Electrical conductivity and vibrational studies induced phase transitions in [(C2H5)4N]FeCl4

The compound, tetraethylammonium tetrachloroferrate [(C2H5)4N]FeCl4, was prepared by slow evaporation at room temperature. It was characterized by X-ray powder diffraction, thermal analysis, and impedance and vibrational spectroscopy. X-ray diffraction data confirmed formation of a single phase material which crystallized at room temperature in the hexagonal system (P63mc space group). DSC showed the existence of two phase transitions at 413 K and 430 K. Electrical conductivity was measured in the temperature and frequency ranges of 390 K to 440 K and 40 Hz to 110 MHz, respectively. Nyquist plots revealed the existence of grains and grain boundaries that were fitted to an equivalent circuit. AC conductivity plots were analyzed by Jonscher's power law. Variations in the “s” values indicated that CBH models describe the conduction mechanism in regions I and II. Temperature dependence of Raman spectra showed that the most important changes were observed in the cationic parts ([(C2H5)4N]+). The activation energy value obtained from the line width decreased which indicated an order–disorder model.


Introduction
Recently, material science has mainly concentrated on multifunctional materials. Obtaining such a material in the form of solids with a continuous lattice was found to be very complicated. However, a material with a multifunctional character can be obtained by building up hybrid solids formed by two lattices consisting of organic and inorganic parts. Much attention has been paid to organic-inorganic hybrid materials due to the possibility of each moiety contributing its own characteristic properties. [1][2][3][4][5] This large family exhibits several phase transitions related to the reorientation dynamic of alkyl chains. [6][7][8] In fact, they present interesting properties such as ferromagnetic, ferroelectric, ferroelastic, and thermal ones. [9][10][11][12][13] Special attention is paid to compounds based on iron. Owing to the presence of the high-spin d 5 in their molecules. Compounds containing tetrahalogenferrate(III) units may also be used as attractive magnetic materials. 14, 15 Moreover, it was found that some of the iron(III) complexes have been used in bioinorganic chemistry as substances for synthesizing model compounds, such as [Fe 2 S 2 Cl 4 ] 2À . 16 With this aim, we wish to report the growth of [(C 2 H 5 ) 4 N] FeC1 4 crystals, and a description of basic information about their properties. This compound is of interest due to the presence of Fe(III) in a tetrahedral coordination structure that mainly provides the existence of magnetic, electric, and elastic anomalies. 17 At room temperature, the system belongs to the hexagonal system (space group P6 3 mc) with four formulae per unit cell, which has dimensions of a ¼ b ¼ 8.198Å, c ¼ 13.183Å. 18 In this contribution, the synthesis, X-ray powder diffraction, differential scanning calorimetry, impedance measurements, and vibrational study as a function of temperature were carried out.

Synthesis
Mixing a stoichiometric molar ratio of FeCl 3 (purity 98%; FLUKA) and [N(C 2 H 5 ) 4 ]Cl (purity 97%; FLUKA) was performed in aqueous solution. Aer few days, yellow prismatic crystals were obtained by slow evaporation at room temperature. The sequence of the chemical reaction is the following:

Characterisations
Phase purity and homogeneity were checked using X-ray powder diffraction analysis. Using a Phillips PW 1710 powder diffractometer operating with CuK a (l ¼ 1.5405Å), the XRD pattern was recorded in a wide range of Bragg angles (10 # 2q # 60 ). Structural renements ware carried out by the Rietveld renement method. 19 Differential scanning calorimetry, DSC, was executed with a Perkin Elmer DSC-7 instrument in a temperature range from 300 K to 470 K with a 5 K min À1 rate. Thermogravimetric analysis (TGA) was performed with an ATG-Q500 SETARAM in a heating process from room temperature up to 772 K with a heating rate of 10 K min À1 .
To study the electrical proprieties, the [(C 2 H 5 ) 4 N]FeCl 4 powder was pressed at 5 t cm À2 ton pressure, forming a circular disc with a 1.1 mm thickness and 8 mm diameter. Measurements were executed in the frequency range of 40 Hz to 110 MHz using a 4294A impedance analyzer. The measurements were carried out under an excitation voltage of 50 mV. In the present study, we found that aer several tests our pellet became soer aer 430 K, which proved that these organicinorganic crystals of tetraethylammonium tetrachloroferrate show plastic behavior at high temperature. 6 Therefore, the sample is not in the form of an electrical dipole, which shows that measurement aer 430 K is not possible.
Using a Perkin Elmer FT-IR 1000 spectrophotometer, the infrared spectrum of [(C 2 H 5 ) 4 N]FeCl 4 was recorded at room temperature in the frequency range of 500-3500 cm À1 .
Raman scattering measurements were analyzed by a Horibe Jobin-Yvon T64000 spectrometer over the frequency range 50-3500 cm À1 with a resolution of 3 cm À1 in the temperature range 303-428 K. The program LABSPEC5 soware was used for tting the spectra with a combination of Lorentzian-Gaussian functions. The tting procedure was performed in order to quantitatively analyze the evolution of Raman bands as a function of temperature.

Results and discussion
3.1 X-ray powder diffraction analysis Fig. 1 shows the XRD patterns of [(C 2 H 5 ) 4 N]FeCl 4 . The Rietveld renement was performed using the FULLPROOF soware program. The circles symbolize the experimental data and the line presents the simulated pattern. The purity of the studied compound was proved and the reection peaks were indexed in the hexagonal system with the P6 3 mc space group. The corresponding lattice parameters were found to be: a ¼ b ¼ 8.218Å, c ¼ 13.203Å and the cell volume was V ¼ 772.2Å 3 . The quality of the renement was evaluated through the goodness of t where c 2 ¼ 1. 23. The values of the reliability factors obtained from the renement are R up ¼ 13.5, R p ¼ 18.5 and R exp ¼ 12.04 and the tted parameters were found to be in a good agreement with those in the literature. 18 Table 1.

Thermal analysis
From the Boltzmann equation, (DS ¼ R ln(U)), where U is the rapport number of distinguishable orientations allowed in the high-and the low temperature phases (N 1 /N 2 ).
The obtained values of U were 1.14 and 1.16 at T 1 and T 2 , respectively (U 1,2 < 2), which reveals that these two phase transitions are not purely "order-disorder". 20 The thermogravimetric analysis (TGA) curve in Fig. 3 shows that this compound started to decompose at 615 K. Besides, no weight losses were observed between 300 and 615 K.

Electrical measurements
Impedance spectroscopy is one of the most suitable techniques to investigate electrical conductivity and to analyze the charge transport processes in grains, grain boundaries, and electrode effects in materials in terms of thermal and frequency ranges. 21 Fig . 4 displays the obtained Nyquist plots from experimental results at several temperatures. With respect to these curves, the experimental points show semi-circles where their diameters decrease with temperature increase indicating that the conduction mechanism is thermally activated. 22 In addition, they are centered below the abscissa axis indicting that the relaxation process in the material is of a non-Debye type. 23 (The Debye model presents the ideal response 24 where all the dipoles participating in the relaxation phenomenon have the same relaxation time s). The Nyquist diagram is a perfect semicircle centered on the abscissa axis but there are other cases where all dipoles do not have the same relaxation time (distribution of relaxation time). There are several empirical models derived from the Debye equation that correctly describe these types of relaxations including the Cole-Cole model 25-27 and the Nyquist plot described by a attened arc with its center located below the real axis on a line deviated from the angle of (1 À a)p/2 where a describes the interactions between dipoles.
Nyquist plots were analyzed using Zview Soware. The best ts were obtained using an equivalent circuit (inset Fig. 4) realized by two cells which consisted of a parallel combination of bulk resistance R 1 and fractal capacity CPE 1 in series with a parallel combination of grain boundary resistance R 2 and fractal capacity CPE 2 . The constant phase element (CPE) impedance is given by the following equation: 28 where Q presents the capacitance value of the CPE fractal capacity and a relates to the deviation degree with respect to the pure capacitor value.
The theoretical impedance of real (Z 0 ) and imaginary (ÀZ 00 ) parts linked to the equivalent circuit were calculated according to the following eqn (2) and (3):  The frequency dependence of the impedance of real (Z 0 ) and imaginary (ÀZ 00 ) at various temperatures, are depicted in Fig. 5 and 6, respectively. It was noted that the magnitude of Z 0 decreased, where increases in both frequency and temperature indicated an increase in AC conductivity of the sample. At frequencies higher than 10 6 Hz, the coincidence of the impedance (Z 0 ) at all temperatures showed a possible freeing of space charge 29 whereas, the Z 00 peak maximum decreased with a rise in temperature. The peak frequency u max shied to higher values and the later reected a non-Debye type relaxation. 30 Fig. 4-6 show good conformity between experimental data and the theoretical line indicating that the equivalent circuit described the electric properties of the investigated compound quite well. As a matter of fact, details of tted values for different temperatures are gathered in Table 2. It is obvious that all the capacitance values (Q 1 and Q 2 ) are in the range of picofarads (pF) and nanofarads (nF), respectively, implying a single semicircle response is from grain interiors and grain boundaries. The values of a vary in the range of 0.81-0.99 showing a capacitive behavior of the fractal phase CPE. 31 Electrical conductivity spectroscopy is a well-founded method for characterizing hopping dynamics of the charge carriers. Based on the equivalent circuit parameters, grain conductivity is expressed according to the following expression: 29 where e and S are the thickness and area of the sample, respectively, and R 1 is the bulk resistance. The dependence of ln(s g T) versus 1000/T is presented in Fig. 7. The experimental data evinced a linear variation whose s g decreased as temperature decreased. This indicated that electrical conduction in the material is a thermally activated process and was tted well by the Arrhenius relation as described by eqn (5): where s 0 is the pre-exponential factor, E a is the activation energy, and k B is the Boltzmann constant. The activation energies obtained by the linear t at T 1 (413 AE 5 K) are E a (I) ¼ 0.74 eV in region I and E a (II) ¼ 1.13 eV in region II. The observed variation in the activation energies between the two temperature domains can be explained by movement of the cationic and anionic parts with temperature. 32 However, the discontinuity at 413 AE 5 K agrees with the phase transition observed in the DSC measurements.

AC conductivity studies
The variation of AC conductivity with angular frequency for [(C 2 H 5 ) 4 N]FeCl 4 is shown in Fig. 8 at different temperatures. Each conductivity plot exhibits two distinct regions. First, it remained almost constant at lower frequencies; this plateau corresponds to dc conductivity. It is seen that an increase of temperature is closely related to an increase of the AC conductivity which suggests that electrical conduction in the material is a thermally activated process and suggests semiconductor properties of this compound. Second, at higher frequencies, the AC conductivity dependence occurred with changes in slope and increased gradually with an increase in frequency.
Besides, the dispersive region shied to higher frequencies with an increase in temperature. This phenomenon of conductivity dispersion is generally analyzed using Jonscher's universal power law 33 expressed by eqn (6): where s dc is dc conductivity, A is a frequency independent preexponential factor that depends only on temperature and s is the dimensionless frequency exponent having a value between 0 and 1; s is the degree of interaction between mobile ions with the environments surrounding them. In order to identify the predominant conduction mechanism for [(C 2 H 5 ) 4 N]FeCl 4 , different theoretical models proposed by Long et al. were used to correlate the conduction mechanism of AC conductivity with the predicted exponent s(T) behavior. [34][35][36][37] These different models are: QMT, the quantum mechanical tunneling model, OLPT, the overlapping large polaron tunneling model, NSPT, the non-overlapping small polaron tunneling model, and CBH, the correlated barrier-hopping model. Comparing the obtained results with the extracted exponent s temperature dependence behavior (Fig. 9) for the different models, the conduction mechanism for [(C 2 H 5 ) 4 N] FeCl 4 was best interpreted with the correlated barrier hopping (CBH) model in region I and II. According to this model of conduction 38 (CBH), the thermal dependence of S, is given by eqn (7): where W M is the polaron binding energy and s 0 is the characteristic relaxation time. By a rst approximation (at higher binding energy), eqn (8) is written in the form: The AC conductivity as a function of frequency (s ac (u)) can be expressed according to this model 39,40 by eqn (9): where n is the number of polarons participating in the hopping process (n ¼ 1 for single polarons or 2 for bipolarons), N is the density of localized states in which carriers exist and R u is the hopping distance for the condition us ¼ 1 which is calculated using eqn (10): The potential barrier W M was calculated from the linear t of the curve (1s) as a function of temperature from eqn (8). In the general case, if W M ¼ E a /2, then bipolaron hopping is the dominating conduction mechanism and if W M ¼ E a /4, then a single polaron is dominating. The obtained values of W M are 0.12 eV in region I and 0.25 eV in region II. These values are proximate to E a /4, which proves that single polaron hopping is the dominating conduction mechanism in the material. Temperature dependence of conductivity (ln(s ac )) at different frequencies is shown in Fig. 10. There is good agreement between experimental and theoretical curves. The density of localized states (N) obtained by t are understood between 5.45  Â 10 34 to 5.12 Â 10 32 cm À1 in region I and between 3.02 Â 10 32 to 3.7 Â 10 31 cm À1 in region II. From a qualitative analysis of these values, we noted that the density of localized states decreased with increasing frequency. This reduction is explained by an increase in the disorder which decreased stabilities of states with non-localization of the latter. 41

Vibrational study at room temperature
The IR and Raman spectra of tetraethylammonium tetrachloroferrate are presented in Fig. 11. Tentative assignments for a majority of the vibrational bands using previously reported data in the literature on similar compounds are: [(C 2 H 5 ) 4 Table 3.
The internal vibrations of the [(C 2 H 5 ) 4 N] + cations. The Raman spectrum above 3000 cm À1 displays one band (at ca. 3022 cm À1 ) attributable to the (n as (CH 3 )) vibration. The Raman and IR bands at 2990 and 2989 cm À1 , respectively, are attributed to the CH 2 asymmetric stretching mode (n as (CH 2 )). The IR peak at 2979 cm À1 is assigned to the CH 3 symmetric bending mode (d s (CH 3 )). On the other hand, the symmetric bending mode (d s (CH 2 )) is observed at 2952 and 2950 cm À1 in the Raman and IR spectra, respectively. The asymmetric bending of CH 2 groups (d as (CH 2 )) is found at 1460 and 1440 cm À1 in the Raman and at 1455 cm À1 in the IR spectra. The CH 3 symmetric bending (d s (CH 3 )) mode appears at 1353 cm À1 in the Raman spectrum. The observed Raman band at 1307 cm À1 and IR band at 1302 cm À1 are assigned to CH 2 twitching mode (t(CH 2 )). The CH 3 rocking vibration (r r (CH 3 )) is in the Raman spectrum at 1185 and 1008 cm À1 and also as doublet IR bands at 1183 and 1006 cm À1 . The asymmetric stretching mode (n as (C-C)) is identied at 1082 cm À1 in Raman and at 1079 in IR, whereas the symmetric stretching mode (n s (C-C)) presents a Raman band at 895 cm À1 . The N-C asymmetric stretching vibration (n as (N-C)) is observed at 1022 and at 1033 cm À1 in Raman and IR, respectively, while the symmetric bending modes (n s (N-C)) are   n 2 (FeCl 4 ) a n s , n 1 : Symmetric stretching; n as , n 3 : asymmetric stretching; d s , n 2 : symmetric bending; d as, n 4 : asymmetric bending; t: twitching; r r : rocking.
located at 665 cm À1 in the Raman spectrum. A strong transmission band appearing in IR near 791 cm À1 and Raman band at 794 cm À1 are assigned to the CH 2 rocking vibration (r r (CH 2 )).
The band related to the CNC skeleton deformation (d s (CNC)) is detected in the Raman spectrum at 554 cm À1 .

Temperature dependence of the Raman spectra
In order to gain more information on the crystal dynamics and on the mechanism involved in the transition, we undertook a vibrational study using Raman scattering between 303 and 428 K. Fig. 12 illustrates the Raman spectra of [(C 2 H 5 ) 4 N]FeCl 4 recorded in three spectral ranges ([50-400 cm À1 ], [500-1600 cm À1 ], and [2800-3200 cm À1 ]). A deconvolution of all spectra was necessary to follow the temperature dependence of the wavenumber and half maximum. This deconvolution was carried out by means of Labspec soware with a combination of two Lorentzian and Gaussian functions. Fig. 14(a and b) shows the temperature dependence of the position and half maximum for some bands issued from the internal modes of the anionic part [FeCl 4 ] À observed between 50 and 400 cm À1 . We noticed that this gure indicates weak changes near 418 K where the phase transition has been observed. The line at 121 cm À1 associated with n 2 (FeCl 4 ) mode underwent a shi toward high frequency by 2 cm À1 , with a half maximum decrease by 5 cm À1 . The two bands at 379 and 397 cm À1 attributed to n 3 (FeCl 4 ) vanished at the temperature transition.
In Fig. 13(a and b), signicant changes were obtained for some peaks located in the 500-1600 cm À1 frequency range which issued from the internal modes of the cationic parts. The two bands around 554 and 1185 cm À1 assigned to the d s (CNC) and r r (CH 3 ), respectively, vanished aer the phase transition (418 K), while three bands appeared in the vicinity of 595, 750, and 1528 cm À1 at 418 K. A large change was detected for the peak at 665 cm À1 (n s (N-C)), where it broke into two bands aer 418 K. Another important change in the position was observed near 1440 and 1460 cm À1 (d as (CH 2 )). These two bands merged  into a single line at 418 K while the half maximum of them increased to 15 cm À1 above the transition. The bands observed between 2800 and 3200 cm À1 , which were assigned to the symmetric and asymmetric vibration of CH 2 and CH 3 groups, did not change signicantly with temperature; their position and half maximum underwent weak changes (a few cm À1 ) which means that these modes are not directly connected to a phase transition.
Spectral anomalies observed in Raman spectra of the [(C 2 H 5 ) 4 N]FeCl 4 crystals are due to a phase transition at T ¼ 418 K which is in good agreement with DSC measurements and electrical proprieties. The most pronounced changes were found to be connected with vibration of the cationic part. In order to conrm the main role of the organic part in the phase transition point, we focused our study on the band around 1440 cm À1 associated with the CH 2 asymmetric bending mode d as (CH 2 ).
3.6.1 Temperature dependence of the Raman wavenumbers. According to Andrade and Porto, 48 the thermal dependence of the Raman shi of a phonon linked to an orderdisorder mechanism can be expressed by eqn (11): where n 0 is the so-called 'hard-core wavenumber' at T ¼ T tr , g is a thermal coefficient of the substance, and T tr is the transition temperature. In the general case where g is very weak, then eqn (11) can be written 49 as eqn (12): The thermal coefficient g associated with variation of the crystal volume and the wavenumber is given by eqn (13): where n is the band position and V is the volume of the crystal at room temperature. We adjusted the evolution of the frequency of the studied modes using eqn (12) in the temperature range that extends above and below the phase transition temperature (Fig. 15). The variation of the frequency shows two linear regimes, one below and the other above 418 K which conrms that this temperature is characterized by a phase transition. The value obtained from the coefficient (g) at the level of the two temperature domains is in the order of 0.0047 K À1 for T < T tr and 0.058 K À1 for T > T tr . We noticed that the parameter g depends on the frequency and it increased with an increase in temperature, which makes it possible to identify that the volume of the crystal decreases for T > T tr . 50 3.6.2 Temperature dependence of the Raman at half maximum. The width of the Raman lines of a photon related to the order-disorder mechanism as a function of the correlation time (s c ) can be obtained 51 from the generalized Langevin eqn (14): where s c is the correlation time (the time necessary to jump from one potential to another); it is related to orientational activation energy given by eqn (15):  where s 0 represents the value of s c at high temperature, E a is the activation energy for the concerned mode with the orderdisorder transition, and k B is the Boltzmann constant. Generally, the term (us c 2 ) [ 1 so that eqn (14) can be reduced 52 to eqn (16): in which a, b, c, and E a are parameters that should be tted. Fig. 16 shows the adjustment of the width at half maximum of the band at 1440 cm À1 using eqn (16). This variation is characterized by an enlargement at high temperature due to the reorientation dynamics of the disordered crystal. The activation energies determined from this spectrum are in the order of E a (I) ¼ 1.1 eV for T < T tr and E a (II) ¼ 0.92 eV for T > T tr which are in good agreement with the activation energies obtained by electrical conductivity.
The decrease of these values with increasing temperature is explained by the gradual evolution from an ordered state to a disordered phase resulting from an increase of the dynamics [(C 2 H 5 ) 4 N] + cation. 53 This allows us to conclude that the observed phase transition is related to the reorientation dynamical disorder of the tetraethylammonium cation.

Conclusion
Tetraethylammonium tetrachloroferrate with a hexagonal system (P6 3 mc space group) was prepared and investigated as a function of temperature and frequency. One phase transition at 413 K was detected by differential scanning calorimetry (DSC). Additionally, Nyquist plots revealed the existence of grains and grain boundaries that were tted by an equivalent circuit. The AC conductivity spectrum was found to obey Jonscher's power law.
The temperature dependence of the exponents s(T) indicated that a correlated barrier hopping (CBH) was the most suitable model for the conduction mechanism. Signicant changes of several bands for the internal modes of the organic cation were observed within the phase transition temperature. Temperature dependence analysis of the frequency and the width of the d as (CH 2 ) mode proved that there is an anomaly around T ¼ 418 K, a consequence of an order-disorder phase transition. The decrease of E a values below the order-disorder phase transition can be understood as a change in the dynamical states of the cation.

Conflicts of interest
There are no conicts to declare.