to describe these 3d electrons in antiferromagnetic insulators.28,29The spin originates from unpaired 3d electron at dxy, dyz, or dzxorbitals of Cu2+ions. Below the Néel temperature of 25 K, the superexchange interactions among them keep themselves against the thermal destruction, to arrange them in a long-range antiferromagnetic order.20Above the Néel tempera- ture, these electrons are thermally activated as the charge carrier to gradually transition from short-range hop to long-range motion.22 They move through copper-titanium sublattices via electronic mixing pathways, such as dCu2zx !tTi2g!dCu1xy , because the running- wave functions of these orbitals overlap each other. They are charged particles, carrying the clouds of correlated electronic polar- izations by themselves. Thus, they behave as the polarons. Above 150 K, these quasiparticles distort the copper-titanium sublattice,14 correlate to the local lattice, and finally are pinned at the grain surface for the bulk dielectric polarization. The pinned electrons contribute to the electrostatic potential of the Schottky barriers across grain boundaries and at electrode-interfaces. Also, the motion of these charge quasiparticles induces the fabrication-process-related presence of Cu1+ and Ti3+ cations and oxygen vacancies at room temperature.30Every Cu ion has the same number of polaronlike 3d electrons. Thus, the real mole ratio of polaronlike 3d electrons among CaCu3Ti4O12, Ca2Cu2Ti4O12, and Ca3CuTi4O12 should be close to the stoichiometric proportion ratio of Cu, i.e., 3:2:1.
Tentatively, the relation between the permittivity magnitude and the mole ratio of polaronlike 3d electrons can be described using the formula [lg (ε0)](xþ1), where [ ] is the integral function.
The comprehensive model mentioned above was proposed in our previous work,20 which is supported by dielectric-, antiferromagnetic-, optical-, and photo-related phenomena. The dielectric properties below 200 K have been quantitatively and well characterized on the basis offinite-correlated off-center dis- placements of B-site Ti ions. Above 200 K, the thermal activation of polaronlike 3d electrons results in the appearance of the electri- cal heterogeneity. However, no quantitative studies have been per- formed to clarify their permittivity contribution. In the work, the contribution is determined quantitatively. The effect of polaron- like 3d electrons is further supported by a recent experiment that CaCu3Ti4O12polycrystalline ceramics were sintered under different oxygen atmospheres.30 Oxygen vacancies change the quantity of polaronlike 3d electrons because of the charge conservation, and thus, the permittivity is affected significantly.
IV. CONCLUSION
In summary, Ca4−xCuxTi4O12(x = 3, 2, and 1) polycrystalline ceramics were prepared by a solid-state reaction in order to investi- gate the effect of Ca/Cu atomic disorder on the giant permittivity.
At room temperature, CaCu3Ti4O12and Ca3CuTi4O12are single-
phase compounds, while Ca2Cu2Ti4O12is a composite. The Ca/Cu atomic ordered state exists in all grains of CaCu3Ti4O12 and Ca2Cu2Ti4O12, as well as some grains of Ca3CuTi4O12, while the Ca/Cu atomic disorder is observed only in the remaining grains of Ca3CuTi4O12. The permittivity magnitude of CaCu3Ti4O12, Ca2Cu2Ti4O12, and Ca3CuTi4O12 is 104, 103, and 102, and the minimum loss tangent is about 0.09, 0.08, and 0.04, respectively.
Ca/Cu atomic disorder does not result in the giant permittivity of CaCu3Ti4O12. The permittivity magnitude is related to the mole ratio of the polaronlike 3d electrons.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11004106, 11501293, 51522212, 51421002, and 51672307) and by the National 973 Program of China (Grant No. 2015CB654600).
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