# Structural Characterization and Infrared and Electrical Properties of the New Inorganic-Organic Hybrid Compound[N(C3H7)4]2[Hg2Cl6]

Authors: A. Oueslati; I. Chaabane; K. Adil; F. Hlel
Journal: Journal of Chemistry
 (2013)

---

## Abstract

New inorganic-organic hybrid [(C3H7)4N]2Hg2Cl6 compound was obtained and characterised by single-crystal X-ray diffraction, infrared, and impedance spectroscopy. The latter crystallizes in the monoclinic system (space group C 2/c, Z=8) with the following unit cell dimensions: a=18.489(1) Å, b=13.0419(6) Å, c=29.162(2) Å, and β=91.686∘(2). Besides, its structure was solved using 84860 independent reflections leading to R=0.038. Electrical properties of the material were studied using impedance spectroscopic technique at different temperatures in the frequency range of 209 Hz to 5 MHz. Detailed analysis of the impedance spectrum suggested that the electrical properties of the material are strongly temperature-dependent. The Nyquist plots clearly showed the presence of bulk and grain boundary effect in the compound.


---

## Body

## 1. Introduction

The contemporary deep interest for inorganic-organic hybrid materials is due to various reasons. An obvious advantage of hybrids is that they favorably combine the properties of the organic materials to that of the inorganic one and thus to exhibit specific properties, such as electronic, optical, thermal, and catalytic [1–4]. Among halometallates (II), chloromercurates (II) have been of special interest for their structural flexibility. In fact the spherical d10 configuration of Hg2+ ion is associated with a flexible coordination environment so that the geometries of these complexes can vary from tetrahedral to octahedral and severe distortions in the ideal polyhedron occur easily, depending on crystal packing and hydrogen bonding, as well as halide dimensions [5–11]. In the last years, the structural and electrical properties of [(C3H7)4N]2Cu2Cl6 and [(C3H7)4N]2Cd2Cl6 compounds have been reported [12, 13]. In spite of attractive properties of mercury(II) compounds in terms of their potential applications in thermometers, manometers, energy efficient fluorescent light bulbs, and mercury batteries (although somehow limited due to mercury’s toxicity), we have successfully synthesized a new compound of formula [(C3H7)4N]2Hg2Cl6.In the present paper we report on the synthesis, the structural, and spectroscopic characterizations of the [(C3H7)4N]2Hg2Cl6 compound.


## 2. Experimental

### 2.1. Preparation of [N(C3H7)4]2Hg2Cl6

The synthesis of [N(C3H7)4]2Hg2Cl6 was performed from precursors [N(C3H7)4]Cl (purity 97%; FLUKA) and HgCl2 (purity 99.5%; FLUKA). The reactions sequence for the synthesis is shown in the following equation:
(1)2[N(C3H7)4]Cl+2HgCl2→(1M)HCl[N(C3H7)4]2Hg2Cl6
The solution was obtained by mixing 0.441 g of [N(C3H7)4]Cl and 0.218 g of HgCl2 in 10 ml of HCl (1 M) aqueous solution. After few days, crystalline samples were obtained by slow evaporation at room temperature.


### 2.2. Crystallographic Studies

Single crystals of [(C3H7)4N]2Hg2Cl6 are obtained by slow evaporation, at room temperature, of an hydrochloric acid solution containing stoichiometric amounts of [N(C3H7)4]Cl (purity 97%; FLUKA) acidified with HCl (1 M) and HgCl2 (purity 99.5%; FLUKA).A single crystal with 0.2 × 0.19 × 0.17 mm3 dimensions was selected by optical examination. The crystal data were collected on a Siemens APEX II four-circles diffractometer using a monochromatic Mo Kα radiation (λ = 0.71073 Å). The absorption corrections were based on multiple and symmetry-equivalent reflections in the data set using the SADABS program [14]. The structure was solved by direct methods and refined in the anisotropic approximation using SHELXS-97 [15] and SHELXL-97 [16]. The main crystal data, the parameters used for intensity data collection, and the reliability factor are gathered in Table 1. The obtained solution permits us to localize the positions of mercury and chlorine atoms. Positions of N and all carbon atoms were located after subsequent Fourier series analysis. The nitrogen H-atoms were successively located in a difference Fourier maps. The other hydrogen atoms were placed in calculated positions. Main geometrical features, bond distances, and angles are reported in Table 2.Table 1
Summary of crystal data, X-ray diffraction intensity measurements, and      refinement parameters for [N(C3H7)4]2Hg2Cl6.
Formula: [(C3H7)4N]2Hg2Cl6
Fw = 986.6 g·mol-1
Color/shape
Colorless/prismatic
Crystal dimensions
0.22× 0.18 × 0.11 mm
Crystal system
Monoclinic
Space group
C 2/c (N° 15)
a
=
18.489
(
1
) Å, b=13.0419(6) Å,
V = 7409.0(7) Å3
c
=
29.162
(
2
)  Å, β =91.686(2)
Z = 8, μ = 8.726 mm−1
Temperature (K)
173(2)
Radiation,λ (Å), monochromator
MoKα, 0.71069, graphite
Scan angle (°)
θ-θ
θ Range (°)
1.4–30
Range ofh, k, l
−26→27, −16→18, −40→40
Reflections collected/unique
42266/10658 (Rint  = 0.047)
Observed reflections [Fo > 2σ(Fo)]
8486
Absorption correction
Multiscan (SADABS)
T
min, Tmax
0.542, 0.823
Structure resolution
Paterson methods: SHELXS-86
Structure refinement with
SHELXL-97
Refinement
F
2 full matrix
Refined parameters
348
Goodness of fit
1.177
FinalR and Rw
0.038, 0.087
FinalR and Rw (for all data)
0.057, 0.097
Largest feature diff. map
1.565, −1.354 e−/Å3
w = 1/[ σ2(Fo)2 + (0.035 P)2 + 0P]
P = [Fo2 + 2Fc2]/3Table 2
Selected bond distances (Å) and bond angles (°) of [N(C3H7)4]2Hg2Cl6 (e.s.d.     are given in parentheses).
Distances  (Å)
Angles  (°)
Hg(1)Cl4
Hg1−ClE1
2.387
(
1
)
ClE1−Hg1−ClE2
133.30
(
6
)
Hg1−ClE2
2.388
(
1
)
ClE1−Hg1−ClL1
102
.
13
(
5
)
Hg1−ClL1
2.638
(
1
)
ClE1−Hg1−ClL2
111.83
(
6
)
Hg1−ClL2
2.662
(
1
)
ClE2−Hg1−ClL1
108.56
(
5
)
ClE2−Hg1−ClL2
103.25
(
4
)
ClL1−Hg1−ClL2
88
.
87
(
4
)
Hg(2)Cl4
Hg2−ClE3
2.393
(
1
)
ClE3 −Hg2−ClE4
131.45
(
6
)
Hg2−ClE4
2.399
(
1
)
ClE3 −Hg2−ClL1
101
.
18
(
5
)
Hg2−ClL1
2.632
(
1
)
ClE3 −Hg2−ClL2
111.18
(
5
)
Hg2−ClL2
2.659
(
1
)
ClE4 −Hg2−ClL1
109.11
(
5
)
ClE4 −Hg2−ClL2
106.44
(
5
)
ClL1−Hg2−ClL2
89
.
07
(
4
)
(C3H7)4N+(1)
N1− C21
1.525
(
5
)
C21−N1−C41
108.2
(
3
)
N1−C41
1.524
(
5
)
C21−N1−C11
108.8
(
3
)
N1−C11
1.527
(
5
)
C41−N1−C11
111.9
(
3
)
N1−C31
1.531
(
6
)
C21−N1−C31
111.6
(
3
)
C11−C12
1.524
(
7
)
C41−N1−C31
108.6
(
3
)
C12−C13
1.528
(
7
)
C11−N1−C31
107.8
(
3
)
C21−C22
1.522
(
7
)
C12−C11−N1
116.4
(
4
)
C22−C23
1.510
(
7
)
C11−C12−C13
108.9
(
4
)
C31−C32
1.520
(
7
)
C22−C21−N1
116.3
(
4
)
C32−C33
1.521
(
7
)
C23 −C22−C21
109.8
(
4
)
C41−C42
1.521
(
6
)
C32−C31−N1
115.6
(
3
)
C42−C43
1.535
(
7
)
C33 −C32−C31
109.0
(
4
)
C42−C41−N1
116.8
(
4
)
C41−C42−C43
108.7
(
4
)
(C3H7)4N+(2)
N2−C81
1.519
(
5
)
C81−N2−C51
111.1
(
3
)
N2−C51
1.522
(
6
)
C81−N2−C61
108.6
(
3
)
N2−C61
1.524
(
6
)
C51−N2−C61
109.9
(
3
)
N2−C71
1.532
(
6
)
C81−N2−C71
108.9
(
3
)
C51−C52
1.534
(
7
)
C51−N2−C71
107.7
(
3
)
C52−C53
1.520
(
7
)
C61−N2−C71
110.8
(
3
)
C61−C62
1.515
(
6
)
N2−C51−C52
116.1
(
4
)
C62−C63
1.524
(
7
)
C53 −C52−C51
110.6
(
4
)
C71−C72
1.512
(
7
)
C62−C61−N2
116.3
(
4
)
C72−C73
1.531
(
7
)
C61−C62−C63
108.5
(
4
)
C81−C82
1.531
(
7
)
C72−C71−N2
116.8
(
4
)
C82−C83
1.532
(
7
)
C71−C72−C73
107.9
(
4
)
N2−C81−C82
115.2
(
4
)
C81−C82−C83
108.7
(
4
)


### 2.3. Infrared Spectroscopies

The infrared spectrum was recorded in the 400–4,000 cm−1 range with a Perkin-Elmer FT-IR 1000 spectrometer using samples pressed in spectroscopically pure KBr pellets. Spectral resolution is better than 4 cm−1.


### 2.4. Impedance Spectroscopy Analysis

The finely grain samples were pressed into pellets of 8 mm diameter and 1.1 mm thickness using a hydraulic press. The pellet discs were coated with Ag paste to ensure good electrical contact. 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 293–375 K.


## 2.1. Preparation of [N(C3H7)4]2Hg2Cl6

The synthesis of [N(C3H7)4]2Hg2Cl6 was performed from precursors [N(C3H7)4]Cl (purity 97%; FLUKA) and HgCl2 (purity 99.5%; FLUKA). The reactions sequence for the synthesis is shown in the following equation:
(1)2[N(C3H7)4]Cl+2HgCl2→(1M)HCl[N(C3H7)4]2Hg2Cl6
The solution was obtained by mixing 0.441 g of [N(C3H7)4]Cl and 0.218 g of HgCl2 in 10 ml of HCl (1 M) aqueous solution. After few days, crystalline samples were obtained by slow evaporation at room temperature.


## 2.2. Crystallographic Studies

Single crystals of [(C3H7)4N]2Hg2Cl6 are obtained by slow evaporation, at room temperature, of an hydrochloric acid solution containing stoichiometric amounts of [N(C3H7)4]Cl (purity 97%; FLUKA) acidified with HCl (1 M) and HgCl2 (purity 99.5%; FLUKA).A single crystal with 0.2 × 0.19 × 0.17 mm3 dimensions was selected by optical examination. The crystal data were collected on a Siemens APEX II four-circles diffractometer using a monochromatic Mo Kα radiation (λ = 0.71073 Å). The absorption corrections were based on multiple and symmetry-equivalent reflections in the data set using the SADABS program [14]. The structure was solved by direct methods and refined in the anisotropic approximation using SHELXS-97 [15] and SHELXL-97 [16]. The main crystal data, the parameters used for intensity data collection, and the reliability factor are gathered in Table 1. The obtained solution permits us to localize the positions of mercury and chlorine atoms. Positions of N and all carbon atoms were located after subsequent Fourier series analysis. The nitrogen H-atoms were successively located in a difference Fourier maps. The other hydrogen atoms were placed in calculated positions. Main geometrical features, bond distances, and angles are reported in Table 2.Table 1
Summary of crystal data, X-ray diffraction intensity measurements, and      refinement parameters for [N(C3H7)4]2Hg2Cl6.
Formula: [(C3H7)4N]2Hg2Cl6
Fw = 986.6 g·mol-1
Color/shape
Colorless/prismatic
Crystal dimensions
0.22× 0.18 × 0.11 mm
Crystal system
Monoclinic
Space group
C 2/c (N° 15)
a
=
18.489
(
1
) Å, b=13.0419(6) Å,
V = 7409.0(7) Å3
c
=
29.162
(
2
)  Å, β =91.686(2)
Z = 8, μ = 8.726 mm−1
Temperature (K)
173(2)
Radiation,λ (Å), monochromator
MoKα, 0.71069, graphite
Scan angle (°)
θ-θ
θ Range (°)
1.4–30
Range ofh, k, l
−26→27, −16→18, −40→40
Reflections collected/unique
42266/10658 (Rint  = 0.047)
Observed reflections [Fo > 2σ(Fo)]
8486
Absorption correction
Multiscan (SADABS)
T
min, Tmax
0.542, 0.823
Structure resolution
Paterson methods: SHELXS-86
Structure refinement with
SHELXL-97
Refinement
F
2 full matrix
Refined parameters
348
Goodness of fit
1.177
FinalR and Rw
0.038, 0.087
FinalR and Rw (for all data)
0.057, 0.097
Largest feature diff. map
1.565, −1.354 e−/Å3
w = 1/[ σ2(Fo)2 + (0.035 P)2 + 0P]
P = [Fo2 + 2Fc2]/3Table 2
Selected bond distances (Å) and bond angles (°) of [N(C3H7)4]2Hg2Cl6 (e.s.d.     are given in parentheses).
Distances  (Å)
Angles  (°)
Hg(1)Cl4
Hg1−ClE1
2.387
(
1
)
ClE1−Hg1−ClE2
133.30
(
6
)
Hg1−ClE2
2.388
(
1
)
ClE1−Hg1−ClL1
102
.
13
(
5
)
Hg1−ClL1
2.638
(
1
)
ClE1−Hg1−ClL2
111.83
(
6
)
Hg1−ClL2
2.662
(
1
)
ClE2−Hg1−ClL1
108.56
(
5
)
ClE2−Hg1−ClL2
103.25
(
4
)
ClL1−Hg1−ClL2
88
.
87
(
4
)
Hg(2)Cl4
Hg2−ClE3
2.393
(
1
)
ClE3 −Hg2−ClE4
131.45
(
6
)
Hg2−ClE4
2.399
(
1
)
ClE3 −Hg2−ClL1
101
.
18
(
5
)
Hg2−ClL1
2.632
(
1
)
ClE3 −Hg2−ClL2
111.18
(
5
)
Hg2−ClL2
2.659
(
1
)
ClE4 −Hg2−ClL1
109.11
(
5
)
ClE4 −Hg2−ClL2
106.44
(
5
)
ClL1−Hg2−ClL2
89
.
07
(
4
)
(C3H7)4N+(1)
N1− C21
1.525
(
5
)
C21−N1−C41
108.2
(
3
)
N1−C41
1.524
(
5
)
C21−N1−C11
108.8
(
3
)
N1−C11
1.527
(
5
)
C41−N1−C11
111.9
(
3
)
N1−C31
1.531
(
6
)
C21−N1−C31
111.6
(
3
)
C11−C12
1.524
(
7
)
C41−N1−C31
108.6
(
3
)
C12−C13
1.528
(
7
)
C11−N1−C31
107.8
(
3
)
C21−C22
1.522
(
7
)
C12−C11−N1
116.4
(
4
)
C22−C23
1.510
(
7
)
C11−C12−C13
108.9
(
4
)
C31−C32
1.520
(
7
)
C22−C21−N1
116.3
(
4
)
C32−C33
1.521
(
7
)
C23 −C22−C21
109.8
(
4
)
C41−C42
1.521
(
6
)
C32−C31−N1
115.6
(
3
)
C42−C43
1.535
(
7
)
C33 −C32−C31
109.0
(
4
)
C42−C41−N1
116.8
(
4
)
C41−C42−C43
108.7
(
4
)
(C3H7)4N+(2)
N2−C81
1.519
(
5
)
C81−N2−C51
111.1
(
3
)
N2−C51
1.522
(
6
)
C81−N2−C61
108.6
(
3
)
N2−C61
1.524
(
6
)
C51−N2−C61
109.9
(
3
)
N2−C71
1.532
(
6
)
C81−N2−C71
108.9
(
3
)
C51−C52
1.534
(
7
)
C51−N2−C71
107.7
(
3
)
C52−C53
1.520
(
7
)
C61−N2−C71
110.8
(
3
)
C61−C62
1.515
(
6
)
N2−C51−C52
116.1
(
4
)
C62−C63
1.524
(
7
)
C53 −C52−C51
110.6
(
4
)
C71−C72
1.512
(
7
)
C62−C61−N2
116.3
(
4
)
C72−C73
1.531
(
7
)
C61−C62−C63
108.5
(
4
)
C81−C82
1.531
(
7
)
C72−C71−N2
116.8
(
4
)
C82−C83
1.532
(
7
)
C71−C72−C73
107.9
(
4
)
N2−C81−C82
115.2
(
4
)
C81−C82−C83
108.7
(
4
)


## 2.3. Infrared Spectroscopies

The infrared spectrum was recorded in the 400–4,000 cm−1 range with a Perkin-Elmer FT-IR 1000 spectrometer using samples pressed in spectroscopically pure KBr pellets. Spectral resolution is better than 4 cm−1.


## 2.4. Impedance Spectroscopy Analysis

The finely grain samples were pressed into pellets of 8 mm diameter and 1.1 mm thickness using a hydraulic press. The pellet discs were coated with Ag paste to ensure good electrical contact. 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 293–375 K.


## 3. Results and Discussions

### 3.1. Crystal Structure Description

The representations of asymmetric unit showing the ellipsoid thermal mean square displacements are represented in Figure1. The structural arrangement of [N(C3H7)4]2Hg2Cl6 is layered organization of organic-inorganic sheets staked along  [010] direction, Figure 2. Each layer is translated via its neighbor by  ((a+c)/4). The organic-inorganic layer can be described as an alternation of inorganic chain and organic double chain parallel to the [1¯01] direction. The organic double chain is made up of two crystallographic different [N(C3H7)4]+ cation, Figure 3. Unlike the reported structure, atomic arrangement of similar compound, [N(C3H7)4]2Cu2Cl6 [17] and [N(C3H7)4]2Cd2Cl6 [13], can be described as a sequence of alternating organic-inorganic layers. In the organic layer, N(C3H7)4 groups orient their aliphatic chains parallel to organic sheets. For [N(C3H7)4]2Hg2Cl6 structure, the alkylammonium cation shows a tetrahedral environment. However, each (C3H7)4 fragment develops along the N–C direction of the NC4 tetrahedra. Consequently, each two fragments made a “V” shape and were observed in the same plane. Plans contain all (C3H7)4 are perpendicular. Two (C3H7)4 chains are observed in the plane of the organic-inorganic layer. The other fragments, localized in the plan perpendicular to layer, are oriented in both sides of the inorganic chain. Both cations have C1 point group symmetry. C–C–C, C–N–C and N–C–C angles and C–C and C–N distances, Table 2, are commonly observed [17].Figure 1
Representation of the ellipsoid of thermal mean square displacements of nonhydrogen atoms at 50% of the asymmetric unit.Figure 2
[
101
]  view showing the organic-inorganic layers staked along b direction; Hg2Cl6 schematized by grey tetrahedra, grate empty, and small and full circles represent nitrogen, hydrogen, and carbon atoms, respectively.Figure 3
View of an organic-inorganic layer of [N(C3H7)4]2Hg2Cl6.The inorganic chain is made up of one Hg2Cl6 dimers. The anion is built up by two independent HgCl4 tetrahedra and shares one bridging chlorine atoms (ClL1 and ClL2) as shown in Figure 1. The Hg2Cl6 dimers can be described as two strongly distorted HgCl4 tetrahedra. The Hg2Cl6 tetrahedron presents a C1 punctual symmetry. The M2X6 groups are commonly observed in this family. Two types of ligands are usually mentioned, XE (external) and XL (linkage). Moreover, bibliographic investigations show that M–X distances and X–M–X angles verify (M–XL > M–XE) (I) and (XL–M–XE and XE–M–XE are generally bigger than XL–M–XL) (II) [18, 19]. The geometry of Hg2Cl6 dimers verifies the reported relations, Table 2. The Hg2Cl62-  anion, ClL–Hg–ClL–Hg, is pseudosquare. These results are in agreement with the above comparison (I and II).


### 3.2. Infrared Spectra

The infrared spectrum of the [N(C3H7)4]2Hg2Cl6 compound at room temperature is shown in Figure 4. A detailed assignment of most important bands is realized by comparison with similar compounds [20–27]. The wavenumbers and proposed band assignments are listed in Table 3.Table 3
Observed IR frequencies (in cm−1) for [N(C3H7)4]2Hg2Cl6 at room temperature.
IR wavenumbers(cm−1)
Assignment
516
609
755
ν
3(NC4)
851
ρ
r(CH2)
874
ρ
r(CH3) + ρr (CH2)
920
ρ
r(CH2)
968
ν
1(NC4)
986
ν
as(C–C)
1038
ν
s(C–C–N)
1107
1138
ν
s(C–C–C–N)
1173
1274
τ(CH2)
1328
ω(CH2)
1357
δ
s(CH3)
1392
1458
δ
as(CH3)
1471
2413
2734
2878
ν
s(CH2)
2940
ν
as(CH2)
2972
ν
as(CH3)
3701Figure 4
Infrared spectrum of the [N(C3H7)4]2Hg2Cl6 compound at room temperature.The principal bands are assigned to the internal modes of the propyl group: strong absorption band appears near 2972 cm−1 which was assigned to the asymmetric methyl stretching mode νas(CH3). Two bands are observed at 2940 and 2878 cm−1, which were assigned to the νas(CH2) and νs(CH2) stretching modes, respectively. A strong absorption band appears near 1458 cm−1 which was assigned to the asymmetric methyl deformation mode δas(CH3). Another band, assigned to the symmetric methyl δs(CH3) deformation modes, was observed near 1357 cm−1. The splitting (C–C–C–N) bending mode at 1138 cm−1 may correspond to different conformers of the organic chains. The bands observed around 968 cm−1 were assigned to ν1(NC4) stretching modes. A weak band which appeared at 874 cm−1 is related to the ρr(CH3) +ρr(CH2) rocking vibration mode, while the deformation mode ν3(NC4) appears below 755 cm−1.


### 3.3. Electrical Properties

#### 3.3.1. Impedance Studies

Impedance spectroscopy is a useful method to resolve the contributions of various processes such as bulk, grain boundary, and electrode effect in the specified frequency domain. In addition, the resistance and the capacitance associated with the solids could be estimated using impedance spectroscopy.Figure5 shows the plot of (-Z′′) versus  Z′  taken over the frequency range (209 Hz to 5 MHz) at different temperatures (293 K ≤ T ≤ 375 K). The inset in Figure 5 shows the plot of (-Z′′) versus  Z′  at 338 K.Figure 5
Impedance spectra of [(C3H7)4N]2Hg2Cl6sample at different temperature. The inset shows the plot of (-Z′′) versus  Z′ at 338 K.Two arcs are obtained which may be ascribed to the circuit shown in Figure6 where Rgb   and  CPEgb, are respectively, the resistance and the constant phase elements arising out from the grain boundaries response of the sample showed by the second arc observed at low frequency, while Rb  and  CPEb  are, respectively, the resistance and the constant phase elements due to the bulk response of the compound showed by the first arc observed at high frequency [28–30].Figure 6
Equivalent circuit model of the [(C3H7)4N]2Hg2Cl6 compound.The impedance of CPE isZCPE=1/Q(jω)α. Usually ZCPE 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. (Note that there are known cases when ZCPE cannot be treated this way; e.g., the Warburg impedance, which is connected with diffusion, is a CPE element with α=0.5.)The real and the imaginary components of the whole impedance of this circuit were calculated according to the following expressions:(2)Z′=Rb2Qbωαbcos(αbπ/2)+Rb(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbcos(αgbπ/2)+Rgb(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQωαgbsin(αgbπ/2))2(3)-Z′′=Rb2Qbωαbsin(αbπ/2)(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbsin(αgbπ/2)(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQgbωαgbsin(αgbπ/2))2The curves ofZ′ and -Z′′versus frequency at several temperatures are fitted by (2) and (3), respectively. Figures 7 and 8 represent Z′ and -Z′′  versus frequency at several temperatures together with fits to the equivalent circuit represented 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.Frequency dependence of real part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)Frequency dependence of imaginary part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)The temperature dependences of the fitted parametersRb, Rgb, Qb, Qgb, αb, and αgb are given in Table 4. As temperature decreases, the grain boundaries resistance Rgbincreases with the arc increasing. The bulk resistance Rb increases as temperature decreases as is expected for an activated conduction mechanism that is reflected as an increase in the radius of the arc as temperature is lowered.Table 4
Fitting parameter obtained from impedance spectroscopy at different temperature ranges.
T(K)
R
gb (MΩ)
Q
gb (10−9 F)
α
gb
R
b (MΩ)
Q
b(10−12 F)
α
b
323
5.12
1.57
0.745
2.64
12.2
0.77
326
5.10
1.42
0.759
2.24
21.8
0.78
328
4.82
1.47
0.761
1.87
28.0
0.78
331
4.26
1.53
0.764
1.47
34.2
0.82
333
3.56
2.07
0.751
0.853
34.7
0.83
338
3.09
2.77
0.739
0.689
38.5
0.87
343
2.40
3.74
0.725
0.531
61.9
0.89
348
1.98
4.98
0.705
0.407
67.8
0.91
353
1.44
8.86
0.665
0.255
88.7
0.92
358
1.22
11.8
0.647
0.221
89.2
0.95
363
0.859
18.8
0.626
0.237
1.05
0.97
368
0.588
22.7
0.628
0.254
1.13
0.97The variation of fitted parametersαb versus temperature (0.77<α<0.97) shows that the constant phase elements (CPE) represents a leaking (non ideal) capacitor as it contains both imaginary and real parts and constitutes energy dissipation because of the presence of the impedance real part.The capacitance values(Q) 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 literatures that the dispersion in the grain boundaries and in the bulk has a capacitance value in the range of nF and pF, respectively. In our case the capacitance values (Qb) vary between 1.05 pF and 89.2 pF and Qgb vary in the range 1.42 nF–22.7 nF. This implies that the first arc response is due to grain interiors response and the second arc arising out from the grain boundaries response.The temperature dependence of the conductivity obtained from the fits of the first arc observed at high frequency is shown in Figure9. It is noted that the variation of the conductivity with temperature obeys an Arrhenius equation as follows:
(4)σp=ATexp(EbKβT),
where σp  is the conductivity at temperature T,A  the preexponential factor, Kβ the Boltzmann’s constant, and Eb  is the thermal activation energy. The value of the activation energy Eb is about 0.46 eV obtained from the least squares straight line fits.Figure 9
Temperature dependence ofLn(σpT) versus reciprocal temperature for [N(C3H7)4]2Cu2Cl6.


#### 3.3.2. Modulus Studies

The modulus formalisma is particularly suitable to extract phenomena such as electrode polarization and conductivity relaxation times [31, 32].Consider the following:(5)M*=1ε*=jωC0Z*(ω)=M′(ω)+jM′′(ω).The dependence of electric modulus on frequency can be written also as [33]:
(6)M=Ms[1-∫0∞e-jωt(-dφ(t)dt)dt]=Ms[1-φ(ω)],
where φ(t) gives the time evolution of the electric field with in the dielectric.Figure10 shows the variation of M′ as a function of frequency at various temperatures. At lower frequencies, M′ tends to be very small, confirming that the electrode effects make a negligible contribution and hence may be ignored when the data are analyzed in modulus formalism. M′ attains a maximum below 107 Hz and decrease above for all temperatures. The decreases of M′  above 107 Hz may be interpreted as the accumulation of charges at the interface between the sample and the electrode, that is, space charge polarization [34, 35].Figure 10
Variation of real part of electric modulus(M′) with frequency for [(C3H7)4N]2Hg2Cl6 at several temperatures.Figure11 shows the temperature-frequency dependence of imaginary part of electric modulus (M′′). The asymmetric modulus peaks shifts towards higher frequency side indicating correlation between motions of mobile ions charges [36]. The asymmetry in peak broadening shows the spread of relaxation times with different time constant, and hence relaxation is of non-Debye type. The existence of low frequency peaks suggests that the ions can move over long distances whereas high-frequency peaks suggest confinement of ions in their potential well. The peak in the  M′′  plot shifts toward higher frequencies with increase in temperature and also the peak height increases. This reveals that when the frequency is high, the temperature for which the measuring frequency is equal to  fp  is also high.Figure 11
Variation of imaginary part of modulus(M′′) with frequency for [(C3H7)4N]2Hg2Cl6 at different temperatures.The conductivity relaxation frequencyfp   is given by the relation fp=f0exp(Em/(KβT)), where f0 is the characteristic phonon frequency, Em is the activation energy for conductivity relaxation,  Kβ is the Boltzmann’s constant, and T is the temperature. The temperature dependence of the conductivity relaxation frequency is plotted in Figure 12. It is well described by the Arrhenius relation. The activation energy Em  obtained from the modulus spectra is about 0.4 eV.Figure 12
Dependence of Ln(fp) versus reciprocal temperature for [(C3H7)4N]2Hg2Cl6 sample.The activation energies issued from the impedanceEb (0.46 eV) and modulus Em (0.4 eV) spectra are not very different, to suggest that the ion transport in polycrystalline sample is probably due to a hopping mechanism [37].


## 3.1. Crystal Structure Description

The representations of asymmetric unit showing the ellipsoid thermal mean square displacements are represented in Figure1. The structural arrangement of [N(C3H7)4]2Hg2Cl6 is layered organization of organic-inorganic sheets staked along  [010] direction, Figure 2. Each layer is translated via its neighbor by  ((a+c)/4). The organic-inorganic layer can be described as an alternation of inorganic chain and organic double chain parallel to the [1¯01] direction. The organic double chain is made up of two crystallographic different [N(C3H7)4]+ cation, Figure 3. Unlike the reported structure, atomic arrangement of similar compound, [N(C3H7)4]2Cu2Cl6 [17] and [N(C3H7)4]2Cd2Cl6 [13], can be described as a sequence of alternating organic-inorganic layers. In the organic layer, N(C3H7)4 groups orient their aliphatic chains parallel to organic sheets. For [N(C3H7)4]2Hg2Cl6 structure, the alkylammonium cation shows a tetrahedral environment. However, each (C3H7)4 fragment develops along the N–C direction of the NC4 tetrahedra. Consequently, each two fragments made a “V” shape and were observed in the same plane. Plans contain all (C3H7)4 are perpendicular. Two (C3H7)4 chains are observed in the plane of the organic-inorganic layer. The other fragments, localized in the plan perpendicular to layer, are oriented in both sides of the inorganic chain. Both cations have C1 point group symmetry. C–C–C, C–N–C and N–C–C angles and C–C and C–N distances, Table 2, are commonly observed [17].Figure 1
Representation of the ellipsoid of thermal mean square displacements of nonhydrogen atoms at 50% of the asymmetric unit.Figure 2
[
101
]  view showing the organic-inorganic layers staked along b direction; Hg2Cl6 schematized by grey tetrahedra, grate empty, and small and full circles represent nitrogen, hydrogen, and carbon atoms, respectively.Figure 3
View of an organic-inorganic layer of [N(C3H7)4]2Hg2Cl6.The inorganic chain is made up of one Hg2Cl6 dimers. The anion is built up by two independent HgCl4 tetrahedra and shares one bridging chlorine atoms (ClL1 and ClL2) as shown in Figure 1. The Hg2Cl6 dimers can be described as two strongly distorted HgCl4 tetrahedra. The Hg2Cl6 tetrahedron presents a C1 punctual symmetry. The M2X6 groups are commonly observed in this family. Two types of ligands are usually mentioned, XE (external) and XL (linkage). Moreover, bibliographic investigations show that M–X distances and X–M–X angles verify (M–XL > M–XE) (I) and (XL–M–XE and XE–M–XE are generally bigger than XL–M–XL) (II) [18, 19]. The geometry of Hg2Cl6 dimers verifies the reported relations, Table 2. The Hg2Cl62-  anion, ClL–Hg–ClL–Hg, is pseudosquare. These results are in agreement with the above comparison (I and II).


## 3.2. Infrared Spectra

The infrared spectrum of the [N(C3H7)4]2Hg2Cl6 compound at room temperature is shown in Figure 4. A detailed assignment of most important bands is realized by comparison with similar compounds [20–27]. The wavenumbers and proposed band assignments are listed in Table 3.Table 3
Observed IR frequencies (in cm−1) for [N(C3H7)4]2Hg2Cl6 at room temperature.
IR wavenumbers(cm−1)
Assignment
516
609
755
ν
3(NC4)
851
ρ
r(CH2)
874
ρ
r(CH3) + ρr (CH2)
920
ρ
r(CH2)
968
ν
1(NC4)
986
ν
as(C–C)
1038
ν
s(C–C–N)
1107
1138
ν
s(C–C–C–N)
1173
1274
τ(CH2)
1328
ω(CH2)
1357
δ
s(CH3)
1392
1458
δ
as(CH3)
1471
2413
2734
2878
ν
s(CH2)
2940
ν
as(CH2)
2972
ν
as(CH3)
3701Figure 4
Infrared spectrum of the [N(C3H7)4]2Hg2Cl6 compound at room temperature.The principal bands are assigned to the internal modes of the propyl group: strong absorption band appears near 2972 cm−1 which was assigned to the asymmetric methyl stretching mode νas(CH3). Two bands are observed at 2940 and 2878 cm−1, which were assigned to the νas(CH2) and νs(CH2) stretching modes, respectively. A strong absorption band appears near 1458 cm−1 which was assigned to the asymmetric methyl deformation mode δas(CH3). Another band, assigned to the symmetric methyl δs(CH3) deformation modes, was observed near 1357 cm−1. The splitting (C–C–C–N) bending mode at 1138 cm−1 may correspond to different conformers of the organic chains. The bands observed around 968 cm−1 were assigned to ν1(NC4) stretching modes. A weak band which appeared at 874 cm−1 is related to the ρr(CH3) +ρr(CH2) rocking vibration mode, while the deformation mode ν3(NC4) appears below 755 cm−1.


## 3.3. Electrical Properties

### 3.3.1. Impedance Studies

Impedance spectroscopy is a useful method to resolve the contributions of various processes such as bulk, grain boundary, and electrode effect in the specified frequency domain. In addition, the resistance and the capacitance associated with the solids could be estimated using impedance spectroscopy.Figure5 shows the plot of (-Z′′) versus  Z′  taken over the frequency range (209 Hz to 5 MHz) at different temperatures (293 K ≤ T ≤ 375 K). The inset in Figure 5 shows the plot of (-Z′′) versus  Z′  at 338 K.Figure 5
Impedance spectra of [(C3H7)4N]2Hg2Cl6sample at different temperature. The inset shows the plot of (-Z′′) versus  Z′ at 338 K.Two arcs are obtained which may be ascribed to the circuit shown in Figure6 where Rgb   and  CPEgb, are respectively, the resistance and the constant phase elements arising out from the grain boundaries response of the sample showed by the second arc observed at low frequency, while Rb  and  CPEb  are, respectively, the resistance and the constant phase elements due to the bulk response of the compound showed by the first arc observed at high frequency [28–30].Figure 6
Equivalent circuit model of the [(C3H7)4N]2Hg2Cl6 compound.The impedance of CPE isZCPE=1/Q(jω)α. Usually ZCPE 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. (Note that there are known cases when ZCPE cannot be treated this way; e.g., the Warburg impedance, which is connected with diffusion, is a CPE element with α=0.5.)The real and the imaginary components of the whole impedance of this circuit were calculated according to the following expressions:(2)Z′=Rb2Qbωαbcos(αbπ/2)+Rb(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbcos(αgbπ/2)+Rgb(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQωαgbsin(αgbπ/2))2(3)-Z′′=Rb2Qbωαbsin(αbπ/2)(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbsin(αgbπ/2)(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQgbωαgbsin(αgbπ/2))2The curves ofZ′ and -Z′′versus frequency at several temperatures are fitted by (2) and (3), respectively. Figures 7 and 8 represent Z′ and -Z′′  versus frequency at several temperatures together with fits to the equivalent circuit represented 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.Frequency dependence of real part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)Frequency dependence of imaginary part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)The temperature dependences of the fitted parametersRb, Rgb, Qb, Qgb, αb, and αgb are given in Table 4. As temperature decreases, the grain boundaries resistance Rgbincreases with the arc increasing. The bulk resistance Rb increases as temperature decreases as is expected for an activated conduction mechanism that is reflected as an increase in the radius of the arc as temperature is lowered.Table 4
Fitting parameter obtained from impedance spectroscopy at different temperature ranges.
T(K)
R
gb (MΩ)
Q
gb (10−9 F)
α
gb
R
b (MΩ)
Q
b(10−12 F)
α
b
323
5.12
1.57
0.745
2.64
12.2
0.77
326
5.10
1.42
0.759
2.24
21.8
0.78
328
4.82
1.47
0.761
1.87
28.0
0.78
331
4.26
1.53
0.764
1.47
34.2
0.82
333
3.56
2.07
0.751
0.853
34.7
0.83
338
3.09
2.77
0.739
0.689
38.5
0.87
343
2.40
3.74
0.725
0.531
61.9
0.89
348
1.98
4.98
0.705
0.407
67.8
0.91
353
1.44
8.86
0.665
0.255
88.7
0.92
358
1.22
11.8
0.647
0.221
89.2
0.95
363
0.859
18.8
0.626
0.237
1.05
0.97
368
0.588
22.7
0.628
0.254
1.13
0.97The variation of fitted parametersαb versus temperature (0.77<α<0.97) shows that the constant phase elements (CPE) represents a leaking (non ideal) capacitor as it contains both imaginary and real parts and constitutes energy dissipation because of the presence of the impedance real part.The capacitance values(Q) 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 literatures that the dispersion in the grain boundaries and in the bulk has a capacitance value in the range of nF and pF, respectively. In our case the capacitance values (Qb) vary between 1.05 pF and 89.2 pF and Qgb vary in the range 1.42 nF–22.7 nF. This implies that the first arc response is due to grain interiors response and the second arc arising out from the grain boundaries response.The temperature dependence of the conductivity obtained from the fits of the first arc observed at high frequency is shown in Figure9. It is noted that the variation of the conductivity with temperature obeys an Arrhenius equation as follows:
(4)σp=ATexp(EbKβT),
where σp  is the conductivity at temperature T,A  the preexponential factor, Kβ the Boltzmann’s constant, and Eb  is the thermal activation energy. The value of the activation energy Eb is about 0.46 eV obtained from the least squares straight line fits.Figure 9
Temperature dependence ofLn(σpT) versus reciprocal temperature for [N(C3H7)4]2Cu2Cl6.


### 3.3.2. Modulus Studies

The modulus formalisma is particularly suitable to extract phenomena such as electrode polarization and conductivity relaxation times [31, 32].Consider the following:(5)M*=1ε*=jωC0Z*(ω)=M′(ω)+jM′′(ω).The dependence of electric modulus on frequency can be written also as [33]:
(6)M=Ms[1-∫0∞e-jωt(-dφ(t)dt)dt]=Ms[1-φ(ω)],
where φ(t) gives the time evolution of the electric field with in the dielectric.Figure10 shows the variation of M′ as a function of frequency at various temperatures. At lower frequencies, M′ tends to be very small, confirming that the electrode effects make a negligible contribution and hence may be ignored when the data are analyzed in modulus formalism. M′ attains a maximum below 107 Hz and decrease above for all temperatures. The decreases of M′  above 107 Hz may be interpreted as the accumulation of charges at the interface between the sample and the electrode, that is, space charge polarization [34, 35].Figure 10
Variation of real part of electric modulus(M′) with frequency for [(C3H7)4N]2Hg2Cl6 at several temperatures.Figure11 shows the temperature-frequency dependence of imaginary part of electric modulus (M′′). The asymmetric modulus peaks shifts towards higher frequency side indicating correlation between motions of mobile ions charges [36]. The asymmetry in peak broadening shows the spread of relaxation times with different time constant, and hence relaxation is of non-Debye type. The existence of low frequency peaks suggests that the ions can move over long distances whereas high-frequency peaks suggest confinement of ions in their potential well. The peak in the  M′′  plot shifts toward higher frequencies with increase in temperature and also the peak height increases. This reveals that when the frequency is high, the temperature for which the measuring frequency is equal to  fp  is also high.Figure 11
Variation of imaginary part of modulus(M′′) with frequency for [(C3H7)4N]2Hg2Cl6 at different temperatures.The conductivity relaxation frequencyfp   is given by the relation fp=f0exp(Em/(KβT)), where f0 is the characteristic phonon frequency, Em is the activation energy for conductivity relaxation,  Kβ is the Boltzmann’s constant, and T is the temperature. The temperature dependence of the conductivity relaxation frequency is plotted in Figure 12. It is well described by the Arrhenius relation. The activation energy Em  obtained from the modulus spectra is about 0.4 eV.Figure 12
Dependence of Ln(fp) versus reciprocal temperature for [(C3H7)4N]2Hg2Cl6 sample.The activation energies issued from the impedanceEb (0.46 eV) and modulus Em (0.4 eV) spectra are not very different, to suggest that the ion transport in polycrystalline sample is probably due to a hopping mechanism [37].


## 3.3.1. Impedance Studies

Impedance spectroscopy is a useful method to resolve the contributions of various processes such as bulk, grain boundary, and electrode effect in the specified frequency domain. In addition, the resistance and the capacitance associated with the solids could be estimated using impedance spectroscopy.Figure5 shows the plot of (-Z′′) versus  Z′  taken over the frequency range (209 Hz to 5 MHz) at different temperatures (293 K ≤ T ≤ 375 K). The inset in Figure 5 shows the plot of (-Z′′) versus  Z′  at 338 K.Figure 5
Impedance spectra of [(C3H7)4N]2Hg2Cl6sample at different temperature. The inset shows the plot of (-Z′′) versus  Z′ at 338 K.Two arcs are obtained which may be ascribed to the circuit shown in Figure6 where Rgb   and  CPEgb, are respectively, the resistance and the constant phase elements arising out from the grain boundaries response of the sample showed by the second arc observed at low frequency, while Rb  and  CPEb  are, respectively, the resistance and the constant phase elements due to the bulk response of the compound showed by the first arc observed at high frequency [28–30].Figure 6
Equivalent circuit model of the [(C3H7)4N]2Hg2Cl6 compound.The impedance of CPE isZCPE=1/Q(jω)α. Usually ZCPE 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. (Note that there are known cases when ZCPE cannot be treated this way; e.g., the Warburg impedance, which is connected with diffusion, is a CPE element with α=0.5.)The real and the imaginary components of the whole impedance of this circuit were calculated according to the following expressions:(2)Z′=Rb2Qbωαbcos(αbπ/2)+Rb(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbcos(αgbπ/2)+Rgb(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQωαgbsin(αgbπ/2))2(3)-Z′′=Rb2Qbωαbsin(αbπ/2)(1+RbQbωαbcos(αbπ/2))2+(RbQbωαbsin(αbπ/2))2+Rgb2Qgbωαgbsin(αgbπ/2)(1+RgbQgbωαgbcos(αgbπ/2))2+(RgbQgbωαgbsin(αgbπ/2))2The curves ofZ′ and -Z′′versus frequency at several temperatures are fitted by (2) and (3), respectively. Figures 7 and 8 represent Z′ and -Z′′  versus frequency at several temperatures together with fits to the equivalent circuit represented 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.Frequency dependence of real part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)Frequency dependence of imaginary part of impedance of [(C3H7)4N]2Hg2Cl6 at different temperatures.
(a)
(b)The temperature dependences of the fitted parametersRb, Rgb, Qb, Qgb, αb, and αgb are given in Table 4. As temperature decreases, the grain boundaries resistance Rgbincreases with the arc increasing. The bulk resistance Rb increases as temperature decreases as is expected for an activated conduction mechanism that is reflected as an increase in the radius of the arc as temperature is lowered.Table 4
Fitting parameter obtained from impedance spectroscopy at different temperature ranges.
T(K)
R
gb (MΩ)
Q
gb (10−9 F)
α
gb
R
b (MΩ)
Q
b(10−12 F)
α
b
323
5.12
1.57
0.745
2.64
12.2
0.77
326
5.10
1.42
0.759
2.24
21.8
0.78
328
4.82
1.47
0.761
1.87
28.0
0.78
331
4.26
1.53
0.764
1.47
34.2
0.82
333
3.56
2.07
0.751
0.853
34.7
0.83
338
3.09
2.77
0.739
0.689
38.5
0.87
343
2.40
3.74
0.725
0.531
61.9
0.89
348
1.98
4.98
0.705
0.407
67.8
0.91
353
1.44
8.86
0.665
0.255
88.7
0.92
358
1.22
11.8
0.647
0.221
89.2
0.95
363
0.859
18.8
0.626
0.237
1.05
0.97
368
0.588
22.7
0.628
0.254
1.13
0.97The variation of fitted parametersαb versus temperature (0.77<α<0.97) shows that the constant phase elements (CPE) represents a leaking (non ideal) capacitor as it contains both imaginary and real parts and constitutes energy dissipation because of the presence of the impedance real part.The capacitance values(Q) 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 literatures that the dispersion in the grain boundaries and in the bulk has a capacitance value in the range of nF and pF, respectively. In our case the capacitance values (Qb) vary between 1.05 pF and 89.2 pF and Qgb vary in the range 1.42 nF–22.7 nF. This implies that the first arc response is due to grain interiors response and the second arc arising out from the grain boundaries response.The temperature dependence of the conductivity obtained from the fits of the first arc observed at high frequency is shown in Figure9. It is noted that the variation of the conductivity with temperature obeys an Arrhenius equation as follows:
(4)σp=ATexp(EbKβT),
where σp  is the conductivity at temperature T,A  the preexponential factor, Kβ the Boltzmann’s constant, and Eb  is the thermal activation energy. The value of the activation energy Eb is about 0.46 eV obtained from the least squares straight line fits.Figure 9
Temperature dependence ofLn(σpT) versus reciprocal temperature for [N(C3H7)4]2Cu2Cl6.


## 3.3.2. Modulus Studies

The modulus formalisma is particularly suitable to extract phenomena such as electrode polarization and conductivity relaxation times [31, 32].Consider the following:(5)M*=1ε*=jωC0Z*(ω)=M′(ω)+jM′′(ω).The dependence of electric modulus on frequency can be written also as [33]:
(6)M=Ms[1-∫0∞e-jωt(-dφ(t)dt)dt]=Ms[1-φ(ω)],
where φ(t) gives the time evolution of the electric field with in the dielectric.Figure10 shows the variation of M′ as a function of frequency at various temperatures. At lower frequencies, M′ tends to be very small, confirming that the electrode effects make a negligible contribution and hence may be ignored when the data are analyzed in modulus formalism. M′ attains a maximum below 107 Hz and decrease above for all temperatures. The decreases of M′  above 107 Hz may be interpreted as the accumulation of charges at the interface between the sample and the electrode, that is, space charge polarization [34, 35].Figure 10
Variation of real part of electric modulus(M′) with frequency for [(C3H7)4N]2Hg2Cl6 at several temperatures.Figure11 shows the temperature-frequency dependence of imaginary part of electric modulus (M′′). The asymmetric modulus peaks shifts towards higher frequency side indicating correlation between motions of mobile ions charges [36]. The asymmetry in peak broadening shows the spread of relaxation times with different time constant, and hence relaxation is of non-Debye type. The existence of low frequency peaks suggests that the ions can move over long distances whereas high-frequency peaks suggest confinement of ions in their potential well. The peak in the  M′′  plot shifts toward higher frequencies with increase in temperature and also the peak height increases. This reveals that when the frequency is high, the temperature for which the measuring frequency is equal to  fp  is also high.Figure 11
Variation of imaginary part of modulus(M′′) with frequency for [(C3H7)4N]2Hg2Cl6 at different temperatures.The conductivity relaxation frequencyfp   is given by the relation fp=f0exp(Em/(KβT)), where f0 is the characteristic phonon frequency, Em is the activation energy for conductivity relaxation,  Kβ is the Boltzmann’s constant, and T is the temperature. The temperature dependence of the conductivity relaxation frequency is plotted in Figure 12. It is well described by the Arrhenius relation. The activation energy Em  obtained from the modulus spectra is about 0.4 eV.Figure 12
Dependence of Ln(fp) versus reciprocal temperature for [(C3H7)4N]2Hg2Cl6 sample.The activation energies issued from the impedanceEb (0.46 eV) and modulus Em (0.4 eV) spectra are not very different, to suggest that the ion transport in polycrystalline sample is probably due to a hopping mechanism [37].


## 4. Conclusion

Crystals of a new hybrid material, [(C3H7)4N]2Hg2Cl6, have been prepared by slow evaporation of aqueous solution HCl (1 M), N(C3H7)4,  and HgCl2 at room temperature. The atomic arrangement is layered organization of organic-inorganic sheets staked along b direction. Those layers spreading in this network are interconnected by van Der Waals interaction. 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 [(C3H7)4N]2Hg2Cl6. The temperature dependence of conductivity was analyzed using the Arrhenius approach. Impedance spectra revealed the presence of grain and grain boundary contribution whereas electric modulus spectra showed only bulk (grain) contribution in the electrical properties.The analysis of the temperature variation ofM′′ peak indicates that the observed relaxation process is thermally activated. The near value of activation energies is obtained from the relaxation times (0.4 eV) and conductivity data (0.46 eV) suggesting that the ionic transport in the investigated material can be described by a hopping mechanism.



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*Source: 435462-2012-10-18.xml*