AC conductivity and mechanism of conduction study of α-Sr 2 P 2 O 7 using impedance spectroscopy

The ceramic sample Sr2P2O7 was prepared by a solid-state reaction technique at high temperature. Electrical properties and modulus analysis were studied using complex impedance spectroscopy in the frequency range 200 Hz–5 MHz and temperature range 602-714 K. The difference of the value of activation energy for the bulk obtained from analysis of equivalent circuit (0.81 eV) and modulus relaxation (0.69 eV) confirms that the transport is not due from a simple hopping mechanism. The average of the power law exponent s is reasonably interpreted by the overlapping large polaron tunneling (OLPT) model. The mechanism of conduction is probably due from the displacements of the Sr 2+ ion in the tunnel-type cavities along the b axis.


INTRODUCTION
The metal phosphate is a wide field of research that currently operates a large numbers of laboratories around the world for their enormous importance in scientific and commercial photonic applications.They exist in several areas such as glass, ceramic, electrochemical solid.Among them pure and doped pyrophosphates have variety of applications, such as lamp industry, color display, radiation dosimetry and X-ray imaging because of their luminescent, dielectric, semiconductive, catalyst, magnetic, fluorescent, and ion-exchange properties [1][2][3][4][5].
Alkaline-earth-metal pyrophosphates with the general formula of A2P2O7 (A=Ca, Sr, Ba) are well-known for their potential applications as luminescent materials, for example Sr2P2O7: Er 3+ etc [6][7][8][9].A2P2O7(A=Ca, Sr, Ba; Mg, Zn) is a large family of pyrophosphate compounds, which have been found to crystallize in two structural types that can be predicted from the ionic radius of A cation.When radius of A 2+ is smaller than 0.97 A˚(A=Mg, Zn), A2P2O7 is of the thortveitite structure, in which [P2O7] groups are in stagger configuration; and when the radius of A 2+ is larger than 0.97 A˚(A=Ca, Sr, Ba), the [P2O7] groups are in eclipsed configuration [10].
In our study we have the interest to study strontium pyrophosphate which is a promising phosphate that is used broadly in the industry as a result of its luminescent, fluorescent, dielectric, semi-conductor, catalyst, magnetic and ion exchange properties.In this paper the ac conductivity has been investigated using impedance spectroscopy to determine the electrical, dielectrical properties and mechanism of conduction by examining the observed experimental results.

Experimental details 2.1 Solid-state syntheses
The Sr2P2O7 was prepared by conventional solid-state reaction technique.Stoichiometric quantities of strontium carbonate (Sr2CO3) and ammonium di-hydrogen phosphate (NH2H4PO4) with high purity (99%) were well grounded into fine powders using mortar and pestle, thoroughly mixed and heated first to 473 K for 8h to expel NH3, H2O and CO2, the calcined powder was pressed into cylindrical pellets using 3 T/cm 2 uniaxial pressure and heated at 1123 K for 10 hours.

X-ray powder diffraction
X-ray powder diffraction pattern was recorded using a Philips PW 1710 diffractometer operating with copper radiation Kα=1.5418Å. Unit cell parameters of the synthesized compound have been refined by the least square method from the powder data.

Impedance measurements
The electrical measurements were performed using a two platinum electrode configuration.The polycrystalline Sr2P2O7 sample was pressed into pellets of 8-mm diameter and 1-mm thickness using 3t/cm2 uniaxial pressure.Electrical impedances were measured in the frequency ranging from 200 Hz to 5 MHz with the TEGAM 3550 ALF automatic bridge monitored by a microcomputer between 602 K and 714 K.

Complex electrical impedance analysis
The impedance in its standard definition means quotient of vector voltage and vector current calculated from small single sinusoidal measurement.When an ac signal is applied to a system, the impedance of the system obeys Ohm's law, as ratio of voltage to current in the time domain.
The irnpedance is a complex quantity, having both magnitude Z and phase angle  expressed as: (3) Where Z' and Z" are the real and imaginary parts of complex impedance.In impedance technique, the real and imaginary parts of impedance of the sample were measured simultaneously as a function of frequency.The impedance data were successfully modeled by an equivalent circuit, which is given in the inset of Fig. 4.This later is composed by two elements consisting of series of combination of two parallel circuits.At higher frequencies, the observed shapes due to the grain response are expressed by Rg-Cg parallel circuits while the grain boundary response evidenced at the lower frequencies is modeled by Rgb-CPEgb parallel circuits.The impedance of the capacity of the fractal interface CPE is giving by the following equation: (4) Where Q indicates the value of the capacitance of the CPE element and α the degree of deviation with respect to the value of the pure capacitor.This behavior is typical of an ionic ally conducting polycrystalline material [17].
The experimental data for the real (Z') and imaginary (-Z") components of the whole impedance were calculated from the theoretical expression established with equivalent circuit are: Z', -Z″ data measured at 649 K and their fits according to the above equations versus frequency are represented in Fig. 4.
The good conformity of calculated lines with the experimental measurement indicates that the suggested equivalent circuit describes the crystal-electrolyte interface reasonably well.Fitted values (grain and grain boundary) parameters for different temperature are listed in Table 2.The capacitance values for the high and the low frequency semicircles are found to be in the range of pF and nF, respectively, proving that the observed semicircles represented the grain and the grain boundary response of the system, respectively.

Electric modulus analysis
The complex electric modulus, M*(ω) is an alternative approach to investigate the electrical response of materials that present some degree of ionic conductivity.M*(ω) has been used in the analysis of the electrical properties since it provides the response due to the bulk and eliminates the electrode polarization effect.The complex electric modulus is represented by the following expression [18-21] Where C0 is the vacuum capacitance of the cell.The variation of the imaginary part of electric modulus M″ with the frequency at various temperatures is shown in Fig. 6.
Double peaks are observed in the patterns.The peaks in higher and lower frequency region are basically related to the relaxation process of grains and grain boundaries, respectively.The position of these relaxation peaks are found to shift to higher frequencies with the increase of the temperature showing a temperature-dependent relaxation.
The modulus plot can be characterized by full width at half height or in terms of a non exponential decay function [22,23].
In this fact, the stretched exponential function is defined by the empirical Kohlrausch-Williams-Watts function [24]: Where  the characteristic relaxation time and  is the well known Kohlrausch parameter, which decreases with an increase in the relaxation time distribution.Indeed, its value for a practical solid electrolyte is clearly less than 1. (t) is related to the modulus in the angular frequency domain by the equation: Among these functions, the Havriliak-Negami (HN) one has been the most extensively used in literature [25,26].The HN function is: Being the corresponding relationship between  and HN parameters given by: (1/1.23) β=(αγ) (11) In this event, the modulus expression becomes: The β parameter is most often interpreted as a result of correlated motions between ions.Its value represents the deviation from the linear exponential (β =1).In the present case, the shape of each spectrum has been quantified with a β M a r c h 1 5 , 2 0 1 4 value obtained by fitting the curve to Eq.8.Thus, to achieve the fit to Eq. ( 8) at each temperature, β ,  and M  value have been taken free parameters.It is worthy to note that the best fits for M" at different temperatures for the compound are shown in Fig. 6.Additionally, in Fig. 7 we represent the average value of the parameter β for the bulk (0.64-0.72) with temperature.Which suggests that all possible relaxation mechanisms occurring at different frequencies are driven by the thermal energy and that the dynamical processes are temperature dependent.

M''
 (rad s -1 ) On the other hand, the conductivity relaxation frequency fp is given by the relation: Where f0 is characteristic phonon frequency, Em is the activation energy for conductivity relaxation, KB is the Boltzmann constant and T is the temperature.The temperature dependence of the conductivity relaxation of angular frequency (p) for the grain and grain boundaries is plotted in Fig. 8.It is well described by the Arrhenius relation.The obtained activation energy in bulk is 0.69(2) eV.This obtained value (from modulus analysis) is different from impedance measurement study (0.81(1) eV).We conclude that the ion transport is not due to a hopping mechanism.

Dielectric study
The study of the dielectric properties is another important source of valuable information about conduction processes since it can be used to understand the origin of the dielectric losses, the electrical and dipolar relaxation time and its activation energy [38].
The complex dielectric response of the system exposed to an external oscillating electric field is expressed as: Where, the real ‫׳‬ and imaginary ‫״‬ components are respectively the storage and loss of the energy.The dielectric spectra show a non-Debye type behavior in the high frequency range, it can be described as [39]: Where 0 is the specific conductivity, ∞ is the dielectric constant at infinite frequency and s is the static dielectric constant.M a r c h 1 5 , 2 0 1 4 Fig. 9 shows the variation of ‫״‬ with frequency at various temperatures.It is observed that ‫,״‬ decreases with increasing frequency for all temperatures.At low frequencies, as the temperature increases, ‫״‬ shows a dispersive behavior, while it merges at frequency above 100 KHz.The higher values of ‫״‬ at low frequency suggest the existence of electrode polarization [40,41].dielectric constant exhibits larger dispersion at low frequencies while it decreases to a constant value and becomes temperature independent at higher frequencies.This behavior is well explained by the Maxwell-Wagner type relaxation, often occurring in the heterogeneous systems [42].When an electric current passes through interfaces between two different dielectric media, because of their different conductivities, surface charges pile up at the interfaces giving rise to interfacial polarization at the boundaries.These space charges align with the applied electric field at lower frequencies but as frequency increases the dipoles cannot synchronize with the frequency of the applied field so their contribution is reduced, giving rise to low dielectric constant.According to this model the sample consists of perfectly conducting grains separated by insulating grain boundaries.The Koop's phenomenological theory postulates that grain boundaries are effective at low frequencies and grains are effective at high frequencies.Thus low polarization at higher frequencies, leads to decrease in dielectric constant.Where S is the conductivity at low frequencies,   is an estimate of conductivity at high frequencies,=2f is the angular frequency,  represents the characteristic relaxation time, A is a constant temperature dependent and s is the power law exponent, where 0 < s < 1.The s represents the degree of interaction between mobile ions with the environments surrounding them, and A determines the strength of polarisability.
The above Eq.15 has been used to fit the AC conductivity data.In the fitting procedure, A and s values have been varied simultaneously to get the best fits (Fig. 12).
The values of exponent s lie in the range 0.45-0.94, the correlation motion is sub-diffusive and indicates a preference on the part of ions that has hopped away to return to where it started [30].Jonscher [31] has shown that a non-zero s in the dispersive region of conductivity is due to the energy stored in the short-range collective motion of ions.A higher s implies that large energy is stored in such collective motions.In this work, exponent s decreases with increasing temperature at a minimum 680 K and then increase.According to the QMT model, the exponent s is almost equal to 0.8 and increases slightly with temperature or independent of temperature [32].The exponent s could be calculated using the formula: where τ0 is the characteristic relaxation time.That is, in the QMT model, the frequency exponent s is temperature independent but frequency dependent.A temperature dependent frequency exponent can be obtained within the framework of the QMT model in the pair approximation by assuming that the carriers form non-overlapping small polarons (NSPT) [32] where s, in this case, is given by: Where WH is the polaron hopping energy.That is, s in the NSPT model is temperature dependent, increasing with increasing temperature.
In the CBH model that describes charge carrier hops between sites over the potential barrier separating them, s is found to decrease with increasing temperature [33,34] as: In the OLPT model, the exponent s depends on both frequency and temperature and drops with rising temperature to a minimum value and then increases, as temperature rises [35].The variation of frequency exponent s as a function of temperature is shown in Fig. 10.This result suggests that OLPT model is the most suitable model to characterize the electrical conduction mechanism in the ceramic compound Sr2P2O7.
If overlapping large polarons are formed, the expression for a.c.conductivity and exponent s is given as [36,37]: Where Rω the hopping length at angular frequency ω (is the tunneling distance), rp the polaron radius, α is inverse localization length, N is density of defect states, and WHO is activation energy associated with charge transfer between the overlapping sites.

Conclusion
The

Fig. 3 (Fig 3
Fig. 3(a.b) shows the complex impedance spectroscopy measurement of the Sr2P2O7 simple at various temperatures.There are mainly two overlapping semicircles, which correspond to grains (the semicircle at low frequency) and grain boundary (the semicircle at high frequency)[16].

Fig 4 :
Fig 4: Variation of Z′ and -Z″ with frequency at 649 K with electrical equivalent circuit

Fig 5 :
Fig 5: Dependence of ln(dcT) on temperature for Sr2P2O7  are shape parameters ranging between 0 and 1.The Cole-Cole function corresponds to the case 0 < α < 1 and  = 1 and the Cole-Davidson to α = 1 and 0 < < 1.The Debye case is recovered again with α = = 1.Alvarez et al. established that for HN function which approximately corresponds to the Fourier transform of d(t)/dt, these two shape parameters, α and  are related as[27,28]

Fig 6 :Fig 7 :
Fig 6: Variation of imaginary part of modulus (M″) with angular frequency for Sr2P2O7 at different temperatures.Solid lines represent the fitted data

Fig 8 :
Fig 8: Temperature dependence of relaxation frequency h (bulk) obtained from the frequency dependent plots of M″ for Sr2P2O7 compound

Fig 9 :
Fig 9: Variation of dielectric loss, ‫״‬ versus frequency at various temperatures Fig. 10 illustrate the frequency dependence of the dielectric constant (‫)׳‬ in the temperature range 561 and 696 K. the

Fig 10 : 3 . 5 Frequency dependent conductivity measurements 3 . 5 . 1
Fig 10: Variation of dielectric constant, ‫׳‬ versus frequency at various temperatures 3.5 Frequency dependent conductivity measurements 3.5.1 AC electrical conductivity The a.c.conductivity ac study gives information on the time dependent movement of charges.Such time dependent movements of charges lead to conductivity and dielectric relaxation phenomena.The study of dielectric properties with frequency gives a good insight into the distribution of electric field in the system and the field induced perturbations.The frequency dependence of a.c.conductivity in Sr2P2O7 at different temperatures is shown in Fig. 11.The phenomenon of the conductivity dispersion is analyzed by the equation [29]:

Fig 11 :Fig 12 : 2
Fig 11: Frequency dependence of AC conductivity at various temperatures strontium diphosphate Sr2P2O7 has been synthesized and identified by X-ray diffraction.The sample crystallizes in orthorhombic symmetry with Pnma space group.Two semicircles are observed in impedance plot indicating the presence of two relaxations processes in the compound associated with the grain and grain boundary.The relaxation behavior of the grain and grain boundary of the Sr2P2O7 are also obtained from the analyzed electrical modulus data.AC conductivity has been measured in the frequency range of 200 Hz-5 MHz and in the temperature range of 602-714 K. Activation energy for bulk from the impedance (0.81 eV), and the modulus (0.69eV) are determinate.The displacements of the Sr 2+ ion are probably due to OLPT mechanism in the tunnel-type cavities along the b axis.The OLPT model was found to explain the mechanism of charge transport in Sr2P2O7.