Synthesis, crystal structure, thermal analysis, dielectric properties and electrical conduction mechanisms of the new mixed solid solution of thallium rubidium sulfate selenate tellurate

Journal of Alloys and Compounds 749 (2018) 448e464

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Synthesis, crystal structure, thermal analysis, dielectric properties and electrical conduction mechanisms of the new mixed solid solution of thallium rubidium sulfate selenate tellurate Atef Elferjani a, *, Santiago Garcia-Granda b, Mohamed Dammak a a b

Laboratory of Inorganic Chemistry, LR 17ES07, University of Sfax, B. P. 1171, Sfax, 3000, Tunisia Department of Physical and Analytical Chemistry, University Oviedo-CINN, 33006, Oviedo, Spain

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 November 2017 Received in revised form 1 March 2018 Accepted 16 March 2018 Available online 22 March 2018

The new mixed compound Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 (TlRbSSeTe) has been synthesized in order to determine the temperature transitions and to specify the electrical properties as well as the conduction mechanism. It is obtained by slow evaporation at room temperature and prove to crystallize in the monoclinic system with P21/c space group using X-ray diffractometer data. The basic property of 2
6
these atomic arrangements is the coexistence of three different anions (SO2
4 , SeO4 and TeO6 groups) in the unit cell, related by O
H…O hydrogen bonds building up the crystal. Thermal analysis (DSC, DTA and TG) of the title compound confirms the presence of the phase transitions and the temperature of the decomposition of the studied salt. In order to characterize the phase transitions, Raman spectra have been recorded at various temperatures in the wavenumber range from 50e1200 cm
1. Detailed dielectric and electrical properties of the material have been analyzed as a function of frequency (100 Hze10 MHz) and temperature (383e518 K). Besides, the analysis of Nyquist plots were well fitted to an equivalent circuit consisting of a series of combination of grains and grain boundary elements. The variation of the DC and AC conductivity confirms all the transitions of our sample. Furthermore, The frequency dependence of alternative current (AC) conductivity is interpreted in terms of Jonscher's law (developed). The alternative current (AC) electrical conduction in TlRbSSeTe material is accounted for in terms of two processes that can be assigned to a hopping transport mechanism. These processes are the correlated barrier hopping (CBH) model in some regions, as well as the non-overlapping small polaron tunneling (NSPT) model in the other regions. The conduction mechanism for each phase is determined with the help of Elliot's theory. © 2018 Elsevier B.V. All rights reserved.

Keywords: Structure study Thermal analysis AC conductivity Dielectric properties

1. Introduction In recent years, much interest has been shown to the inorganic compounds with hydrogen bonds, which are known for not only their high-temperature phase transition with high proton mobility showing superprotonic conduction [1] but also their low temperature phases showing ferroelectricity [2,3]. The different attempts to explore this novel class of the compound refer basically to their interesting applications, such as multilayer capacitors, microelectronic components, material of storage of energy… etc.

* Corresponding author. E-mail address: [email protected] (A. Elferjani). https://doi.org/10.1016/j.jallcom.2018.03.211 0925-8388/© 2018 Elsevier B.V. All rights reserved.

In fact, many inorganic acids such as telluric acid have the property of forming stable adduct with a wide range of organic and inorganic compounds of considerable importance like Te(OH)6 which acts as both an acceptor and a donor of hydrogen bonds [4e9]. Various authors have shown that certain added compounds with sulphuric and selenic acid have drawn considerable attention for their structural phase transitions and their associated physical properties like ferroelectricity, dielectric relaxation and especially a phase transition into a state characterized by a high protonic conductivity. All these interesting properties are linked to the presence of 2
2
some anionic groups (TeO6
6 , SO4 and SeO4 ) in the same unit cell favoring the presence of different load centers as well as protons Hþ in telluric groups, which are at the origin of the network hydrogen

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

bonds formed in the crystal structure of these materials. Many research works have been performed on the growth characterization of inorganic compounds such as these with the general formula M2AO4Te(OH)6 (where M is a monovalent cation: þ þ þ Naþ, Kþ, NHþ 4 , Tl , Rb and Cs , A ¼ S, Se and P). They usually display structures resting on the coexistence of different and independent anions in the same crystal connected by hydrogen bonds and structural arrangement of all the polyhedra which are at the origin of structural phase transition accompanied by significant physical properties [4e9]. However, many attempts were also carried out to explore these families in depth so as to synthesize and examine new materials by changing the cation or anionic group in the hope of obtaining compounds with improved structural and physical properties, or even a new functionality. The influence of anionic substitution on the structural parameters has been reported in previous studies. For instance, while thallium sulfate selenate tellurate Tl2(SO4)0.61(SeO4)0.39Te(OH)6 (TlSSeTe), and rubidium sulfate selenate tellurate, Rb2(SO4)(SeO4) Te(OH)6 (RbSSeTe), which are centrosymmetric, crystallize in the monoclinic system with P21/c space group [10,11]. The thallium selenate tellurate (TlSeTe) displays the space group P21/a [12]. Actually, RbSSeTe presents two phase transitions at 420 and 598 K, which is confirmed through DSC analysis and dielectric measurements [11]. The first transition is of ferroelectriceparaelectric phase and the second one is of protonic conduction phase. However, TlSeTe material is characterized by successive phase transitions at 373, 395 and 437 K, respectively [12]. These transitions are of a structural type and are related to several physical properties such as ferroelectricity and superionicprotonic conduction, which refers essentially to the motion of the Hþ ions via the O
H…O hydrogen bonds [4,9]. The present paper is devoted to the preparation and characterizations of the new mixed crystal Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 (TlRbSSeTe) based on the structural characterization by Xray diffraction, thermal analysis and vibrational studies at different temperatures. In addition, this research work investigates the electrical and dielectric properties of the new mixed compound by means of impedance spectroscopy. Indeed, it provides valuable information on the electrical conductivity which is significant in terms of practical applications.

449

The density average value Dm ¼ 3.85 g cm
3 proved to be in good agreement with the calculated one Dcal ¼ 3.41 g cm
3. 2.2. Diffraction data collection and refinement Single crystal X-ray diffraction intensity data was obtained on an EnrafeNonius Kappa CCD diffractometer using Mo Ka radiation (l ¼ 0.71073 Å) [13]. The unit cell dimensions were specified and refined using the indexation of diffraction markings collected with a Bruker-Nonius X8-APEX2 CCD area-detector diffractometer using the APEX2 program [14]. The title compound crystallizes at room temperature in the monoclinic system with the space group P21/c. 1878 reflections were computed, 1295 of which had an intensity of I > 3s(I). The structure was analyzed with the crystallographic CRYSTALS program [15]. TlRbSSeTe structure was solved by conventional Patterson and difference-Fourier techniques. Te, Tl and Rb atom positions were refined by Patterson methods. The O atom positions were set up from difference Fourier maps, and H atoms were geometrically placed. Once all atoms were anisotropically refined, the agreement factors R and wR converged respectively to 0.077 and 0.079. The structural graphics were created using the DIAMOND program [16]. The details of data collection, the final atomic positions and the Ueq parameters for the new material are depicted respectively in Tables 1 and 2. The main interatomic distances (Å) and bond angles ( ) for our solid solution are displayed in Tables 3 and 4. 2.3. Thermal behavior measurements The DSC measurement was performed on 7 mg of the samples from 300 to 550 K on a NETZSCH apparatus (Model 204 Phoenix) at a heating rate of 5 K min
1. Besides, the simultaneous TG and DTA analyses were conducted with Mettler Toledo model TGA851ELF and Setaram model Setsys Evolution 16 thermobalances. The samples whose masses in TG and DTA measurements correspond to 24.55 mg, were placed inside uncovered alu-mina crucibles. They were heated from 350 K to 550 K at a heating rate of 5 K min
1. In the TG test, a Pfeiffer Vacuum ThermoStarTM GSD301 T mass spectrometer was used to determine the evacuated vapors. 2.4. Infrared and Raman measurements

2. Experimental detail 2.1. Chemical preparation Colorless and transparent single crystals of the thallium rubidium sulfate selenate tellurate Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 (TlRbSSeTe) were synthesized by slow evaporation, at room temperature, from a mixture of telluric acid H6TeO6, rubidium carbonate Rb2CO3, thallium carbonate Tl2CO3 and sulfuric and selenic acid corresponding respectively to H2SO4 and H2SeO4 in the stochiometric ratio. Schematically, the reaction is as follows: (1-y) Tl2CO3þ y Rb2CO3þ (1-x) (H2SO4) þ x H2SeO4 þ H6TeO6 / Tl2-2yRb 2y(SO4)1-x(SeO4)x.Te(OH)6þ CO2 þ H2O (1) Several recrystallizations were necessary to obtain single crystals suitable for the structural study. A fortnight after, the solutions resulted into colorless and transparent single crystals. The obtained crystals are pure with appropriate size and stable under normal conditions regarding temperature and humidity. The chemical material formula was identified by chemical analysis and confirmed by the refinement of the crystal structure. Density was measured, at room temperature, by flotation in CCl4.

The Infrared absorption spectra of crystalline suspension in KBr were recorded using Jasco-FT-IR-420 spectrophotometer in the frequency range of 400e4000 cm
1. The Raman spectra of polycrystalline samples sealed in glass tubes were recorded at various temperatures on a Labrama HR 800 instrument using 632.81 nm radiations from a physics argon ion laser. The spectrum was stored in the range of wave number from 50 to 1200 cm
1. 2.5. Dielectric measurements Dielectric Spectroscopy experiments were carried out in a Novocontrol Broadband Dielectric Spectrometer, based on an Alpha analyzer and a Quatro temperature controller. The samples were gold coated in order to obtain a better contact between the sample and the electrodes. Isothermal and isochronal measurements were carried out at frequencies between 100 Hz and 10 MHz from 110  C to 245  C, in 5  C steps, using brass electrodes of 8 mm in diameter at an oscillation voltage of 1 V. The accuracy of Alpha impedance measurement is of 0.01%. The measured dielectric permittivity data was collected and evaluated by WinDETA impedance analysis software. According to the planar capacitor rule, the complex dielectric function for the polymer is expressed as [17e20]:

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Table 1 Main crystallographic, feature X-ray diffraction data parameters results of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6. Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 512.44 293 Monoclinic P21/c a ¼ 13.6323(9) Å b ¼ 6.6656(5) Å c ¼ 11.5010(7) Å b ¼ 107.076(4) V ¼ 999.00(12) Å3 4 3.41 3.126e26.431 3.407
16  h  12
8  k  8
14  l  12 Kappa CCD 0.71073 1878 1295 R ¼ 0.077 and Rw ¼ 0.079 1,01
3.50 < Dr <2.64

Formula Formula weight (gmol
1) T (K) Crystal system Space group Unit cell dimensions

Z Dx (g.cm
3) q range for data collection ( ) m (mm
1) hkl range

Data collection instrument Wavelength (Å) Measured reflections Observed reflections I > 3s(I) R indices Goodness-of-fit on (F2) Highest peak/deepest hole(eÅ3) w ¼ 1/[s2 (Fo2)þ(0.0800P)2 þ0P] where P ¼ (Fo2þ2Fc2)/3 CCDC deposition number

1580919

Table 2 Atomic coordinates and equivalent thermal parameters. Atomes

x

y

1.0000
0.5000 0.5000
1.5000 0.64199(4)
0.98139(4) 0.64199(4)
0.98139(4) 0.85730(10)
0.50265(10) 0.85730(10)
0.50265(10) 0.74846(5)
0.49005(5) 0.74846(5)
0.49005(5) 0.9715(18)
0.414(3) 1.1330(13)
0.387(3) 1.0405(16)
0.755(3) 0.5474(15)
1.364(3) 0.3658(13)
1.407(3) 0.4776(15)
1.731(3) 0.7838(16)
0.274(3) 0.8374(15)
0.623(3) 0.6700(15)
0.508(3) 0.7034(18)
0.552 (3) 0.9606
0.4298 1.1955
0.4574 1.0909
0.8330 0.6087
1.4385 0.3004
1.4635 0.5170
1.8519 PP Ueq ¼ 1/3 i j Uij ai*aj*aiaj. Te1 Te2 Tl1 Rb1 Tl2 Rb2 S1 Se1 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 H1 H2 H3 H4 H5 H6

z

Ueq

Occupation

1.0000 0.5000 0.34302(4) 0.34302(4) 0.59734(10) 0.59734(10) 0.23441(5) 0.23441(5) 1.1389(19) 1.0669(17) 1.0676(18) 0.3850(16) 0.4159(16) 0.4003(16) 0.2558(19) 0.2381(16) 0.1107(16) 0.3292(19) 1.2166 1.1037 1.1256 0.3938 0.3755 0.4159

0.0232(5) 0.0222(5) 0.0107(5) 0.0107(5) 0.0143(5) 0.0143(5) 0.0096(5) 0.0096(5) 0.0511(5) 0.0348(5) 0.0448(5) 0.0335(5) 0.0310(5) 0.0303(5) 0.0444(5) 0.0358(5) 0.0420(5) 0.0494(5) 0.0594 0.0412 0.0539 0.0394 0.0369 0.0361

1.0000 1.0000 0.95031(5) 0.05030(5) 0.95013(4) 0.05013(4) 0.92026(5) 0.08026(5) 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

00

ε* ðuÞ ¼ ε0 ðuÞ þ ε ðuÞ

(2)

The alternative current conductivity of all samples has been calculated from the dielectric losses according to the relation:




s* ¼ jε0 uε*ðuÞ ¼ jε0 u ε0
jε

00



00

¼ ε0 uε þ jε0 uε0

The real part of s* ðuÞ is given by:

(3)

00

sAC ðuÞ ¼ ε0 uε ðuÞ

(4)

where ε0 is the dielectric permittivity in vacuum (8.85  10
12 F m
1) and u is the angular frequency. 3. Results and discussion 3.1. Description of the structure The X-ray single crystal analysis of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 (TlRbSSeTe) at room temperature, shows that this compound crystallizes in monoclinic system with P21/c space group. The unit cell parameters a ¼ 13.6323(9) Å, b ¼ 6.6656(5) Å, c ¼ 11.5010(7) Å, b ¼ 107.076(4) , Z ¼ 4, V ¼ 999.00(12) Å3 and Dx ¼ 3.41 g cm
3. The asymmetric unit of the title compound, presented in Fig. 1, is formed by Tlþ/Rbþ cations, S/SeO4 tetrahedra and Te(OH)6 octahedra. The structural arrangement of the title compound projected onto the ab plan is depicted in Fig. 2. An examination of the structure clearly reveals the coexistence of three and different an2
2
ions (TeO6
6 , SO4 and SeO4 ) in the unit cell. They are connected by hydrogen bonds building up the crystal. The S and Se atoms are statistically distributed over the same site. This structure type can be at the origin of the ferroelectric polar phases in this compound. For this reason dielectric measurements were performed to prove this hypothesis. Indeed, the structure is being built by planes of pure TeO6 octahedra parallel to the (1 0 0) plane at x/a ¼ 0 and x/a ¼ 1/2 and to the (0 1 0) one at x/a ¼ 0 and x/ a ¼ 1/2 alternating with planes of pure S/SeO4 tetrahedra at x/a ¼ 1/ 4, x/a ¼ 3/4, x/b ¼ 1/4 and x/b ¼ 3/4. Moreover, the Tlþ and Rbþ cations are intercalated between these kinds of polyhedra.

3.1.1. Geometry and environment of TeO6 groups In the structure of the new compound TlRbSSeTe, the Te atom occupies two special positions. Therefore, the structure shows two types of octahedra Te(1)O6 and Te(2)O6. In the octahedral group, the TeeO distances range from 1.84(2) to 1.904(2) Å and OeTeeO angles between 86.5(1) and 93.5(8) . As a matter of fact, we realize that these values are different from those observed in the previously studied materials. However, in the Tl2(SO4)0.61(SeO4)0.39Te(OH)6 (TlSSeTe) material, the TeeO distances are between 1.886(10) to 1.979(11) Å and the OeTeeO angles vary from 86.2(2) to 93.8(2) [10]. On the other hand, in the Rb2(SO4)0.5(SeO4)0.5Te(OH)6 (RbSSeTe) structure, the TeeO distances vary from 1.908(7) to 1.923(7) Å with OeTeeO angles between 87.05(3) and 92.95(3) [11]. 3.1.2. Geometry and environment of S/SeO4 groups The structure of TlRbSSeTe presents one type of S/SeO4 tetrahedra. The tetrahedral coordination of S/Se atoms is built up with four oxygen atoms. The S and Se atoms, in this structure, occupy the same crystallographic sites. Indeed, in the present compound, the sulphur and selenium atoms occupy the same site of a statistical manner in respective proportions 92% and 8%. In fact, the S/Se
O distances in the (RbSSeTe) structure, vary between 1.519 (7) and 1.543 (6) Å with OeSe/SeO angles ranging between 108.2(3) and 110.6(3) [11]. The S/SeeO distances vary from 1.512(11) to 1.562(9) Å for the (TlSSeTe) structure [10]. Yet, in the mixed (TlRbSSeTe) material, the S/SeeO bonds vary from 1.46(2) to 1.518(2) Å and the OeS/SeeO angles range from 108.9(1) to 110.1(1) . The bond lengths and angles for the S/SeO4 tetrahedra are depicted in Table 4. The difference between these values and those obtained in the

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451

Table 3 Anisotropic displacement parameters of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 material. Atomes

U11

U22

U33

U12

U13

U23

Te1 Te2 Rb1 Tl1 Rb2 Tl2 S1 Se1 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10

0.01883(5) 0.01977(5) 0.01095(4) 0.01095(4) 0.01605(10) 0.01605(10) 0.00688(5) 0.00688(5) 0.071(18) 0.010(9) 0.046(16) 0.050(14) 0.014(10) 0.042(13) 0.039(15) 0.039(13) 0.062(15) 0.083(19)

0.02178(5) 0.02101(5) 0.01294(4) 0.01294(4) 0.01455(10) 0.01455(10) 0.00966(5) 0.00966(5) 0.045(14) 0.035(11) 0.023(11) 0.032(11) 0.037(10) 0.023(9) 0.031(11) 0.044(12) 0.045(12) 0.038(13)

0.02594(5) 0.02355(5) 0.00943(4) 0.00943(4) 0.01679(10) 0.01679(10) 0.01264(5) 0.01264(5) 0.066(15) 0.052(12) 0.057(14) 0.031(10) 0.041(10) 0.029(9) 0.064(15) 0.028(10) 0.045(11) 0.060(14)


0.00332(5)
0.00263(5)
0.00154(4)
0.00154(4)
0.00059(10)
0.00059(10) 0.00227(5) 0.00227(5)
0.038(13)
0.008(8) 0.001(9) 0.002(10) 0.006(8)
0.004(8) 0.003(10)
0.004(10)
0.007(13) 0.013(13)

0.00122(5) 0.00208(5) 0.00513(4) 0.00513(4) 0.01178(10) 0.01178(10) 0.00322(5) 0.00322(5) 0.029(13)
0.006(8)
0.017(10) 0.012(9)
0.001(8) 0.015 (9)
0.004(11) 0.003(9) 0.026(10) 0.026(13)


0.00312(5)
0.00238(5) 0.00105(4) 0.00105(4) 0.00049(10) 0.00049(10)
0.00004(5)
0.00004(5)
0.004(11)
0.004(9) 0.013(9) 0.003(8) 0.008(8)
0.014(7)
0.002(10)
0.001(8)
0.009(11)
0.006(10)

The anisotropic displacement exponent takes the form: exp[-2p2

P P i

jUij

hihj aiaj* ].

Table 4 Selected bond lengths (Å) and bond angles ( ). a-Thallium/rubidium groups Tl/Rb(1)dO4 ¼ 2.95(2) Tl/Rb(1)dO5(iv) ¼ 2.98(2) Tl/Rb(1)dO9(v) ¼ 2.99(2) Tl/Rb(1)dO2(iii) ¼ 2.99(2) Tl/Rb(1)dO10 ¼ 3.00(2) Tl/Rb(1)dO6(vi) ¼ 3.00(2) Tl/Rb(1)dO7(vii) ¼ 3.11(2) Tl/Rb(1)dO4(iv) ¼ 3.20(2) Tl/Rb(1)dO6(iv) ¼ 3.26(2)

Tl/Rb(2)dO7(ix) ¼ 2.96(2) Tl/Rb(2)dO8(v) ¼ 3.02(2) Tl/Rb(2)dO5(x) ¼ 3.06(2) Tl/Rb(2)dO3(xi) ¼ 3.08(2) Tl/Rb(2)dO3(viii) ¼ 3.13(2) Tl/Rb(2)dO1(xii) ¼ 3.16(2) Tl/Rb(2)dO10 ¼ 3.19(2) Tl/Rb(2)dO2(iii) ¼ 3.21(2) Tl/Rb(2)dO1(i) ¼ 3.28(2)

b-Sulfate/selenate groups S/SedO7 ¼ 1.53(2) S/SedO8 ¼ 1.51(2) S/SedO9 ¼ 1.49(2) S/SedO10 ¼ 1.44(3)

O7dS/SedO8 ¼ 110.00(12) O7dS/SedO9 ¼ 109.60(13) O8dS/SedO9 ¼ 108.00(11) O7dS/SedO10 ¼ 109.90(13) O8dS/SedO10 ¼ 108.70(12) O9dS/SedO10 ¼ 110.70(14)

c-Tellurate groups Te1dO2(i) ¼ 1.90(2) Te1dO3(i) ¼ 1.88(2) Te1dO1(i) ¼ 1.84(2) Te1dO1 ¼ 1.84(2) Te1dO2 ¼ 1.90(2) Te1dO3 ¼ 1.88(2) Te2dO5(ii) ¼ 1.90(2) Te2dO6(ii) ¼ 1.89(2) Te2dO4(ii) ¼ 1.87(2) Te2dO4 ¼ 1.87(2) Te2dO5 ¼ 1.90(2) Te2dO6 ¼ 1.89(2)

O2(i)dTe1dO3(i) ¼ 93.1(9) O2(i)dTe1dO1(i) ¼ 93.5(1) O3(i)dTe1dO1(i) ¼ 88.8(1) O2(i)dTe1dO1 ¼ 86.5(1) O3(i)dTe1dO1 ¼ 91.2(1) O1(i)dTe1dO1 ¼ 180 O2(i)dTe1dO2 ¼ 180 O3(i)dTe1dO2 ¼ 86.9(9) O1(i)dTe1dO2 ¼ 86.5(1) O1dTe1dO2 ¼ 93.5(10) O2(i)dTe1dO3 ¼ 86.9(9) O3(i)dTe1dO3 ¼ 180 O1(i)dTe1dO3 ¼ 91.2(1) O1dTe1dO3 ¼ 88.8(11) O4(ii)dTe2dO5 ¼ 91.8(9) O4dTe2dO5 ¼ 88.2(9) O5(ii)dTe2dO6 ¼ 89.6(9) O6(ii)dTe2dO6 ¼ 180 O4(ii)dTe2dO6 ¼ 90.5(8) O4dTe2dO6 ¼ 89.5(8) O5dTe2dO6 ¼ 90.4(9) O6(ii)dTe2dO4(ii) ¼ 89.5(8) O5(ii)dTe2dO4 ¼ 91.8(9) O6(ii)dTe2dO4 ¼ 90.5(8) O4(ii)dTe2dO4 ¼ 180

Symmetry codes: (i)
xþ2,
y
1,
zþ2; (ii)
xþ1,
y
3,
zþ1; (iii)
xþ2, y
1/2,
zþ3/2; (iv)
xþ1, yþ1/2,
zþ1/2; (v) x,
y
3/2, zþ1/2; (vi) x, yþ1, z; (vii) x, y
1, z; (viii)
xþ2, yþ1/2,
zþ3/2; (ix) x,
y
1/2, zþ1/2; (x)
xþ1,
y
2,
zþ1; (xi) x,
y
3/2, z
1/2; (xii) x,
y
1/2, z
1/2.

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Fig. 1. The asymmetric unit with atom labels and 50% probability displacement ellipsoids for non-H atoms of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6.

Fig. 2. Projection of crystal structure Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 on the ab plane.

TlSSeTe and RbSSeTe compounds are related to the size of the cation radii, which can be attributed to the partial cationic substitution.

3.1.3. The thallium/rubidium cations environment In the unit cell, the Tl and Rb atoms in the studied TlRbSSeTe solid solution are distributed on two sites that are sandwiches between the S/SeO4 tetrahedral and Te(OH)6 octahedral planes. In the present case, nine oxygen atoms coordinate the Tl(1)/Rb(1) and Tl(2)/Rb(2) cations in the mixed structure (TlRbSSeTe). Indeed, the

environment of Tl(1)/Rb(1) is composed by one oxygen atom belonging to Te(1)O6, five oxygen atoms of second octahedral Te(2) O6 and three oxygen atoms belonging to S/SeO4 tetrahedra (Fig. 3a). The Tl(1)/Rb(1) eO distances vary from 2.95 (2) Å to 3.26 (2) Å. The environment of Tl(2)/Rb(2) is formed by five oxygen atoms belonging to Te(1)O6, one oxygen atom of second octahedral Te(2) O6 and the others belonging to S/SeO4 tetrahedra (Fig. 3b). Tl(2)/ Rb(2)eO distances are included between 2.96(2) and 3.28(2) Å. Table 4 depicts the thallium/rubidium coordination. Compared to thallium sulfate tellurate compound (TlSSeTe), the

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

thallium atoms are surrounded by 6 and 7 oxygen atoms, respectively, with distance lengths between 2.842(12) and 3.151(9) Å [10]. Hence, the high coordination of the thallium/rubidium cations in the studied structure explains the stability of this new mixed (TlRbSSeTe) structure in view of the high interaction between cationic and anionic groups. 3.1.4. The O
H…O hydrogen bonds The OeH…O hydrogen bonds belong to the most important intermolecular bonding phenomena in inorganic materials. In fact, hydrogen bonds stand for the linking interactions between hydrogen atoms and negatively charged atoms with (or without) lone pairs [21]. The examination of the vibrational study of hydrogen bonded systems in condensed phases is a very important topic in physics

453

and chemistry. The presence of the O
H…O hydrogen bond gives many unusual properties. Indeed, infrared IR spectroscopy is a very powerful tool to explore H bonded systems. Numerous results of experimental and theoretical studies on hydrogen bonds have been examined [10,11,22,23]. In fact, IR spectrum of hydrogen-bonded systems is considered as a wealthy source of information on the dynamics of weak and medium strength hydrogen bonds. Over the last several studies, a theoretical of the IR and Raman spectroscopy of hydrogen bond has emerged, which has proven to be useful for interpreting the main features of the hydrogen bond in our sulfate selenate tellurate compound [24]. The O
H…O hydrogen bond ensures the connection between the S/SeO4 tetrahedra and the TeO6 octahedra. The stability of the crystal structure of TlRbSSeTe is guaranteed by protons which belong to hydroxide groups combining them. Thus, the presence of the O
H…O hydrogen bonds confirms that the studied material shows interesting physical properties [9,11,22e24]. Fig. 4 depicts a projected view of the new crystal structure, highlighting the hydrogen bonding in TlRbSSeTe. The geometrical characterizations of the hydrogen bonds network are stated in Table 5. It's noticeable that the hydrogen bonds, described in this ! structure, contribute to form tunnels parallel to b direction (Fig. 4). As a result, one oxygen atom O(8) of the tetrahedral groups S/ SeO4 is linked to two hydrogen atoms of the octahedra group (TeO6) and three oxygen atoms, O(7), O(9) and O(10). Each one is linked to one hydrogen atom uniquely (Fig. 4). In fact, the O…O distances are between 2.648 and 3.131 Å. The O
H distances in this compound vary from 1.828 Å to 2.285 Å with O
H…O angles ranging between 121.4 (1) and 146.9 (1) . The hydrogen atoms are located geometrically in this structure. According to the NOVAK criterion, the crystal structure of our compound exhibits two types of hydrogen bonds. Strong bonds for O…O distances which are smaller than 2.7 Å and weaker bonds in the other case [25]. All these results are reported in Table 5. These values are slightly higher than those found in RbSSeTe structure. Thus, the insertion of Tlþ with Rbþ in RbSSeTe can serve to decrease the stability of this structure. In TlRbSSeTe material, the presence of the O
H…O hydrogen bonds, and all these O…O, O…H values prove to be at the origin of very interesting physical properties such as protonic conduction at high temperature. This interpretation was confirmed by conductivity and dielectric study. 3.2. Thermal analysis

Fig. 3. a The coordination of Tl(1)/Rb(1) cations. b The coordination of Tl(2)/Rb(2) cations.

3.2.1. Calorimetry study The differential scanning calorimetry (DSC) measurements of TlRbSSeTe powder was taken upon heating scans in the 300e550 K temperature range with a scanning speed of 5 K min
1 in order to determine the phase transitions. The results of the calorimetric study of our compound are presented in Fig. 5. An overview of this thermogram curve shows the existence of three endothermic peaks. Hence, the calculated transition enthalpies, for the first transition at T1 ¼ 398 K is DH1 ¼ 25.65 Jg
1. However, the second and the third peaks are stacked with other peaks. Thus, the enthalpy corresponding to these peaks is DH2 ¼ 213.42 Jg
1. Compared to other similar compounds, the first transition of the title compound at 398 K can be attributed to the structural phase transition, which can favor a non-centro-symmetric phase at high temperature [12,23]. On the other side, the second one observed at 448 K can be related to ferro-paraelectric phase transition [21e23]. As for the third endothermic peak at 475 K, it corresponds to the

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Fig. 4. Projection of the structure Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 showing the Hydrogen bonds.

Table 5 Hydrogen-bond and short contact geometry (Å,  ). DdH$$$A

DdH

H$$$A

D$$$A

DdH$$$A

O1dH1$$$O8(iii) O2dH2$$$O8(iv) O2dH2$$$O10(iv) O3dH3$$$O7(v) O6dH6$$$O9(vi)

0.955 0.958 0.958 0.949 0.950

2.176 1955 2285 1.828 1. 913

2.795 2.792 3.131 2.648 2.720

121.4(1) 144.7(1) 146.9(1) 142.9(1) 141.3(1)

Symmetry codes: (iii) x, y, zþ1; (iv)
xþ2, yþ1/2,
zþ3/2; (v)
xþ2, y
1/2,
zþ3/2; (vi)
xþ1, y
3/2,
zþ1/2.

protonic conduction phase transition in view of the breaking of O
H…O hydrogen bonds which connect tellurate groups to S/SeO4 one [11,12,23]. It's worth noting, after this thermal analysis, our material preserves its solid state, which confirms that the material has not achieved the melting temperature [9,23].

3.2.2. Thermogravimetric (TG) and differential thermal analysis (DTA) At this stage of analysis, Such a structural arrangement is observed in the new TlRbSSeTe structure which is characterized by the presence of three independent and different anions (SO2
4 , 6
SeO2
4 and TeO6 groups) connected by (O
H…O) hydrogen bond. Investigating the thermal behavior of this material is quite interesting. In order to get further information about these phase transitions, we have undertaken thermo-differential and thermogravimetric measurements from 350 to 550 K. According to the superposition of TG/DTG, DTA curves report in Fig. 6, we conclude that DTA presents three peaks at 403, 438 and 480 K respectively. In fact, we notice that the first peak observed in DTA at T1 ¼ 403 K, is not accompanied by a weight loss and does not correspond to the melting point, which indicates that the (TlRbSSeTe) undergoes structural changes over the same temperature.

Fig. 5. Differential Scanning Calorimetry of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6.

This result is in good agreement with the previous calorimetric study (DSC) presenting an endothermic peak at 398 K. Moreover, the weight loss occurs over the temperature range 448e475 K. Approximately 7.52% of the mass is lost, which corresponds to the loss of two water molecules per chemical formula, associated with endothermic peak at 480 and 475 K on the DTA and DSC curves, respectively. Comparing the obtained results with the already conducted studies, we infer that the telluric acid Te(OH)6 decomposes to release the two water molecules as well as the orthotelluric acid H2TeO4 [23,26]. The decomposition of the new material can be described by the following reaction: Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 / Tl1.90Rb0.10(SO4)0.92(SeO4)0.08 H2TeO4 þ 2H2O

(5)

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455

Fig. 6. TGeDTGeDTA curves of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 material.

This result is confirmed by the dielectric and Raman studies at different temperatures.

Fig. 7. IR spectrum at room temperature of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound.

3.3. Vibrational spectroscopy study To provide further information about the new TlRbSSeTe crystal structure, we referred back to previous studies on this sample using infrared absorption and Raman scattering. We have undertaken IR and Raman spectroscopic studies for this material in order to confirm the presence and the indepen2
2
dence of the three anions (TeO6
6 , SO4 and SeO4 ) groups, and elucidate the hydrogen bonds in their crystal lattice. The study of IR and Raman spectra of this mixed compound at room temperature which has been conducted in the frequency range (400e4000) cm
1 and (50e1200) cm
1 is displayed in Figs. 7 and 8; whereas, the Raman spectra performed at various temperatures are exhibited in Fig. 9. The observed bands and their assignment to different modes for TlRbSSeTe compound are presented in Table 6.

3.3.1. Interpretation of IR spectrum The infrared spectroscopy is one of the major physical methods of investigation for molecular structures. At room temperature, the absorption of TlRbSSeTe compounds exhibits a monoclinic symmetry with space group P21/c with four formula unit. The attribution of TeO6, SO4, SeO4, bands (Table 6) is carried out by comparison to other materials having similarity with the new compound (TlRbSSeTe). In fact, the bands observed at 642 cm
1 are assigned to the symmetric stretching (n1) mode of TeO6 [22,23,26]; whereas, the intense peak detected at 583 cm
1 is associated with the asymmetric stretching of n3(TeO6) [22,23,26]. The tetrahedral SeO4 group has all the vibration modes which are IR active, whereas only n4 is Raman active. The symmetric stretching vibration n1 of (SeO4) appears in the spectra at 826 cm
1. The line observed at 863 cm
1 is assigned to the asymmetric stretching (n3) mode of (SeO4). n2(SeO4) vibration appears in IR spectra at 847 cm
1 [23]. For SO4 groups, the internal vibration of SO4 tetrahedra has four vibrational modes, two stretching modes n1, n3 and two bending modes n2 and n4 of a regular tetrahedron. The intense peak detected at 971 cm
1 is associated with the symmetric stretching (n1) mode of (SO4). The line at 1030 cm
1 is attributed to the asymmetric stretching vibration (n3) of (SO4) tetrahedral [22]. The two stretching modes n2 and n4 SO4 are active

Fig. 8. Raman spectra at room temperature of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound.

in Raman spectra [22,23]. As for the strong band at 2970 cm
1 in IR spectra, it can be assigned to the OeH stretching vibration [21,23,27]. 3.3.2. Interpretation of Raman spectrum 3.3.2.1. Raman spectra at room temperature. In the present investigation, a Raman spectroscopic measurement of this new compound was identified and analyzed. In order to gain additional information on crystal dynamics about the degree of disorder in the different phases and to confirm the mechanisms involved in the transition, we have undertaken a Raman study between 300 and 490 K in the range 50e1200 cm
1. The increase of the temperature affects the Raman spectra, indicating the presence of different phase transitions in the TlRbSSeTe compound. Compared to previous works focusing on 2
2
similar materials containing TeO6
6 , SO4 and SeO4 ions, we proposed certain assignment attempts of the observed different bands [8,23,24]. The stretching and bending vibrations for materials containing

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In the Raman spectra, the totally strongest symmetric stretching mode n1(SO4) tetrahedral groups occur at 969 cm
1 [8,22e24]. The bands observed at 470, 628 cm
1 correspond to n2(SO4) and n4(SO4) [22,23]. In (<200 cm
1) Raman spectral region, the low-frequency including the translation modes of Rbþ cations is observed at 57 cm
1 [8,26], while the very weak band at 109 cm
1 correspond to the lattice modes [8,26]. The peak which appears at 172 cm
1 can be attributed to the vibration and translation modes of S=SeO2
4 and TeO6
6 ) anions [23].

Fig. 9. Raman spectra of Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound at different temperatures.

TeO6 group usually occur in regions 550e750 and 350e450 cm
1, respectively [8,23]. At room temperature, the Raman spectrum of our mixed compound is very resolved, which confirms the presence of the polar phase. In fact, the intense peak around 642 cm
1 is assigned to the symmetric stretching n1(TeO6) [8,21e23], while the peak appearing at 628 cm
1 is attributed to the n2 vibration of TeO6. Moreover, the two vibration modes n3(TeO6) [8,21e24] and n4(TeO6) occur at respectively 596 cm
1 and 331 cm
1. The band observed at 357 cm
1 corresponds to n5(TeO6) [22,23]. However, n6(TeO6) vibration appearing in the spectra at 245 cm
1, is in pffiffiffi agreement with Wilson's rule n5(TeO6) ¼ 2 n6(TeO6) [22,23]. Besides, the peak detected at 827 cm
1 is attributed to n1(SeO4) tetrahedral groups. The n4(SeO4) [23,24] vibration appears in this spectra at 470 cm
1. Only n2 and n3 are IR active.

3.3.2.2. Temperature evolution of the Raman spectra. Fig. 9 reveals the temperature evolution of the low frequency (50e1200 cm
1) Raman spectrum of our addition compound (TlRbSSeTe) in the temperature range from 300 K to 490 K where DSC results confirm three phase transitions. Departing from the spectrum, we can deduce that when temperature increases, many bands present a decreasing intensity and an increasing width, which is in agreement with the establishment of a disorder with the paraelectric phase. This fact proves our last interpretation as well as the presence of the superprotonic phase transition observed in this compound which refers basically to the breaking of the hydrogen bond favoring the disorder phase. Thus, two phase transitions at 448 and 475 K have been confirmed in this salt by Raman spectroscopy. On heating the sample, the lines at 642, 331 and 245 cm
1 assigned to n1(TeO6), n4(TeO6) and n6(TeO6), respectively, broaden and decrease in intensity. Furthermore, the peak that appears at 357 cm
1 attributed to n5(TeO6) decreases considerably with the increase in temperature. However, the bands at 628 and 596 cm
1 corresponding to n2(TeO6) and n3(TeO6), respectively, decrease progressively and disappear completely at 440 K. On the other side, the vibration mode of SO4 tetrahedra shows an important fluctuation at a high temperature. In fact, the band relative to n1(SO4) at 969 cm
1 and n2(SO4) at 470 cm
1 remains constant in both intensity and wavelength number but it decreases in intensity and broadens in the neighborhood of the second transition then disappears at high temperature. However, the

Table 6 Observed IR and Raman frequencies (cm
1) and band assignments for Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6. IR

Raman

Assignment

T ¼ 300 K

T ¼ 300 K

T ¼ 340 K

T ¼ 380 K

T ¼ 400 K

T ¼ 420 K

T ¼ 440 K

T ¼ 490 K

2970 s 2356 s 1418 vs 1030 vs 971 vs 863 s 847 s 826 s 647 s

e e e e 969 vs

e e e e 968 vs

e e e e 968 vs

e e e e 968 vs

e e e e 968 vs

e e e e 968 vs

e e e e 968 vs

e 827 m 642 vs 628 m

828 m 641 vs 628 m

827 m 641 vs 630 m

827 m 641 vs 629 w

827 m 641 s 628 w

827 w 642 s e

827 vs 641 m e

596 w 470 m

593 w 470 m

591 w 470 m

592 w 477 m

593 vw 470 m

598 vw e

e e

e 583 s

n(O
H) of Te(OH)6 e e n3(SO4) n1(SO4) n3(SeO4) n2(SeO4) n1(SeO4) n1(TeO6) n2(TeO6) and n4(SO4)

e

357 m

359 m

361 w

356 w

356 vw

355 vs

e

e

331 m 312 w

334 m 313 w

336 w 314 w

336 w 316 w

333 vw 313 vw

332 vw 312 vw

e e

e

245 s

259 s

258 s

258 s

259 m

261 m

261 w

e

171 w

170 w

174 vw

173 vw

172 vw

e

e

n3(TeO6) n2(SO4) and n4(SeO4) n5(TeO6) n4(TeO6) n2(SeO4) n6(TeO6) nOH…O

e

109 w

108 w

106 vw

105 vw

108 vw

e

e

6
T(S/SeO2
4 ;TeO6 )

e

57 w

57 w

56 vw

55 vw

55 vw

e

e

T(Rbþ)

e

Relative intensities: vs: very strong; s: strong; m: medium; w: weak; vw: very weak.

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457

stretching mode n4(SO4) decreases in intensity and disappears at high temperature [22]. As for the vibration mode of SeO4, n1(SeO4), it keeps the same place with a progressive decrease in intensity, and broadens in the neighborhood of the first transition, then disappears at high temperature, but the vibration n4(SeO4) decreases in intensity and disappears at the first transition. However, the band at 312 cm
1 attributed to n2(SeO4), decreases progressively and disappears entirely at high temperature. These findings are in accordance with the previous study [9,24]. When temperature increases, we remark that the peaks show an increase in their full width at half height for this new mixed compound (TlRbSSeTe), then these peaks disappear at high temperature. Consequently, the result observed in these curves of our material goes in agreement with these phase transitions detected by 2
2
DSC, involving mainly (TeO6
6 , SO4 and SeO4 ) motions and the breaking of O
H…O hydrogen bonds.

3.4. Electrical properties The electrical properties of the new mixed material (TlRbSSeTe) were analyzed by complex impedance spectroscopy over a range of frequencies and temperatures. The main objective of this study is to analyze the electrical processes of the grain and grain boundary effects by making an interpretation of the microscopic process which allows discerning the role of grain and grain boundary [28]. Furthermore, it also offers an insight about the electrical processes taking place within the system and their correlation with the sample when modeled in terms of their equivalent electrical circuit [29]. The Nyquist plots drawn between imaginary part of complex 00 impedance (Z ) versus real part of complex impedance (Z 0 ) for the TlRbSSeTe compound at different temperatures are presented in Fig. 10. a, b. It is worth noting that there are two semicircles in each impedance spectrum. The first semicircle at lower-frequencies refers to the grain boundary, whereas the second at higher frequencies refers to the bulk grain effect [30]. The impedance data is fitted to an equivalent circuit that consists of a series combination of grains and grains boundary elements [30e34]. The Zview program was used to fit the measured impedance data alongside with typical equivalent circuit formed by a series combination of two cells: a parallel combination of a resistance (Rg ) and a fractal capacitance constant phase element (CPE) forming together the first equivalent circuit configuration related to the grain, while the second is obtained by connecting parallel combinations of resistance (Rgb ) and constant phase elements (Cgb ) related to grain boundary (insets of Fig. 11). The impedance of the capacity of fractal interface CPE is expressed by the following equation [35]:

ZCPE ¼

1 Q ðjuÞa

Fig. 10. a, b Nyquist plots (Z00 vs. Z0 ) at different temperatures for TlRbSSeTe compound.

equations:

Z0 ¼

Rgb

1 þ uRgb Cgb

2


 aP R2g Qg uag cos g2 þ Rg þ

2

2 aP aP 1 þ Rg Qg uag cos g2 þ 1 þ Rg Qg uag sin g2 (7) 2

(6)

where Q indicates the value of capacitance of the CPE element and a is the fractal exponent. The previous equation shows that if: a ¼ 1, ZCPE ¼ 1=jQ u, it means that CPE involves a pure capacitance, and if: a ¼ 0, ZCPE ¼ 1=Q , it means that CPE involves a pure resistance. The values of a vary in the range 0.84e0.98, showing a capacitive behavior of the fractal phase CPE. The real and imaginary components of the impedance of the equivalent circuit were calculated according to the following




6 Z ¼ Rgb 4 00

3

uRgb Cgb


1 þ uRgb Cgb

7 2 5


 aP R2g Qg uag sin g2 þ

2

2 aP aP 1 þ Rg Qg uag cos g2 þ 1 þ Rg Qg uag sin g2 (8) 00

Fig. 12 represents Z 0 and Z versus frequencies together with fits to the equivalent circuit portrayed in Fig. 11. At 423 K temperature,

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The phase transitions observed in the calorimetric study are confirmed by the change of the curve slope in Fig. 13 at T1, T2, T3 and   T4 as well as, an Arrhenius type behavior, sdc ¼ A exp
kEaT , that B

Fig. 11. Simulated Nyquist plots with equivalent circuit elements for TlRbSSeTe compound at 423 K.

an excellent agreement between the experimental (scatter) and the theoretical curve (line) of the real and imaginary impedance is recorded. All fitted curves at each temperature indicate the good conformity of the calculated lines with the experimental data, confirming that the suggested equivalent circuit describes the crystaleelectrolyte interface reasonably well. The extracted parameters for the circuit elements are summarized in Table 7.

3.5. Conductivity analysis 3.5.1. DC electrical conductivity The values of resistance (R) obtained by data fit of the impedance spectra, the area of the sample S and the sample thickness e are used to determine the dc conductivity, which is given by the following equation:

sdc ¼


e  R*S

(9)

The thermal evolution of the conductivity in TlRbSSeTe compound as a fonction of inverse temperature ðlnðsdc :TÞ ¼ð1000=TÞÞ is represented in Fig. 13.

is shown for regions (I), (II), (III) and (V), revealing the conduction phase transition in this material [1,24]. Furthermore, the activation energy calculated by the linear fit of the curve conductivity from (Fig. 13) in regions (I), (II), (III) and (V), are Ea I ¼ 1.38 eV, Ea II ¼ 3.07 eV, Ea III ¼ 0.04 eV and Ea V ¼ 0.24 eV, respectively. In region (IV), the conductivity plot is just ready constant, which can be assigned to the phase transition. DTA shows the existence of an endothermic peak in this temperature range. Since this region presents a metastable state, any conduction mechanism can be found [36]. The superionic-protonic conduction appears in this compound at a temperature above 475 K. Regarding the crystal structure and the chemical composition, it is inferred that this drastic increase refers to the ionic conductivity [37]. The conductivity plot proves that the proposed material presents a superionic-protonic conduction that may be assigned to the breaking of O
H…O hydrogen bonds which link octahedral and tetrahedral groups, building up the stability of crystalline edifice [24,38]. Departing from this behavior, we distinguish two main mechanisms of proton transport are distinguished. The first one, is the proton motion within a hydrogen bond from one potential minimum to another. The second mechanism, is the proton motion between oxygen molecules. During this process, the liberation or even rotation of TeO6 octahedra, SO4 and SeO4 tetrahedra leads to the breaking of the hydrogen bond and the transfer of the proton to the nearest vacant position with the formation of a new hydrogen bond. 3.5.2. AC electrical conductivity The study of electrical conductivity sac is important for any dielectric material. It affords reliable information about the transport phenomenon in compound. AC measurements are of extreme importance in terms of distribution of electric field in the system and the induced field perturbations. The variation of the AC electrical conductivity versus the angular frequency at different temperatures for our sample is detailed in Fig. 14. As a matter of fact, the conductivity curves for the studied sample reveal two different regions: low angular frequency region and high angular one. The first one proves the presence of direct current conductivity (AC); whereas, in the second region, the AC conductivity, sac, rises with the increase in frequency at different temperatures, which is a characteristic of us . The conductivity results of the TlRbSSeTe material are fitted by Table 7 Equivalent circuit parameters for the Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound at different temperatures.

Fig. 12. Variation of Z0 and Zʺ with the angular frequency of TlRbSSeTe compound at 423 K.

T(K)

Rg (U)

Qg (F)

ag

Rgb (U)

Qgb (F)

383 393 413 423 448 458 468 478 498 508 518

6.67  108 1.29  108 2.01  106 6.38  105 7.07  105 5.21  105 1.34  106 1.64  106 1.16  106 9.01  105 6.70  105

2.24  10
11 2.81  10
11 1.75  10
10 2.51  10
10 1.34  10
10 1.68  10
10 1.50  10
10 1.72  10
10 1.86  10
10 1.91  10
10 1.95  10
10

0.98 0.79 0.88 0.88 0.90 0.89 0.90 0.89 0.89 0.88 0.87

3.68  106 2.08  106 2.35  103 1.87  104 8.23  102 4.97  102 1.83  103 4.67  103 7.25  103 6.56  103 5.37  103

1.19  10
10 7.97  10
10 1.40  10
10 6.41  10
11 1.98  10
10 2.68  10
10 1.10  10
10 1.08  10
10 9.90  10
10 9.90  10
10 1.01  10
10

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459

(Fig. 15). This variation is well described by the Arrhenius relation and characterizes the five regions which are confirmed by the change of the curve slope at T1 ¼ 400 K, T3 ¼ 450 K and T4 ¼ 480 K. The variation of the slope at T2 ¼ 420 K is not observed by calorimetric study. Such transition may be due to a change of conduction mechanism. With regard to the activation energy obtained, the values of Ea determined from linear fit to the data points in the different regions as well as R2 values are reported in Table 8. As for the frequency variations of the obtained activation energy Ea , they are shown in Fig. 16. In addition, It is clear that the activation energy usually decreases with the increase in frequency. This result suggests that the applied field frequency improves the electronic jumps between the localized states. Consequently, the smaller activation energy values and the increase in AC conductivity as well as applied frequency suggest the hopping mechanism for the conduction in this compound. Fig. 13. Variation of the ln (sdc.T) versus 1000/T for the TlRbSSeTe compound.

3.6. Theory investigation of the conduction mechanism the following equation referred to as Jonscher's universal power law [28]:

sðuÞ ¼ sdc þ Aus

(10)

where sdc is the direct current (AC) conductivity, A is a constant that depends upon temperature and s is the power law exponent with values in the range 0 < s < 1. The exponent (s) represents the degree of interaction between mobile ions with the environments surrounding them [39,40]. On the other side, Fig. 15 illustrates the temperature dependence of AC conductivity for TlRbSSeTe compound at different frequencies in the form of lnðsac :TÞ versus ð1000=TÞ, which clearly shows five distinct regions presumably corresponding to different conduction mechanisms. Besides, the experimental values of AC conductivity are fitted to the Arrhenius-type behavior described by the following expression [41]:



sac ¼ A exp


Ea kB T



where A is the pre-exponential factor, Ea is the activation energy, T is the absolute temperature and kB is the Boltzmann's constant

Fig. 14. Frequency dependence of AC conductivity at various Temperatures.

In order to find the predominant conduction mechanism of the AC conductivity of the new mixed crystal (TlRbSSeTe), the convenient mode for the conduction mechanism is suggested taking into account the several theoretical models which associate the conduction mechanism of AC conductivity with s(T) comportment [42] (Fig. 17). In literature, different models have been considered based on two distinct processes, namely, classical hopping over a barrier and quantum-mechanical tunneling, or some certain variations or combinations of the two processes. It has been differently assumed that electrons (or polarons) or atoms are the responsible carriers [43]. These different models are: - The quantum mechanical tunneling (QMT) model, wherein the exponent “s” is almost equal to 0.8 and temperature independent or increases slightly with temperature [44,45]. - The correlated barrier hopping(CBH) model, wherein the exponent “s” decreases with the increase in temperature [46]. - The overlapping large-polaron tunneling (OLPT) model, wherein the exponent “s” depends on both frequency and temperature

Fig. 15. Variation of the ln (sac.T) as a function of temperature of the TlRbSSeTe compound.

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Table 8 Frequency dependence of activation Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6.

energy

of

AC

conduction

Ea

Phases

Frequency (Khz)

Activation energy DE (eV)

R2

Phase I

1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000

0.9 0.8 0.35 0.27 0.15 2.48 0.2 1.72 1.37 0.65 0.3 0.36 0.32 0.25 0.41 0.21 0.26 0.18 0.08 0.15

0.9029 0.9239 0.9403 0.9689 0.9726 0.9301 0.9609 0.9736 0.9685 0.9858 0.9755 0.9864 0.9795 0. 9767 0.9675 0.9861 0.9881 0.9935 0.9905 0.9959

Phase II

Phase III

Phase V

in

Fig. 17. Temperature dependence of the exponent s and (1-s) for the TlRbSSeTe compound.

Though the variation of the slope at 420 K is observed in ln sigma (ac) and s for the sample, it is not observed by Calorimetric study. This obtained result suggests that this transition refers to the change of conduction mechanism. As a consequence, NSPT and CBH models are the most suitable ones to characterize the electrical conduction mechanism of our sample in regions I, II, III, IV and V respectively.

Fig. 16. Frequency dependence of activation energy at different regions of TlRbSSeTe.

and decreases with a rise in temperature to a minimum value and then increases as temperature rises [47]. - The non-overlapping small polaron tunneling (NSPT) model, wherein the exponent s increases with temperature increase [48]. Fig. 17 depicts the variation of the exponent “s” and the fitted values of (1-s) as a function of temperature. These values prove to be conversely varied. It is obvious from this figure that two fundamental mechanisms are observed. First of all, the values of (s) increase with temperature increase in regions (I) and (III) suggesting that the non-overlapping small Polaron tunneling (NSPT) model is the suitable one to characterize the electrical conduction mechanism in these regions, indicating in turn the activated behavior of polarons, which is independent of interstice separation [48]. Secondly, the values of (s) decrease with the rising temperature in phase (II), (IV) and (V), indicating that the Correlated Barrier Hopping (CBH) model is the appropriate model for these regions, in which the charge carrier hops between the sites over the potential barrier separates them [47].

3.6.1. The CBH model regions (II), (IV) and (V) According to the correlated barrier hopping (CBH) model, the values of s decrease with the increase in temperature. This goes in good agreement with the obtained results for TlRbSSeTe compound, as shown in Fig. 17. In CBH model, carrier motion occurs by means of hopping over the Coulomb barrier separating two defect centers. This model, was first developed by Pike [49] for single polaron hopping, and has been further improved by Elliot [50] for simultaneous bipolaron hopping. Based on the CBH model, the ac conductivity is given by the expression [51,52]:

sac ¼

np2 NNP ε0 uR6u 24

(12)

where n is the number of polarons involved in the hopping process (n ¼ 1 or 2 for a single or bipolaron transport, respectively), NNP is proportional to the square of states concentration and ε0 is the dielectric constant. Ru is the hopping distance for conduction (ut ¼ 1). Where the hopping length Ru is determined by the quadratic equation [53]:

Ru ¼

pε0 ε0

e2

 1 WM
kB T ln ut 0

(13)

where kB is the Boltzmann constant and t0 is the characteristic relaxation time, which is in the order of atom vibrational period t0 ¼ 10
13 s. WM is the height of binding energy (or maximum barrier) which has to surmount the charges trapped in localized sites [53]. NNP is given by Ref. [54]:

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

NNP ¼ NT 2

(14)

Rw ¼

461

  1 1 W ln þ M 2a ut0 kB T

(21)

(for bipolaron hopping) where where NT is the number of states density.

NNP ¼ NT 2

 
Ueff exp 2KB T

(15)

(for single polaron hopping) The value of frequency exponent s in the CBH mode is calculated with reference to Eqs. (12) and (13), and is equal to

s¼

d lnðsac Þ ¼1
d lnðuÞ W

M

a
1 : is the spatial extension of the polaron (¼1  1010 m). WM : is the polaron hopping energy. t0 : is the characteristic relaxation time (10
13 s). NðEF Þ: is the density of states near from the Fermi level. Rw : is the tunneling distance.

6kB T
 1
kB TLn ut 0

(16)

This equation implies that s is both frequency and temperatureM dependent. It is worth noting that, at least for small values of W ,s k T B

M ,s increases with increasing frequency. While for large values of W k T B

is closer to unity and the increase is so small that s is effectively frequency independent. So, Eq. (16) is reduced to [55]:

3.7. Complex modulus analysis The complex modulus formalism is an important theory, created by Macedo et al. [57,58]. This formalism has been used as a tool in the analysis of the electrical properties which is particularly suitable to detect such phenomena as electrode polarization and apparent conductivity relaxation time [59]. The complex electrical modulus (M*) stands for the reciproque of the dielectric permittivity (ε*) using the following relation [60].

M* ¼

6k T s¼1
B WM

(17)

Fig. 17 exhibits the variation of (1-s) as a function of temperature. The linear fit of these curves in the different regions is carried out to calculate the value of the binding energy WM , equaling 0.374, 0.398, and 0.172 eV for the regions II, IV and V, respectively.

s¼1þ

4kB T


 1 WM
kB T ln ut 0

(18)

where kB is the Boltzmann's constant, t0 is a characteristic relaxation time, which is in the order of an atom vibrational period and WM is the polaron hopping energy. For large values of

s¼1þ

WM , kB T

Eq. (18) becomes:

4kB T WM

(19)

The values of the barrier height WM are extracted from the linear fit of the two plots regions (I) and (III) in graph (1-s) versus T (Fig. 17). They are found to be equal to 0.14 and 0.58. For this model of conduction, NSPT, the AC conductivity expression is given by Ref. [56]:



sac

 e2 p kB T ua
1 ðNðEF ÞÞ2 R4u ¼ 12

with

(20)

(22) 00

The real M 0 and the imaginary M parts of electric modulus are obtained from the impedance data using the following expressions:

M0 ¼

00

3.6.2. The NSPT model (regions I and III) Small polaron tunneling (NSPT) model for conduction mechanism in this sample is described in the two regions I and III where the exponent (s) increases with increasing frequency. This goes in good agreement with the obtained results for TlRbSSeTe compound, as shown in Fig. 17. As a matter of fact, NSPT mechanism can occur in a covalent solid provided that the addition of a charge carrier to a site causes a large degree of local lattice distortion. According to this model, the frequency exponent (s) could be computed using the formula [48]:

00 1 ¼ juC0 Z* ¼ M 0 þ jM ε*

M ¼

ε0 ðε0 Þ2

þ ðε Þ2 00

¼ uC0 Z

00

(23)

00

ε

ðε0 Þ2 þ ðε Þ2 00

¼ uC0 Z 0

00

(24)

00

where ðM 0 ; Z Þ and ðM ; Z 0 Þ are the real and imaginary parts of the electric modulus and impedance, respectively, j ¼ ð
1Þ1=2 , u angular frequency ðu ¼ 2pf Þ and C0 (vacuum capacitance of the cell) C0 ¼ ε0 A=t (where ε0 is the permittivity for free space, A is the area of the electrode surface and t is the thickness) [61,62]. The variation of the experimental and simulated data of the 00 imaginary M part of the electrical modulus as a function of the angular frequency of TlRbSSeTe sample at several temperatures is represented in Fig. 18. The plots reported in this figure are characterized by the presence of two relaxation peaks. Thus, the low frequency domain corresponds to the grain boundaries effect, while that of the high frequency, it is associated with grain effect, which proves the observed result in the impedance spectra. 00 The two peaks of M shift to higher frequency with increasing temperature, which suggests an ionic conductor character of the compound [63]. Usually, the general method to study nature of the dielectric relaxation in such materials is to fit the measured data by KohlrauscheWilliamseWatts (KWW) decay function. As a matter of fact, the stretched exponential function of a solid is defined by the empirical KWW function [64,65]:

 fðtÞ ¼ exp




t

tKWW

b !

ð0 < b < 1Þ

(25)

where t is the characteristic relaxation time, and b is the well known Kohlrausch parameter. This parameter indicates the degree of non-Debye behavior which decreases with an increase in the

462

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

ε* ¼

1 00 ¼ ε0 þ jε juC0 Z *

(28)

00

Fig. 18. Angular frequency dependence of the imaginary part M00 of the electric modulus at different temperatures.

relaxation time distribution. fðtÞ is associated with the modulus in the frequency domain by the equation [58]:

2 M ðuÞ ¼ M∞ 41
00

*

Z∞

e
jut






dfðtÞ dt dt

(26)

0 00

00

where M∞ (M∞ ¼ 1=ε∞ ) is the asymptotic value of the real part of the dielectric constant. 00 Indeed, The imaginary part M of the complex modulus for different temperatures has been fitted with an approximate frequency representation of the (KWW) function, suggested by Bergman (Eq. (2)) [66]: 00

M ¼h

} Mmax   i b umax  þ umax b ð1
bÞ þ ð1
ð b u u bÞ




(27)

} where Mmax and umax are the peak maximum and the peak angular frequency of the imaginary part of modulus, respectively. A typical curve of imaginary parts of Modulus M} is plotted at 423 K in Fig. 19. A good agreement is recorded between experimental and theoretical values as shown in this spectrum. In the studied frequency range, two relaxation peaks of the sample are observed. So, the smaller peak at lower frequency is associated with the grain boundaries effect and the well defined higher frequency is correlated with grain effect, which confirms the obtained result in the impedance spectra.

whereε0 and ε are the real and imaginary parts of the dielectric constant, respectively. We have studied the temperature dependence of the real (ε0 ) 00 and imaginary (ε ) parts of the dielectric permittivity for (TlRbSSeTe) material at different frequencies. These are reported in Figs. 20 and 21. It is observable from these figures that there are four regions, region I (T < 398), region II (398 < T < 448), region III (448 < T < 475) and region IV (T > 475). 00 At T < 398 K, the variations of ε0 and ε with temperature are almost constant. This may be explained by the restricted reorientational motions of the proton, which cannot orient themselves with respect to the direction of the applied electric field, but they acquire a weak contribution to polarization. Over the transition temperature, T > 398 K, the reorientational dynamics of protons is activated. The cation gets enough excitation thermal energy to be able to obey the change in the external electric field more easily. This in return enhances their contribution to the polarization leading to an increase in dielectric behavior. Two peaks are observed at low frequencies in these spectra: The first peak of low intensity at around T ¼ 423 K associated with the ferroelectric-paraelectric phase transition, which coincides with the temperature observed by DSC at 448 K [4,23]. Tc temperature is independent of frequency suggesting that the sample does not present any type of dielectric relaxation at this frequency range [6,7]. The second peak observed at T ¼ 467 K can be attributed to ioniceprotonic phase transition [67,68]. The obtained curves reveal the peak shifts to higher frequencies. The peak height decreases with the increase in temperature as expected for a dipolar relaxation. The important evolution of the dielectric constant with decreasing frequencies is connected to the great contribution of the conductivity in this material. The decrease of ε0r and ε}r with increasing frequency is linked to the large conductivity in our compound due to charge carriers and to the fast mobility of the proton Hþ [67,68]. Furthermore, at T > 475 K, as the frequency increases, the peak located at 467 K becomes less pronounced. This can be explained by

3.8. Dielectric properties The study of the dielectric properties is one of the important sources helping researchers to gain more information about the conduction mechanisms in the compounds and the origin of the dielectric relaxation. The dielectric relaxation analysis has been performed to reveal significant information of chemical as well as physical behavior. The complex dielectric function can be represented by the following expression [66]:

Fig. 19. Angular frequency dependence of M00 fitted using two Bergman functions and the inset showing the experimental spectra of M00 at 423 K.

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

463

Fig. 22. This figure, reveals that the dielectric loss exhibits similar values of the dissipation factor (tan d) with ε0 and ε00 . The obtained values of the dissipation factor (tan d) are greater with the important contribution of conductivity in the title compound. In fact, the dielectric loss rises from low temperature until it reaches a maximum, then decreases and presents a minimum in the vicinity of Tc (Curie temperature). The minimum of tan d found for temperatures between 439 and 469 K are associated with the maximum of ε0 (Fig. 22). The behaviors of the dielectric permittivity ε0 and Tand confirm the existence of ferroelectriceparaelectric phase transition in TlRbSSeTe material at T ¼ 439 K. Consequently, the values of ferroelectriceparaelectric temperature phase transition do not change with the rise in frequency, which suggests that this material does not present a dipolar-type relaxation in this frequency range. This phase transition appears also in the similar compound TlKSSeTe of our new sample at 468 K [23]. Fig. 20. Variation of ε0 r with temperature Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound.

Fig. 21. Variation of ε00 r with temperature Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6 compound.

at

different

frequencies

of

4. Conclusion

at

different

frequencies

of

In this work, we have synthesized the new mixed solid solution TlRbSSeTe by the slow evaporation technique. X-ray studies show that the title material has an interesting three dimensional network. Besides, the new structure of (TlRbSSeTe) at room temperature crystallizes in the monoclinic system with P21/c space group. The structure is made up of planes of mixed TeO6 octahedra and S/SeO4 tetrahedra, with Tlþ and Rbþ cations intercalating between them. TlRbSSeTe structure is stabilized with O
H…O hydrogen bonds assured by protons belonging to hydroxide groups linking octahedral and tetrahedral groups. The thermal investigation of the title compound indicates the presence of three-phase transitions and the decomposition of the sample at about 448 K. The performed studies enable us to identify the electrical properties of TlRbSSeTe compound. Two semicircles are observed in the impedance plot, indicating the presence of two relaxation processes in the studied material associated with the grain and grain boundary. The variation of AC conductivity as a function of frequency at different temperatures is found to obey Jonscher's universal power law. In order to give an idea about the conduction mechanism in this compound, we have investigated the variation of the exponent (s) in function of the temperature. This mechanism in

the fact that beyond a certain frequency of external field, the charge carriers cannot follow the alternating electric field. Hence, when we have a solid which presents long-range ion diffusion, the real part of dielectric ε0 r constant can be expressed as the sum of two contributions:

ε0r ¼ ε0r ðlatt:Þ þ ε0r ðcarr:Þ

(29)

The first contribution ε0r (latt.), presents the lattice response owing to permanent dipole orientations or other motions that do not involve long-range displacement of mobile charge carriers, where its peak characterizes the ferroelectriceparaelectric phase transition [68,69]. However, the second contribution, ε0r (carr.), presents the conductivity, or carrier response, connected to long migration. This contribution firmly relates to frequency and especially the lower one. So, this part of the permittivity for the (TlRbSSeTe) compound characterizes the conductivity mechanisms.   ε0 The variation of the loss tangent (tan d ¼ ε00r ) of the sample as r

a function of temperature at different frequencies is presented in

Fig. 22. Thermal evolution of the dissipation factor as a function of frequency. for Tl1.90Rb0.10(SO4)0.92(SeO4)0.08Te(OH)6.

464

A. Elferjani et al. / Journal of Alloys and Compounds 749 (2018) 448e464

our sample is explained by two approaches with the help of Elliot's theory, which can be attributed to the correlated barrier hopping (CBH) model in regions II, IV and V. In regions I and III, the nonoverlapping small polaron tunneling (NSPT) model proves to be the suitable one to account for the electrical conduction mechanism for TlRbSSeTe. Acknowledgments This work is supported by the Ministry of Higher Education and Research of Tunisia. We would like to express our sincere thanks to Pr. H. Khemakhem for his help as far as Raman measurements are concerned. References [1] H. Litaiem, M. Dammak, T. Mhiri, A. Cousson, J. Alloys Compd. 396 (2005) 34. [2] L. Ktari, M. Dammak, A. Hadrich, A. Cousson, M. Nierlich, F. Romain, T. Mhiri, Solid State Sci. 6 (2004) 1393. [3] L. Ktari, M. Dammak, A. Madani, T. Mhiri, Solid State Ion 145 (2001) 225. [4] H. Khemakhem, Ferroelectrics 234 (1999) 47. [5] R. Zilber, A. Durif, M.T. Averbuch-Pouchot, Acta Cryst. B 36 (1980) 2743. [6] R. Zilber, A. Durif, M.T. Averbuch-Pouchot, Acta Cryst. B 37 (1981) 650. [7] R. Zilber, A. Durif, M.T. Averbuch-Pouchot, Acta Cryst. B 38 (1982) 1554. [8] M. Dammak, H. Khemakhem, T. Mhiri, A.W. Kolsi, A. Daoud, J. Alloys Compd. 280 (1998) 107. [9] M. Dammak, H. Khemakhem, T. Mhiri, J. Phys. Chem. Solids 62 (2001) 2069. [10] M. Abdelhedi, M. Dammak, A.W. Kolsi, A. Cousson, Anal. Sci. X-ray Struct. Anal. Online 24 (2008) 93. [11] M. Abdelhedi, M. Dammak, A. Cousson, A.W. Kolsi, J. Alloys Compd. 398 (2005) 55. [12] L. Ktari, M. Dammak, T. Mhiri, A.W. Kolsi, Phys. Procedia 2 (2009) 729. [13] Nonius, in: B.V. Nonius (Ed.), Kappa CCD Sever Software, 1999. Delft, The Netherlands. [14] APEX2 version 1. 0e8, Bruker AXS, Madison, WI, 2003. [15] D.J. Watkin, C.K. Prout, J.R. Carruthers, P.W. Betteridge, R.I. Cooper, CRYSTALS Issue 11, Chemical Crystallography Laboratory, Oxford, UK, 2001. [16] K. Brandenburg, M. Berndt, DIAMOND Version 2.1.b, Crystal Impact, Gb R, Bonn, Germany, 1999. [17] H. Rekik, Z. Ghallabi, I. Royaud, M. Arous, G. Seytre, G. Boiteux, A. Kallel, Compos. B Eng. 45 (2013) 1199. [18] E. Ozkazanc, S. Zor, H. Ozkazanc, H.Y. Guney, U. Abaci, Mater. Chem. Phys. 133 (2012) 356. [19] A. Sarkar, P. Ghosh, A.K. Meikap, S.K. Chattopadhyay, S.K. Chatterjee, P. Chowdhury, K. Roy, B. Saha, J. Appl. Polym. Sci. 108 (2008) 2312. [20] Y.-N. Qi, F. Xu, H.-J. Ma, L.-X. Sun, J. Zhang, T. Jiang, J. Therm. Anal. Calorim. 91 (2008) 219. [21] H. Frikha, M. Abdelhedi, M. Dammak, S. Garcia-Granda, J. Saudi Chem. Soc. 21 (2017) 324. [22] M. Djemel, M. Abdelhedi, L. Ktari, M. Dammak, J. Mol. Struct. 1047 (2013) 15. [23] A. Elferjani, M. Abdelhedi, M. Dammak, A.W. Kolsi, J. Appl. Phys. A 122 (2016) 742. [24] M. Dammak, A. Hadrich, T. Mhiri, J. Alloys Compd. 428 (2007) 8. [25] A. Novak, Hydrogen Bonding in Solids 18, Spring-Verlag, Berlin, Heidelberg, New York, 1974, p. 177. [26] K. Ghorbel, H. Litaiem, L. Ktari, S. Garcia-Granda, M. Dammak, J. Mol. Struct. 1079 (2015) 225. [27] H. Frikha, M. Abdelhedi, B. Louati, M. Dammak, S. Garcia-Granda, J. Therm.

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