Co composites

Journal of Non-Crystalline Solids 385 (2014) 89–94

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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol

Positive temperature coefficient and high Seebeck coefficient in ZnO–P2O5/Co composites O. Oabi a, A. Maaroufi a,⁎, B. Lucas b, S. Degot c, A. El Amrani d a

University of Mohammed V Agdal, Laboratory of Composite Materials, Polymers and Environment, Department of Chemistry, Faculty of Sciences P.B. 1014, Rabat - Agdal, Morocco XLIM UMR 7252 - Université de Limoges/CNRS 123 avenue Albert Thomas - 87060 Limoges Cedex, France SPCTS, CNRS UMR 6638, European Ceramic Center, 12, rue Atlantis, 87068 Limoges Cedex, France d LPSMS, FST Errachidia, University Moulay Ismail Meknès, B. P. 509, Boutalamine, Errachidia, Morocco b c

a r t i c l e

i n f o

Article history: Received 10 July 2013 Received in revised form 30 October 2013 Available online 26 November 2013 Keywords: Glass ceramics; Electrical properties; Volume expansion; Phase transition; PTC devices

a b s t r a c t This article reports a study of electrical properties of new Zinc Phosphate glass/Cobalt composites (45 mol.% ZnO–55 mol.%P2O5) (ZP/Co). The measurements of electrical conductivity at room temperature as a function of cobalt's concentration showed a non-conducting to conducting phase transition at percolation threshold of 27 vol.%. The Seebeck coefficient obtained under the same conditions, accompanies a sign, with high positive and negative values below and above the percolation threshold respectively, depicting a p- to n-type conducting phase transition, confirming the conductivity measurements. Then, the measurements of electrical conductivity and Seebeck coefficient above the percolation threshold as a function of temperature showed an original conducting to insulating phase transition, called Positive Temperature Coefficient (PTC) at T = 420 K, associated to a high negative value of S ≤ −8000 μV/K, with the highest power factor PF = σS2 ≈ 8 × 10−3 W m−1 K−2. The thermal measurements of volume expansion confirm this transition, indicating matrix dilation around this temperature. However, the thermal behavior of the electrical conductivity and Seebeck coefficient data obtained below the percolation threshold showed different mechanisms i.e.; Small Polaron Hopping (SPH) mechanism at high temperatures and Mott's Variable Range Hopping (VRH) at low temperatures. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The phosphate glasses have interesting physical properties, i.e. low melting temperatures, large glass areas [1], low glass transition temperatures (Tg) and optimizing coefficient of thermal expansion (CTE) [2]. That is why, they find ever-increasing applications in many emerging technologies e.g.; stable storage medium for high level nuclear waste [1,3], laser glasses [4,5], magneto-optical devices [6], energy transfer materials [7], glasses for sealing in electronics [8], biomaterials [9], battery materials for ultra-fast charging and discharging [10]. Moreover, they are effectively applicable in photovoltaic applications; which are already obtained in amorphous phases of other systems [11]. The use of phosphate glasses in the composite form can open up new horizons for the development of this kind of materials. In accordance with our previous findings, composites of zinc-phosphate glasses filled with metallic powders are not only capable to improve the glasses' electrical characteristics but also can provide interesting industrial applications [12,13]. It is a well-known fact that the thermoelectric applications are evaluated with the figure of merit ZT defined as: ZT = S2σT/κ; where, σ is the electrical conductivity, T is the temperature, k is the thermal conductivity, and S is the Seebeck coefficient. A high ZT indicates a high ⁎ Corresponding author. Tel./fax: +212 537 77 54 40. E-mail address: maaroufi@fsr.ac.ma (A. Maaroufi). 0022-3093/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2013.11.003

thermodynamic efficiency. Recently, the best reported ZT values have been in the range 2–3 [14,15]. Moreover, the materials exhibiting Positive Temperature Coefficient (PTC) are still of great interest due to their technological applications, like very sensitive detectors obtained with their nanocomposites [16,17]. The objective of the present work is to develop new materials with controlled structural and electrical properties. Therefore, composites of zinc-phosphate glasses loaded with cobalt powder have been elaborated and electrically studied. In our previous work on zinc-phosphate glasses filled with nickel, very interesting results have been obtained [12,13]. Indeed, a high power factor (PF = σS2) and PTC effect have been shown for the first time in the phosphate glasses' composites. The thermoelectric parameters obtained are higher than measured in case of oxide glasses [18–21]. It would be beneficial to compare this work with our earlier one, in order to explore the composites of this kind of materials with the highest thermoelectric characteristics for eventual applications.

2. Experimental procedures 2.1. Composite preparation The xZnO–(100 − x)P2O5 matrix, where, x is ZnO molar fraction percent, was prepared using the classical quenching technique [12,13].

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Powder of ammonium di-hydrogen phosphate ((NH4)H2PO4 from Panreac type, 98%) and zinc oxide (ZnO from Panreac type, 99%) are mixed in adequate molar proportions. Then, thin particles of cobalt (from Sigma-Aldrich with average particle size 149 μm, and a purity of 99.9 %) are mixed in adequate proportions with zinc phosphate glass matrix (45 mol%ZnO–55 mol%P2O5). The obtained powder microcomposites were transferred into a cylindrical mould and pressed at 7 tons to decrease the porosity and to obtain fine compact discs, each one with 13 mm of diameter and 2–3 mm of thickness. The disks obtained were sintered at 300 °C for 2 hours in order to increase the cohesion of composites. Series of composites were prepared with filler contents ranging from 1 to 40 vol% into the matrix. 2.2. Electrical conductivity and thermoelectric power measurements The measurements of dc electrical conductivity (σdc) at room temperature were performed with a Keithley 224 current source and a Keithley 616 voltmeter, by four-point technique of Valdes [22]. The measurements of the conductivity and the Seebeck coefficient versus temperature were performed between 150 K and 450 K [23]. The operating conditions are mentioned in the previous work [13]. The Seebeck coefficient S is then determined by the equation: S¼−

ΔV ΔT

ð1Þ

where, ΔT and ΔV are the difference of temperature and the difference of potential respectively, between two points of the sample. 2.3. Volume expansion measurements The volume expansion of the composites was obtained with a SETARAM TMA 92 thermo-mechanical analyzer, using a programmed heating rate of 2 K/min in a temperature range varying from 300 to 500 K. The thickness of composites was measured before and after thermal treatments. 3. Results 3.1. Non-conducting to Conducting Phase Transition The zinc phosphate glass matrix (45 mol%ZnO–55 mol%P2O5) or ZP is used because it showed a good thermal stability. The glass temperature transition Tg determined with DSC scan is 430 °C [12]. Fig. 1 shows electrical conductivity (σdc) obtained with square four-point probe technique on the surface of the samples and Seebeck coefficient (S) data as a function of filler volume percent (ϕCo) for ZP loaded with cobalt powder (ZP/Co). The obtained percolation behavior has been discussed in our previous study [12]. As in our previous study [12], the percolation behavior is obtained. However, the value of conducting percolation threshold is slightly different, because this is probably related to sandwich method used in earlier and square four-point probe technique on the surface of the samples used in present study. Thus, three regions are observed: – Region below the percolation threshold ϕc or ϕCo b ϕc: The conductivity is almost constant and equal or slightly higher than that of zinc phosphate glass matrix (~ 10− 8 S/cm). The Seebeck coefficient remains constant and taking high positive value of S ≈ 5500 μV/K. The power factor PF deduced is low and takes 10−10 to 10−11 W/m K2. Such behavior is a characteristic of dielectric materials. – Region around the percolation threshold or ϕCo ≈ ϕc: The electrical conductivity of the composites jumps by eight orders in a very small region of ϕCo, showing a phase transition from insulator to conductor materials around percolation threshold of ФC ≈ 27 vol.%, slightly different than that obtained with two points

Fig. 1. Dependence of the Seebeck coefficient (○) and electrical conductivity (●) of ZP/Co composites versus cobalt volume fraction percentage. The lines are drawn as guides to the eyes.

sandwich method [12]. The small deviation is probably due to the nature of current flow in the sample which is associated to the difference in technical measurements. The Seebeck coefficient data confirm the percolating behavior. The conduction threshold is almost the same as the one obtained with the conductivity. Moreover, the coefficient S changes its sign from positive to negative for lower and higher level fillings, respectively. This behavior indicates a passing from p- to n -type semiconductor material or insulator/conductor phase transition, which is in good accord with conductivity results. – Region above the critical percolation threshold or ϕCo N ϕc: Above the percolation threshold (ϕ ≈ 30 vol.%), the conductivity becomes constant and takes σ ≈ 1 S/cm. The round figure value of S− 40 μV/K emphasizes that the composite starts behaving like a typical metal. The corresponding power factor jumps at percolation threshold and takes values greater than 10−7 W/m K2. 3.2. Positive Temperature Coefficient (PTC) phase transition According to the fixed values of filler content above (or below) the percolation threshold, different behaviors can be observed. Fig. 2a reports the data of the conductivity above the percolation threshold of ZP/Co(40 vol.%) composite as a function of temperature from 293 to 440 K. As shown in this figure, the conductivity decreases slightly and linearly when the temperature increases, with a slope of −1.5 × 10−4 (S cm− 1 K−1) showing metallic behavior. However, at 420 K, it falls abruptly indicating a conducting to non-conducting phase transition, called Positive Temperature Coefficient (PTC) effect. This phenomenon is observed at higher amounts of metal in composites (i.e. ϕCo N ϕc) and below Tg. The temperature of transition TPTC increases slightly with a metallic amount (ϕ N ϕc) incorporated in ZP-matrix. The PTC intensity is given as:   σ
I PTC ¼log low σ RT

ð2Þ

where σRT is the room temperature conductivity and σlow is the lowest conductivity after PTC transition. It may be noticed that the PTC effect is even higher when the filler content in ZP is significant and greater than the percolation threshold; the PTC intensity is found approximately 1.5 decades. After crossing the PTC transitions, the conductivity decreases insubstantially and finally stabilizes. Moreover, the conductivity behavior versus heating/cooling temperature of ZP/Co (40 vol.%) composite shows an important hysteresis (Fig. 2a), indicating that the observed phase transitions are of first

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Fig. 3. Variation of Seebeck coefficient with temperature for (a) ZP/Co(40 vol.%) and (b) ZP/Co(27 vol.%) composites. The lines are drawn as guides to the eyes.

Fig. 2. a) Electrical conductivity of ZP/Co (40 vol.%) composite versus temperature, heating (●) and cooling (○); b) Electrical conductivity of ZP/Co(27 vol.%) composite versus temperature (●). The lines are drawn as guides to the eyes.

order (with respect to latent heat), in accordance with the Ehrenfest classification [24]. It is obvious that the previously observed transition is reversible (return to initial state). It seems that a quick disconnect of the infinite percolating clusters occurred. On the other hand, a stationary regime has been established (with a shift in temperature of about 64 K) for the reconnection of the junctions without apparent degradation of the conductive paths in the composite. However, at conduction threshold ϕc or below, this phenomenon is not visible (Fig. 2b). The conductivity decreases slightly with temperature, like metals with the absence of any evident phase transition. To confirm the PTC transition, the Seebeck coefficient of ZP/ Co(40 vol.%) has been investigated in the same range of temperature. The result is given in Fig. 3a. In the 300–393 K temperature range, S varies between − 30 and − 40 μV/K and is almost independent of temperature. However, at TPTC ≈ 393 K, an abrupt decrease is observed confirming the PTC transition as demonstrated by the conductivity measurements. Furthermore, a high negative value of S (≤ − 8000 μV/K) is obtained around 420 K, with the power factor PF ≈ 8 × 10− 3 W/m.K2. However, the measured Seebeck coefficient of ZP/Co (27 vol.%) composite (Fig. 3b) is similar to metals with negative values (between about − 10 and − 30 μV/K), which decreases almost linearly with the increase in temperature and do not show any phase transition in the temperature range, under consideration. The linear dependence of S on temperature is known as a characteristic temperature dependence of degenerate semiconductors, which is generally related to the free electron-like behavior of the carriers in the composite; this is consistent with the metallic behavior. In order to examine the origin of the PTC transition, the volume expansions of pure ZP-matrix and composites of ZP/Co, with different filling above and below the percolation threshold (19, 27 and 40 vol.%) have been investigated as functions of temperature (Fig. 4). The volume expansion of pure matrix ZP (Fig. 4a) increases slightly with temperature between 300 K and approximately 393 K (expansion), corresponding to the PTC transition and then, it decreases to become negative

(compression) after 417 K. On cooling from 500 to 300 K, it decreases continuously until around 370 K; changes slope and starts increasing below this temperature, showing a big hysteresis. However, for the ZP-matrix filled with 19 vol.% of Co, the volume expansion increases almost linearly on heating to 500 K and shows the same behavior on cooling from 500 to 340 K (Fig. 4b). The decreasing values are slightly lower to the increasing ones at high temperature, showing a small hysteresis. The filler seems to modify the thermal behavior of the matrix by passing from expansion to compression. This phenomenon seems to be related to the fact that the filler modify by improving or lowering the mechanical properties of matrix and its resistance to the thermal effects. This effect becomes important when the filler fraction rises to the critical value (percolation threshold) or above that. Hence, the mechanical properties of matrix seem to tend progressively to these of pure matrix, as can be seen in the ZP/Co27 and ZP/Co40 vol.% case (Fig. 4c–d). Indeed, it has been shown [12] that the porosity decreases inside the composites with the increase in filler volume fraction and then increases around 30 vol.%. The SEM pictures showed cracking at high limit filling [12].

Fig. 4. Volume expansion coefficient of composites: a) ZnO-P2O5 matrix, b) ZP/Co (19 vol.%), c) ZP/Co (27 vol.%) and d) ZP/Co(40 vol.%) versus temperature, heating (→) and cooling (←).

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3.3. Electrical behavior below percolation threshold Depending upon the amount of filler inside the matrix, different behaviors could be seen. On this basis, the PTC transition is obtained only when the filler concentration is higher than the percolation threshold. The dependence of the electrical conductivity of ZP/Co(19 vol.%) on temperature is given in Fig. 5a. The conductivity increases linearly from 300 to approximately 370 K, and then it changes the slope for the high temperatures. Probably, several mechanisms of conduction occur. 4. Discussion The thermal behavior of electrical conductivity (Fig. 1) shows a phase transition from insulating to conducting state by important jump of more than eight orders at conduction threshold of cobalt filler around 27 vol.%. This result is in fair agreement with earlier study, which showed a percolation threshold about 30 vol.% of cobalt [12]. This discrepancy is probably associated to the difference of technical measurements. The observed transition was effectively interpreted with statistical percolation theory [12]. Indeed, in the insulating phase the conducting clusters of cobalt filler are small and disconnected. However, when the amount of filler increases, the size of conducting clusters grows progressively and becomes infinite path at percolation threshold (ϕc ≈ 27 vol.%), leading to the conducting phase. This behavior seems to be confirmed by the Seebeck coefficient measurements. Indeed, it is well known that, the Seebeck coefficient is a weighted average of the conductivity associated with the two ‘p’ and ‘n’ types of carriers, as: S¼

Sn σ n þ Sp σ p σn þ σp

ð3Þ

According to this equation, it is clear that the measurement of the Seebeck coefficient gives the type of the charge carriers and the electrical conduction mechanisms that take place in the materials [25]. Likewise, the experimental data given in Fig. 1 showing the change of sign of S, indicate that the electrical transport mechanism in the composite is governed by free electron carriers due to the conductive filler above

Fig. 5. (a) Inverse temperature dependence of electrical conductivity of ZP/Co (19 vol.%) composite data (●) and linear line (——) fit with Eq. (5); (b) Ln(σT1/2) versus T−1/4 (■) and linear line (——) fit with Eq. (6).

the percolation threshold. The conducting state results from the connected conductive infinite paths of filler. A similar behavior of passing from p to n type conductor carriers was obtained by Dong-Souk [26] on solid solutions of (1 − x)NiO–xZnO (x is volume fraction of ZnO) calcined at 600 °C, followed by sintering at 1200–1300 °C. It has been found that the change from p to n of Seebeck coefficient depends upon the composition x and temperature. This solution has also been studied by Lisjak et al. [27] showing PTC phase transition around 673 K above 20 wt.% of ZnO. The amplitude of transition decreases for high values of x and disappears around 80 wt.%. However, the mechanism of conduction in such materials seems to be different from that observed in ZP/Ni [13] or ZP/Co composites. Indeed, in recent investigations, the mechanism of the electrical conduction in Zn1 − xNixO (x is atomic fraction of Ni) micro or nano-solid solutions was clarified [28,29]. It has been remarked that the increase of both the Seebeck coefficient and electrical conductivity is related to the substitution of Zn by Ni in the crystalline structure of ZnO, until the solubility limit of 3Ni at%. In consequences, the electrical conduction mechanism of ZP/ Co compounds seems the same as observed in ZP/Ni composites [13] and no exchange between Co and Zn has been evidenced. The electrical conduction is merely related to the metallic filler percolating clusters connection. The obtained power factor of ZP/Co (40 vol.%) sintered at 300 °C is PF ≈ 8 × 10−3 W/m K2 at 420 K. This value is higher than determined at the compared temperature of ZP/Ni (40 vol.%) composite, PF ≈ 2 × 10− 4 W m− 1 K-2, sintered at same temperature [13] and Zn0.97Ni0.03O (PF ≈ 1.4 × 10− 4 W m− 1 K− 2) [29], Al(1–4at.%)-doped ZnO (PF ≈ 1.5 × 10− 4 W m− 1 K− 2) [30,31], or ZnO/TiB2 (10 vol.%) composite (PF ≈ 1.07 × 10−4 W m−1 K−2) [32], sintered at high temperature. Moreover, it would be possible that sintering at high temperature of ZP/metals composites gives higher values of PF. The large variation in S at PTC phase transition (420 K), giving highest negative values (≤ − 8000 μV/K) could be used in advantageous applications. However, is not clearly understood yet. It could have different origins. The probable first one is the PTC transition mechanism or the migration of negative oxygen ions (O−), which more probably originates from the residual vacuum in the chamber. It reacts with the material surface following a chemisorption process. Such an effect of oxygen on the evolution of S against temperature has already been observed with amorphous germanium and silicon [33]. An alternative to the oxygen effect is the phonon drag [34,35]: phonons move towards the cold end of the sample (subjected to a temperature gradient) and take the electrons with them towards this end. This effect overlaps the electron diffusion effect associated to the concentration gradient produced by the thermal gradient, showing an intense decrease in S, which may be explained on the basis of Fig. 3a. The PTC transition with a high negative thermoelectric power (from about −6000 to −8000 μV/K) observed in the ZP/Co composites confirms the one already observed in ZP/Ni, with a value around −4000 to −5000 μV/K [13]. Such phenomenon demonstrated by ZP/ metal composites could provide an opportunity for important industrial applications. Verily, the power factor PF of ZP/Co (40 vol.%) composite is lower than ZP/Ni [13] below the PTC transition and takes values around ~ 10−7 W m−1 K−2. However, above the PTC phase transition, a long jump is observed giving PF ≈ 8 × 10−3 W m−1 K−2 at 420 K. Therefore, the figure of merit ZT could achieve higher values with the decrease in the thermal conductivity of a material. Regarding the origin of the PTC effect showed for the first time in zinc-phosphate glass/metal composites, different and complex mechanisms could take place. The mechanism described by Heywang model [36] considers the electron conduction at the interface of grain boundaries. This model allows a good interpretation of the PTC effect observed in the BaTiO3 ferroelectric material families [37]. In this theory the electrical resistivity is an exponential function of potential barrier created by the interface of grain boundaries. The increase of this potential above the ferroelectric transition by the traps of electron along the grain boundaries induces an important increase in electrical resistivity,

O. Oabi et al. / Journal of Non-Crystalline Solids 385 (2014) 89–94

inferring the PTC transition. It is also noticed that the thermal volume expansion has an important effect on the PTC transition, characterized by Mott type transition as observed in vanadium compounds [38], or the volume expansion of the semi-crystalline or amorphous matrix of the polymer/conducting filler composites [39,40]. In this case and above the percolation threshold, the electrical conductivity is high because the conducting particles are connected by infinite pathway. The PTC transition is due to the disconnection of the infinite clusters induced by a large volume expansion near the melting point for the semicrystalline and at glass phase transition for the amorphous polymers. Similar phenomenon was observed on cristobalite/graphite ceramic composite [41]. The thermosetting polymer composites show a different and complex behavior. The PTC transition may occur above or below the glass transitions [42,43]. The PTC phase transition seems to associate with the volume expansion of the matrix, inducing the decrease of internal constraints and a consequent disconnection of conductive particles. It has been shown that this effect was at the origin of PTC transition in ZP/Ni composites [13]. Therefore, it would be interesting to verify its occurrence during the PTC transition, observed in the ZP/ Co composites. The investigated thermal volume expansion depicts hysteresis in all tested composites of ZP/Co around 400 K, close to the temperature of PTC transition (Fig. 4). Like ZP/Ni composites, the observed PTC transition in ZP/Co composites seems related to the volume expansion in matrix. As mentioned above, the volume expansion of the composite under the temperature effect increases the inter-particle distances, breaking the conducting particles connectivity which finally results in inducing transition. The effect of the thermal volume expansion on the electrical conductivity of composites has been shown by Gul et al. [42], as: σ ¼ σ 0 expð−αT Þ

ð4Þ

where σo is the electrical conductivity of the composite at room temperature and α is the thermal volume expansion coefficient. According to this equation, the electrical conductivity can drop down when α takes important values, giving the PTC phase transition as observed in ZP/ Metal composites. The thermal dependence of electrical conductivity of ZP/Co 19 vol.% (composite with ϕCo b ϕc) given in Fig. 5a shows two different behaviors by changing in slope around 370 K, suggesting at least two mechanisms of conduction. It has been shown [12] that the studied composites are formed with amorphous glass matrix filled with metallic fillers. When the amount of fillers becomes critical, a crystallized network of these fillers is obtained. Hence, the investigated composites are partially ordered materials. Like this, the analysis with theoretical models, which have been proposed to explain the electrical conductivity in amorphous semi-conductors, is justified. The most used is the band model postulated by Mott-Davis [44]. In this model the electrical conduction takes place by hopping between first neighbors' localized states near the Fermi level and in the tails of valence and conduction bands. Consequently, different behaviors can be observed as a function of temperature and depending upon the distribution of energies in these localized state bands. Thus, the data were fitted with Arrhenius law:  .  W σ ¼ σ o exp − kT

ð5Þ

where σo is the conductivity of the composite at room temperature, W is the activation energy for hopping, k the Boltzmann constant and T absolute temperature. The linear fit of the conductivity data versus (1/T) (Fig. 5a) gives two different values of activation energies, 0.31 for T ≤370 K and 0.26 eV for T N 370 K respectively. This shows good consistency with Arrhenius law, confirming the thermally activated hopping mechanism at high temperature between localized states near the Fermi level and in the tails of conduction and valence bands. The corresponding activation

93

energy obtained at high temperature is lower than that obtained in ZP/Ni (26 vol.%) composite [13]. The mechanism of activation is complex and depends on several parameters; like the importance of contribution of localized states in tail of bands or near the Fermi-level [45], the composition of glass materials [46,47] and more. Moreover, the conductivity of ZP/Ni (26 vol.%) is about ten times higher than that of ZP/Co (19 vol.%). The values in the same orders were obtained in similar phosphate materials [48,49]. The change of slope of the thermal dependence conductivity indicates that at low temperature the Mott's variable range hopping (VRH) theory [44] is more appropriate to interpret the conductivity behavior. This theory is given by:  1= 2

σT

¼Aexp

−B

. T

1= 4

Þ

ð6Þ

hence, " 

#

e2

A¼

2ð8πÞ

1

=2

ν ph

"  B ¼ 2:1

α

3

h

N ðE F Þ

. αkT

#1 =

4

kNðE F Þ

2

ð7Þ

ð8Þ

 R¼

1 = 4 9 8παN ðE F ÞkT

i1 =

Wo ¼

3

. ½4πR3 NðE F Þ

ð9Þ ð10Þ

A represents the conductivity at infinite temperature, T is absolute temperature and B is the characteristic temperature of system, k is the Boltzmann constant, α is the decay of the localized state wave functions (i.e. the inverse localization length of the localized wave functions), Wo is the hopping energy, R is the mean hopping distance, e is the electron charge, N(EF) is the state density at the Fermi level EF, and νph is optical phonon frequency, which can to be obtained from the Debye temperature θD as: kθD ¼ hν ph

ð11Þ

where, h is the Plank's constant. As can be seen from Eq. (8), larger B implies a stronger localization of the charge carriers, shown by decrease of the conductivity at low temperatures, whereas a low B implies a weak localization. Thus, the linear fit of Ln(σT1/2) versus T−1/4 given in Fig. 5b, obtained with correlation factor of R2 = 0.996, indicates a three-dimensional process of conduction, taking place in the ZP/Co(19 vol.%) composite, which is in good agreement with the variable range hopping mechanism [44]. The obtained parameters of fit are A = 22.74 (S cm− 1 K1/2) and B = 164.34 K1/4 (i.e. 7.3 × 108 K). The value of B obtained in this composite is of the same order of magnitude as that found in ZP/Ni (26 vol.%) composite [13] and slightly higher than that of an amorphous material (B ≈ 108 K), this indicates a weak value of N(EF) [44,45]. The observed high temperature mechanisms was interpreted with non-adiabatic small Polaron Hopping (SPH) theory [50] which predicts a change of slope at critical temperature θD/2 of the linear behavior of conductivity versus inverse temperature, showing a transition from SPH to VRH (Fig. 5a). At low temperatures, the Polaron binding energy becomes smaller than the disorder energy WD, which can attain approximately the value of Wo [51]. Thus, taking in consideration the temperature of 370 K of change in slope, θD may be of order 740 K. Hence, from Eq. (11), the value of νph can be calculated and it gives νph ≈ 1.54 × 1013 Hz, which seems realistic because the optical phonon frequency is of order 1012– 1013 Hz. Employing Eqs. (7), (8), (9), (10) and the slope of Ln(σT1/2)

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O. Oabi et al. / Journal of Non-Crystalline Solids 385 (2014) 89–94

vs. T − 1/4 , the α, N(E F ), R and Wo were estimated respectively. At T = 300 K; α ≈ 1.2 × 10 9 cm − 1, N(EF ) ≈ 5.5 × 10 23 eV− 1 cm− 3 , R ≈ 120.8 × 10 − 10 cm and W D ≈ Wo ≈ 0.25 eV. The obtained state density is higher than that found in semiconducting glasses (1021 eV−1 cm−3) [46,47,52]. However, these results confirm the occurrence of VRH because the term αRN N 1 and WDN N kT (=0.0255 eV) at T = 300 K [44]. 5. Conclusion In this work, the 45mol%ZnO-55mol%P2O5 matrix loaded by cobalt has been studied by electrical conductivity measurements and Seebeck coefficient as a function of filler content and temperature. The results showed a jump of the electrical conductivity above a critical value of the filler's volume fraction. This behavior was fairly interpreted in statistical percolation frame. The obtained values of Seebeck coefficient are high and change a sign at critical conduction percolation threshold, showing the transition from p- to n-type conduction. The thermal behavior of the conductivity above the critical threshold showed an original PTC effect phase transition at 420 K, linked with a high negative value of Seebeck coefficient with the highest power factor. However, the thermal electrical conductivity behavior below the percolation threshold showed a non-adiabatic -SPH conduction at high temperature and VRH mechanism conduction at intermediate temperatures, in good agreement with earlier studies. Acknowledgments This work was carried out in the frame of the scientific projects (SPM10/10, 11) under 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. References [1] [2] [3] [4] [5] [6]

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