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A low-temperature specific heat study of giant dielectric constant materials
View the table of contents for this issue, or go to the journal homepage for more 2008 J. Phys.: Condens. Matter 20 285214
(http://iopscience.iop.org/0953-8984/20/28/285214)
J. Phys.: Condens. Matter 20 (2008) 285214 (5pp) doi:10.1088/0953-8984/20/28/285214
A low-temperature specific heat study of
giant dielectric constant materials
C P Sun
1, Jianjun Liu
2,3, J-Y Lin
4, Chun-gang Duan
3,5, W N Mei
2,3and H D Yang
1,61Department of Physics, Center for Nanoscience and Nanotechnology, National Sun Yat-Sen University, Kaoshiung 804, Taiwan, Republic of China
2Department of Physics, University of Nebraska at Omaha, NE 68182-0266, USA
3Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
4Institute of Physics, National Chiao-Tung University, Hsinchu 300, Taiwan, Republic of China
5Department of Physics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
E-mail:yang@mail.phys.nsysu.edu.tw
Received 9 April 2008, in final form 29 May 2008 Published 17 June 2008
Online atstacks.iop.org/JPhysCM/20/285214
Abstract
A low-temperature specific heat study has been performed on the insulating giant dielectric constant material CaCu3Ti4O12and two related compounds, Bi2/3Cu3Ti4O12and
La0.5Na0.5Cu3Ti4O12, from 0.6 to 10 K. From analyzing the specific heat data in a very
low-temperature range, 0.6–1.5 K, and moderately low-temperature range, 1.5–5 K, in addition to the expected Debye terms, we observed significant contributions originating from the linear and Einstein terms, which we attributed as the manifestation of low-lying elementary
excitations due to lattice vibrations occurring at the grain boundaries and induced by local defects. Together with the findings on electronic and mechanical properties, a
phenomenological model is proposed to explain the high dielectric constant behavior in both low and high frequency regions.
(Some figures in this article are in colour only in the electronic version)
CaCu3Ti4O12 (CCTO) and related compounds have attracted
much attention because of its extraordinary dielectric behavior. The ceramic samples were first found to have a gigantic dielectric constant (K , up to 104) independent of frequency
and temperature in the range of DC-105 Hz and 100–600 K,
dropping steadily down to about 100 at 106 Hz and then
remaining constant until high frequency ∼109 Hz [1, 2]. A giant value of 105was later reported in a CCTO single crystal; yet twin and domains still existed [3].
Usually, a large dielectric constant results from atomic displacements in a non-centrosymmetric structure near its phase transition temperature, e.g. in a ferroelectric. However, CCTO is of body-centered cubic perovskite structure, no deformations associated with dipole formation and no soft modes in the phonon spectra down to 35 K [4, 5] have been noted. In addition, the values of the dielectric constant seem to be dependent upon the preparation methods and post
6 Author to whom any correspondence should be addressed.
treatments of the ceramic samples [6,7]. Many experiments on thin-film single crystal samples only had values about 100 [8]. In addition there is a group of single crystal and polycrystalline metal oxide samples with rock salt and fluorite structures, such as MnO, CoO [9], ZrO2 and HfO2 [10], which exhibit high
dielectric constants K ∼ 25–40. Extensive theoretical studies, including first principles calculations and lattice dynamics, have been performed on ZrO2and HfO2, and the results agreed
well with experiments.
A similar approach was applied to CCTO, the sub-IR frequency dielectric constants were estimated to be at most 70–80 [11,12] when using the effective charges, static dielectric constant, and optical frequencies calculated from lattice dynamics of a perfect crystal. This is smaller than the high frequency dielectric constant, thus it is vital to examine the structural details of the samples.
Several proposals have been put forward that the high di-electric constant of CCTO could originate from the creation
J. Phys.: Condens. Matter 20 (2008) 285214 C P Sun et al of barrier layer capacitances at twin boundaries [1,3], or at
the interfaces between grains and grain boundaries [13, 14], or between the sample and the electrodes [2, 15]. Current– voltage measurements show that the grain boundaries in the ceramics samples play an important role in the CCTO electri-cal properties [16]. We have made an effort to characterize the temperature dependence of the permittivity and impedance of CCTO and related compounds such as Bi2/3Cu3Ti4O12,
La2/3Cu3Ti4O12, and Y2/3Cu3Ti4O12 [14,17]. We found that
all these compounds have similar dielectric and electric behav-ior; i.e. they are insulators and all have large dielectric con-stants, though perhaps not as high as that of CCTO. In all these compounds we detected a Debye-like relaxation in the permit-tivity and frequency-dependent current/voltage measurements with dielectric constants independent of the temperature and frequency over a wide range. In the impedance frequency-dependent voltage/current measurements, we observed some evidence for two electric responses with very different inten-sity and response frequencies. One relates to the semiconduct-ing grains and the other insulatsemiconduct-ing grain boundaries that we as-cribed to the Maxwell–Wagner relaxation of the interfacial po-larization. These are due to oxygen deficiency occurring at the regions between grains and grain boundaries that generates the detected Debye-like relaxation and large dielectric constants.
Based on the impedance and scanning electron mi-croscopy (SEM) studies (figure 1), we suggested [14, 17] a shell–core model where the ceramic samples consist of semi-conducting grains partitioned from each other by poorly insu-lating grain boundaries. To establish this model as a source of the extraordinary dielectric behavior, we combined x-ray diffraction and high- pressure techniques [18] and found the ce-ramic CCTO samples behaved differently under the hydrostatic and uniaxial compression condition, which we explained in terms of the same model as samples being composed of grains with shells stiffer than the cores. Recently, a study [19] uti-lizing x-ray spectroscopy techniques provided another support to this scenario, and a new high-K material KxTiyNi1−x−yO
was also well described using the insulating grain boundary model [20].
What now needs to be explored is the nature of the low-lying excitations of the microstructures in these high-K materials. This would offer us clues to unravel the origin the extraordinary dielectric behavior: it is well known that low-temperature specific heat data provides information for different elementary excitations of the ground state. The specific heat data can contain several independent contributions, such as electronic, magnetic ordering contributions, and lattice vibrations that are derived from dispersion relations. The latter contributions are conventionally separated into two parts: the Debye and Einstein modes [19, 21–23] that relate to two issues of key interest pertinent to this study. First, at the interface region of the grain boundaries, it was proposed that there may exist corrugated phonon modes with an elementary excitation spectrum behaving as ω ∼ k2, where ω and k are the frequency and wavevector, respectively. This mode was used to portray bending motion of the long-chain molecules [24], and bond angle vibration in the Cu–O plane
Figure 1. SEM image of the CCTO sample. Notice the grains are of
the size of few microns, determined by using a JOELJSM840A scanning electron microscope set at 5 kV. The sample surfaces were gold-coated prior to examination.
of high Tc superconductors [25] due to the corrugation that
the z coordinates of O and Cu are different, the z direction being perpendicular to the Cu–O planes, that is the Cu–O planes are not flat. Furthermore, there was a report that grain boundary layers of samples are Ti-rich and Cu-poor [19], in effect that would lead to a structure deviating from the perfect cubic lattice of CCTO then rendering the boundary layers to corrugate. Hence we anticipate it would offer a basis for the stiff insulating grain boundaries that are capable of sustaining large amounts of charge and facilitating the giant dielectric constant at low frequency region. Hence this mode could be used to support the existing theories [13–15] and profound features would emerge in the LTSH data. Second, low-lying optical modes caused by the lattice defects during fabrication might assist us in exploring the nature of those reasonably high dielectric constants in the higher frequency region (106–109 Hz), which are about 100 or higher [11,12].
Because the evaluation of the sub-IR dielectric constant requires a summation of all the optical modes, especially those low energy localized modes, it is conceivable that these values would be enhanced as we could identify those low-lying modes caused by defects.
In this work, we performed low-temperature specific heat (LTSH) studies of CCTO and two other high-K compounds, from 0.6 to 10 K. Of the three high-K compounds, Bi2/3Cu3Ti4O12 contains 1/3 of vacancies while
La0.5Na0.5Cu3Ti4O12 is a mixture of equal amounts of La and
Na ions, at the sites originally occupied by Ca ions in CCTO. These polycrystalline samples were prepared by heating mixed stoichiometric amounts of the oxides CaCO3, CuO, and TiO2
for CCTO or Na2CO3, La2O3, Bi2O3 when fabricating other
compounds in an oxygen atmosphere at 1000◦C for 30 h and with intermediate grinding. The final samples were ground into powder and verified to be in a single phase by Scintag PADV powder x-ray diffractometer. The LTSH C(T ) was measured by using a3He heat-pulsed thermal relaxation
calorimeter [21–23] whose essential method of calculating the heat capacity is to reach the thermal equilibrium of the sample and background in less than a characteristic time following the applied heat pulse. In figure2, we present the specific heat data C(T ) of our samples after subtracting the addenda contribution 2
Table 1. Fitting parameters for the low-temperature specific heat data of CaCu3Ti4O12. The equation we used is C(T ) = Chyp+
Clinear+ Clattice= A/T2+ T + βT3+ δT5+ D(TE/T )2exp(TE/T )/[exp(TE/T ) − 1]2and the values in the parentheses are the error bars of the fit. A (mJ K mol−1) (mJ mol−1K−2) β
(mJ mol−1K−4)δ(mJ mol−1K−6) (J molD −1K−1) T
E(K) SD
1.2 (0.64) 0 0.559 (0.031) 0.0206 (0.0004) 0 0 16.30
1.27 (0.10) 0 0.489 (0.016) 0.0082 (0.0005) 9.0 (0.5) 53.8 (0.4) 0.46 0 2.32 (0.19) 0.259 (0.025) 0.0110 (0.0005) 7.0 (0.4) 50.7 (0.5) 0.43
Table 2. Best fitting parameters (same formula as table1) for the three high-K compounds.
ACu3Ti4O12 ε ( f = 1 Hz) A (mJ K mol−1) (mJ mol−1K−2) β (mJ mol−1K−4) δ (mJ mol−1K−6) D (J mol−1K−1) TE(K) SD CaCu3Ti4O12 9340 0.74 (0.11) 1.45 (0.20) 0.343 (0.024) 0.0100 (0.0005) 7.6 (0.4) 51.8 (0.5) 0.29 La0.5Na0.5Cu3Ti4O12 3560 1.63 (0.23) 6.67 (0.37) 0.906 (0.054) 0.0128 (0.0007) 6.7 (0.3) 43.2 (0.4) 1.35 Bi2/3Cu3Ti4O12 2150 0 22.85 (0.36) 2.730 (0.060) 0.0060 (0.0005) 4.2 (0.1) 39.5 (0.4) 1.39
Figure 2. Low-temperature specific heat data (black circles), plotted
as C(T )/T3versus T , from 0.6 to 10 K, and the best fit containing all the contributions is the solid line (SD= 0.29).
determined from a separate measurement. In order to classify different contributions in the LTSH data, we fit the data by using the equation C(T ) = Chyp+ Clinear+ Clattice[26], where
Chyp is the hyperfine contribution (∼1/T2) appearing in the
lowest temperature region and is caused by the interaction between the crystal field and nuclear magnetic moments, such as those from Cu ( A= 63) with 69% abundance and magnetic moment 2.2 μB. Clinear is a linear T term normally originating
from the free electrons, and Clattice = CD+ CE corresponds
to Debye and Einstein modes, where CD = βT3 + δT5
includes a linear frequency dispersion at low energy and an anharmonic term of lattice vibration, whereβ depends on the Debye temperature and atom number per unit cell, and might contain the contribution of the antiferromagnetic magnon with Neel temperature TN ∼ 25 K, because they have the same
temperature dependence of specific heat. Moreover, CE is
caused by the low-lying dispersionless optical modes given as CE = D(TE/T )2exp(TE/T )/[exp(TE/T ) − 1]2, where D
relates to the Einstein temperature TEand number of Einstein
modes per unit cell. In tables1and2, we listed the acceptable
Figure 3. Specific heat data, plotted as C(T )T2versus T3, from 0.6 to 1.5 K, and different fits: the model contains (i) Chypand Clinearis the dotted line, (ii) Chypand CDis the dashed line, and (iii) Chyp,
Clinear, and CDis the solid line.
fits: the parameters are positive, within a reasonable range and the standard deviations (SD) are small.
Since the three samples studied share similar character-istics, we choose to focus first on the CCTO results. Af-ter careful examination, we noticed two inAf-teresting features: (1) the appearance of Einstein modes at a low-temperature range T < 5 K and (2) the manifestation of a linear term in this good insulator (∼0.45 M cm at room temperature [11], similar for other reports and samples). Starting by analyzing the LTSH data using known contributions, we found that it was impossible to omit CE and Clinear. The standard deviation for
the best fit 16.30 could be obtained without incorporating lin-ear and Einstein terms. But after we added CE, SD decreased
immediately to 0.46. Then by adding Clinear, values of the
stan-dard deviation dropped down to around 0.3. In figure2, the entire low-temperature (0.6–10 K) specific heat data is shown together with the best fit including all the contributions. Later, in order to evaluate the relative merits between Chyp, CD and
CEcontributions, we present the data as following: in figure3,
J. Phys.: Condens. Matter 20 (2008) 285214 C P Sun et al
Figure 4. Specific heat data, plotted as C(T )/T versus T2, from 1.5 to 5 K, and different fits: the model contains (i) Clinearand CDterms is the dashed line, (ii) Clinear, CDand CEterms is the solid line.
temperature region from 0.6 to 1.5 K, we observe clearly that Chyp+ Clinear describes the data better than Chyp+ CD
(cu-bic term only). Finally, when combining the three terms, we reached a satisfactory agreement. Then in figure4, we plotted C(T )/T versus T2from 1.5 to 5 K. We would like to
empha-size that CEstarts to rise above Clinear+CDaround 3–4 K. Thus,
from the above analysis, we deduce that there are other excita-tions on top of the Debye term that originate from the conven-tional acoustical modes. We know well the linear T term used to connect with the conduction electrons; however, CCTO is identified to be a good insulator. However, we observe sharp x-ray patterns that indicate our samples are in single phase, we thus correlate this linear T term in the low-temperature spe-cific heat data with the corrugated phonon modes located at the grain boundaries as proposed earlier; and we deduce that the samples are composed of grains with tough shells that can be regarded as quasi-two-dimensional lattices. These corrugated phonon modes constitute the linear T term in the specific heat data. In addition, we find this picture matches with many ex-isting theories [14,17,18]. Similar phenomena were reported in C60studies [27], which were attributed to the disordered
in-duced localized state but not a special feature in its excitation spectrum.
Usually, the Einstein term is related to the low-lying optical modes. According to the previous studies [11, 12], optical mode frequencies for the cubic phase CCTO ranged from 125 to 560 (cm−1), so they are much higher than those observed in our specific heat data, in which the Einstein term started to appear about 3–4 K, around 2–5 (cm−1). Thus, these modes are not generated from lattice vibrations of a perfect solid; rather they are expected to arise from local defects at the grain boundaries caused by oxygen deficiency inside the grains, which are produced during the heating process. Hence including these modes would increase the high frequency dielectric constants and provide an insight into the high dielectric constant at higher frequency as we expected.
In order to demonstrate that the above studied low-lying excitations are common in many similar materials, LTSH measurements and analysis of high-K materials such
as La0.5Na0.5Cu3Ti4O12and Bi2/3Cu3Ti4O12were carried out
and compared with those of CCTO in table 2. We notice that contributions from the linear term are prominent in all the samples; CCTO is the smallest among them. This may imply that its grain boundary shell is the thinnest, and their Einstein temperatures TEare of the same order of magnitude; yet CCTO
is the largest among them, at this point it is our belief that more studies are needed to develop a reliable theory.
In conclusion, we present low-temperature specific heat studies on the giant dielectric constant material CCTO from 0.6 to 10 K. Clear indications of linear and Einstein term contributions were observed on top of the commonly detected Debye term that originated from the conventional acoustic phonons. We examined the data at different ranges, 0.6– 1.5 K and 1.5–5 K, separately to stress their contributions. Similar results were obtained for other high-K materials such as La0.5Na0.5Cu3Ti4O12, Bi2/3Cu3Ti4O12, and two distinct
batches of CCTO with different oxygen pressure and baking temperatures, with only few per cent changes in the fitting coefficients. We found two main features in the low-temperature specific heat data: there are linear and Einstein contributions. We have reason to believe that the linear contribution to the specific heat at low temperatures is caused by the corrugated phonon modes. These phonon modes lead to stiff grain boundaries that are capable of holding large amounts of charge hence facilitating the observed low frequency high dielectric constants. Whereas the Einstein contributions suggest that the effects from the low energy optical modes, generated due to imperfections, is non-trivial and in turn provides an explanation for the origin of the high frequency high dielectric constants. Thus, combined with the previous theoretical and experimental studies on the electronic and mechanical properties of CCTO and the related high dielectric constant compounds, we put forward a phenomenological model consistent with many current theories that, in addition to the material, the microstructure and the associated elementary excitations are endemic to the high dielectric constant behavior.
Acknowledgments
We are grateful for the fruitful discussions with Professors Morrel H Cohen and Peter A Dowben. This work was partially supported by the National Science Council of Republic of China under contract NSC96-2112-M110-001 and the Nebraska Research Initiative.
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