# Characterization and Electrical Properties of [C6H9N2]2CuCl4 Compound

Authors: M. Hamdi; A. Oueslati; I. Chaabane; F. Hlel
Journal: ISRN Condensed Matter Physics
 (2012)

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## Abstract

We report measurements of X-ray powder diffraction, vibrational study, the differential scanning calorimetry (DSC), and the electric properties of a made-up [C6H9N2]2CuCl4 sample. The alternative current (ac) conductivity of the compound [C6H9N2]2CuCl4 has been measured in the temperature range 356–398 K and the frequency range 209 Hz–5 MHz. The Cole-Cole (the imaginer part (Z′′) versus real part (Z′) of impedance complex) plots are well fitted to an equivalent circuit model which consists of a parallel combination of a bulk resistance (R) and constant phase elements (CPE). The single semicircle indicates only one primary mechanism for the electrical conduction within [C6H9N2]2CuCl4. The variation of the value of these elements with temperatures confirmed the result detected by DSC and dielectric measurements. Thus the conduction in the material is probably due to a hopping or a small polaron tunneling process.


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## Body

## 1. Introduction

Organic-inorganic hybrid compounds can be designed to utilize synergistic interactions between the dissimilar components, which can yield new properties and/or an enhanced performance. Indeed, synergy will be critical in achieving targeted physical properties (e.g., electronic, optical and transport properties). Thus, organic-inorganic hybrid materials combine the advantageous properties characteristic of inorganic solids (e.g., high carrier mobilities, thermal stability) with those of organic molecules (e.g., ease of processing, high fluorescence efficiency, and large polarizability) [1–11]. A novel group of crystals, containing heteroaromatic cations like, pyridinium, substituted pyridinium, and imidazolium ones, have been recently synthesized and characterized [11–13]. Since aromatic heterocyclic cations are bestowed a significant electric dipole moment; thus some halogenoantimonates(III) and halogenobismuthates(III) containing these cations form strongly polar structures. Inorganic component can introduce some special structural units, such as distorted tetrahedron and octahedron. In an attempt to study the electric behavior in this class of compounds we have successfully synthesized a compound of formula bis(2-amino-4-methylpyridinium) tetrachloridocuprate(II) ([C6H9N2]2[CuCl4]). At room temperature, the synthesized compound crystallizes in the monoclinic system (C2/c space group) with Z=4 and the following unit cell dimensions: a=11.313 (3) Å, b=12.272 (3) Å, c=14.264 (4) Å, and β=113.201 (17)° [11]. The crystal structure contains chains of cations C6H9N2+ alternating with stacks of tetrahedra anions of tetrachloridocuprate CuCl42- (Figure 1(a)). Both N–H⋯Cl and π-π stacking interactions cause the formation of a three-dimensional supramolecular architecture.(i)
The bonding between inorganic and organic layer is established by four different hydrogen bonds ([N1–H1A⋯(Cl1,Cl2i), N2–H2A⋯Cl1, and N2–H2B⋯Cl2ii). The N⋯Cl distances vary between 3.294 (6) and 3.359 (6) Å. These interactions and the symmetrically related ones connect the anion to four surrounding cations (Figure 1(b)).(ii)
The cations interact via offset face-to-face,π-π stacking interactions leading to chains along the crystallographic c axis (Figure 1(c)) [11].Figure 1
(a) Crystal packing diagram showing alternating stacks of anions and chains of cations. (b) The structure of the title compound, viewed downc. N–H⋯Cl–Cu intermolecular interactions are shown as dashed lines. (c) Cationic chains along the crystallographic c axis, assembled via offset face-to-face (π-π stacking; double broken lines) motifs.In the present paper we report the synthesis, X-ray powder diffraction patterns, DSC, infrared, Raman, and impedance spectroscopy characterizations of the [C6H9N2]2CuCl4 compound.


## 2. Experimental

[C6H9N2]2CuCl4 sample was prepared by mixing CuCl2 (purity 98%; FLUKA), dissolved in hydrochloric acid solution (1 M), and the organic compound bis(2-amino-4-methylpyridinium) (purity 99%; FLUKA), in molar ratio 1 : 2. After six days, crystalline samples were obtained by slow evaporation at room temperature.Schematically the reaction proposed in order to justify the obtaining [C6H9N2]2CuCl4 sample is shown in the following equation:
(1)2·[C6H8N2]+CuCl2→HCl(1M)[C6H8N2]2CuCl4.
Powder X-ray diffraction was carried out initially to confirm the presence of the [C6H9N2]2CuCl4 compound. A Siemens D500 was employed, using CuKα radiation. A scanning rate of 0.028° s−1 was employed.Differential scanning calorimetry analysis was performed using a DSC NETZSCH 204 between 220 and 475 K at the heating rate of 5 K/min.The infrared spectrum was recorded in the 400–4000 cm−1 range with a JASCO FT-IR 420 1000 spectrometer using samples pressed in spectroscopically pure KBr pellets.The Raman spectrum of [C6H9N2]2CuCl4 sample is recorded on a Kaiser Optical System spectrometer model-Hololab 5000R in the region 80–2000 cm−1 at room temperature.The pellets of [C6H9N2]2CuCl4 sample were prepared (diameter 8 mm; thickness 0.6 mm) by compressing the powder in a die using a hydraulic press at a pressure of 3000 kg/cm2. The samples of the appropriate shape were sandwiched between two silver electrodes of the configuration Ag/electrolyte/Ag. The ac impedance data, |Z|, and phase angle were obtained in the frequency range 209 Hz–5 MHz using TEGAM 3550 impedance analyzer over the temperature range 356–398 K.


## 3. Results and Discussion

### 3.1. X-Ray Powder Diffraction Patterns

The room temperature X-Ray diffraction pattern of [C6H9N2]2CuCl4 is shown in Figure 2. Lattice parameters were calculated with reference to the single-crystal X-ray study of bis(2-amino-4-methylpyridinium) tetrachloridocuprate(II) and using a computer program package Celref 2 based on the least square refinement method. The refined, in the monoclinic system (C2/c space group), of observed interplanar spacing d-values from the diffractograms show that refined lattice parameters are a=11.26 (2) Å, b=12.22 (2) Å, c=14.25 (4) Å, and β=113.47 (3)°. From these, it is found that [C6H9N2]2CuCl4 is in a good agreement with the literature values [11].Figure 2
X-ray diffractogram of [C6H9N2]2CuCl4 compound.


### 3.2. Infrared and Raman Vibrational Study

Figures3(a) and 3(b) show infrared (IR) and Raman spectra, respectively, of the reported compound at room temperature. A detailed assignment of all the bands is difficult, but we can attribute some of them by comparison with similar compounds [12–15]. The assignments are listed in Table 1.Table 1
Infrared and Raman spectral data (cm−1) and band assignments for [C6H9N2]2[CuCl4] sample.
IR wavenumbers(cm−1)
Raman wavenumbers(cm−1)
Assignments
81
ν
2[CuCl4]2−
135
ν
4 [CuCl4]2−
180
223
ν
3[CuCl4]2−
279
428
430
τ C=C
512
N=C–N
572
565
δ NH
590
718
Torsion of the cycle
762
840
860
ρ CH
940
962
961
984
989
1036
C–C
1180
1179
δ CH3
1224
1224
ν C–N
1300
1297
δ (CH) + δ (NH) and ν (CN)
1436
1416
1482
1484
ν (C–C), δ (CH) and δ (NH)
1528
1624
ν C=C
1658
2361
ν CH (−)
2956
ν CH
3010
ν CH (+)
3094
3166
ν
as NH (−)
3188
ν
as NH2
3226
3296
ν
s NH2
3366
3732
ν
as NH (+)
ν
2: bending, ν3: asymmetric stretching, ν4: asymmetric bending, ν: stretching, ρ: rocking, δ: deformation, τ: torsion, (−): out of plane, (+): in plane.(a) Infrared spectrum of [C6H9N2]2CuCl4, (b) Raman spectrum of [C6H9N2]2CuCl4 compound.
(a)
(b)The principal bands are assigned to the internal modes of organic cation. The C=C bands exhibit torsion vibration at 425 cm−1 in IR and 430 cm−1 in Raman the stretching vibration appears at 1624 and 1658 cm−1 in IR. The bands observed at 762, 940, 961, 989 and 840, 860, 962, and 984 cm−1 in Raman and IR, respectively, are attributed to CH wagging modes. The CH stretching vibrations are observed at 2362, 2956, and 3010 cm−1 in IR. The bands observed at 3094 and 3166 cm−1 in IR are associated to the asymmetric NH stretching out of plane those observed at 3366 and 3732 cm−1 in IR are ascribed to asymmetric NH stretching in plane.A freeCuCl42- ion under Td symmetry has four fundamental vibrations the symmetric stretching mode ν1, the bending mode ν2 observed at 77 cm−1. The average frequencies observed at 267, 248 and 136, 118 cm−1 are ascribed to the asymmetric stretching mode ν3 and asymmetric bending mode ν4, respectively. All the modes are Raman active, whereas only ν3 and ν4 are active in the IR [16]. Meanwhile, the vibrations of the CuCl42- in this structure are shown in Raman spectra. The ν2 mode appears as one strong band at 81 cm−1. The ν3 mode appears as one strong band at 279 cm−1 and one shoulder at 223 cm−1. The ν4 mode is observed as one strong band at 180 and one shoulder at 135 cm−1. The higher frequency value obtained for the ν2,ν3, and ν4 modes than those in a free CuCl42- ion confirms the distortion of CuCl4 tetrahedra as is evident from different Cu–Cl bond lengths determined by the X-ray diffraction study [11]. The presence of hydrogen bonds and Jahn-Teller effect may be the reason for the observed distortion in the CuCl4 tetrahedra in this structure [11].The infrared and Raman studies confirm the presence of the organic group C6H9N2 and the tetrahedral anion CuCl42-.


### 3.3. D.S.C Analysis

Results of differential scanning calorimetry measurements, recorded in the temperature range 220–475 K, are presented in the thermogram shown in Figure4. It shows the presence of an endothermic peak located at 436.71 K corresponding to the fusion of the compound [C6H9N2]2CuCl4.Figure 4
Differential scanning calorimetry of [C6H9N2]2CuCl4 sample.


### 3.4. Electrical Properties

Complex impedance spectroscopies have been used to study electrical properties of the [C6H9N2]2CuCl4 compound. It is useful for analyzing the electrical processes occurring in a compound on the application of a small ac signal as input perturbation. In our case the resultant response (when plotted in a complex plane shown in Figures 5(a) and 5(b)) appears in the form of depressed semicircles. The observed depressed semicircles can usually be reproduced with an equivalent circuit formed by parallel combination of resistance polarization (Rp) and constant phase elements (CPEs) [2]. Usually ZCPE (ZCPE=1/A0(jω)α) is considered to be a dispersive capacitance. α is the measure of the capacitive nature of the element: if α=1 the element is an ideal capacitor, if α=0 it behaves as a frequency independent ohmic resistor, whereas if α=-1 it behaves as an inductance.(a), (b) Impedance spectra of [C6H9N2]2CuCl4 sample at different temperature ranges.
(a)
(b)The impedance of the equivalent circuit shown in Figure6 can be expressed as follows: Z=Z′-jZ′′ where
(2)Z′=Rp(1+RpA0ωαcos(απ/2))(1+RpA0ωαcos(απ/2))2+(RpA0ωαsin(απ/2))2,(3)-Z′′=Rp2A0ωαsin(απ/2)(1+RpA0ωαcos(απ/2))2+(RpA0ωαsin(απ/2))2.
The curves of Z′ and -Z′′ versus frequency at several temperatures are fitted by (2) and (3), respectively. In Figures 7(a) and 7(b) are represented Z′ and -Z′′ versus frequency at 381 K, respectively, together with fits to the equivalent circuit presented in Figure 6. All fitted curves at each temperature show the good conformity of calculated lines with the experimental data indicating that the suggested equivalent circuit describes the crystal-electrolyte interface reasonably well.Figure 6
Equivalent circuit model of [C6H9N2]2CuCl4 sample.(a), (b) Experimental plot fitted with the corresponding electrical equivalent model ofZ′ and Z′′, respectively, with frequency (T=381 K). circles and line represent the experimental and fitted data, respectively.
(a)
(b)The resistanceRp, the capacitance A0, and α have been simulated using a mean square method which consists to minimize the difference between the experimental and calculate data. The values of the equivalent circuit elements have been listed in Table 2.Table 2
Equivalent circuit parameters obtained at some temperatures.
T (K)
R
p (106Ω)
A
0 (10−12 F)
α
356
100.37
50.584
0.816
358
103.36
51.548
0.812
362
68.36
50.615
0.819
366
41.46
61.505
0.806
369
27.17
72.764
0.798
373
14.97
94.271
0.783
375
10.18
114.14
0.773
379
7.06
132.9
0.765
381
5.24
142.07
0.764
388
3.19
173.71
0.751
398
1.74
234.86
0.729The temperature dependences of the fitted parametersα  (0.72<α<0.81) show that the constant phase elements (CPEs) represent a leaking (nonideal) capacitor as it contains both imaginary and real parts and constitute energy dissipation because of the presence of the impedance real part.The capacitance values (A0) of the equivalent circuit element are critical to the identification of the grain boundary and grain interior contribution. It has already been established in the literature that the dispersion in the boundaries and in the grain bulk interior has a capacitance value in the range of nF and pF, respectively, [17–20]. In our case the capacitance values (A0) vary between 50.584 pF and 234.86 pF in the temperature range 356 K–398 K. This implies that the single semicircular response is from grain interiors, which is expected from the sample where no grain boundaries are involved.Knowing the bulk resistance, obtained from equivalent circuit parameter values, and the dimensions of the sample, the conductivity (σdc) has been calculated at each temperature by means of the relation:
(4)σdc=eRpS,
where e/S represents the sample geometrical ratio. The temperature dependence of the conductivity is represented in the form of log(σdcT) versus 1000/T plot in Figure 8. An Arrhenius type behaviour, σdcT=Bexp(-E/kβT), is shown in the temperature range 355K<T<400 K, where σdc is the dc conductivity at temperature T, B the preexponential factor, Kβ the Boltzmann’s constant, and E is the thermal activation energy for the ion migration. The activation energies obtained from the slopes of [C6H9N2]2CuCl4 sample are Ea = 1.347 eV. The variation of electrical conductivity versus the angular frequency of [C6H9N2]2CuCl4 sample at various temperatures is plotted in Figure 9. The electric response of the low conductivity materials is usually characterized by the well-known universal dynamic response [21]. Consider
(5)σac=σdc+Aωn,
where σdc is the dc conductivity in the particular range of temperature, A is a temperature dependent parameter, and n is the temperature-dependent exponent in the range of 0≤n≤1 [21–23]. The exponent n represents the degree of interaction between mobile ions with the lattices around them and the prefactor exponent A determines the strength of polarizability.Figure 8
Temperature dependence ofln(σ·T).Figure 9
Frequency dependence of the ac conductivity at various temperatures.In order to explain the behaviour ofσ with both frequency and temperature, different theoretical models have been proposed to correlate the conduction mechanism of AC conductivity with n(T) behaviour. According to quantum mechanical tunneling model [22, 24, 25], the exponent n is temperature independent. The large overlapping polaron model [25] predicted that n decreases with increasing temperature up to a certain temperature degree, after which, it begins to increase with further rise in temperature. The small polaron tunneling model and the classical hopping model over a barrier separating two sites [26] predicted that n decreases with increasing the temperature.The temperature dependence on the fitted frequency exponentn is shown in Figure 10. The n values decreases with increasing the temperature. Comparing our results of n(T) shown in Figure 10 with the abovementioned models, it can be concluded that the classical hopping or small polaron tunneling model is the most probable conduction mechanism for the [C6H9N2]2CuCl4 crystal.Figure 10
Temperature dependence of the frequency exponentn.


## 3.1. X-Ray Powder Diffraction Patterns

The room temperature X-Ray diffraction pattern of [C6H9N2]2CuCl4 is shown in Figure 2. Lattice parameters were calculated with reference to the single-crystal X-ray study of bis(2-amino-4-methylpyridinium) tetrachloridocuprate(II) and using a computer program package Celref 2 based on the least square refinement method. The refined, in the monoclinic system (C2/c space group), of observed interplanar spacing d-values from the diffractograms show that refined lattice parameters are a=11.26 (2) Å, b=12.22 (2) Å, c=14.25 (4) Å, and β=113.47 (3)°. From these, it is found that [C6H9N2]2CuCl4 is in a good agreement with the literature values [11].Figure 2
X-ray diffractogram of [C6H9N2]2CuCl4 compound.


## 3.2. Infrared and Raman Vibrational Study

Figures3(a) and 3(b) show infrared (IR) and Raman spectra, respectively, of the reported compound at room temperature. A detailed assignment of all the bands is difficult, but we can attribute some of them by comparison with similar compounds [12–15]. The assignments are listed in Table 1.Table 1
Infrared and Raman spectral data (cm−1) and band assignments for [C6H9N2]2[CuCl4] sample.
IR wavenumbers(cm−1)
Raman wavenumbers(cm−1)
Assignments
81
ν
2[CuCl4]2−
135
ν
4 [CuCl4]2−
180
223
ν
3[CuCl4]2−
279
428
430
τ C=C
512
N=C–N
572
565
δ NH
590
718
Torsion of the cycle
762
840
860
ρ CH
940
962
961
984
989
1036
C–C
1180
1179
δ CH3
1224
1224
ν C–N
1300
1297
δ (CH) + δ (NH) and ν (CN)
1436
1416
1482
1484
ν (C–C), δ (CH) and δ (NH)
1528
1624
ν C=C
1658
2361
ν CH (−)
2956
ν CH
3010
ν CH (+)
3094
3166
ν
as NH (−)
3188
ν
as NH2
3226
3296
ν
s NH2
3366
3732
ν
as NH (+)
ν
2: bending, ν3: asymmetric stretching, ν4: asymmetric bending, ν: stretching, ρ: rocking, δ: deformation, τ: torsion, (−): out of plane, (+): in plane.(a) Infrared spectrum of [C6H9N2]2CuCl4, (b) Raman spectrum of [C6H9N2]2CuCl4 compound.
(a)
(b)The principal bands are assigned to the internal modes of organic cation. The C=C bands exhibit torsion vibration at 425 cm−1 in IR and 430 cm−1 in Raman the stretching vibration appears at 1624 and 1658 cm−1 in IR. The bands observed at 762, 940, 961, 989 and 840, 860, 962, and 984 cm−1 in Raman and IR, respectively, are attributed to CH wagging modes. The CH stretching vibrations are observed at 2362, 2956, and 3010 cm−1 in IR. The bands observed at 3094 and 3166 cm−1 in IR are associated to the asymmetric NH stretching out of plane those observed at 3366 and 3732 cm−1 in IR are ascribed to asymmetric NH stretching in plane.A freeCuCl42- ion under Td symmetry has four fundamental vibrations the symmetric stretching mode ν1, the bending mode ν2 observed at 77 cm−1. The average frequencies observed at 267, 248 and 136, 118 cm−1 are ascribed to the asymmetric stretching mode ν3 and asymmetric bending mode ν4, respectively. All the modes are Raman active, whereas only ν3 and ν4 are active in the IR [16]. Meanwhile, the vibrations of the CuCl42- in this structure are shown in Raman spectra. The ν2 mode appears as one strong band at 81 cm−1. The ν3 mode appears as one strong band at 279 cm−1 and one shoulder at 223 cm−1. The ν4 mode is observed as one strong band at 180 and one shoulder at 135 cm−1. The higher frequency value obtained for the ν2,ν3, and ν4 modes than those in a free CuCl42- ion confirms the distortion of CuCl4 tetrahedra as is evident from different Cu–Cl bond lengths determined by the X-ray diffraction study [11]. The presence of hydrogen bonds and Jahn-Teller effect may be the reason for the observed distortion in the CuCl4 tetrahedra in this structure [11].The infrared and Raman studies confirm the presence of the organic group C6H9N2 and the tetrahedral anion CuCl42-.


## 3.3. D.S.C Analysis

Results of differential scanning calorimetry measurements, recorded in the temperature range 220–475 K, are presented in the thermogram shown in Figure4. It shows the presence of an endothermic peak located at 436.71 K corresponding to the fusion of the compound [C6H9N2]2CuCl4.Figure 4
Differential scanning calorimetry of [C6H9N2]2CuCl4 sample.


## 3.4. Electrical Properties

Complex impedance spectroscopies have been used to study electrical properties of the [C6H9N2]2CuCl4 compound. It is useful for analyzing the electrical processes occurring in a compound on the application of a small ac signal as input perturbation. In our case the resultant response (when plotted in a complex plane shown in Figures 5(a) and 5(b)) appears in the form of depressed semicircles. The observed depressed semicircles can usually be reproduced with an equivalent circuit formed by parallel combination of resistance polarization (Rp) and constant phase elements (CPEs) [2]. Usually ZCPE (ZCPE=1/A0(jω)α) is considered to be a dispersive capacitance. α is the measure of the capacitive nature of the element: if α=1 the element is an ideal capacitor, if α=0 it behaves as a frequency independent ohmic resistor, whereas if α=-1 it behaves as an inductance.(a), (b) Impedance spectra of [C6H9N2]2CuCl4 sample at different temperature ranges.
(a)
(b)The impedance of the equivalent circuit shown in Figure6 can be expressed as follows: Z=Z′-jZ′′ where
(2)Z′=Rp(1+RpA0ωαcos(απ/2))(1+RpA0ωαcos(απ/2))2+(RpA0ωαsin(απ/2))2,(3)-Z′′=Rp2A0ωαsin(απ/2)(1+RpA0ωαcos(απ/2))2+(RpA0ωαsin(απ/2))2.
The curves of Z′ and -Z′′ versus frequency at several temperatures are fitted by (2) and (3), respectively. In Figures 7(a) and 7(b) are represented Z′ and -Z′′ versus frequency at 381 K, respectively, together with fits to the equivalent circuit presented in Figure 6. All fitted curves at each temperature show the good conformity of calculated lines with the experimental data indicating that the suggested equivalent circuit describes the crystal-electrolyte interface reasonably well.Figure 6
Equivalent circuit model of [C6H9N2]2CuCl4 sample.(a), (b) Experimental plot fitted with the corresponding electrical equivalent model ofZ′ and Z′′, respectively, with frequency (T=381 K). circles and line represent the experimental and fitted data, respectively.
(a)
(b)The resistanceRp, the capacitance A0, and α have been simulated using a mean square method which consists to minimize the difference between the experimental and calculate data. The values of the equivalent circuit elements have been listed in Table 2.Table 2
Equivalent circuit parameters obtained at some temperatures.
T (K)
R
p (106Ω)
A
0 (10−12 F)
α
356
100.37
50.584
0.816
358
103.36
51.548
0.812
362
68.36
50.615
0.819
366
41.46
61.505
0.806
369
27.17
72.764
0.798
373
14.97
94.271
0.783
375
10.18
114.14
0.773
379
7.06
132.9
0.765
381
5.24
142.07
0.764
388
3.19
173.71
0.751
398
1.74
234.86
0.729The temperature dependences of the fitted parametersα  (0.72<α<0.81) show that the constant phase elements (CPEs) represent a leaking (nonideal) capacitor as it contains both imaginary and real parts and constitute energy dissipation because of the presence of the impedance real part.The capacitance values (A0) of the equivalent circuit element are critical to the identification of the grain boundary and grain interior contribution. It has already been established in the literature that the dispersion in the boundaries and in the grain bulk interior has a capacitance value in the range of nF and pF, respectively, [17–20]. In our case the capacitance values (A0) vary between 50.584 pF and 234.86 pF in the temperature range 356 K–398 K. This implies that the single semicircular response is from grain interiors, which is expected from the sample where no grain boundaries are involved.Knowing the bulk resistance, obtained from equivalent circuit parameter values, and the dimensions of the sample, the conductivity (σdc) has been calculated at each temperature by means of the relation:
(4)σdc=eRpS,
where e/S represents the sample geometrical ratio. The temperature dependence of the conductivity is represented in the form of log(σdcT) versus 1000/T plot in Figure 8. An Arrhenius type behaviour, σdcT=Bexp(-E/kβT), is shown in the temperature range 355K<T<400 K, where σdc is the dc conductivity at temperature T, B the preexponential factor, Kβ the Boltzmann’s constant, and E is the thermal activation energy for the ion migration. The activation energies obtained from the slopes of [C6H9N2]2CuCl4 sample are Ea = 1.347 eV. The variation of electrical conductivity versus the angular frequency of [C6H9N2]2CuCl4 sample at various temperatures is plotted in Figure 9. The electric response of the low conductivity materials is usually characterized by the well-known universal dynamic response [21]. Consider
(5)σac=σdc+Aωn,
where σdc is the dc conductivity in the particular range of temperature, A is a temperature dependent parameter, and n is the temperature-dependent exponent in the range of 0≤n≤1 [21–23]. The exponent n represents the degree of interaction between mobile ions with the lattices around them and the prefactor exponent A determines the strength of polarizability.Figure 8
Temperature dependence ofln(σ·T).Figure 9
Frequency dependence of the ac conductivity at various temperatures.In order to explain the behaviour ofσ with both frequency and temperature, different theoretical models have been proposed to correlate the conduction mechanism of AC conductivity with n(T) behaviour. According to quantum mechanical tunneling model [22, 24, 25], the exponent n is temperature independent. The large overlapping polaron model [25] predicted that n decreases with increasing temperature up to a certain temperature degree, after which, it begins to increase with further rise in temperature. The small polaron tunneling model and the classical hopping model over a barrier separating two sites [26] predicted that n decreases with increasing the temperature.The temperature dependence on the fitted frequency exponentn is shown in Figure 10. The n values decreases with increasing the temperature. Comparing our results of n(T) shown in Figure 10 with the abovementioned models, it can be concluded that the classical hopping or small polaron tunneling model is the most probable conduction mechanism for the [C6H9N2]2CuCl4 crystal.Figure 10
Temperature dependence of the frequency exponentn.


## 4. Conclusions

The diffraction of X-rays powder shows that the compound [C6H9N2]2CuCl4 crystallizes in the monoclinic system (space group C2/c, Z=4) with the following unit cell dimensions: a=11.26 (2) Å, b=12.22 (2) Å, c=14.25 (4) Å, and β=113.47 (3)°, similar of the X-ray diffraction data collection described by Al-Far and Ali.The differential calorimetric analysis shows the presence of only one endothermic peak located at 436.71 K which corresponds to the fusion of material. The analysis by infrared and Raman spectroscopy made it possible to check the presence of the functional groupings, of the ionic groupings of material.The analysis of the frequency dispersion of the real imaginary components of the complex impedance allowed us to determine an equivalent electrical circuit for the electrochemical cell with [C6H9N2]2CuCl4. The variations of the values of elements of this equivalent circuit with temperature confirmed the result detected by DSC and dielectric measurements. The temperature dependence of conductivity was analyzed using the Arrhenius approach.The AC conductivity is analyzed by Jonscher's law, and suggests that the classical hopping or small polaron tunneling model is the most probable conduction mechanism for the [C6H9N2]2CuCl4 crystal.



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