Broadband dielectric spectroscopy of BaTiO3–Ni0.5Zn0.5Fe2O4 composite ceramics

Accepted Manuscript Broadband dielectric spectroscopy of BaTiO3-Ni0.5Zn0.5Fe2O4 composite ceramics A. Sakanas, R. Grigalaitis, J. Banys, L. Mitoseriu, V. Buscaglia, P. Nanni PII: DOI: Reference:

S0925-8388(14)00618-5 http://dx.doi.org/10.1016/j.jallcom.2014.03.041 JALCOM 30812

To appear in: Received Date: Revised Date: Accepted Date:

12 December 2013 14 February 2014 5 March 2014

Please cite this article as: A. Sakanas, R. Grigalaitis, J. Banys, L. Mitoseriu, V. Buscaglia, P. Nanni, Broadband dielectric spectroscopy of BaTiO3-Ni0.5Zn0.5Fe2O4 composite ceramics, (2014), doi: http://dx.doi.org/10.1016/ j.jallcom.2014.03.041

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Broadband dielectric spectroscopy of BaTiO3-Ni0.5Zn0.5Fe2O4 composite ceramics A. Sakanasa), R. Grigalaitisa, J. Banysa, L. Mitoseriub, V. Buscagliac, and P. Nannic, d a

Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania Department of Physics, Al. I. Cuza University, Bv. Carol 1, no. 11, Iasi 700506, Romania c Institute for Energetics and Interphases, CNR, Via de Marini no. 6, Genoa 1-16149, Italy d Department of Chemistry and Process Engineering, University of Genoa, P-le Kennedy no. 1,Genoa, Italy b

The behavior of three xBaTiO3 – (1-x)Ni0.5Zn0.5Fe2O4 composites (x = 0.50, 0.60 and 0.70 molar ratios) were studied using the broadband dielectric spectroscopy methods in the broad frequency and temperature ranges. x = 0.70 composition clearly exhibits similar dielectric response to that of pure barium titanate, while the response of the composite with the highest concentration of nickel-zinc ferrite is largely influenced by the conductivity, especially at the highest temperatures and lowest frequencies. In the non-dispersive region the permittivity gradually increases with increasing level of high-permittivity barium titanate material as a result of the “sum property”, while the low frequency behavior described by complex contributions do not show a systematical modification with the changing composition. At around 10 8 – 10 10 Hz frequencies the dispersion process was observed and approximated with the Cole-Cole equation, finding the parameters describing the process. Presumably, lattices of barium titanate in close vicinity to nickel-zinc ferrite could lead to the distortion and some shifting of ions in barium titanate lattice, possibly affecting the states that Ti can occupy. The conductivity process was approximated with the recently suggested generalized Joncher’s relationship, which manages to describe both low and high frequency conductivity processes observed. The computed corresponding activation energies for all the samples were found to be similar to oxide composites containing ferrites with ionic conduction contributions.

Keywords: composite materials, ferroelectrics, dielectric response.

I.

Introduction

Technological and experimental progress in recent years initiated very rapid increase of interest in the field of multiferroic and magnetoelectric materials. Despite the precursory research in 1950s and 1960s, the main difficulty of their exploration was the lack

Corresponding author: [email protected], Phone number: +37062478591

of explanation of basic physical principles underlying the rarity of such materials. The popularity of multiferroics has grown significantly over the past decade [1]. A material is considered multiferroic if it possesses at least two of the three main “ferroic” properties: ferroelectricity, ferromagnetism and ferroelasticity. The latter is the least known and studied property in practice, and only recently became more interesting by the material requirement to have the so-called ferrotoroidic order [2]. On the other hand, magnetoelectric multiferroics should possess an electrical order parameter (polarization) switchable by magnetic fields and vice-versa, while more generally, magnetoelectric coupling refers to the ability of the material to change one of its electrical characteristics (polarization, permittivity, resistivity) by a magnetic field and vice-versa. Such properties are rarely met in single-phase magnetoelectric multiferroics, due to very contrasting requirements for the electron configuration in the d shell [3]. Additionally, the magnetoelectric coupling in most cases is rather weak and significant only at cryogenic temperatures [4, 5]. Two-phase systems use the principle of strain-mediated coupling of electric and magnetic properties. Multiferroics are promising for a broad range of applications, including fourstate random access memory, various sensors, bi-tunable devices, microwave materials and so on. In order to successfully prepare two-phase composite materials, certain compatible structure materials must be used. It is known from various reports of magnetoelectric composites [6, 7] that perovskite and spinel ferrites have such required high structural compatibility and it allows combining perovskite ferroelectrics with magnetic spinel structures and makes the sintered di-phase composites as one of the most attractive materials able to achieve the two ferroic properties in the same structure. BaTiO3-based ceramics are among the most used perovskite materials in microelectronic industry. Good chemical and mechanical stability, high dielectric permittivity, and low losses in a wide range of frequencies are the features of one of the longest known and most popular ferroelectric. The ferroelectric-paraelectric phase transition in BaTiO3 is generally considered to be a classical example of a displacive soft-mode type phase transition, which can be described by anharmonic lattice dynamics. Nevertheless, the question of the possible existence of a displacive to order-disorder crossover close to the paraelectric-ferroelectric phase transition is however still open [8]. On the other hand, nickel ferrites combine a wide range of useful magnetic properties with a relatively low electrical conductivity; they exhibit low eddy current loss in alternating-current applications and have numerous applications in electric devices. They have been employed in the last years as magnetic counterpart in various ferroelectricmagnetic composites with BaTiO3, Pb(Zr,Ti)O3 or other ferroelectrics [9 – 11]. As in case of other magnetoelectric composites, the dielectric losses were still high, in spite of multiple efforts dedicated to improve the microstructures and to ensure clean interfaces and good contact between the two phases. The magnetic component (ferrite) has a lower resistivity by comparison with the ferroelectric oxides as due to the hopping of charge carriers (electrons or holes) between cations presented by more than one valence state occupying the octahedral sites [12]. The dielectric properties of ferrites can still be improved by substitutions. It was reported that Zinc substituent into NiFe2O4, has stable valency (+2) and hence, it does not contribute to the conduction mechanism [13], which results into ferrites of higher resistivity. Moreover, Zinc ion in spinel ferrites occupies tetrahedral (A) site [14] and hence, it cannot contribute to the electrical conductivity. Therefore, Zn (and other diamagnetic ions) substitution of Ni ferrite usually show improved resistivity. From structural point of view, NiFe2O4 have inverse spinel structure while ZnFe2O4 has normal spinel structure. Hence, the incorporation of Zn into the NiFe2O4 spinel cell pushes the inverse structure to acquire mixed spinel and the most interesting composition from magnetic point of view is Ni0.5Zn0.5Fe2O4, because Zn+2 cations preferentially substitute 2

for Fe3+ ions in tetrahedral sites. Due to this, an increase in the saturation magnetization with the Zn/Ni content up to x=0.5 and a decrease for x>0.5 was noticed due to the increase in the concentration of the Fe3+ ions in the octahedral sites. The maximum magnetisation was found in the range of 50% Zn substitution, in the range of 100-140 emu/g at room temperature [15 – 17]. The choice of the ferrite composition is related to both electrical and magnetic properties in single phase, which are expected to improve the final functional characteristics in composite. Since the addition of a non-magnetic phase (ferroelectric) in the composite will result anyway in a reduction of the effective magnetization, it is better to start with a good magnetic material with high magnetization and good magnetostrictive properties. In order to apply composite materials successfully, the physical properties need to be well determined. The main problem in understanding the dielectric properties of such materials is that the dielectric permittivity is mostly studied up to the megahertz frequency range, and in many cases not exceeding 1 MHz [7, 18, 19], where the electrical conductivity phenomena typically dominate the electrical response and are not intrinsic to the composite materials, but are mostly related to the relaxations due to uncompensated charges, to polaron hopping phenomena associated with the spontaneous fluctuations of Fe3+/Fe2+, different local oxygen stoichiometry, etc. In such a way, other very important mechanisms functioning at much higher frequencies are left out and not considered. A more complete characterization over a broadband frequency range and at various temperatures is necessary in order to disclose the dielectric relaxation and conductivity mechanisms of such complex materials. Thus, the main task of this work is to present a broadband dielectric dispersion study of composites formed by barium titanate and nickel-zinc ferrite xBaTiO3 – (1-x)Ni0.5Zn0.5Fe2O4 (BT-NZF) in a broad range of frequencies and temperatures. BT-NZF two-phase composites have gathered attention due to their multiferroic and magnetoelectric coupling properties [20]. The magnetic properties of these composite materials were presented elsewhere [18, 20], and are not discussed in this paper. Although recently it has been concluded that the ferrimagnetic and ferroelectric phases in BT-NZF are independent on each other [21], if the properties of both ferroic phases are preserved in the composite and in addition, a magnetoelectric coupling mediated by stress resulted, such composites are still viable candidates for magnetoelectric applications. From the previous studies concerning ferrite-BT or ferrite-PZT composites [22 – 24] it was demonstrated that, while the magnetic properties of such composite are simply derived as a “sum property” from ones of the ferrite, the dielectric, ferroelectric and magnetoelectric properties are determined not only by composition and microstructures, but mostly by extrinsic properties which are not controlled at all by the available processing methods in ceramic composites. Therefore, a deeper insight in understanding the specific relaxation mechanisms as revealed from a detailed investigation by broadband dielectric spectroscopy is still lacking in such magnetoelectric composites composites and this need justifies the proposed research study.

II.

Experimental Methods

Ceramic barium titanate and nickel-zinc ferrite composites were prepared by coprecipitating Fe, Ni, Zn nitric salts in a NaOH solution in which BaTiO3 fine powders previously prepared by solid state have been dispersed (as described in detail in Ref. 19). After washing and drying, the mixture was calcined at 400 °C/1h to promote the formation of ferrite phase. The composite powders were milled, sieved, isostatically pressed at 2·108 Pa 3

and then sintered at 1150 °C/1h. Only two phases: the perovskite BaTiO3 and ferrite were found by XRD [20, 25, 26], with no traces of secondary phases possibly resulted at interfaces during sintering. The microstructures were characterized by scanning electron microscopy (SEM, LEO 1450VP, LEO Electron Microscopy Ltd., Cambridge, UK). Quite homogeneous microstructures with good dispersion of BT perovskite grains and spinel NZF octahedral crystals, high density (above 97% relative density) were found (Figure 1). For all the compositions, ferrite phase shows much larger grains, even accompanied by fine grains as well (from 500 nm to several microns), while BaTiO3 phase is always finer, with grain sizes in the range of 100-500 nm. A detailed microscopic study by electron backscatter diffraction of similar composites prepared by following the same strategy revealed small microstructural differences for various compositions and changes in the degree of texturing (i.e. preferential orientation) of the ferrite grains when modifying compositions, which means that by this method the microstructures cannot be strictly controlled [27], and therefore, the functional properties might be influenced both by composition and microstructural characteristics. FIG. 1. Three compositions of xBaTiO3 – (1-x)Ni0.5Zn0.5Fe2O4 ceramics (with x = 0.50, 0.60 and 0.70 molar ratios, or volume fractions of 0.466, 0.567 and 0.67, respectively) have been investigated. Dielectric experiments were carried out in the wide frequency (20 Hz – 50 GHz) and temperature (100 – 500 K) ranges, using appropriate measurement technique for each range. To ensure favorable experimental conditions, surfaces of ceramic specimens were thoroughly polished and electroded with silver paste, in order to ensure the best electrical contact. Measurements were performed in the cooling regime, keeping less than 1 K/min temperature change rate. Dielectric measurements in 20 Hz – 1 MHz frequency range were performed with HP 4284 LCR spectrometer. The samples were placed into the special holder, forming the capacitor and the capacity along with the loss tangent values were adapted for the permittivity calculations. At higher frequencies, from 1 MHz up to 2 GHz, Agilent 8714ET vector analyzer coupled with coaxial line was used. In such regime dielectric permittivity was calculated from the measured amplitude and phase of the reflected signal. The 20 – 50 GHz frequency range was covered by a waveguide setup with the scalar network analyzer R2400, specially manufactured by the company “Elmika”. In these measurements, scalar reflection and transmission values are detected. The detailed description of the method is given in Ref. 28.

III.

Results and discussions

Figure 2 shows temperature dependencies of the real and imaginary parts of dielectric permittivity at a few selected frequencies. Three peaks in the real part of permittivity occur at approximately 410, 300 and 200 K temperatures (more visible at high frequencies) for each composition, which are associated with the structural phase transitions of pure barium titanate. Perovskite barium titanate undergoes three first-order phase transitions (rhombohedral-orthorhombic-tetragonal-cubic), reflected by abrupt and sharp peaks of the dielectric permittivity vs. temperature dependence [29]. The peaks found in the present composites are slightly shifted towards higher temperatures, although preserving the 4

same sequence as in BaTiO3 pure material. Moreover, much more gradual change of permittivity vs. temperature was observed. The combination of few effects can help in explaining the broadening of peaks in the vicinity of phase transition temperatures: (a) the “sum property”, (b) grain size effect, and (c) the presence of impurities. First of all, the reduction of permittivity with the decreasing part of high permittivity barium titanate in the composite (and subsequently, the increase of nickel-zinc ferrite) is expected in the measured dielectric response – the “sum property” effect [18]. Furthermore, grain size effect in high permittivity ceramics with grain sizes below ~1.5 µm is known [30, 31] to reduce permittivity and to flatten the dielectric peaks in the vicinity of the structural phase transitions: in our case, all the composites present submicronic grain sizes (below 500 nm) of BaTiO3 phase. Finally, the doping of BaTiO3 with Ni and Fe ions at interfaces in the preparation process are highly probable as well. Presence of impurities and defects may lead to modifications of the local Curie temperatures, resulting in a broadening of peaks. All the mentioned effects can play significant role in discussing the measured dielectric response. By comparison with barium titanate, nickel-zinc ferrite is much less resistive [7] and its presence in composites will strongly influence the conductivity of composites. According to Bruggeman EMA model developed to describe spherical inclusions embedded into a continuous background with the effective dielectric permittivity of both components, the percolation threshold is reached when the volume filling factor of the inclusions is close to 1/3 [32]. In conformity with this model, the concentration of ferrite of BT-NZF composites is already above percolation threshold for all the investigated three compositions, hence it is clear that the conductivity greatly affects the dielectric permittivity data. The conductivity is enhanced at low frequencies and higher temperatures, because it is a thermally-activated process. Therefore, at the lowest frequencies and highest temperatures of the present measurements, the effect can be observed as the mutual rise of the real and imaginary parts of dielectric permittivity (Figure 2), where the values of permittivity increase greatly and hide the temperature peaks. This effect is stronger for the highest low-resistivity ferrite concentration (x = 0.50), for which the dielectric peak at ~400 K is almost suppressed by the increase due to conduction. FIG. 2. The frequency dependencies of dielectric permittivities are presented in Figure 3. At the lowest measured frequencies, the dispersion in the real as well as imaginary parts is observed for all the compositions. The most popular model in explaining such behavior is Maxwell-Wagner polarization mechanism [33]. A huge number of interfaces between the ferroelectric and ferrimagnetic phases act as traps for the ions and electrons. These can be caught at such inter-grain boundaries, leading to the formation of inner depolarizing field and causing huge dielectric loss, especially at low frequencies where the separation distances between the positive and negative charges can be significant. Although Maxwell-Wagner contribution should be predominating in case of multiphase materials, such high dielectric response at the lowest frequencies could be also influenced by the interaction of conduction electrons and the dielectric polarization, the so called electron-relaxation-mode coupling [34]. Measurements at the highest frequencies reveal the presence of the dipolar relaxation process. No appreciable dielectric dispersion up to at least 60 GHz was evidenced in pure barium titanate crystals in paraelectric phase [35], although some earlier papers [36] reported some dispersion in the 108 – 10 10 Hz range in the ferroelectric phase. The strong dielectric dispersion observed in BT-NZF composites could be enhanced by the presence of 5

the ferrite phase. Considering the off-center Ti model in barium titanate [8], lattices of BT in the neighborhood of NZF could lead to the distortion and some shifting of ions in BT lattice, which could affect the possible states that Ti can occupy. In the non-dispersive region (10 6 – 108 Hz), the permittivity regularly increases with increasing level of high-permittivity material (BT) as a result of the “sum property”, as discussed previously, and shows values of hundreds (about 139, 227, 325 at 250 K for x = 0.50, 0.60, and 0.70, respectively). These can be considered as the intrinsic values of permittivity in this frequency range. The relaxation process was approximated in the range of 10 MHz – 40 GHz using the empirical Cole-Cole equation with an additional conductivity term to take into consideration the conductivity loss observed in the imaginary part of permittivity: (1) The additional conductivity is included to describe the growth of the imaginary part of permittivity at lower frequency side, where the real part still displays non-dispersive behavior. The conductivity will be discussed separately. FIG. 3. The temperature dependencies of the parameters determined from the Cole-Cole equation are plotted in Figure 4, and express the behavior of high frequency dispersion in more detail. The high frequency parameter, ε∞ (Figure 4, a) clearly shows some increase in the region of the ferro-para phase transition of BT. It is not surprising having in mind that the meaning of this parameter is the contribution of electronic and ionic polarization to the total dielectric permittivity. It is well known from the previous investigations [31] that the contribution of soft modes in pure barium titanate can reach values up to few thousands and in nanograined BT they are not significantly suppressed. The fitting parameter ∆ε (Figure 4, b) has the meaning of the contribution of the relaxation process to the total dielectric permittivity, and in this case shows an increase near the phase transition temperature and then remains nearly constant. Parameter α (Figure 4, c) represents the width of the distribution of relaxation times (Figure 4, d). Despite some scattering of the calculated values, a common trend of approaching zero (which means that the Cole-Cole equation reduces to the Debye-type relaxation) above the temperature of approximately 400 K can be observed. Below this temperature its value starts to grow slightly, possibly due to some additional contributions to the dielectric permittivity. In Figure 4 (d), it is shown that the temperature dependence of the mean relaxation time τcc provides similar results: an increase below 400 K followed by an almost linear behavior below 350 K. At high enough temperatures the relaxation originates from the displacement of Ti ions between different equivalent positions in the perovskite lattice. When approaching the temperature corresponding to the phase transition, relaxation time starts to grow due to additional contributions to the dielectric properties. This is supported by the increase of α parameter and nearly constant ∆ε, followed by the simultaneous decrease of ε∞. It is possible that the behavior of the Cole-Cole parameters described above is due to the formation of domains in the ferroelectric phase. Relaxation process in GHz frequency for polycrystalline barium titanate, presumably associated with the inertial effect of domain wall movement was firstly calculated by Kittel [37]. Later, the dependence of the microwave dispersion on temperature and grain size of barium titanate, lead zirconate titanate and doped ferroelectric ceramics was explained as a result of the emission of elastic shear waves from the vibrating domain walls [38]. The contribution of

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domain state of the ferroelectrics to the relaxation processes at GHz frequencies was pointed out in many other papers [39 – 41]. Unfortunately, no analysis on the domain structure of our samples were carried out, thus it is not possible to decisively prove the origin of relaxation mechanism. Nevertheless, qualitative similarities between the dispersion observed in BTNZF composites and results published by other authors suggest the contribution of domain state to be important in our case as well. FIG. 4. Conductivity data presented in Figure 5 reveals two dispersion processes. The low frequency conductivity adds up with the high frequency conductivity in the range of tens of kHz and presents a “kink” in the typical behavior following the classical Jonscher’s relationship for conductivity. In the literature [42], where the similar conductivity processes of barium titanate and nickel-zinc ferrite were reported, the high frequency process was associated with a short distance charge carrying (inside the grains of the ceramics), while the low frequency process – with a long distance carrying (in-between the grains). Recently, a new approach to interpret similar conductivity behavior in the nonhomogeneous systems was suggested [43]. The main idea of the authors was that the relaxation process can be described by the equations containing non-integer operations of differentiation and integration if a disordered medium contains self-similar (fractal) structures. Fractal current is included to the total current alongside with the usual polarization current, leading to a delayed response of the considered self-similar structure. The generalized Jonscher’s relationship for conductivity then takes the form: (2) in which parameter σDC stands for the DC conductivity, τ is the mean relaxation time, generally characterizing some collective motions in self-correlated clusters (in our case it can be interpreted as the movement of conducting species within the grains of the composite) and χ defines the strength of the process. The last two parameters A and ν come from the classical Jonscher’s relationship. The solid lines in Figure 5 correspond to the fitting results obtained by adapting the equation (2) and they perfectly describe the present experimental data for suitable fitting parameters. FIG. 5. The values of DC conductivity for the low frequency process were obtained from the classical part of the Jonscher’s relationship, while the fractal part yielded DC conductivity of the high frequency process (assuming that ω→0). The results of DC conductivities and the relaxation times for the high frequency process and their approximations using Arrhenius law are presented in Figure 6. FIG. 6. The computed corresponding activation energies are for all the samples in the range of 0.30-0.80 eV, similar as for other ceramics and for oxide composites containing ferrites with ionic conduction contributions [7, 18, 44, 45]. Values of about 0.50 eV for the activation energy was usually reported for O-vacancy hopping associated to the spontaneous 7

transition Fe3+-Fe2+ in ferrites or in iron oxides and similar phenomena might also play a role in the low-frequency properties of the present composites, although their role cannot be separated by other possible contributions to the dielectric response. The low-frequency activation energy does not vary in a systematical manner, for reasons already discussed (extrinsic contributions), while the high-frequency dipolar relaxation process is described by an increase with the increasing of NZF composition (0.33, 0.41, 0.68 eV for x = 0.70, 0.60, and 0.50, respectively). Therefore, the dipolar relaxation process (probably specific to the ferroelectric phase) needs a lower activation energy when the amount of non-ferroelectric phase is smaller.

IV.

Conclusions

Dielectric measurements of barium titanate and nickel-zinc ferrite composites display a great variety of different kinds of dispersions, including a few conductivity mechanisms at low frequencies and a dipolar relaxation at high frequencies. Dielectric permittivity peaks, present in pure barium titanate are still conserved, although they are much more suppressed as high as the nickel-zinc ferrite amount is greater. The high frequency permittivity respects the rule of the “sum property” as described by the effective field models, while the low frequency permittivity and conductivity are described by complex contributions and do not show a systematical modification vs. composition. Consequently, NZF in these composites contributes not only to the low frequency dielectric properties (as conductivity), but also to the high frequency dielectric relaxation by increasing the dipolar relaxation activation energy.

Acknowledgements: The authors gratefully acknowledge the financial support for this work by the European Social Fund under the Global Grant measure (project VP1-3.1-SMM-07-K-03-011) and Romanian PNII-ID-PCE-2011-3-0745 grant. The collaboration in the frame of COST MP0904 Action is highly acknowledged.

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Figure captions: FIG. 1. SEM micrograph of the: (a) fractured surface, (b) and (c) backscattered image obtained for xBaTiO3 – (1-x)Ni0.5Zn0.5Fe2O4 ceramic (x = 0.60 mol.); white: BaTiO3, dark zones: Ni0.5Zn0.5Fe2O4. FIG. 2. Temperature dependencies of real (ε’) and imaginary (ε’’) parts of permittivity at various frequencies (concentrations from top to bottom: x = 0.70, 0.60, 0.50) FIG. 3. Frequency dependencies of ε’ and ε’’ at various temperatures. Solid lines are approximations with formula (1.1) (concentrations from top to bottom: x = 0.70, 0.60, 0.50) FIG. 4. Temperature dependencies of the fitting parameters used in Cole-Cole equation (1.1): (a) high frequency parameter (ε∞); (b) the dielectric strength (∆ε); (c) parameter α, and (d) the mean relaxation time τcc. FIG. 5. Frequency dependencies of σ‘ at various temperatures (concentrations from left to right: (a) x = 0.70, (b) x = 0.60, (c) x = 0.50) FIG. 6. (a) DC conductivities (squares – the low frequency, circles – the high frequency process) and (b) the high frequency conductivity process mean relaxation times and their approximations using Arrhenius law

11

12

24 kHz

150 kHz

1 MHz

60 MHz

750 600

x=0.70

45

300

30

150

15

0 750

0 75

x=0.60

60 45

'

''

450 300

30

150

15

0 750

0 75

600

40 GHz

60

450

600

1 GHz

75

x=0.50

60

450

45

300

30

150

15

0 100

150

200

250

300

350

400

450

500

0 100

T, K

13

150

200

250

300

350

400

450

500

410 K 10

4

10

3

10

370 K 10

6

10

4

2

10

2

1

1 6 10

x=0.70

104 10

x=0.60

3

10

4

''

10

'

10

250 K

2

10

1

16 10

104 10

10

3

10

2

x=0.50

1

10 1 10

10

2

10

3

10

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10

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10

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10

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10

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10

9

10

10

10

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10

12

2

10

4

10

2

1 1 10

, Hz

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10

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10

4

10

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10

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10

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10

10

10

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10

12

x=0.7

x=0.6

300

(a)

250 200

150

150

∆

200

100

100

50

50

0 0.5

0 60

(c)

50

, ps

0.4 0.3

(b)

(d)

40 30

CC

∞

250

x=0.5

300

0.2

20 0.1

10

0.0 150 200 250 300 350 400 450 500

0 150 200 250 300 350 400 450 500

T, K

15

477 K

-1

451 K

417 K

10

x=0.70

x=0.60

x=0.50

-2

', S/m

10

-3

10

-4

10

-5

10

1

10

2

10

3

10

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5

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, Hz

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10 10

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10

8

10

1

-11 x=0.5 x=0.6 x=0.7

-1

-12 -13

-2

ln( , s)

10

-3

10

DC

, S/m

10

x=0.5 x=0.6 x=0.7

-4

x=0.5 x=0.6 x=0.7

-14 -15 -16 -17

10

-18

-5

10

-19

-6

-20 10 0.0020 0.0021 0.0022 0.0023 0.0024 0.0025 0.0020 0.0021 0.0022 0.0023 0.0024 0.0025

(a)

1 -1 T, K

17

(b)

Highlights: • • •

High frequency dielectric relaxation process is observed and interpreted Multiple conductivity processes analyzed by fractal Jonscher’s relationship Calculated conductivity activation energies fall in 0.30-0.80 eV range

18