Rietveld refinements, impedance spectroscopy and phase transition of the polycrystalline ZnMoO4 ceramics

Abstract The triclinic phase of zinc molybdate α-ZnMoO 4 (ZMO) was synthesized by a simple co-precipitation method at 600 °C. The crystal structure of the obtained polycrystalline sample of ZMO was characterized by X-ray diffraction (XRD) and Rietveld calculations using the space group P-1. The electrical properties of α-ZnMoO 4 compacted pellets were determined at room temperature from electrical impedance spectrometry (EIS), in the temperature range of 400–700 °C. Nyquist representations were interpreted in terms of two types of electrical circuits, involving a high frequency bulk component and a low frequency Warburg component. Analyses of the frequency dependence of the real and imaginary impedance show a non-Debye type relaxation. A phase transition corresponding to the allotropic transformation triclinic–monoclinic (α→β) of ZnMoO 4 was observed in the temperature range of 450–500 °C, with a variation of activation energies. The Warburg component is discussed in terms of electrode surface reactions.


Introduction
Tungstates and molybdates have multiple properties with interesting applications in various fields. It is well known that these types of materials overcome several phase transitions, thus they attracted considerable attention. For instance the Bi 2 WO 6 compound has two phase transitions: one structural phase transition occurs at 660°C with a change in space group from P2 1 ab to B2cb, and another phase transition takes place at 960°C with the space group changing to A2/m [1][2][3].
Likewise, a phase transition occurs for the Bismuth molybdate Bi 2 MoO 6 compound (space group P2 1 ab ) at 640°C [4] or 680°C [1], also this irreversible phase transition takes place with a space group changing to P2 1 /c. Zinc Molybdate ZnMoO 4 (ZMO) is one of the molybdate family and presents some similarities with these Aurivillius-Type compounds.
Electrical Impedance spectroscopy (EIS) was used by many researchers to explain materials behavior: Ben Mohamed et al [5] used the EIS to identify the slope change in conductivity, they concluded that the two phase transitions of their compound are accompanied by a change of the conduction mechanism observed in the difference of activation energies. Bourja et al have also determined some phase transitions in the cerium and bismuth mix oxides using the impedance spectroscopy [6].
In the case of the stabilized α phase, Goake et al. [36] observed a slight change in DSC analyses, they inferred a phase transition at Tc = 735 K or Θc=462°C. This phase transition corresponded to the transformation of a low temperature triclinic structure (the -phase), into a high temperature monoclinic structure (the -phase). The triclinic -phase [37,38]  (low temperature phase) into molecular groups MoO 6 . The β-phase was also synthesized directly via hydrothermal route as a metastable phase (obtained at room temperature) [18]. The monoclinic β phase was characterized by an indirect band gap around 2.48-2.68eV, and was evaluated as a photocatalytic material [24]. The triclinic -ZnMoO 4 band gap was determined by Keereeta et al. [34] with a value of 3.3eV.
This present study reports for the first time the electrical behavior at high temperature of ZMO. The main aim of our study is to investigate the effects of the phase transition on the sintered ZMO pellets conductivity. As a first step, we synthesized the polycrystalline sample, we optimized its crystallization, then, we refined the structure using the Rietveld refinements. Finally, in a second step, electrical impedance spectroscopy was used to characterize the evolution of conductivity as a function of temperature.

II. Experimental section.
Synthesis of the material: Zinc molybdate was synthesized via a co-precipitation method using Then sodium molybdate solution was gradually added to the zinc nitrate solution. The resulting white precipitate was filtered and washed several times with distilled water and ethanol, and finally, the obtained powder were calcined during 3 hours at 600°C with a cooling rate of 20°C/min.

X-Ray diffraction:
The X-Ray diffraction (XRD) patterns were collected using an Empyrean Panalytical diffractometer operating at 45 kV/35 mA, using Cu-K radiation with Ni filter, and working in continuous mode with a step size of 0,013°2θ. Data suitable for Rietveld refinements were collected over a range 5-80° 2θ.

Electrical Impedance Spectroscopy (EIS):
The electrical impedance spectroscopy is currently used to describe electrical properties in polycrystalline samples. This technique was recently applied to a phase transition [5,6]. Our study was performed using an electrical impedance spectrometer (Solartron Impendance meter SI 1260) coupled to an electrical cell operating under air. All Accepted Manuscript measurements were carried out in the temperature range of 100 to 750°C. The ZMO-600 sample was a cylindrical pellet (diameter 13.02±0.1 mm, thickness 2.17 ± 0.05 mm) initially compacted under ambient conditions. The experimental density of 3.87g.cm -3 represents 90% of the theoretical density 4.3g.cm -3 . The pellet was placed between two cylindrical platinum electrodes and was pressed in a specific cell. The cell was placed in an isotherm furnace operating up to 750°C.
The electrical analyses were carried out in the frequency range ( = 2 ) 1 to 10 7 Hz, with an alternating current associated with a maximum voltage of 1 V. The sample was stabilized for 20 minutes at a fixed temperature and the recording time for the frequency range was of 20 minutes. To ensure thermal stabilization, the sample was subjected to three successive measuring cycles (one temperature rise and drop for each cycle). The final impedance data were chosen during heating mode of the third cycle, as being representative of a stabilized sample.  The results of the Rietveld refinements are presented in Table 1 where the refined lattice parameters are reported. The initial atom coordinates have been exported from the structural results of authors [38] on single crystal. These coordinates have been refined: oxygen and zinc/molybdenum coordinates were refined, which led to a significant goodness of fit. Moreover, the fit parameters (R wp , R p , R exp , and χ²) are quite reliable. The main interatomic distances are given in Table 2 All these results are in full agreement with the crystal structure proposed by Reichelt et al. [38], determined from X-ray diffraction on a single crystal.    The Nyquist plots were interpreted and fitted using Zview software [43] by a classical equivalent circuit with impedance including constant phase elements [42] and resistance in parallel. RC parallel circuits and constant phase elements Z(CPE) were tested on Nyquist experimental data. At low temperature Θ <400°C, the impedance of such parallel R/CPE is well fitted. However, in the high Accepted Manuscript temperature range Θ >400°C, the linear contribution at low frequencies corresponds to a specific Warburg model described through a specific impedance Z W depending on the diffusion mechanism at the electrode -material interfaces (Figure 4).

Accepted Manuscript
The electrical analyzes were performed by separating the impedances associated with the core of the material (including grain boundaries) and those related to the electrodes (Z and Z W for bulk and Warburg impedances respectively).  Table 3 reports the parameters relative to the bulk impedance analysis: the parameters R, A and n are respectively the resistance, the polarization parameter and the exponent characteristic of the CPE term (jω) n . The Warburg element [44][45][46][47][48] can be expressed in a generalized form as follows: Accepted Manuscript In this expression, R W is the Warburg resistance depending on diffusion characteristics at the electrode/material interface, m is the characteristic exponent, A W = L 2 /D is related to the chemical diffusion coefficient D (m 2 s -1 ), and to the characteristic length L of reaction process (effective diffusion thickness). Table 4 reports the values of R W , A W and exponent m obtained from this model. 2. Impedance vs. Frequency analysis Figure 5 reports the variation of real and imaginary impedances as a function of frequency and temperature. The real Z' decreases with increasing temperature till a certain fixed frequency suggesting a notable reduction in the bulk resistance. The real impedance Z' attains a plateau at higher frequencies which implies a possible release of space charges meaning the absence of frequency relaxation in the ceramic [49,50]. A peaking behavior can be observed for all the selected spectra, the peak maximum shifts towards higher frequencies as a function of temperature. The imaginary Z" attains a maximum at certain frequency, then it decreases with increasing temperature to a fixed value at higher frequencies with peak broadening. The full width at half maximum (FWHM) calculated from the frequency dependence is greater than 1.141 decade (for ideal Debye type relaxation), this deviation clearly indicates the presence of non-Debye type relaxation in the sample [51]. These results explain the presence of relaxation process and the temperature dependence of the relaxation phenomenon in the pellet sample [52]. The relaxation process occurs due to the presence of immobile charges at low temperatures and of additional defects and vacancies at higher temperatures [53,54].

Conductivity analysis
In Figure 6 representing the logarithm of conductivity σ versus 1/T, or logarithm of σ.T versus 1/T, we clearly observe a modification in the temperature range 440 to 500°C. In the linear part of the curves (at low or high temperatures), the activation energies are different. In the transition range from 440 to 500 °C, the progressive variation of conductivity can be interpreted in terms of specific "progressive jumps" characteristic of a first order transition, with coexistence of two phases (the so called α and β phases). We have evaluated the conductivity variation due to the transition, by extrapolating the two linear parts of log(σ) curves at high and low temperatures: close to the transition point, the two lines are separated by a ∆σ/σ relative variation of about 0.45 ±0.05.
This double modification can be interpreted in terms of coupling of the phase transition at Θc = 450°C with the modification of charge carriers associated with two different activation energies: the first one being due to extrinsic initial defects of the material, and the second one being due to major contribution of additional Schottky defects delivering additional mobile oxygen ions.   To interpret the electrical transition observed in our ZMO-600 sample: two types of models might be proposed. Generally, in the absence of any phase transition, if we assume that at least two types of charge carriers can coexist, the thermally activated conductivity can be expressed as follows:

T).exp(-E 1 /RT) + (K 2 /T).exp(-E 2 /RT)
In the case of a material undergoing a phase transition at a temperature T c , each parameter K i , E i (i=1,2) could be subjected to a modification as a function of T.
However, another more classical model could be proposed in competition with the previous one, where K -, K + are in relation with K 1 and K 2 , and where E -, E + are in relation with E 1 and E 2 :

Accepted Manuscript
This model was used to calculate the activation energies in Table 5. However, this simplified model cannot account for changes in the vicinity of the transition point.
It is the reason why we propose now to consider that the phase transition can have a direct consequence on the various types of charge carriers, due to initial extrinsic defects and on additional defects linked to Schottky-like defects, formed during heating the material and in equilibrium with oxygen of air.
To describe the first order transition at T c = 733 K, we postulate a modification of the (K 1 , E 1 ) and (K 2 , E 2 ) terms, occurring in a small temperature range between T c and T up . In the case of a first order transition, a two-phase domain of temperature can be generally observed. Consequently, the K 1 and K 2 terms are subjected to increasing values of ∆K 1 and ∆K 2 , while the enthalpy terms are subjected to decreasing values of -∆Ε 1 and -∆Ε 2 : these last decreasing values correspond to the structural modification allowing larger space for electron (and vacancy) mobilities, and weaker barriers for electron (and vacancy) jumps. In fact, to correctly describe the transition domain between T c and T up , it was necessary to use empirical continuous evolution of these parameters. All parameters describing the phase transition have been reported in Table 6.

IV. Conclusion
In