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Author’s Accepted Manuscript Ac-conductivity and dielectric response of new zinc-phosphate glass /metal composites A. Maaroufi, O. Oabi, B. Lucas www...

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Author’s Accepted Manuscript Ac-conductivity and dielectric response of new zinc-phosphate glass /metal composites A. Maaroufi, O. Oabi, B. Lucas

PII: DOI: Reference:

S0921-4526(16)30110-7 PHYSB309422

To appear in: Physica B: Physics of Condensed Matter Received date: 27 January 2016 Revised date: 24 March 2016 Accepted date: 26 March 2016 Cite this article as: A. Maaroufi, O. Oabi and B. Lucas, Ac-conductivity and dielectric response of new zinc-phosphate glass /metal composites, Physica B: Physics of Condensed Matter, This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Ac-conductivity and dielectric response of new zincphosphate glass /metal composites A. Maaroufi1,*, O. Oabi1, B. Lucas2 1

University of Mohammed V, Laboratory of Composite Materials, Polymers and

Environment, Department of Chemistry, Faculty of Sciences P.B. 1014, Rabat - Agdal, Morocco, 2

XLIM UMR 7252 - Université de Limoges/CNRS 123 avenue Albert Thomas - 87060

Limoges Cedex, France.

*Corresponding author: [email protected]; [email protected], Phone/Fax: +212 537 77 54 40

ABSTRACT: The ac-conductivity and dielectric response of new composites based on zinc-phosphate glass with composition 45mol%ZnO–55mol%P2O5, filled with metallic powder of nickel (ZP/Ni) were investigated by impedance spectroscopy in the frequency range from 100Hz to 1MHz at room temperature. A high percolating jump of seven times has been observed in the conductivity behavior from low volume fraction of filler to the higher fractions, indicating an insulator – semiconductor phase transition. The measured conductivity at higher filler volume fraction is about 10-1 S/cm and is frequency independent, while, the obtained conductivity for low filler volume fraction is around 10-8 S/cm and is frequency dependent. Moreover, the elaborated composites are characterized by high dielectric constants in the range of 105 for conductive composites at low frequencies (100Hz). In addition, the distribution of the relaxation processes was also evaluated. The Debye, Cole-Cole, Davidson – Cole and


Havriliak–Negami models in electric modulus formalism were used to model the observed relaxation phenomena in ZP/Ni composites. The observed relaxation phenomena are fairly simulated by Davidson -Cole model, and an account of the interpretation of results is given. Keywords: phosphate glass; composite; dielectric; relaxation; conductivity; percolation

1. Introduction Phosphate glasses have potential applications in diverse areas of technology such as matrix for confinement of the waste [1, 2], laser glasses and optics [3-6], magneto-optical devices [7], energy transfer materials [8], glasses for sealing in electronics [9], biomaterials [10-13], battery materials for ultrafast charging and discharging [14],…etc. These applications are due to the facility to varying the glass transition temperature (Tg), lower melting temperatures, and optimizing the coefficients of thermal expansion (CTE) based on the variation in composition. These glasses are also relatively easy to prepare and offer a large range of compositional possibilities, which facilitates tailoring of the physical and chemical properties for specific technological applications. Thus, phosphate glass materials can also provide other new and interesting applications; in particular in the field of materials having high dielectric constants, compared to silicon dioxide, for the energy storage, thermoelectric sensors, etc. Indeed, such materials can be used in the electronics industry applications in order to respond to the needs of land-supply decoupling for secure signal integrity of high speed and to reduce the electromagnetic interference, in capacitor fabrications for energy storage, supplying a burst of power to another component, filtering out noise from signals as part of a resonant circuit, insulating for wires, cabling and sensor devices, etc [15]. The higher the dielectric constant, the more charge the capacitor can store in a given field. The development of new fascinating materials demands high electrical resistivity and low 2

dielectric loss as the most desirable properties [16]. Thus, several studies have been reported on the development of polymers and their composites with high dielectric constants [17-20]. Nevertheless, the thermal stability/degradation issues of polymeric materials reduce their potential applications and therefore their interest. It is for that reason important to develop inorganic materials with high dielectric constant and good thermal resistance to suggest new and attracting opportunities for these applications. Such works were undertaken by several authors, studying the dielectric properties of various phosphate glasses containing transition metal oxides [21-24]. These studies showed increasing of dielectric constants with metallic oxides. The investigation of dielectric properties of composites based on the zinc-phosphate glasses as matrix filled with conducting particles in accordance with the cited applications is so worth interesting. Indeed, it enables measuring the intensity of the electrical parameters and helps to understand the origin of conduction processes. The investigation of the conductivity with frequency gives useful information about the mobility of charges, the distribution of electric field in the system, dielectric relaxation phenomena and the field induced perturbations [25]. The aim of the present work is to study the ac-conductivity and dielectric properties of composites of 45ZnO-55P2O5 (mol%) matrix filled with conducting powder of nickel (Ni) as functions of frequency from 100Hz to 1MHz at room temperature. Indeed, several attempts in literature have been made to study the frequency dependent conductivities and dielectric permittivity of some oxide glasses using various theoretical models proposed for the acconductivity in amorphous semiconductors [24-28]. To our knowledge, there is no published systematic data on the ac-conductivity and the conduction mechanisms of binary zinc phosphate glasses as composites; although, these kinds of composites showed a high Seebeck coefficient and percolating electrical conduction with metallic fillers variation [29, 30]. Moreover, above percolation threshold, the conductivity vs temperature showed an insulator


to semiconductor phase transition, called positive temperature coefficient phase transition. The study of ac-conductivity and dielectric properties of ZP/Ni composites is therefore justified followed by discussion and interpretation of the obtained results. 2. Materials and experimental methods 2.1. Composite preparation The method used to obtain ZnO-P2O5 matrix (ZP) filled with conductive particles has been already described elsewhere [29]. Composites of 45mol%ZnO–55mol.%P2O5 (ZP)/ Ni (3, 11, 23, 30 and 36 vol.%) were elaborated and studied. 2.2. Alternative conductivity measurements The measurements of conductivity versus frequency at room temperature were carried out with a HP 4282A LCR bridge, in the 100Hz–1MHz frequency range. The total electrical conductivity σ is calculated using the conductance G:

t A



Whereas t and A are the thickness and the cross-sectional area of the sample respectively. The dielectric constant ε' and dielectric loss ε" are determined by measuring the capacitance C using the following relations [31]:

t 0 .A

' C

'' 0




Where εo is the permittivity of free space (εo = 8.854 × 10−12 F/m), ω is the angular frequency (ω=2πf) and f is the frequency. 3. Theoretical considerations The total electrical conductivity can be written as: dc




Where the ac-conductivity is given by σac ≈ kωs, with σdc is the direct current conductivity, k is the dose dependent coefficient and s is the exponent factor (0 ≤ s ≤ 1). The dielectric relaxation is often described by the Havriliak–Negami equation [32], *

giving the complex dielectric permittivity *


( ) as:


i '' 1




Where ε' and ε" are real and imaginary parts of the complex dielectric permittivity,



are the dielectric constants for the low and high frequency sides of the relaxation, is the average relaxation time,


are the symmetrical and asymmetrical broadening

parameters respectively. A Debye type relaxation process corresponds to =0 and =1. To investigate interfacial polarization relaxation of composites, the complex electrical modulus is often used. Indeed, these materials are heterogeneous with two or more phases. The heterogeneity implies an important polarization at interface between matrix and filler. When a component is conductive, interfacial relaxation is masked by high conductivity. Therefore, to minimize the effect of the variations of high values of conductivity and permittivity especially at low frequencies, the electric modulus formalism is always used. Moreover, the difficulties due to the space charge injection, nature and the contacting condition of the electrodes and absorbed impurity conduction effects, which can appear to mask relaxation in the dielectric presentation, can be suppressed by using modulus formalism [33]. Thus, the dipolar contributions can be revealed. The complex electrical modulus M* is related to the complex dielectric constant by:


1 *

1 i ''


' '2



'' '2


M' iM"

, i





Where M' is the real and M" the imaginary part of electric modulus. Thus, the equation (5) of Havriliak–Negami has been rewritten in the electric modulus formalism by Tsangaris & al. [33] as:

M' M Ms

MsA 2 s



2A M


Ms cos


Ms Mscos



Ms )2


M'' M Ms

2 s



M 2A M

Ms sin A Ms Mscos (M


Ms )2



1 2







1 2


)1 cos



1 (


2 ) sin


corresponds to the value of M' when ω→0 and M


when ω→∞,

1 and


0. The Debye relaxation equation corresponds to =1 and =0, the Cole-Cole relaxation equation to =1 and

0, the Davidson-Cole equation to

1 and

= 0 and Havriliak–

Negami relaxation to

0 and ≠1. All these models will be used to discuss and show which

is more appropriate to account for the results obtained. 4. Results 4.1. Electrical conductivity as a function of frequency In order to clarify the conduction mechanisms in the studied composites, the electrical conductivity as a function of frequency has been investigated. The total conductivity


determined by the conductance measurements using the Eq. (1). Fig.1 represents the behavior of

as a function of frequency from 100Hz to 1MHz of ZP/Ni composite series at room

temperature. The conductivity behavior as function of the frequency can be analyzed using the Eq.(4), where


is the

0 limiting value. As can be seen, two behaviors are obtained,

showing transition from low to high Ni filled in the ZP-matrix. The total conductivity is independent of frequency and equals to the dc-conductivity (σ≈

dc ≈

10-1S/cm) above the

percolation threshold for =30 and 36Ni vol.% ≥ c, confirming the previous obtained results [29, 30]. Its values were used as experimental dc-conductivities to check the percolation limit for different composites. Thus, for the ZP/Ni (30, 36 vol.%) composites, the observed 6

conductivity is therefore truly σdc component and is frequency independent. The conductivity σdc becomes predominant at a critical filler concentration, known as percolation threshold ( c≈28 vol.%), when continuous conductive networks of filler are formed in the matrix of glass systems. However, for low volume fractions (3, 11 and 23 vol.%), almost linear frequency dependence of conductivity σ was observed, with a slight change in slope around 106 Hz and stabilization at higher frequencies (Fig.1). Taking the dc-conductivity as value observed at zero frequency, the ac-conductivity is therefore deduced from Eq. (4) as: dc




and plotted in Fig. 2. As can be observed, for the ZP/Ni (3, 11 and 23 vol.%) composites, is mainly dependent on polarization and increases almost linearly with increasing

frequency (Fig.2). However some irregularity was observed beyond 106Hz. But the overall behavior is in good agreement with the ac-conductivity behavior of other amorphous phosphate materials [24-28]. 4.2. Real (ε') and imaginary (ε") parts of complex dielectric permittivity The ε' and ε" are determined at room temperature and at different frequencies (100Hz to 1MHz) using the Eqs. (2) and (3) respectively. The results are shown in Fig. 3. As can be seen, high values of dielectric constant approaching to 105 at 100Hz have been obtained in conductive composites. However, for the semiconducting composites corresponding to 3, 11 and 23 Ni vol.%, the obtained values are similar to the amorphous phosphate materials [2128]. A jump is observed above 23 vol.% of Ni corresponding to the percolation conducting threshold ( c≈28 vol.% of Ni) [29]. The dielectric constant ' was also determined as function of Ni volume fraction at room temperature and at a frequency of 100 Hz. The obtained result is given in Fig. 4. A nonlinear relationship between the values of ε' and filler volume fraction is observed. A jump from less 100 to almost 105 is shown, indicating a percolating behavior. The composites having volume fraction of 3, 11 and 23 vol.% of Ni, lower than the already observed 7

conducting percolation threshold of


vol.% [29, 30] show at low frequency a similar

dielectric behavior to that of amorphous semiconductors [21-28]. The increase of Ni filler amount into the phosphate glass matrix leads to increase of ε' and a large values are observed for the high volume fraction of Ni (30 and 36 vol.%) over the percolation threshold. Similar phenomenon has been observed for the composites of spherical metal Ni particles in a dielectric of BaTiO3/PVDF matrix [34]. 4.3. Electric modulus formalism and relaxation The real M' and imaginary M" parts of complex electric modulus M* are determined with


values as function of frequency using Eq. (6). The results are plotted with

scatter points in Fig.5. A special care has been taken to achieve good electrical contact between electrodes and specimen. It can be seen that a low values approaching to zero of M' corresponding to Ms are obtained at low frequencies, indicating the electrodes polarization makes a negligible contribution (Fig.5a). Then, two different behaviors with frequency increasing are observed for low and above percolation threshold. For the composites having lower filler's amount than the percolation threshold value (ϕ<ϕ c), M' starts to increase with frequency, shows a change in slope above 106 Hz and diminishes in increasing after. Limit values corresponding to M∞ are reached at high frequency (Fig.5a). The high limit value of M' decreases slightly with increase of metallic or polarons concentration. However, for the composites with high filler concentration (30 and 36Ni vol.%), the obtained values of M' are very low and change slightly between 10-13 at low frequency and 10-7 at higher, indicating a semiconductor behavior. The results obtained for the M" component are given in Fig.5b. Peaks are appeared in the M" behavior as function of frequency for all studied composites loaded with filler concentration less than the percolation threshold, indicating clearly dielectric relaxation dispersion processes over 105Hz. These peaks were not evident in permittivity's formalism 8

(Fig.3b). The observed relaxation phenomenon depends on filler's content. The maximum of M" decreases with the increase in conducting filler's concentration, ultimately shifting toward higher frequency. These M" maximum occur between two crossover conduction region: σdc for the low frequency and conducting limit σac at the high frequency (Fig.2). 5. Discussion In Fig.1, the direct electrical conductivity value obtained at room temperature and low frequency for low filler volume fraction (3,11 and 23vol.%) is low (about 10-8 S/cm). Thus, the frequency variation of total electrical conductivity σ corresponds approximately to an alternative conductivity (σ ≈


The increase of the conductivity at higher frequencies (>105

Hz) is probably due to activated localized charges, which leads to mobility increase [35]. The observed jump in the case of ZP filled with different amounts of nickel, confirms the previous data [29, 30] by showing the nonconductor to semiconductor phase transition at percolation threshold. The direct conductivity σdc increases by several decades when the percentage of nickel reaches its critical value of


vol.%. Indeed, the metal particles are

better interconnected enhancing charge carrier’s mobility through well defined conduction pathways which in turns increases conductivity. Beyond the percolation threshold, the total conductivity becomes independent of frequency. This phenomenon is a typically conducting behavior. However, below the critical threshold of percolation, the conductivity with power law




ac was fitted

in the whole frequency range considered (100Hz-1MHz). The result

is showed by solid line in Fig.2. The fit was obtained with a correlation factor of R2= 0.98, showing good consistency with the frequency power law behavior of


The obtained values

of k and s given in Table 1 seem coherent. The parameter k which is the amplitude coefficient, increases with amount of metallic filler and the parameter s is lower than 1. This means that below the percolation threshold, the conductivity increases continuously with frequency as


for 23 vol.% and


for 3 and 11 vol.% concentration of Ni. The exponent 9

s passes from 0.3 for a high filling to 0.5 for a low filling; indicating the characteristic of finite conductive size clusters for low filler's concentration, consistent with variable range hopping (VRH) theory [36, 37] and progressive dominance of σdc component when the filler's amount increases. Elsewhere, as showed the dielectric constant ε' measured at room temperature is dependent of filler concentration and frequency. It diverges when a critical threshold is reached, showing a percolating behavior. Thus, the experimental data were fitted by the general percolation theory as follows [34, 38, 39]: q '

c m c


Where εm is the real part of the complex dielectric constant of the matrix, fraction of the filler (Ni),


is the volume

is the percolation threshold (with < c), and q is the critical

exponent. This equation has been successfully applied to several organic and inorganic percolating composites [40, 41]. The fit was obtained with a correlation factor of R2=1, showing good consistency with the percolation law behavior of ' (Fig.4). The obtained parameters q,


and εm are q≈1.94,


30.5 and εm≈21.5. The power exponent and critical

percolation threshold values are in good agreement with these already obtained by electrical conductivity measurements [29, 30], showing a three dimensional system behavior. The obtained εm=21.5 value seems coherent, because the matrix is an insulator material. The dielectric constant ε' is enhanced by the metallic inclusion. Moreover, it was also shown that, the real (ε') and imaginary (ε") parts of complex dielectric permittivity decrease for all the samples when the frequency of the applied field increases. The reducing of ε' with the frequency may be due to several reasons: i) the electrode polarization resulting from accumulation of electric charges at the electrode- glass interface. 10

These charges are trapped by the metal electrode, which prevents their movement in the external circuit, leading to bulk polarization of the composites, ii) the increase of ε' at lower frequency can be explained on the basis of dipoles behavior under alternative field. Indeed, when the frequencies of applied field are low, the dipole moments in the system can easily follow the change of electric field orientation, inducing a high value of polarization expressed in a large values of ε'. As frequency of the applied field increases, the dipoles begin to show difficulties to follow the movement of the field orientation, the polarization decreases and hence the values of ε' decrease and a limit value ε∞ will be reached at high frequency. Thus, the space charges cannot sustain with the field; as theoretically predicted [38] and experimentally observed in various glasses materials [23, 24, 27, 28]. The dielectric loss ” decreases almost linearly with frequency, showing a small change of slope over 105Hz. It seems that is a sign of a relaxation process. This behavior is typically associated to the dominance of losses by conduction (ε"≈ σdc/εoω). It should be better clarified with electrical modulus treatment. Indeed, the transport mechanism is determined by the frequency region of M" behavior. Below the maximum of M" peak, the conduction is due to the hopping mechanism of charge carriers or polaron from site to the neighboring one [23, 42]. However, above the frequency peak of M", the carriers are localized in potential wells and having a short distance of motion as can be seen by the ac conductivity behavior (Fig.2). Thus, the behavior suggests that below percolation threshold, the relaxation mechanism is dominated by dipolar relaxation orientation under the electric field. The large dipoles developed cannot follow the electric field when the frequency is high. These dipoles are probably originated from the polar bonding between Zn2+, probably Ni2+ and oxygen of peroxide phosphate network by opening the P=O bonds, in addition to the induced dipoles. The relaxation process corresponds to the energy loss dispersion as frequency dependence. It decreases when the material becomes


electrically semiconductor or when the mobility of carriers into the matrix increases, and disappears above the percolation threshold. Moreover, the Fig.5b shows that the peaks are asymmetric with respect to the maxima and are considerably broader on both sides of these maxima indicating a non ideal Debye relaxation behavior. The broad nature of peaks can be understood as being the consequence of the distributions of relaxation time due to the non-Debye relaxation nature. This should be more clarified by plotting the M"/M"max with log (f/fmax) (Fig.6). This normalized curve called modulus master indicates the dielectric process occurring in the material. As showed in Fig.6, the modulus master is characterized by broad asymmetric pattern with a cross over from long range mobility to short range mobility of carriers. The full width half maximum (FWHM) of peaks are greater than the typically Debye peak. This non-symmetric behavior of normalized modulus is well described by the Kohlraush-William-Watts stretching function as:

(t) exp



Whereas, τ and β are the relaxation time and kohlraush or stretching exponent respectively. The parameter β measures the extent of non-exponential behavior and tends toward unity for Debye -type relaxation. The experimental data of M" vs frequencies were fitted using Debye, Cole-Cole Davidson-Cole and Havriliak–Negami models, using the Eqs. (7) and (8) respectively. The best fit is obtained with Davidson –Cole equation. Indeed, the electric field relaxation for average single relaxation time in the frequency domain mode, corresponding to DavidsonCole’s dispersion equations is obtained by putting the parameters ≠1 and =0 in Eqs. (7) and (8) [33] as:

M' M Ms

Ms Ms2



Ms (cos ) cos( )

Ms (cos ) 2Ms cos( ) (M - Ms )(cos )



M'' M Ms



2 s



M Ms (cos ) sin( ) Ms (cos ) 2Ms cos( ) (M - Ms )(cos )


) ; 0<β≤1 and the relaxation time τ is given by: =tg(π/2(1+β))/ωmax

The parameter β is introduced in ideal Debye's dielectric equation to account of an asymmetric distribution of relaxation times resulting from dielectric dispersion due to the dipoles orientations. The fits of experimental data of M' and M" versus the frequency with Eqs. (11) and (12) are given by solid lines in Fig.5a and Fig.5b respectively. All fits are obtained with a high factor correlation showing a good agreement between experiment and theory. The relaxation process seems in good accordance with the Davidson-Cole’s dispersion. The obtained fitting parameters (Ms, M∞, β, τ) are given in table 2. The obtained values of Ms and M∞ are close to that extracted from the experimental data. The parameter β measures the asymmetry in the distribution of relaxation time and the value of β=1 corresponds to pure Debye type relaxation or a single relaxation time. The determined values of parameter β are all high and around 0.7 (table 2) indicating a rather narrow distribution of relaxation times. This observation is confirmed by the normalized plots of M" (Fig.6). This means that the heterogeneity effect showed by the amplitude asymmetry is not so large. The physical situation is close to the pure dipolar Debye relaxation process. The reducing of relaxation time with filler amount becoming greater (table 2) can be explained using the approximate relation between τ and σdc as τ~εoε∞/σdc [43], showing that when the system becomes semiconductor the relaxation time decreases and tends to zero for conductor phase. Thus, the decrease of M" maximum with increase of filler amount seems attributed to the conductor state growing.


Elsewhere, the Fig.5 shows that the electrode-sample interfacial polarization becomes negligible by using electric modulus formalism. Moreover, no evidence of interfacial Maxwell-Wagner-Sillars (MWS) relaxation type is showed at low frequency explored upper 100Hz. Such phenomenon is often observed in heterogeneous materials which have multiple phases and interfaces. It is well known that the interfaces may lead to a polarization. The MWS relaxation arises from the fact that the free charges (impurities, catalysts), generated during the material processing are immobilized (trapped) in the material. For sufficiently high temperatures (usually above the glass transition) charges can migrate under the effect of the applied electric field. These free charges will be blocked at the interfaces that have different conductivities and dielectric constants. Thus, macroscopic induced dipoles are formed. The MWS mechanism explains the increase in dielectric constant with the lowering of the frequency. This phenomenon is therefore related to the heterogeneity of system. It is described theoretically by adding to HN Eq. (5) the conduction term-iσdc/ωε0 [33]. It well showed that the heterogeneity increase and consequently MWS effect shift the relaxation process to lower frequencies [33, 44]. In the present case, the absence of interfacial effects may be explained by the delocalized process that is dominated at low frequency, as showed in the conductivity section (σ≈σdc), and the decrease of M" maximum and its shift to higher frequency when the filler concentration increases. Structurally, the absence of this kind of relaxation in the present investigation may be justified by the constituents of these composite materials based on the same symmetrical chemical inorganic nature of matrix and filler, which may give homogenous material. Indeed, it has been shown that the inclusion of asymmetrical particles in the matrix, such as fibers, induces inhomogeneity giving MWS relaxation [33]. The SEM observations confirm this assumption showing almost homogeneous phase of the studied composites [29, 30]. 14

Moreover, in order to confirm this conclusion, the M' and M" are plotted in Cole-Cole diagram (Fig.7). To fit the obtained curve, the Davidson-Cole’s semi-circle equation can be obtained by rearranging the Eqs. (11) and (12) as:

M' Ms M Ms




M" M Ms




Using Davidson [45] result obtained on dielectric constants semi-circle equation (ε″=f(ε')), the Eqs. (11)’ and (12)’ become: 1

M' Ms M Ms









M" M Ms





Combining Eqs. (13) and (14), leads to the equation of a circle: 2(1

(M' Ms )

















This equation represents a quasi-semi-circle having a radius as: 2(1















and with center coordinates (Ms/2,0). The Fig.7 representing M" versus M' shows, in all studied composites that at low frequency, the formed semicircles pass by the origin, confirming the removal of electrode polarization and no presence of other relaxation process in the investigated composites [46]. Furthermore, it can be seen also that the effect of the filler content is indicated by the variation of the semicircles radius. The best fit of experimental data corresponds to Davidson- Cole model. 15

The obtained fitting parameters are in good comparison with these obtained by fitting of experimental points of M' and M" as frequency variation using Eqs. (11) and (12) respectively. The slight deviation from the pure Debye's model is indicated by a little divergence of observed semicircles. Finally, this study shows that the Davidson-Cole approach is most suitable for the description of dielectric relaxation in the composites with moderate heterogeneity in good agreement with earlier studies [33]. 6. Conclusion The electrical properties of 45mol.%ZnO–55mol.%P2O5/Ni composites have been studied in the frequency range 100Hz–1MHz at room temperature. The electrical conductivity as a function of frequency has been analyzed in additive law of real and imaginary components. The real part of conductivity is found frequency independent corresponding to σdc. However the imaginary part shows frequency dependence obeying to power law. It is showed that the mechanism of the conduction is dominated by hopping of carriers between neighboring sites. Moreover, the investigation of dielectric constant ε' shows an increase with the increase in filler concentration which has been well interpreted in the percolation theory frame. The fit parameters are coherent with comparable 3D systems and are in good agreement with these obtained in literature. Concerning the behavior with the frequency, ε' and ε" decrease when the frequency increases and considerably higher value for ε’ has been obtained. This should be giving an industrial application for this kind of materials. The decrease in ε' and ε" with frequency seems related to the mobility of dipoles under the applied electrical field. The investigation of the electric modulus formalism allowed the minimization of the electrode polarization effect and clarified the nature of small broad peaks observed in dielectric loss vs frequency. The relaxation observed at high frequency was interpreted like dipolar orientation under external electrical field and well fitted with Davidson-Cole equation. The obtained parameters are coherent and in good agreement with those found for this type of


composite materials. These materials showed a moderate heterogeneity and no interfacial relaxation (MWS) has been found at low investigated frequencies. Acknowledgements This work was performed in the frame of the scientific projects supported by the collaboration of Centre National pour la Recherche Scientifique et Technique (CNRST), Morocco and Centre National de la Recherche Scientifique (CNRS), France. These organizations are gratefully acknowledged for their partial financial support.

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Table 1: Fitting parameters obtained from power law for different Ni volume fraction (3, 11 and 23 Ni vol.%) in ZP/Ni composites. ZP/Nivol.%












Table 2: Fitting parameters obtained from Davidson-Cole electric modulus equations for different Ni volume fraction (3, 11 and 23vol.%) in ZP/Ni composites. Samples





















Figure legends Fig.1: Total conductivity of the ZP/Ni(3,11,23,30 and 36vol.%) composites as function of the frequency. The lines are guide eyes. Fig.2: Scatter points are the ac-conductivity dependent frequency of ZP/Ni(3,11 and 23vol.%) composites. The solid lines represent the fit with power law. Fig.3: a) dielectric constant (ε’) and b) dielectric loss (ε’’) versus frequency of ZP/Ni(3,11,23,30 and 36vol.%) composites. The lines are guide eyes. Fig.4: Dielectric constant (ε’) as function of Ni filler percent in ZP/Ni composites. The solid line is the fit with percolation Eq. (9). Fig.5: Scatter points are a) Real part M' and b) imaginary part M" of electric modulus versus frequency of ZP/Ni(3,11,23,30 and 36vol.%) composites. The lines are the fit of M' and M" with Eqs. (11) and (12) respectively. Fig.6: Normalized plots of M"/M"max versus log(f/fmax) of the ZP/Ni(3,11 and 23vol.%) composites. Fig.7: Cole-Cole plots of the ZP/Ni(3,11 and 23vol.%) composites. The solid lines are the fit with Davidson-Cole semicircle Eq. (15).


List of figures: Figure 1

Figure 2


Figure 3a

Figure 3b

Figure 4


Figure 5a

Figure 5b

Figure 6


Figure 7

Graphical abstract:


Highlights: ► Composites of ZnO-P2O5/metal were investigated by impedance spectroscopy. ► Original ac-conductivity behavior was discovered in ZnO-P2O5/metal composites. ► High dielectric constant is measured in ZnO-P2O5/metal composites. ► Dielectric constant as filler function is well interpreted with percolation theory. ► Observed relaxation processes are well described using electric modulus formalism.