# Electrical and Vibrational Studies of Na2K2Cu(MoO4)3

Authors: Wassim Dridi; Mohamed Faouzi Zid; Miroslaw Maczka
Journal: Advances in Materials Science and Engineering
 (2017)

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## Abstract

The complex impedance of Na2K2Cu(MoO4)3 material has been investigated in the temperature range of 653–753 K and in the frequency range of 40 Hz–5 MHz. Electrical behavior of the studied material is explained through an equivalent circuit model which takes into account the contributions of grains and grains boundaries. The number of vibrational modes was calculated using group theoretical approach. The infrared and Raman spectra have also been measured and vibrational assignment has been proposed.


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## Body

## 1. Introduction

A great deal of interest has been devoted to the chemistry of molybdenum; a significant number of new molybdates have been synthesized and characterized. Molybdate chemistry has developed rapidly and this development can be explained by several factors, especially the improvement of the structural X-ray diffraction analysis, which has been a fundamental tool used for determination of crystal structures. But this renewed interest is also explained by the fact that many molybdates are suitable materials for technological applications. Molybdates exhibit various physicochemical properties, which are related to both the nature of the elements associated with the molybdate groups and the degree of opening of the formed framework. In these materials, the anionic framework is usually built from MoO4 tetrahedra linked to the transition metal polyhedra, leading to a large variety of crystal structures with a high capacity for cationic substitution. The chemistry of inorganic molybdate materials has been significantly advanced thanks to their valuable electrical and optical properties, which make them promising for various applications such as photoluminescence [1], ionic conductivity [2–4], laser materials [5, 6], and piezoelectrics [7]. The high-temperature superconductivity present in the copper-oxygen ceramic systems resulted in an increasing structural and physicochemistry interest of materials containing Cu-O [8]. Among these materials we can mention the copper molybdate Cu3Mo2O9 doped with lithium, which displays high coulombic efficiency in lithium-ion batteries and excellent charge-discharge stability [9]. Another example is Li2Cu2(MoO4)3 material, which presents a high ionic conductivity (σ = 5.810−3 Ohm−1·cm−1 at 400 K, Ea = 0.33 eV) [10].The vibrational spectroscopic studies of molybdates have attracted particular attention of a large number of researchers [11–16]. This attention is due to the catalytic activity of (MoO42-) groups in hydrocarbons oxidations [17–20] and due to negative thermal expansion, ferroelasticity, and pressure-induced amorphization [21]. Furthermore, the interpretation of laser properties needs knowledge of vibrational level distribution [22]. According to this approach, we have decided to explore system A-Mo-Cu-O (A = alkali metal). The purpose of this study is to analyze the electrical response of the grain and grains boundaries effects, which greatly influence the electrical properties, and to understand the molecular structure at microscopic level of novel Na2K2Cu(MoO4)3 compound. This study can provide important information on the conductivity, which is very important for practical applications. In this paper, we will describe the synthesis method and the characterization of Na2K2Cu(MoO4)3 by Infrared, Raman, and complex impedance spectroscopies. Raman and IR selection rules will be also analyzed using factor group analysis.


## 2. Experimental

### 2.1. Polycrystalline Powder Synthesis of Na2K2Cu(MoO4)3

The Na2K2Cu(MoO4)3 polycrystalline powder was prepared by a conventional solid-state reaction from high-purity starting reagents of Na2CO3, K2CO3, Cu(CO2CH3)·H2O, and (NH4)6Mo7O24·4H2O. These reagents were weighted according to the stoichiometric ratio. They were mixed and ground together in an agate mortar and heated progressively to 773 K in porcelain crucible with intermittent cooling and regrindings. The powder was analyzed by X-ray powder diffraction, using a PAN-analytical X’Pert PRO X-ray diffractometer equipped with copper anticathode (λKα = 1.5406 Å). The unit cell parameters were refined using Celref 3.0 program and calculated to be as follows: a = 7.5010(7) Å, b = 9.3411(4) Å, and c = 9.3670(7) Å and α = 92.59(3)°, β = 105.32(9)°, and γ = 105.44(6)°. The powder X-ray diffraction pattern was in agreement with single-crystal structure (Figure 1).Figure 1
Calculated and experimental powder X-ray diffraction patterns of Na2K2Cu(MoO4)3.


### 2.2. Complex Impedance Spectroscopy

Pellet was prepared by isostatic pressing at 4 kbar and sintering at 773 K for 12 h in air with 10 Kmin−1 heating and cooling rates. The thickness and surface of pellet were about 0.22 cm and 1.25 cm2 having a geometric factor of e/s = 0.176 cm−1. Electrical measurements were carried out in air by complex impedance spectroscopy using Agilent 4294A Precision Impedance Analyzer in the 40 Hz–5 MHz frequency range and 653–753 K temperature range. The sinusoidal AC voltage applied is of 0.5 V. The measuring cell having the sample inserted between two platinum discs used as ion-blocking electrodes is heated in an electric oven under dry air. The measurements were carried out after temperature stabilization of the device every 30 min with a pitch of 10 K. The advantage of this method lies in the fact that it is possible to separate the physical phenomena according to their speed; the fast phenomena will take place at high frequencies and the slow ones at low frequencies. Analysis of impedance spectroscopy data can provide information on charge carrier dynamics in ionic conductors [23].


### 2.3. Vibrational Spectroscopies

The infrared spectrum was recorded at room temperature using Thermo Scientific Nicolet iS50 FT-IR Spectrometer. The frequency range was from 400 to 4000 cm−1 and the spectral resolution was 3 cm−1. We are interested only in the domain 400–1100 cm−1 containing the most significant solid-state absorption bands. To obtain the Raman spectrum of the powdered sample, LAB RAMAN HR800 spectrometer was used. The frequency range was from 100 to 1100 cm−1 and the spectral resolution was 2 cm−1. The measurement was carried out on a thin pellet. The sample was analyzed with an excitation wavelength of 632.81 nm and a power was adjusted to 1 mW in order to avoid any degradation. Spectroscopic studies are used to obtain the distribution of vibrational levels and assignment to the respective normal modes of Na2K2Cu(MoO4)3.


## 2.1. Polycrystalline Powder Synthesis of Na2K2Cu(MoO4)3

The Na2K2Cu(MoO4)3 polycrystalline powder was prepared by a conventional solid-state reaction from high-purity starting reagents of Na2CO3, K2CO3, Cu(CO2CH3)·H2O, and (NH4)6Mo7O24·4H2O. These reagents were weighted according to the stoichiometric ratio. They were mixed and ground together in an agate mortar and heated progressively to 773 K in porcelain crucible with intermittent cooling and regrindings. The powder was analyzed by X-ray powder diffraction, using a PAN-analytical X’Pert PRO X-ray diffractometer equipped with copper anticathode (λKα = 1.5406 Å). The unit cell parameters were refined using Celref 3.0 program and calculated to be as follows: a = 7.5010(7) Å, b = 9.3411(4) Å, and c = 9.3670(7) Å and α = 92.59(3)°, β = 105.32(9)°, and γ = 105.44(6)°. The powder X-ray diffraction pattern was in agreement with single-crystal structure (Figure 1).Figure 1
Calculated and experimental powder X-ray diffraction patterns of Na2K2Cu(MoO4)3.


## 2.2. Complex Impedance Spectroscopy

Pellet was prepared by isostatic pressing at 4 kbar and sintering at 773 K for 12 h in air with 10 Kmin−1 heating and cooling rates. The thickness and surface of pellet were about 0.22 cm and 1.25 cm2 having a geometric factor of e/s = 0.176 cm−1. Electrical measurements were carried out in air by complex impedance spectroscopy using Agilent 4294A Precision Impedance Analyzer in the 40 Hz–5 MHz frequency range and 653–753 K temperature range. The sinusoidal AC voltage applied is of 0.5 V. The measuring cell having the sample inserted between two platinum discs used as ion-blocking electrodes is heated in an electric oven under dry air. The measurements were carried out after temperature stabilization of the device every 30 min with a pitch of 10 K. The advantage of this method lies in the fact that it is possible to separate the physical phenomena according to their speed; the fast phenomena will take place at high frequencies and the slow ones at low frequencies. Analysis of impedance spectroscopy data can provide information on charge carrier dynamics in ionic conductors [23].


## 2.3. Vibrational Spectroscopies

The infrared spectrum was recorded at room temperature using Thermo Scientific Nicolet iS50 FT-IR Spectrometer. The frequency range was from 400 to 4000 cm−1 and the spectral resolution was 3 cm−1. We are interested only in the domain 400–1100 cm−1 containing the most significant solid-state absorption bands. To obtain the Raman spectrum of the powdered sample, LAB RAMAN HR800 spectrometer was used. The frequency range was from 100 to 1100 cm−1 and the spectral resolution was 2 cm−1. The measurement was carried out on a thin pellet. The sample was analyzed with an excitation wavelength of 632.81 nm and a power was adjusted to 1 mW in order to avoid any degradation. Spectroscopic studies are used to obtain the distribution of vibrational levels and assignment to the respective normal modes of Na2K2Cu(MoO4)3.


## 3. Results and Discussion

### 3.1. Structure Description

Na2K2Cu(MoO4)3 crystallizes in the triclinic space group P-1 with a = 7.4946(8) Å, b = 9.3428(9) Å, c = 9.3619(9) Å, α = 92.591(7)°, β = 105.247(9)°, γ = 105.496(9)°, V = 604.7(Å3), Z = 2, R(F2) = 0.022, and Rw(F2) = 0.056. Both cations K1 and K3 are located in the center of inversion, and all other atoms are at general positions. The structure of Na2K2Cu(MoO4)3 can be described as a one-dimensional framework formed by ribbons arranged in parallel to a axis with interribbons spaces containing Na+ and K+ monovalent cations directed to the free vertices of the tetrahedra MoO4 (Figure 2). These structural characteristics encouraged us to study the electrical properties. CIF file containing complete information on the studied structure was deposited with FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crysdata(at)fiz-karlsruhe(dot)de, deposition number CSD-430379).Figure 2
Projection of Na2K2Cu(MoO4)3 structure according to a axis.


### 3.2. Electrical Properties

The Nyquist plots in the temperature range from 653 K to 753 K are shown in Figure3. When temperature increases, the radius of semicircles decreases and consequently the ionic conductivities increase with the temperature. We notice the presence of two hardly distinguishable semicircles, which proves the presence of two relaxation phenomena. The first arc existing towards higher frequencies corresponds to the movement of ions across the grain (bulk), which represents intrinsic conduction and gives rise to an intragranular resistance. The second arc, observed at lower-frequency, corresponds to movement of ions through the grain boundaries [24, 25]. The electrical behavior of Na2K2Cu(MoO4)3 is interpreted through an equivalent electrical circuit formed by two cells arranged in series, constituted by the parallel combination of the following: Rg∥C1andRgb∥ CPE1 corresponding to the contributions of grains and grains boundaries, respectively. Rg and Rgb are the resistances of grains and grains boundaries, respectively. C1 is the pure capacitance of grain and CPE1 is the fractal capacitance constant phase element according to grains boundary. Electrical parameters were measured as a function of temperature. The intercepts of the semicircular arcs with the real axis give an estimation of the resistance of the studied material. Zview software [26] was used to fit these curves. The total resistance, Rtotal, follows the relation Rg+Rgb=Rtotal. The conformity between the experimental and calculated curves (fit) on the whole temperature range proves the validity of the proposed equivalent circuit. Electrical parameters are represented in Table 1.Table 1
Simulated data of the electrical parameters for the proposed equivalent circuit.
T (K)
R
g (Ω)
C
g (F)
R
g
b (Ω)
C
g
b (F)
∑
R
i (Ω)
653
2.087(4)105
1.118(2)10−11
2.874(1)106
8.683(2)10−11
3.083(1)106
663
1.354(1)105
1.078(1)10−11
1.877(2)106
9.442(1)10−11
2.012(2)106
673
9.711(9)104
9.131(4)10−11
1.339(2)106
9.908(4)10−11
1.436(2)106
683
6.797(9)104
9.639(5)10−12
9.159(1)105
1.032(1)10−10
9.838(9)105
693
4.915(3)104
9.010(1)10−12
6.499(8)105
1.078(3)10−10
6.991(3)105
703
2.913(9)104
7.893(2)10−12
3.610(6)105
1.145(4)10−10
3.901(9)105
713
1.283(3)104
6.905(2)10−12
1.677(1)105
1.349(2)10−10
1.805(3)105
723
8.670(1)103
6.781(3)10−12
9.794(8)104
1.518(1)10−10
1.066(1)105
733
6.670(2)103
6.793(4)10−12
6.197(5)104
1.578(2)10−10
6.864(5)104
743
4.831(3)103
7.066(1)10−12
3.464(6)104
1.803(2)10−10
3.947(7)104
753
2.715(2)103
7.954(2)10−12
1.377(1)104
1.984(2)10−10
1.648(6)104Figure 3
Complex impedance spectrum of Na2K2Cu(MoO4)3 over temperature range 653 and 753 K.In order to determine the direct conductivity for the grain interiorσg, grain boundary σgb, and total conductivity σtot, we used the following equation:(1)σi=eRi·1s.Values of ionic conductivities in Na2K2Cu(MoO4)3 material are represented in Table 2.Table 2
Ionic conductivities measurements value as a function of temperature in Na2K2Cu(MoO4)3 material.
T (K)
Conductivities (Ω cm−1)
σ
g
σ
g
b
σ
t
o
t
a
l
653
1.05310−6
7.65210−8
5.70710−8
663
1.62410−6
1.17210−7
8.74510−8
673
2.26510−6
1.64210−7
1.22510−7
683
3.23610−6
2.40110−7
1.78810−7
693
4.47510−6
3.38410−7
2.51710−7
703
7.55010−6
6.09310−7
4.51010−7
713
1.71410−5
1.31110−6
9.74810−7
723
2.53710−5
2.24610−6
1.65010−6
733
3.29810−5
3.54910−6
2.56310−6
743
4.55310−5
6.34910−6
4.45810−6
753
8.10310−5
1.59710−5
1.06710−5The activation energies was obtained by linear fitting of the ionic conductivities values at different temperatures by applying the Arrhenius equation:(2)T=σ0exp⁡-EakbT,where σ is the temperature dependent ionic conductivity, σ0 is the ionic conductivity at absolute zero temperature, Ea is the activation energy of cations migration, kb is the Boltzmann constant, and T is the absolute temperature. The variation of log⁡(σ(S·K·cm−1)) versus 1000/T (K−1) is represented in Figure 4. Activation energies values are represented in Table 3.Table 3
Activation energies in Na2K2Cu(MoO4)3 material.
Contribution
Temperature range (K)
E
a (eV)
Grains
653–673
1.55
673–753
2.02
Grains boundaries
653–673
1.63
673–753
2.86
Total
653–673
1.62
673–753
2.77Figure 4
Arrhenius plot of conductivity of Na2K2Cu(MoO4)3.We note that the total conductivity of our compound is less than the bulk conductivity but higher than the grain boundary one. This reveals the existence of a partial blockage of the charge carriers by the grain boundaries [27]. Therefore, the conductivity of our material is limited by the low conductivity of the grain boundaries. The influence of the grains boundaries conductivity on the total conductivity can be evaluated quantitatively by the blocking factor α. This parameter characterizes the fraction of the load carriers blocked in the case where a direct current flows through the sample. It can also be calculated using the following equation [28, 29]:(3)α=RgbRtot.Figure 5 shows the variation of the blocking factor as a function of the temperature. It is found that the blocking factor decreases with the temperature. Therefore, the increase in temperature causes a decrease in the blocking effect by the limits of the grains.Figure 5
Variation of the blockage factorα with temperature.


### 3.3. Vibrational Study

Na2K2Cu(MoO4)3 crystallizes in the triclinic space group P-1 which corresponds to Ci factor group. There are two molecules per unit-cell, so there are also two molecules per Bravais cell. Mo1, Mo2, Mo3, Cu1, K2, Na1, Na1, and O atoms occupy C1 symmetry whereas K1 and K3 atoms occupy Ci symmetry. The Bravais cell comprises 40 atoms that have 120 zone center degrees of freedom. The structure of Na2K2Cu(MoO4)3 compound is centrosymmetric; a complete assignment of the crystal modes requires both IR and Raman spectra [30]. The crystal vibrational modes are obtained by group theoretical calculations developed by Fateley et al. [31]. Factor group analysis of Na2K2Cu(MoO4)3 is represented in Table 4. The vibrational irreducible representation for the triclinic phase at the center of the Brillouin zone (k=0) is(4)Γvibr=57Ag+63Au,3 acoustic and (3N-3) optic modes, where N is the number of atoms in the unit cell [32]:(5)Γacoustic=3AuΓoptic=57Ag+60Au.Infrared and Raman active modes are as follows:(6)Γraman=57AgΓinfrared=60Au.In the free state tetrahedral MoO4 ion has Td symmetry and four vibrational modes with the following wavenumbers: ν1(A1) nondegenerate symmetric stretching at 936 cm−1, ν2(E) doubly degenerate symmetric bending at 220 cm−1, ν3(F2) triply degenerate asymmetric stretching at 895 cm−1, and ν4(F2) triply degenerate asymmetric bending at 365 cm−1 [33]. Moreover, all four vibrational modes are active in the Raman spectra, but only F2 stretching and bending vibrations are active in the IR spectra. However, when this ion is located in the crystal lattice, its symmetry is lowered due to the constraints imposed by the lattice. So, the local symmetry of the three MoO4 tetrahedra decreases to C1. Because of this lowering of symmetry, all modes become active in Raman and in infrared and degenerate modes raise their degenerations. Therefore, ν3 and ν4 are split into three bands 3A and ν2 into two 2A. The correlation between the point group of Td symmetry of the free anion MoO4, its site-symmetry C1, and its factor group Ci is represented in Scheme 1. According to Basiev et al. [34], the vibrational modes observed in Raman spectra of molybdates can be classified into two groups, internal and external modes. The internal vibrational modes of each type of MoO4 derived from the correlation scheme are equal to Z(3n-6)=18, where n is the number of atoms in the molecular MoO4:(7)ΓMoO4=9AgR+9AuIRΓν1=AgR+AuIRΓν2=2AgR+2AuIRΓν3=3AgR+3AuIRΓν4=3AgR+3AuIR.The external vibrational modes of MoO4 are divided into translational modes which includes acoustic and lattice modes and librational modes [35], presented as follows:(8)Γtranslation=Γacoustic+Γlattice=3AgR+3AuIRΓlibration=3AgR+3AuIR.The comparison of the infrared and Raman bands positions shows that the majority of these bands do not coincide. Indeed, the observed IR bands appear at wavenumbers different from those in the Raman spectrum (Figure 6). This is in agreement with the centrosymmetric character of Na2K2Cu(MoO4)3 structure [36]. The Raman spectrum can be separated into two parts with a wide empty gap in the range 500–700 cm−1 that is commonly observed in molybdates containing MoO4 tetrahedra [22, 37–43]. The proposed assignment of the vibrational spectra of MoO4 in Na2K2Cu(MoO4)3 is realised by considering the following criteria: ν1 bands are generally very strong in the Raman and weaker in the infrared spectra, whereas an opposite behavior is usually observed for ν3 bands. ν2 bands are usually stronger in the Raman spectra than those corresponding to ν4 modes but in the infrared spectra ν4 band is generally more intense [44]. The Mo-O stretching modes are located in the range 720–930 cm−1 whereas the bending modes are situated in the range 380–330 cm−1. Wavenumbers and assignment of the internal vibrational modes of MoO4 tetrahedron are listed in Table 5.Table 4
Factor group analysis of the triclinic phase Na2K2Cu(MoO4)3.
Atoms
Site symmetry
n
s
t
γ
γ
f
γ
ζ
C
ζ
a
ζ
∑
Γ
a
t
o
m
P-1
Γ
t
r
a
n
s
l Mo1, Mo2, Mo3, Cu1, K2, Na1, Na2, 12 O
C
1
2
3
A
(
T
x
,
T
y
,
T
z
)
6
A
g
1
3
19
(
3
A
g
+
3
A
u
)
Z
=
2
A
u
1
3
Z
B
=
2
Γ
t
r
a
n
s
l  K1, K3
C
i
1
3
A
u
(
T
x
,
T
y
,
T
z
)
3
A
u
1
3
2
(
3
A
u
)
Z
B: number of molecules per primitive Bravais cell, ns: number of positions, tγ: number of translations of a site species γ, and fγ: the degree of vibrational freedom present in each site species γ.
C
ζ represents the degeneracy of the species ζ of the factor group, whereas aζ is the number of lattice vibrations of the equivalent set of atoms in species ζ of the factor group.Table 5
Assignment of the internal vibrational modes frequencies of MoO4 tetrahedron.
Assignment
Infrared (ν/cm−1)
Raman (ν/cm−1)
ν
1(MoO4)
914
937, 918, 891
ν
2(MoO4)
344, 331, 273
ν
3(MoO4)
849, 789, 726
871, 829, 758
ν
4(MoO4)
429, 472
378, 360Scheme 1
Correlation scheme for the internal modes of MoO4 in Na2K2Cu(MoO4)3 structure.Figure 6
Infrared and Raman spectra of Na2K2Cu(MoO4)3.In the Raman spectrum, bands located below 300 cm−1 are attributed to external vibrations involving the librational and translational modes of the MoO4 anions and translational modes of cations; the distinguishing between librational and translational modes is difficult. But in general librational modes have higher wavenumbers and intensities than the translational modes [45]. Furthermore, since the atomic mass of molybdenum is larger than that of copper, potassium, and sodium, translations of the MoO4-2 ions should be observed at lower wavenumbers than translations of Cu2+, K+, and Na+ [13]. Based on these rules, we propose assignment of the 273 cm−1 band to T′(Na+) modes, those at 119 and 124 cm−1 to L(MoO4) modes, and the remaining bands in the 138–199 cm−1 range to the coupled modes involving translational motions of the molybdate, potassium, and copper ions.


## 3.1. Structure Description

Na2K2Cu(MoO4)3 crystallizes in the triclinic space group P-1 with a = 7.4946(8) Å, b = 9.3428(9) Å, c = 9.3619(9) Å, α = 92.591(7)°, β = 105.247(9)°, γ = 105.496(9)°, V = 604.7(Å3), Z = 2, R(F2) = 0.022, and Rw(F2) = 0.056. Both cations K1 and K3 are located in the center of inversion, and all other atoms are at general positions. The structure of Na2K2Cu(MoO4)3 can be described as a one-dimensional framework formed by ribbons arranged in parallel to a axis with interribbons spaces containing Na+ and K+ monovalent cations directed to the free vertices of the tetrahedra MoO4 (Figure 2). These structural characteristics encouraged us to study the electrical properties. CIF file containing complete information on the studied structure was deposited with FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crysdata(at)fiz-karlsruhe(dot)de, deposition number CSD-430379).Figure 2
Projection of Na2K2Cu(MoO4)3 structure according to a axis.


## 3.2. Electrical Properties

The Nyquist plots in the temperature range from 653 K to 753 K are shown in Figure3. When temperature increases, the radius of semicircles decreases and consequently the ionic conductivities increase with the temperature. We notice the presence of two hardly distinguishable semicircles, which proves the presence of two relaxation phenomena. The first arc existing towards higher frequencies corresponds to the movement of ions across the grain (bulk), which represents intrinsic conduction and gives rise to an intragranular resistance. The second arc, observed at lower-frequency, corresponds to movement of ions through the grain boundaries [24, 25]. The electrical behavior of Na2K2Cu(MoO4)3 is interpreted through an equivalent electrical circuit formed by two cells arranged in series, constituted by the parallel combination of the following: Rg∥C1andRgb∥ CPE1 corresponding to the contributions of grains and grains boundaries, respectively. Rg and Rgb are the resistances of grains and grains boundaries, respectively. C1 is the pure capacitance of grain and CPE1 is the fractal capacitance constant phase element according to grains boundary. Electrical parameters were measured as a function of temperature. The intercepts of the semicircular arcs with the real axis give an estimation of the resistance of the studied material. Zview software [26] was used to fit these curves. The total resistance, Rtotal, follows the relation Rg+Rgb=Rtotal. The conformity between the experimental and calculated curves (fit) on the whole temperature range proves the validity of the proposed equivalent circuit. Electrical parameters are represented in Table 1.Table 1
Simulated data of the electrical parameters for the proposed equivalent circuit.
T (K)
R
g (Ω)
C
g (F)
R
g
b (Ω)
C
g
b (F)
∑
R
i (Ω)
653
2.087(4)105
1.118(2)10−11
2.874(1)106
8.683(2)10−11
3.083(1)106
663
1.354(1)105
1.078(1)10−11
1.877(2)106
9.442(1)10−11
2.012(2)106
673
9.711(9)104
9.131(4)10−11
1.339(2)106
9.908(4)10−11
1.436(2)106
683
6.797(9)104
9.639(5)10−12
9.159(1)105
1.032(1)10−10
9.838(9)105
693
4.915(3)104
9.010(1)10−12
6.499(8)105
1.078(3)10−10
6.991(3)105
703
2.913(9)104
7.893(2)10−12
3.610(6)105
1.145(4)10−10
3.901(9)105
713
1.283(3)104
6.905(2)10−12
1.677(1)105
1.349(2)10−10
1.805(3)105
723
8.670(1)103
6.781(3)10−12
9.794(8)104
1.518(1)10−10
1.066(1)105
733
6.670(2)103
6.793(4)10−12
6.197(5)104
1.578(2)10−10
6.864(5)104
743
4.831(3)103
7.066(1)10−12
3.464(6)104
1.803(2)10−10
3.947(7)104
753
2.715(2)103
7.954(2)10−12
1.377(1)104
1.984(2)10−10
1.648(6)104Figure 3
Complex impedance spectrum of Na2K2Cu(MoO4)3 over temperature range 653 and 753 K.In order to determine the direct conductivity for the grain interiorσg, grain boundary σgb, and total conductivity σtot, we used the following equation:(1)σi=eRi·1s.Values of ionic conductivities in Na2K2Cu(MoO4)3 material are represented in Table 2.Table 2
Ionic conductivities measurements value as a function of temperature in Na2K2Cu(MoO4)3 material.
T (K)
Conductivities (Ω cm−1)
σ
g
σ
g
b
σ
t
o
t
a
l
653
1.05310−6
7.65210−8
5.70710−8
663
1.62410−6
1.17210−7
8.74510−8
673
2.26510−6
1.64210−7
1.22510−7
683
3.23610−6
2.40110−7
1.78810−7
693
4.47510−6
3.38410−7
2.51710−7
703
7.55010−6
6.09310−7
4.51010−7
713
1.71410−5
1.31110−6
9.74810−7
723
2.53710−5
2.24610−6
1.65010−6
733
3.29810−5
3.54910−6
2.56310−6
743
4.55310−5
6.34910−6
4.45810−6
753
8.10310−5
1.59710−5
1.06710−5The activation energies was obtained by linear fitting of the ionic conductivities values at different temperatures by applying the Arrhenius equation:(2)T=σ0exp⁡-EakbT,where σ is the temperature dependent ionic conductivity, σ0 is the ionic conductivity at absolute zero temperature, Ea is the activation energy of cations migration, kb is the Boltzmann constant, and T is the absolute temperature. The variation of log⁡(σ(S·K·cm−1)) versus 1000/T (K−1) is represented in Figure 4. Activation energies values are represented in Table 3.Table 3
Activation energies in Na2K2Cu(MoO4)3 material.
Contribution
Temperature range (K)
E
a (eV)
Grains
653–673
1.55
673–753
2.02
Grains boundaries
653–673
1.63
673–753
2.86
Total
653–673
1.62
673–753
2.77Figure 4
Arrhenius plot of conductivity of Na2K2Cu(MoO4)3.We note that the total conductivity of our compound is less than the bulk conductivity but higher than the grain boundary one. This reveals the existence of a partial blockage of the charge carriers by the grain boundaries [27]. Therefore, the conductivity of our material is limited by the low conductivity of the grain boundaries. The influence of the grains boundaries conductivity on the total conductivity can be evaluated quantitatively by the blocking factor α. This parameter characterizes the fraction of the load carriers blocked in the case where a direct current flows through the sample. It can also be calculated using the following equation [28, 29]:(3)α=RgbRtot.Figure 5 shows the variation of the blocking factor as a function of the temperature. It is found that the blocking factor decreases with the temperature. Therefore, the increase in temperature causes a decrease in the blocking effect by the limits of the grains.Figure 5
Variation of the blockage factorα with temperature.


## 3.3. Vibrational Study

Na2K2Cu(MoO4)3 crystallizes in the triclinic space group P-1 which corresponds to Ci factor group. There are two molecules per unit-cell, so there are also two molecules per Bravais cell. Mo1, Mo2, Mo3, Cu1, K2, Na1, Na1, and O atoms occupy C1 symmetry whereas K1 and K3 atoms occupy Ci symmetry. The Bravais cell comprises 40 atoms that have 120 zone center degrees of freedom. The structure of Na2K2Cu(MoO4)3 compound is centrosymmetric; a complete assignment of the crystal modes requires both IR and Raman spectra [30]. The crystal vibrational modes are obtained by group theoretical calculations developed by Fateley et al. [31]. Factor group analysis of Na2K2Cu(MoO4)3 is represented in Table 4. The vibrational irreducible representation for the triclinic phase at the center of the Brillouin zone (k=0) is(4)Γvibr=57Ag+63Au,3 acoustic and (3N-3) optic modes, where N is the number of atoms in the unit cell [32]:(5)Γacoustic=3AuΓoptic=57Ag+60Au.Infrared and Raman active modes are as follows:(6)Γraman=57AgΓinfrared=60Au.In the free state tetrahedral MoO4 ion has Td symmetry and four vibrational modes with the following wavenumbers: ν1(A1) nondegenerate symmetric stretching at 936 cm−1, ν2(E) doubly degenerate symmetric bending at 220 cm−1, ν3(F2) triply degenerate asymmetric stretching at 895 cm−1, and ν4(F2) triply degenerate asymmetric bending at 365 cm−1 [33]. Moreover, all four vibrational modes are active in the Raman spectra, but only F2 stretching and bending vibrations are active in the IR spectra. However, when this ion is located in the crystal lattice, its symmetry is lowered due to the constraints imposed by the lattice. So, the local symmetry of the three MoO4 tetrahedra decreases to C1. Because of this lowering of symmetry, all modes become active in Raman and in infrared and degenerate modes raise their degenerations. Therefore, ν3 and ν4 are split into three bands 3A and ν2 into two 2A. The correlation between the point group of Td symmetry of the free anion MoO4, its site-symmetry C1, and its factor group Ci is represented in Scheme 1. According to Basiev et al. [34], the vibrational modes observed in Raman spectra of molybdates can be classified into two groups, internal and external modes. The internal vibrational modes of each type of MoO4 derived from the correlation scheme are equal to Z(3n-6)=18, where n is the number of atoms in the molecular MoO4:(7)ΓMoO4=9AgR+9AuIRΓν1=AgR+AuIRΓν2=2AgR+2AuIRΓν3=3AgR+3AuIRΓν4=3AgR+3AuIR.The external vibrational modes of MoO4 are divided into translational modes which includes acoustic and lattice modes and librational modes [35], presented as follows:(8)Γtranslation=Γacoustic+Γlattice=3AgR+3AuIRΓlibration=3AgR+3AuIR.The comparison of the infrared and Raman bands positions shows that the majority of these bands do not coincide. Indeed, the observed IR bands appear at wavenumbers different from those in the Raman spectrum (Figure 6). This is in agreement with the centrosymmetric character of Na2K2Cu(MoO4)3 structure [36]. The Raman spectrum can be separated into two parts with a wide empty gap in the range 500–700 cm−1 that is commonly observed in molybdates containing MoO4 tetrahedra [22, 37–43]. The proposed assignment of the vibrational spectra of MoO4 in Na2K2Cu(MoO4)3 is realised by considering the following criteria: ν1 bands are generally very strong in the Raman and weaker in the infrared spectra, whereas an opposite behavior is usually observed for ν3 bands. ν2 bands are usually stronger in the Raman spectra than those corresponding to ν4 modes but in the infrared spectra ν4 band is generally more intense [44]. The Mo-O stretching modes are located in the range 720–930 cm−1 whereas the bending modes are situated in the range 380–330 cm−1. Wavenumbers and assignment of the internal vibrational modes of MoO4 tetrahedron are listed in Table 5.Table 4
Factor group analysis of the triclinic phase Na2K2Cu(MoO4)3.
Atoms
Site symmetry
n
s
t
γ
γ
f
γ
ζ
C
ζ
a
ζ
∑
Γ
a
t
o
m
P-1
Γ
t
r
a
n
s
l Mo1, Mo2, Mo3, Cu1, K2, Na1, Na2, 12 O
C
1
2
3
A
(
T
x
,
T
y
,
T
z
)
6
A
g
1
3
19
(
3
A
g
+
3
A
u
)
Z
=
2
A
u
1
3
Z
B
=
2
Γ
t
r
a
n
s
l  K1, K3
C
i
1
3
A
u
(
T
x
,
T
y
,
T
z
)
3
A
u
1
3
2
(
3
A
u
)
Z
B: number of molecules per primitive Bravais cell, ns: number of positions, tγ: number of translations of a site species γ, and fγ: the degree of vibrational freedom present in each site species γ.
C
ζ represents the degeneracy of the species ζ of the factor group, whereas aζ is the number of lattice vibrations of the equivalent set of atoms in species ζ of the factor group.Table 5
Assignment of the internal vibrational modes frequencies of MoO4 tetrahedron.
Assignment
Infrared (ν/cm−1)
Raman (ν/cm−1)
ν
1(MoO4)
914
937, 918, 891
ν
2(MoO4)
344, 331, 273
ν
3(MoO4)
849, 789, 726
871, 829, 758
ν
4(MoO4)
429, 472
378, 360Scheme 1
Correlation scheme for the internal modes of MoO4 in Na2K2Cu(MoO4)3 structure.Figure 6
Infrared and Raman spectra of Na2K2Cu(MoO4)3.In the Raman spectrum, bands located below 300 cm−1 are attributed to external vibrations involving the librational and translational modes of the MoO4 anions and translational modes of cations; the distinguishing between librational and translational modes is difficult. But in general librational modes have higher wavenumbers and intensities than the translational modes [45]. Furthermore, since the atomic mass of molybdenum is larger than that of copper, potassium, and sodium, translations of the MoO4-2 ions should be observed at lower wavenumbers than translations of Cu2+, K+, and Na+ [13]. Based on these rules, we propose assignment of the 273 cm−1 band to T′(Na+) modes, those at 119 and 124 cm−1 to L(MoO4) modes, and the remaining bands in the 138–199 cm−1 range to the coupled modes involving translational motions of the molybdate, potassium, and copper ions.


## 4. Conclusion

Polycrystalline powder of Na2K2Cu(MoO4)3 was obtained by standard solid-state reaction at 773 K. X-ray diffraction studies show that this compound crystallizes in the triclinic symmetry with the P-1 space group. Ionic conductivity of the investigated material is characterized by the existence of a partial blockage of the charge carriers by the grain boundaries. The blocking effect generated by the limits of the grains decreases with temperature. The centrosymmetric space group P-1 of our structure is confirmed by the noncoincidence of majority of Raman and IR bands. Vibrational study indicates the lowering of symmetry of molybdate anion from Td to C1 symmetry.



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