Effects of mixed-alkali oxides on AC conductivity and dielectric properties of xNa2O-(20-x)K2O-30V2O5-50TeO2 glasses

Journal Pre-proofs Effects of mixed-alkali oxides on AC conductivity and dielectric properties of xNa2O-(20-x)K2O-30V2O5-50TeO2 glasses S.J. Japari, A.K. Yahya, R. Hisam PII: DOI: Reference:

S2211-3797(19)32674-9 https://doi.org/10.1016/j.rinp.2019.102905 RINP 102905

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Results in Physics

Received Date: Revised Date: Accepted Date:

6 September 2019 24 December 2019 25 December 2019

Please cite this article as: Japari, S.J., Yahya, A.K., Hisam, R., Effects of mixed-alkali oxides on AC conductivity and dielectric properties of xNa2O-(20-x)K2O-30V2O5-50TeO2 glasses, Results in Physics (2019), doi: https:// doi.org/10.1016/j.rinp.2019.102905

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Effects of mixed-alkali oxides on AC conductivity and dielectric properties of xNa2O(20-x)K2O-30V2O5-50TeO2 glasses S. J. Japari, A. K. Yahya and R. Hisam* School of Physics and Materials Studies, Universiti Teknologi Mara, 40450 Shah Alam, Selangor, Malaysia *corresponding author: [email protected]

Abstract The melt-quenching technique was used to prepare tellurovanadate glasses containing sodium and potassium oxides with compositions of xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 020 mol%) to examine the impact of mixed-alkali oxide on alternating-current (AC) conductivity and dielectric properties. Structural analysis revealed the presence of bridging oxygen (BO) and non-bridging oxygen (NBO). Thermal analysis results demonstrated a minimum value of glass transition temperature (Tg) at x = 10 mol% with an increase in Na2O content. The variation of AC conductivity (σAC) revealed a non-linear behaviour with Na2O at temperature < 383K, where σAC increased to maximum value at x = 15 mol% and shifted to x = 10 mol% at temperature ≥ 383K. This result may be attributed to mixed-alkali effect (MAE) because of the mixing of the two alkali oxides. The increase in 𝜎𝑎𝑐 with Na2O might be due to increase in the carrier pathway caused by the opening up of the glass network as NBO increased. Meanwhile, dielectric constant (ε’) demonstrated an optimal increase at x = 10 mol% prior to the reduction greater than x = 10 mol%. The maximum ε’ value at x = 10 mol% was in accordance with the σAC anomaly, which may also related to the MAE that induced formation of heavy dipoles. Consequently, this facilitated the dipole orientation in the glass network. Conduction mechanism at the dispersion region for all glass samples was found to be the correlated barrier hopping (CBH) model. The electrical modulus of the investigated samples revealed the non-Debye type relaxation, which indicates presence of interaction between ions. Keywords: AC conductivity; dielectric; mixed-alkali effect; tellurite glass

1

1.

Introduction Oxide glasses are known as non-crystalline materials or amorphous solids. Oxide

glasses have been studied extensively owing to their unique properties and potential practical applications in various technological fields [1]. Oxide glasses lack grain boundaries [2] and exhibit high stability to atmospheric moisture [3]. Oxides glasses could be classified as former, intermediate and modifier on the basis of the value of their single bond strength [4]. On that account, a high value of single bond strength corresponds to a higher glass forming tendency [4]. Among the oxide glasses, tellurium dioxide (TeO2)-based glasses have been widely studied because of their potential applications as compared to other conventional glasses. This is due to their high indices of refraction [3, 5], large infrared transparency [3, 5], high density [3, 5], low melting point [6] and good chemical durability as well as low glass transition temperature [3, 5]. In addition, these glasses also have high dielectric constant and electrical conductivity [7, 8] as the results of unshared pair of electrons of the TeO4 [8]. In contrast to phosphate (P2O5) and borate (B2O3) glasses, TeO2-based glasses are relatively non-toxic, resistant to moisture for long periods, and non-hydroscopic [6]. The aforementioned features of the TeO2 glasses have facilitated their diverse applications in photonic devices [9, 10], laser technology [9, 11], optical fiber technology [12], sensor system and CD memory devices [13, 14]. It is well known that TeO2 acts as the conditional glass former that requires the addition of modifier oxides including alkali, alkali earth, and transition metal oxides (TMOs), or additional glass modifiers for the production of a glass [15, 16]. The basic structure of pure TeO2 consists of TeO4 trigonal bipyramids (tbp’s) [7, 17] and TeO3 trigonal pyramids (tp’s) unit structure with a lone pair at the equatorial position where each oxygen is bonded to a Te ion and forms Te-O-Te bond [18-20]. Besides that, addition of modifier oxides into TeO2 based-glasses causes depolymerisation of the network structure and transformation from TeO4 tbp to TeO3 tp unit structure through the formation of an intermediate TeO3+1 polyhedra [21, 22]. Modification of the TeO2 network structure can influence the changes in structural, mechanical, conductivity and optical properties resulting in nonlinear applications of the glass [15]. Transition metal oxides (TMOs) with multivalence states, such as vanadium oxide (V2O5) on tellurite glasses exhibited semiconducting properties and electronic conductivity behaviour as the results of polaron conduction mechanism [23, 24]. Oxide glasses containing V2O5 present in different oxidation states due to the phonon-assisted hopping of electrons during the electrical conduction from the V4+ site to the V5+ site [25-28]. Tellurovanadate 2

glasses were found to exhibit superior electronic conductivity compared to other oxide glasses and have been explored as candidates for cathode materials for Li-ion batteries as well as solidstate devices [29-31]. The addition of V2O5 in binary tellurite glasses has been reported to influence the behaviour of structural, mechanical, and conductivity properties of the glass system [23, 25, 32-34]. On the other hand, the addition of alkali oxides such as Li+, Na+, and K+ ions to tellurite glass has resulted in structural changes by the opening up of the glass network as non-bridging oxygen (NBO) increases, thereby causing higher ionic conductivity [18, 19]. The applications of these glasses have also gained an increased attention owing to their potential use as cathodes in solid-state devices [19]. In addition, studies on ternary xLi2O– (1−x)(0.3V2O5–0.7TeO2) glass system have reported that the minimum conductivity at x = 5 mol% due to the formation of NBO has induced a relative opening structure of the glass network. Consequently, the electronic conductivity was decreased following an increased in the distance during hopping process. As such, this revealed the change in conduction mechanism from predominantly electronic to ionic [2]. The content of one alkali oxide is gradually substituted by another alkali oxide in a glass network, where a nonlinear variation of certain properties was observed such as resistivity, activation energy and glass transition temperature [35, 36, 37]. Such nonlinear variations are known as the mixed-alkali effect (MAE) [35, 38, 39] that has been reported for several glasses such as, (20-x)K2O-xNa2O.80TeO2 [18], A(1-x)BxPO3 [40], (Li1-xAx)2B4O7 [41], 0.2[xNa2O(1-x)Rb2O]0.8B2O3 [1]. For these glass systems, MAE was observed in terms of conductivity that exhibited a minimum as a function of cation replacement. The presence of minimum conductivity at x = 0.5 mol% in the A(1-x)BxPO3 (A-B: Cs-Na, Cs-Li, Rb-Na, RbLi, and K-Na) glass system due to ion hopping was hindered because of the significant difference between the ion sizes of the two alkali ions [40]. For the (Li1-xAx)2B4O7 (A: Na, K, Rb, and Cs) glasses, the minimum conductivity at x = 0.5 mol% was presumably caused by the effective blocking of the migration pathways between two forms of cation sites which were randomly mixed causing local site mismatch involving one alkali ion filling up a vacancy created by hopping of a different type of alkali ion in the glass system [41]. A previous study on 0.3[xLi2O(1-x)R2O]0.7B2O3 (R = Na, K, Rb) glass system indicated that the lowest conductivity was at x = 0.4 mol% as the results of the blocking effect on ions mobility followed by a huge energy mismatch for ions jumping between dissimilar alkali sites [35]. Studies on conductivity properties of quaternary 0.5(xNa2O-(1-x)Li2O)-0.5(0.25(WO3)2-0.75P2O5) glass system demonstrated that the minimum conductivity was attributed to the distinctly different conduction pathways, which was caused by the different local environments of two alkali ions. 3

Consequently, this caused the decrease in conductivity. In the aforementioned glass system, tungsten did not contribute to the conductivity, and the electronic hopping between W5+ and W6+ was omitted. The Electron Paramagnetic Resonance (ESR) spectra of this glass system displayed that there was no EPR spectra in the colourless glass at y = 0.5, whereas EPR signals were observed in the coloured glass at y < 0.5. Thus, the minimum conductivity observed at x = 0.5 mol% was associated with a MAE [42]. On the other hand, maximum conductivity has been reported in xLi2O-(1-x)Na2O-0.3FeO2-49.7B2O3 glass system that could be mainly due to an increase in the mobility of ions [43]. The observation of both minimum and maximum conductivity indicates that the real nature of MAE anomaly remains poorly understood by considering the interaction between two alkali oxides in the glasses. Instead, the structural environment in the mixed-alkali region might be the underlying cause of the MAE. Notably, evidence has shown that the minimum conductivity for xLi2O-(16-x)Na2O-24FeO2-60P2O5 glass system was not caused by MAE. This finding suggested that the electrical conductivity was controlled by the electron hopping from the Fe2+ site to the Fe3+ site, and the mobility of lithium and sodium was slow, resulting in an undetectable impact on the conductivity. This result indicated that studies of MAE might be influenced by TMI elements in this glass system [42]. Nevertheless, these studies were limited to only a number of MAE glass systems, and it is important to perform further investigation on the effects of TMI components in mixed-alkali glasses. On the other hand, studies on dielectric properties of quaternary xLi2O-(1-x)Na2O0.3FeO2-49.7B2O3 glass system that demonstrated an increase in 𝜀 ′ with low frequency was suggested to be attributed to increasing formation of dipoles [43]. Nevertheless, xLi2O-(50x)Na2O-20B2O3-30P2O5 glass system demonstrated the lowest at x = 0.20 mol%, which was in accordance with the conductivity anomaly due to MAE. The decrease in 𝜀 ′ with high frequency was attributed to the reduction in the number of dipoles that contributed to the total polarization [43]. This result indicates that MAE anomaly could facilitate the dielectric changes in addition to influencing the conductivity. Therefore, a comprehensive illustration of the MAE anomaly requires the polarization environment that might be a component of the nature of the peculiarity. The likelihood of a comparable conductivity and dielectric minima that are observed in the xNa2O-(20-x)K2O-30V2O5-50TeO2 glass system require further investigation in order to determine the potential function of dipoles in the conductivity anomaly mechanism. Nonetheless, evidence has shown that information on the alternating-current (AC) conductivity and dielectric properties of xNa2O-(20-x)K2O-30V2O5-50TeO2 glass system have been scant. The current study used impedance spectroscopy to examine AC conductivity and 4

dielectric properties of the xNa2O-(20-x)K2O-30V2O5-50TeO2 glass system in the MAE anomaly region. The current research examined the conductivity and polarization mechanism in the MAE region of xNa2O-(20-x)K2O-30V2O5-50TeO2 tellurovanadate glasses by evaluating the impact of Na2O-K2O mixed-alkali pertaining to AC conductivity and dielectric features. The variations of both MAE regions in AC conductivity and dielectric were analyzed using well-established electrical transport models, such as Correlated Barrier Hoping (CBH), Quantum Mechanical Tunneling (QMT), Overlapping-Large Polaron Tunneling (OLPT) and established relaxation models, respectively.

2.

Experimental details

2.1

Samples preparation Quaternary glass system with starting composition xNa2O-(20-x)K2O-30V2O5-50TeO2

(x = 0, 5, 10, 15 and 20 mol%) glass system were prepared using a standard melt-quenching technique by mixing specified amount of reagent grade tellurium (IV) oxide (TeO2; 99.99 % purity), vanadium (II) pentaoxide (V2O5; 99.95 % purity), potassium carbonate (KCO3, 99.99 % purity), sodium carbonate (NaCO3, 99.99 % purity) at constant heating rate. The materials were weighed prior to mixing. The mixtures were homogenized thoroughly by grinding using an agate mortar. The mixture was then transferred into a alumina crucible and heated in a box furnace at 1100oC for 1 h. The melted mixture was then quickly poured into a stainless steel mold in a second furnace and annealed at 250 oC for about 2 h. Then, the samples were polished using fine sand paper to a thickness of around 3.4 mm to 4.4 mm for impedance spectroscopy measurements. The samples were ground into powder form for X-Ray Diffraction (XRD) spectrometer measurement, Infrared (IR) absorption spectra measurements and Differential Scanning Calorimeter (DSC) measurement.

2.2.

Glass Characterization Density (𝜌) of the glass sample was determined by employing a most convenient

method which is Archimedes principle using toluene as an immersion liquid at room temperature. The bulk 𝜌 of the glass sample was used to calculate molar volume (𝑉𝑎 ) given by the equation below. 𝑉𝑎 = 𝑀𝑔𝑙𝑎𝑠𝑠 /𝜌𝑔𝑙𝑎𝑠𝑠

(1)

5

where 𝑀𝑔𝑙𝑎𝑠𝑠 is the molecular weight of glass sample and 𝜌𝑔𝑙𝑎𝑠𝑠 is the density of glass sample. The amorphous of the glass samples was confirmed by using X-Ray Diffraction (XRD) spectrometer by Panalytical X’Pert Pro diffractometer. The structural measurement was characterized in powder form by Perkin Elmer Model Spectrum One Fourier Transform Infrared (FTIR) spectrometer. Each powdered sample was mixed with KBr in a fixed ration of 10:80 and pressed into a pellet using a hand press. The resulting spectra were deconvulated to obtain information on the structural changes of the basic units of these glasses. 𝑇𝑔 of the glasses was carried out using a Differential Scanning Calorimetry (NETZSCH, DSC 200 F3) at a heating rate of 10 K min-1. The dielectric properties of the sample was characterized using a High-Resolution Dielectric Analyzer (Novocontrol) connected with a BDS 1200 sample holder over a frequency range of 10-2 to 106 Hz with an applied potential of 1V and at temperature range from 300 K to 413 K. A software package WinData control calculated and recorded all measurements. The dielectric constant (𝜀 ′ ), dielectric loss factor (tan 𝛿 ) and AC conductivity (𝜎𝑎𝑐 ) were determined based on the following expression. 𝜀 ′ = Cd / 𝜀𝑜 A

(2)

𝜀 ′′ = 𝜀 ′ tan 𝛿

(3)

𝜎𝑎𝑐 = ω 𝜀𝑜 𝜀 ′′

(4)

where 𝜀𝑜 is the permittivity constant of free space, C is the capacitance, ω is the frequency of the input signal, d is the thickness of the glass sample, and A is the cross-sectional area of the samples.

3.

Results and Analysis The broad humps at about 27° without any discrete or sharp crystalline peaks were

indicated by XRD patterns of xNa2O-(20-x)K2O-30V2O5-50TeO2 glass systems with x = 0, 5, 10, 15, 20 mol%. This reveals the amorphous nature of the glass samples. In Fig. 1, the broad peak was linked to the presence of a mid-range structure that was unable to crystallize. The absence of clear peaks reveals that there was no long-range order that validates the amorphous nature of all glass samples [46, 47]. Thus, the present glass system was demonstrated to comprised of short range order, and the atoms were randomly distributed in lattice space [27].

6

6000

x = 20 mol%

4000 2000 0 6000

x = 15 mol%

4000

Intensity (cps)

2000 0 6000

x = 10 mol%

4000 2000 0 6000

x = 5 mol%

4000 2000 0 6000

x = 0 mol%

4000 2000 0 0

20

40

60

80

100

Angle 2 (degree)

Fig. 1 XRD patterns of the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples Fig. 2 shows the room temperature Infrared (IR) absorption spectra of all glass samples in the frequency range of 400 cm-1 to 1400 cm-1. Fig. 3 shows the deconvolution of the spectrum for 10Na2O-10K2O-30V2O5-50TeO2 glass sample. Five major IR absorption bands were detected in the regions of 488–495 cm-1, 657–673 cm-1, 777–810 cm-1, 928–938 cm-1, and 1089–1096 cm-1. The peaks of the bands at 488–496 cm-1 and 656–673cm-1 were assigned to the bending mode of Te-O-Te or O-Te-Te linkages and stretching vibration mode of Te-O bonds in the TeO4 trigonal bipyramid (tbp) units with bridging oxygen atoms (BO) [16, 17, 48]. The band at 777 cm-1 – 810 cm-1 was assigned to the stretching vibration mode of the TeO3 trigonal pyramid (tp) units containing terminal Te-O bonds with non-bridging (NBO) [16, 17, 46, 48, 49]. The band at 657–673 cm-1 shifted to a higher wavenumber at x ≤ 10 mol% and to a lower wavenumber at x ≥ 15 mol% as the Na2O content increased. Moreover, the peak of the band at 777–810 cm-1 shifted to a higher wavenumber at x ≤ 10 mol%. The IR frequency peak at 928–938cm-1 was assigned to the stretching vibration of the VO4 tetrahedral group [29, 34], whereas the peak at 1089–1096 cm-1 was ascribed to the stretching vibration of the isolated V=O vanadyl group in the VO5 tbp units [29, 34]. 7

0.75

664

0.70

796

928

Absorbance (a.u)

0.65

662 495

0.60

787

1089

657

492

0.55

668

488

777

0.50

800 673

400

1091

937

1094 1096

938

493

0.40

936

810

492

0.45

937

600

800

x = 15 mol%

x = 0 mol% x = 20 mol% x = 5 mol% x = 10 mol%

1095

1000

1200

1400

-1

Wavenumber (cm )

Fig. 2 FTIR spectra of the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples 0.47

TeO4

Absorbance (a.u)

0.46

TeO3

VO4

0.45

TeO4 VO5

0.44

0.43

0.42 400

600

800

1000

1200

1400

-1 Wavenumber (cm )

Fig. 3 Deconvoluted FTIR spectra of the 10Na2O-10K2O-30V2O5-50TeO2 glass sample using a Gaussian-type Function The variations of the density (𝜌) and molar volume (𝑉𝑎 ) of xNa2O-(20-x)K2O-30V2O550TeO2 glass system are listed in Table 1. As shown in Fig. 4, 𝜌 was moderately increased from 3502 kg m-3 (x = 0 mol%) to 3604 kg m-3 (x = 10 mol%) and then was rapidly increased from 3634 kg m-3 (x = 15 mol%) to 3777 kg m-3 (x = 20 mol%) as the Na2O content increased. On the other hand, 𝑉𝑎 was gradually decreased from 4.619 m3 mol-1 (x = 0 mol%) to 4.406 m3 mol-1 (x = 10 mol%) and then was significantly decreased from 4.325 m3 mol-1 (x = 15 mol%) to 3.772 m3 mol-1 (x = 20 mol%).

8

Table 1 Values of density (𝜌) and molar volume (𝑉𝑎 ) of the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples Composition, x (mol%) 𝝆 (kg m-3) 𝑽𝒂 (m3 mol-1) x 10-5 ±2 ± 0.001 0 5 10 15 20

3502 3548 3604 3634 3777

4.619 4.521 4.406 4.325 3.772

3800

4.8

4.6

3700 4.4 3650



4.2

Va 3600

4.0 3550

Molar Volume, Va (m3 mol-1)

Density, (kg m-3)

3750

3.8

3500

3450

3.6 0

5

10

15

20

25

Na2O content (mol%)

Fig. 4 Density (𝜌) and molar volume (𝑉𝑎 ) of the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples The DSC curves of xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass system are shown in Fig. 5. The glass transition temperature (𝑇𝑔 ) values obtained from DSC investigation which was marked by the small endothermic peak corresponding to 𝑇𝑔 as shown in Fig. 5 and listed in Table 2. Table 2 Values of glass transition temperature (𝑇𝑔 ) of the xNa2O-(20-x)K2O30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples Composition, x (mol%) 𝑻𝒈 (°C) 0 5 10 15 20

233 232 227 235 238

9

0.0

Heat Flow (mW)

Exo. -0.2

x = 0 mol%

-0.4

x = 5 mol%

-0.6

x = 10 mol% -0.8 -1.0

x = 15 mol%

-1.2

x = 20 mol%

-1.4 -1.6 Endo. -1.8 50

100

150

200

250

300

350

Temperature (°C)

Fig. 5 DSC curves of the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples. Fig. 6 shows variation of AC conductivity, log (𝜎𝑎𝑐 ) with different Na2O composition at all temperatures. The values of 𝜎𝑎𝑐 is shown to initially increase with increasing Na2O content at x ≤ 15 mol% at room temperature and shifted to x = 10 mol% at higher temperatures. However, the addition of Na2O content at x > 10 mol% reduced 𝜎𝑎𝑐 .

323 343 363 383 403 423 443 463

-8.0

log (ac)

-8.5

K K K K K K K K

-9.0

-9.5

-10.0

0

5

10

15

20

25

Na2O content (mol%)

Fig. 6 The variation of AC conductivity, log (𝜎𝑎𝑐 ) with Na2O content at frequency of 1 kHz at various temperatures

10

Fig. 7 shows the typical plot of the frequency spectra of 𝜎𝑎𝑐 for different glass samples at 383 K. A weak frequency-dependent behavior was observed in region 1 in the low-frequency region of 𝜎𝑎𝑐 , whereas region 2 displayed stronger frequency-dependent behavior as well as for region 3 which also showed much stronger frequency-dependent behavior compared to region 2 at high frequency region of 𝜎𝑎𝑐 for all glass samples. The 𝜎𝑎𝑐 spectra exhibited higher σACslope values when the frequency was increased in the range of 0.1 to 105 Hz. -6 x x x x x

-7

log (ac)

-8

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

Region 2

Region 1 -9

-10

Region 3 -11

-12 -2

0

2

4

6

log f (Hz)

Fig. 7 Plot of AC conductivity, log (𝜎𝑎𝑐 ) in the frequency domain at 383 K for xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples Fig. 8(a) depicts the frequency responses of 𝜎𝑎𝑐 at various temperatures at x = 10 mol%. As shown in Fig. 8(b), (c) and (d), the conductivity-frequency has three regions. In region 1, the low-frequency region (𝜎𝑎𝑐 ) exhibited a weak frequency-dependent behavior and was more visible at higher temperature points. This region was observed between 10-2 Hz and 101 Hz. The intermediate frequency region (𝜎𝑎𝑐 ) had a significant difference with frequency in region 2. Region 3, which is the high frequency region (𝜎𝑎𝑐 ) had a stronger frequency-dependent behavior as compared to the other regions. The frequency dependence of the conductivity of the glasses can be described as follows [50, 51]; 𝜎𝑇𝑜𝑡𝑎𝑙 = 𝜎𝑑𝑐 + 𝜎𝑎𝑐

(5)

where 𝜎𝑑𝑐 is the frequency independent component and 𝜎𝑎𝑐 is the frequency dependent. The frequency dependent can be analyzed using the Jonscher equation [51]; 𝜎𝑎𝑐 = 𝐴𝜔 𝑠

(6)

11

where A is the temperature dependent constant and s is the frequency exponent. The frequency exponent (s) is the decreasing function of temperature. The interpretation frequently involves analysis of temperature dependent, s(T) which is to determine the hopping mechanism in the dispersion of conductivity. The frequency exponent was computed from the slope of the least square linear lines fitted to the log (𝜎𝑎𝑐 ) with the frequency plot in the low frequency regions (Fig. 8(b)), intermediate frequency regions (Fig. 9(c)) and high frequency regions (Fig. 8(d)).

-7

Region 1

log (ac)

-8

-9

323 343 363 383 403 423 443 463

-10

-11

Region 2 -2

0

2

K K K K K K K K

4

log f (Hz)

Fig. 8(a) Plot of AC conductivity, log(𝝈𝒂𝒄 ) in the frequency domain for the 10Na2O-10K2O30V2O5-50TeO2 glass sample at different temperatures. The dashed line separates region 1 and region 2 -8

log (ac)

-9

-10 323 343 363 383 403 423 443 463

-11

-12 -2

-1

0

1

K K K K K K K K

2

log f (Hz)

Fig. 8(b) Plot of AC conductivity, log (𝜎𝑎𝑐 ) in the frequency domain for the 10Na2O-10K2O30V2O5-50TeO2 glass sample at different temperatures in the low frequency region. The lines show the region where least-square fitting was done and the frequency exponent (𝑠1 ) was derived from the slope each line.

12

-7

log (ac)

-8

-9 323 343 363 383 403 423 443 463

-10

K K K K K K K K

-11 1.5

2.0

2.5

3.0

3.5

4.0

4.5

log f (Hz)

Fig. 8(c) Plot of AC conductivity, log (𝜎𝑎𝑐 ) in the frequency domain for the 10Na2O-10K2O30V2O5-50TeO2 glass sample at different temperatures in the intermediate frequency region. The lines show the region where least-square fitting was done and the frequency exponent (𝑠2 ) was derived from the slope each line -6.5

-7.0

log (ac)

-7.5

-8.0 323 343 363 383 403 423 443 463

-8.5

-9.0

K K K K K K K K

-9.5 4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

log f (Hz)

Fig. 8(d) Plot of AC conductivity, log (𝜎𝑎𝑐 ) in the frequency domain for the 10Na2O-10K2O30V2O5-50TeO2 glass sample at different temperatures in the high frequency region. The lines show the region where least-square fitting was done and the frequency exponent (𝑠3 ) was derived from the slope each line As shown in Fig. 9(a), the variation of 𝑠1 at low frequency region was unsystematic for all glass samples with temperature. Meanwhile, the variation of 𝑠2 in Fig. 9(b) at intermediate frequency region was temperature-dependent, where it declined with rising temperature for all glass samples. Fig. 9(c) illustrates similar trend of unsystematic variation for 𝑠3 at high frequency region.

13

0.30 x = 0 mol% x = 5 mol% x = 10 mol% x = 15 mol% x = 20 mol%

Frequency Exponent, s1

0.25

0.20

0.15

0.10

0.05

0.00 300

320

340

360

380

400

420

440

460

480

Temperature (Kelvin)

Fig. 9(a) Variation of frequency exponent (𝑠1 ) with temperature for the xNa2O-(20-x)K2O30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples in the low frequency region. The lines are drawn as guide only

Frequency Exponent, s2

1.0

x x x x x

0.8

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

0.6

0.4

0.2 320

340

360

380

400

420

440

460

Temperature (Kelvin)

Fig. 9(b) Variation of frequency exponent (𝑠2 ) with temperature for the xNa2O-(20-x)K2O30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples in the low frequency region. The lines are drawn as guide only

14

10 x x x x x

Frequency Exponent, s3

8

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

6

4

2

0 300

320

340

360

380

400

420

440

460

480

Temperature (Kelvin)

Fig. 9(c) Variation of frequency exponent (𝑠3 ) with temperature for the xNa2O-(20-x)K2O30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples in the low frequency region. The lines are drawn as guide only Fig. 10 demonstrates the difference in the dielectric constant, log 𝜀 ′ (ω) with frequency for entire glass samples at 383 K. The entire glass samples with frequency between of 0.1 Hz to 100 Hz had dispersion of the log 𝜀 ′ (ω) prior to achieving frequency-independent state, that was achieved constant at higher frequencies (starting at 100 Hz). The difference pertaining to responses concerning the frequencies were moderately analogous among the glass samples. Fig. 11 presents the plot of log 𝜀 ′ (ω) with Na2O content at 383 K for different frequencies ranging from 0.01 Hz to 1 MHz. The dielectric constant (𝜀 ′ ) demonstrated an initial increase at x ≤ 10 mol%. Nevertheless, the addition of Na2O content reduced 𝜀 ′ beyond 15 mol%. 3.2 3.0

x x x x x

2.8 2.6

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

log (')

2.4 2.2 2.0 1.8 1.6 1.4 1.2 -2

0

2

4

6

log f (Hz)

Fig. 10 Variation of dielectric constant (𝜀 ′ ) with frequency at 383 K for the xNa2O-(20x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples

15

2.8

1.9

2.6

log (')

2.4

2.2

1.8

1.7

1.6 2.0

log (')

0.01 Hz 0.1 Hz 1 Hz 10 Hz 1 kHz 10 kHz 100 kHz 1 MHz

1.5 1.8 1.4 1.6 1.3

1.4 0

5

10

15

20

25

Na2O content (mol%)

Fig. 11 Variation of log 𝜀 ′ (ω) with Na2O content at 383 K for different frequencies Fig. 12 demonstrates the temperature dependence of 𝜀 ′ for the 10Na2O-10K2O-30V2O550TeO2 sample at different frequencies. At low frequencies, the 𝜀 ′ values increased in proportion to the temperature increase, whereas at high frequencies, the 𝜀 ′ values remained nearly constant. The results revealed that 𝜀 ′ greatly influenced by frequency and temperature at frequency levels lower than 100 Hz. Fig. 13 illustrates the frequency dependence of 𝜀 ′ in 10Na2O-10K2O-30V2O5-50TeO2 glass at different temperature points. The 𝜀 ′ increased with an increased temperature, however, the increase in 𝜀 ′ was varied according to frequency as it decreased with the increasing frequency. The variations of the responses toward the temperature were moderately comparable among the glass samples.

4.0

0.01 Hz 0.1 Hz 1 Hz 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz

3.5

log(')

3.0

2.5

2.0

1.5

300

320

340

360

380

400

420

440

460

480

Temperature, T (K)

Fig. 12 Temperature dependence of the dielectric constant (𝜀 ′ ) between 0.01 Hz and 100 kHz of the 10Na2O-10K2O-30V2O5-50TeO2 glass sample

16

4.0 323 343 363 383 403 423 443 463

3.5

log (')

3.0

2.5

K K K K K K K K

2.0

1.5

1.0 -2

0

2

4

6

log f (Hz)

Fig. 13 Plot of dielectric constant (𝜀 ′ ) with frequency (Hz) for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperatures Fig. 14 shows the effect of frequency towards dielectric loss factor (tan δ) with different Na2O concentration at 383 K. High dielectric loss was observed at low frequencies (f < 0.1 Hz) which is due to conduction loss of free carriers. The DC loss factor is related to the electrical conductivity through the following expression in terms of conductivity (𝜎𝑑𝑐 ) [52]; 𝜎𝑑𝑐 tan 𝛿 = 2𝜋𝑓′

where tan 𝛿 =

𝜀′′ 𝜀′

(7)

, therefore the loss factor expression can be written as [52]; 𝜀′′ =

𝜎𝑑𝑐 𝜔

𝜎𝑑𝑐 = 𝜔𝜀 ′ tan 𝛿

(8)

(9)

Fig. 15 presents the plot of log (𝜀 ′′ ) values as a function of frequencies for entire glass samples at 383 K. The slope of the least square linear lines fitted in the log (𝜀 ′′ ) versus log f has been found to be in the range of -0.7 to -0.9 which indicates the presence of DC conduction loss in the samples [53]. Fig. 16 demonstrates the frequency dependence of dielectric loss (tan δ) for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperature points. The tan δ increased as temperature was increased. Nevertheless, increase in temperature at higher frequency did not cause any change on tan δ.

17

25

x x x x x

tan 

20

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

15

10

5

0 -2

0

2

4

6

log f (Hz)

Fig. 14 Variation of tan δ with frequency at 383 K for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples 5 x x x x x

log ('')

4

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

3

2

1

0 -2

-1

0

1

2

log f (Hz)

′′

Fig. 15 Dielectric loss (𝜀 ) with frequency at 383 K for the xNa2O-(20-x)K2O-30V2O550TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples. The linear show the region where least square fitting was done

18

120

323 343 363 383 403 423 443 463

100

tan 

80

60

K K K K K K K K

40

20

0 -2

0

2

4

6

log f (Hz)

Fig. 16 Plot of tan δ in the frequency domain for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperatures

The electrical relaxation procedure in the examined glass samples was performed via the complex electrical modulus formalism [54, 55]; (10)

M* (ω) = 1 / ɛ* (ω) = 𝜀 ′ /((𝜀 ′ )2 + (𝜀 ′ ′) 2) +i 𝜀 ′ ′/((𝜀 ′ ) 2 +(𝜀 ′ ′) 2) = 𝑀′ +i𝑀′′

where M* is the complex electrical modulus, 𝜀 ∗ is the complex dielectric permittivity and 𝑀′ and 𝑀′′ is the real and imaginary part, respectively. This formalism is promising for calculating

charge carrier parameters including the conductivity relaxation time (Tm) [55]. Fig. 17 presents the variations of real modulus isotherm 𝑀′ with frequency for entire glass samples at 383 K. The 𝑀′ values noticeably achieved zero at low frequencies for the entire glass samples. Nonetheless, these values started to disperse and reached a plateau as the frequency was increased. The plateau region was increased at x < 10 mol% and decreased at x ≥ 10 mol%. Fig. 18 demonstrates a preliminary weak decline at x ≤ 10 mol%, followed by an increase at x ≥ 15 mol%.

19

5

M'() x 10-2

4

3

2 x x x x x

1

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

0 -2

0

2

4

6

log f (Hz)

Fig. 17 Frequency dependence of 𝑀′ for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples at 383 K 0.055 100 Hz 1 kHz 10 kHz 100 kHz

M' () x10-2

0.050

0.045

0.040

0.035 0

5

10

15

20

Na2O content (mol%)

Fig. 18 Variation of 𝑀′ with the Na2O content at 100 Hz to 100 kHz for 383 K Fig. 19 illustrates the real components of the electrical modulus (𝑀′ ) as a function of temperature and frequency for 10Na2O-10K2O-30V2O5-50TeO2 glass sample. The variations of 𝑀′ with frequency demonstrated comparable patterns for the entire glass samples; that is, 𝑀′ displayed an insignificant amount at minimal frequencies and highly dispersed prior to achieving a plateau at maximal frequencies as the frequency elevated. Fig. 20 depicts the compositional dependence of the imaginary part (𝑀′′ ) spectra for the entire glass samples at 383 K. Fig. 20 indicates that 𝑀′′ shifted to higher frequency for x < 15 mol%, before shifting to lower frequency for x ≥ 15 mol%.

20

5

M' (f) x 10-2

4

3

323 343 363 383 403 423 443 463

2

1

0

-2

0

2

K K K K K K K K

4

6

log f (Hz)

Fig. 19 Plot of real part of the electrical modulus (𝑀′ ) in the frequency domain for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperatures 16 14

x x x x x

12

M'' (x 10-3

10

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

8 6 4 2 0

-2

0

2

4

6

log f (Hz)

Fig. 20 Compositional dependence of 𝑀′′ spectra for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples at 383 K Fig. 21 demonstrates the imaginary part of the electric modulus (𝑀′′ ) as a function of frequency at different temperature points for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample. The plot of 𝑀′′ revealed that the maximum peak shifted to a higher frequency as the temperature was increased in which an asymmetric peak was detected almost in the mid of the dispersion region. This behavior was similarly observed in all of the other glass samples. The ′′ frequency (𝑓𝑚 ) correlated to 𝑀𝑚𝑎𝑥 has the superior probable conductivity relaxation time (𝜏𝑚 )

as of the condition 2𝜋𝑓𝑚 𝜏𝑚 = 1. Fig. 22 demonstrates the log 𝜏𝑚 versus 1000/T plots for relaxation from 𝑀′′ spectra for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20

21

mol%) glass samples at different temperature points. The relaxation time (𝜏𝑚 ) follows the Arrhenius relation [56, 57]; 𝜏𝑚 = 𝜏0 exp (

𝐸𝜔 ) 𝑘𝑇

(11)

where 𝜏0 is the pre-exponential factor, 𝐸𝜔 is the activation energy for conductivity relaxation time. k is the Boltzmann constant and T is the absolute temperature dependence of the conductivity relaxation time. Table 3 demonstrates the values of 𝐸𝜔 for conductivity relaxation time that was derived using the slope of least-square linear fit by applying the Arrhenius relation. The results demonstrated that 𝐸𝜔 was significantly decreased from 0.1511 eV (x = 0 mol%) to 0.1367 (x = 5 mol%), followed by a drop to 0.1288 eV at x = 10 mol%. Nonetheless, above 10 mol%, 𝐸𝜔 demonstrated a large increase from 0.1511 eV (x = 15 mol%) to 0.1813 at x = 20 mol%. Table 3 Values of activation energy for relaxation time (𝐸𝜔 ) of the xNa2O(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples. Composition, x (mol%) 𝑬𝝎 (eV) 0 5 10 15 20

0.1511 0.1367 0.1288 0.1511 0.1813

22

16 323 343 363 383 403 423 443 463

14

M'' (f) x 10-3

12 10 8

K K K K K K K K

6 4 2 0 -2

0

2

4

6

log f (Hz)

Fig.21 Plot of imaginary part of the electrical modulus (𝑀′′ ) in the frequency domain for the 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperatures 1 x = 0 mol% x = 5 mol% 10 vs Col 18 15 vs Col 26 20 vs Col 34

log m (s)

0

-1

-2

-3

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

1000/T (K-1)

Fig. 22 Plot of log 𝜏𝑚 with temperature for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples. Solid lines are the least-square straight lines fit to the data Meanwhile, the scaling plot behavior of 𝑀′′ was analyzed in order to have a deeper understanding of the temperature and composition of relaxation dynamics [28, 54]. Fig. 23 illustrates 𝑀′′ spectra for x = 10 mol% at different temperature points, in which the frequency axis was carried out by peak relaxation frequency (𝑓𝑚𝑎𝑥 ), while the 𝑀′′ axis has been scaled by dividing 𝑀′′ with 𝑀𝑚𝑎𝑥 . A complete overlapping of the entire curves into a single master curve implies that the relaxation process occurring at different frequencies had similar thermal activation energy. This suggests that the temperature independent behavior of dynamical process.

23

1.2 x x x x x

1.0

M" ()/M''max

0.8

= = = = =

0 mol% 5 mol% 10 mol% 15 mol% 20 mol%

0.6

0.4

0.2

0.0

-4

-2

0

2

4

6

log (f/fm)

′′ Fig. 23 The scaled imaginary part of the electric modulus 𝑀′′ / 𝑀𝑚𝑎𝑥 as function of frequency logarithimic for xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples

Fig. 24 illustrates that the modulus spectra for the entire glass samples at 383 K relaxation could be dependent of composition. The scaling modulus plots in Fig. 23 and 24 were asymmetric and corresponding to the non-exponential behavior of the electrical function as proposed by the Kohlrausch-William-Watts exponential function [51]; −𝑡 𝛽 ∅(𝑡) = 𝑒𝑥𝑝 ( ) (0 < 𝛽 < 1) 𝜏

(12)

where 𝜏 is the conductivity relaxation time an 𝛽 is the Kohlrausch exponent, which is lower than one for almost practical solid electrolyte. It should be noted that 𝛽 measures the degree of interaction between the ions. The small value of 𝛽 caused a significant deviation of relaxation pertaining to the Debye-type relaxation. The 𝛽 value could be measured via the full′′ width at half maximum (FWHM) of the 𝑀′′ /𝑀𝑚𝑎𝑥 versus log(f/𝑓𝑚𝑎𝑥 ) plot where (𝛽 =

1.14/FWHM) [28]. In the present glass, 𝛽 values were less than one for both temperature and composition, which reveal that the conductivity relaxation is non-Debye-type relaxation. Moreover, the values of 𝛽 (Table 4) demonstrates a weak rise with temperature at x ≤ 15 mol% prior to a significant elevation was observed at x = 20 mol%, and declined with composition at x ≤ 5 mol% after a decline at x ≥ 10 mol%.

Table 4 Values of beta (𝛽) for the 10Na2O-10K2O-30V2O5-50TeO2 glass at different temperatures and for the xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15, 20 mol%) glass samples at 383K

24

𝜷

Temperature (K)

𝜷

Composition, x (mol%)

383

0.73

0

0.70

403

0.73

5

0.65

423

0.70

10

0.72

443

0.70

15

0.71

463

0.73

20

0.66

1.2 323 343 363 383 403 423 443 463

1.0

M" ()/M''max

0.8

0.6

K K K K K K K K

0.4

0.2

0.0

-4

-2

0

2

4

6

log (f/fm)

′′ Fig. 24 The scaled imaginary part of the electric modulus 𝑀′′ / 𝑀𝑚𝑎𝑥 as function of frequency logarithimic for 10Na2O-10K2O-30V2O5-50TeO2 glass sample at different temperatures

4.

Discussion

4.1

Infrared (IR) Absorption Spectra Studies Analysis of the IR spectra (Fig. 2) revealed the presence of TeO3 trigonal pyramid (tp)

unit and TeO4 trigonal bipyramid (tbp) unit functional groups, indicating that NBO and BO bonds were formed in the glass network, respectively [17, 48, 50]. In addition, the detected VO4 trigonal pyramid (tp) functional groups indicated that NBO bonds were formed, whereas the presence of VO5 trigonal bipyramid (tbp) functional groups implied that BO bonds were formed [31, 34]. In the present glass system, the increase in the relative area of TeO3 tps and VO4 tps at x ≤ 10 mol% indicated that the number of NBO increased in the glass system. 25

Similarly, the increase in relative area of TeO4 tbps also indicated that BO increased in the same glass samples. However, the shift of the TeO4 tbps to a higher wavenumber reflected a structural distortion, which was caused by the transformation of TeO4 tbps to TeO3 tps through TeO3+1 polyhedron structure [58, 59]. This phenomenon contributed to the formation of NBO [16, 48, 59]. Moreover, the relative area of VO5 tbps at x ≤ 10 mol% was accompanied by an increase in the relative area of TeO3 tps and VO4 tps, indicating that both BO and NBO were increased in the glass network. However, TeO3 tps and VO4 tps had higher relative areas than those of VO5 tbps and TeO4 tbps, indicating that a greater amount of NBO was formed than BO in the glass system. The decrease in the relative area of TeO3 tps and VO4 tps as Na2O content increased at x ≥ 15 mol% indicated that NBO decreased, whereas the shift of TeO4 tbps and VO5 tbps to a higher wavenumber indicated an increase in BO number.

4.2

Density and Molar Volume Studies Density (𝜌) is a useful physical parameter for describing the structural compactness of

the glass system [60, 61]. In this study, the increase in 𝜌 (Fig. 4) of the glass composition can be understood by analyzing the changes in both molecular mass (𝑀) and sample volume(𝑉) . As 𝜌 is proportional to 𝑀 and is inversely proportional to 𝑉 of the glass, the increase in 𝑀 is expected to contribute to the increase in 𝜌 [47]. However, the replacement of heavier K2O (94.20 g mol-1) by lighter Na2O (61.98 g mol-1) molecules did not contribute to the increase in 𝜌 because of the decreasing total mass. As such, the increase in 𝜌 was presumed to be due to the decrease in 𝑉. Moreover, the decrease in sample 𝑉 could be due to various factors, such as network modification and differences in the ionic size of alkaline oxides [62, 63]. A previous report suggested that the increase in NBO can increase the total 𝑉 as the effect of NBOs opened up the glass network [16]. However, the FTIR results at x ≤ 10 mol% showed that NBO was formed more dominantly than BO. Therefore, the decrease in 𝑉 can be attributed to the difference in the ionic radius between the larger K+ ion (R = 1.33Å) [64] and the smaller replacing Na+ ion (R = 0.97Å) [64], indicating that the glass network became more compact that led to a decrease in 𝑉. However, beyond 15 mol% of Na2O, a large decrease in 𝑉 was presumably due to the increase in BO number, causing an increase in the compactness of the glass system.

4.3

Glass Transition Temperature Studies

26

The observed variation of 𝑇𝑔 (Fig. 5) correlates with the structural changes, as revealed by the results of FTIR spectroscopy (Fig. 2) and indicates the changes in rigidity where the minimum value of 𝑇𝑔 is at x = 10 mol% in the glass system. This kind of 𝑇𝑔 variation were also reported for several glasses such as, (20-x)K2O-xNa2O.80TeO2 [18], 0.5(xNa2O-(1-x)Li2O)0.5(0.25(WO3)2-0.75P2O5) [44], xLi2O-(30-x)Na2O-65B2O3-5Sm2O3 [65]. The decrease in 𝑇𝑔 with Na2O addition at x ≤ 10 mol% is suggested to be due to increase in the amount of NBO which results in relative opening of glass network [18]. In addition, the decrease in 𝑇𝑔 can also be due to the increase in fragmentation of the glass network via breaking TeO4 and causing formation of TeO3 with corresponding increase in structural defect [18]. However, the increase in 𝑇𝑔 beyond 15 mol% is suggested to be due to increase in the amount of BO. Therefore, the enhancement of BO contributes to increasing the rigidity of glass network which indicates that a larger internal energy barrier for chain mobility during glass transition was involved [63, 66].

4.4

AC Conductivity Properties The nonlinear behaviour of 𝜎𝑎𝑐 with Na2O addition (Fig. 6) can be understood by

considering the concentration of carrier ions together with the structural changes, as revealed by the results of FTIR spectroscopy. This anomalous maximum at x = 15 mol% at room temperature was attributed to mixed-alkali effect (MAE) because of the mixing of the two alkali oxides. The initial increase in 𝜎𝑎𝑐 at x ≤ 15 mol% may not be due to the increase in the ionic concentration as Na+ and K+ both has the same valence and the replacement was on a one to one basis. As such, the increase in 𝜎𝑎𝑐 may also be due to increase in mobility of carrier ions in the glass system because of the replacement of smaller Na+ ions (R = 0.97Å) [64] for larger K+ ions (R = 1.33Å) [664], causing higher probability for the ion to jump to dissimilar alkali’s sites [67]. In addition, the increase in 𝜎𝑎𝑐 was also confirmed by the FTIR results, which showed an increase in the relative area of TeO3 tps and VO4 tps peaks corresponding to the increase in the number of NBO. Therefore, the enhancement of NBO, which induced a relative opening of glass network, increased the carrier pathway, which in turn increased 𝜎𝑎𝑐 . However, the decrease in 𝜎𝑎𝑐 at x ≥ 15 mol% (Fig. 6), which coincided with the decrease in volume of samples (Fig. 4), suggesting that 𝜎𝑎𝑐 was strongly influenced by volume of samples. As the decrease in volume of samples was earlier suggested due to the increase in BO, which enhanced the network linkages and increased the compactness of the glass system, it is further suggested that BO may contribute to reduction of carrier ions which lead to decreasing mobility of the

27

carrier ions and decrease in 𝜎𝑎𝑐 . In addition, the decrease in 𝜎𝑎𝑐 may also be due to blockage by vanadium ions, which participated in the network positions within the VO5 tbps unit. On the other hand, 𝜎𝑎𝑐 for the glass system increased as the temperature increased due to the weakening of the bond in the glass network. It is suggested that as the temperature increased, the mobility of the carrier ions increased due to the increase in kinetic energy and bond weakening that created pathways for the migration of carrier ions, thereby leading to an increase in 𝜎𝑎𝑐 [68]. The shift of the 𝜎𝑎𝑐 maximum point from x = 15 mol% at 323 K to x = 10 mol% at 383 K may be due to the increasing effect of scattering. As the temperature increased, the lattice vibrations increased, and the probability of an electron being scattered by the lattice increased, leading to reduced mobility of carriers and causing an earlier drop in 𝜎𝑎𝑐 [69]. The variation of 𝜎𝑎𝑐 for all samples (Fig. 7) showed the frequency dependence of 𝜎𝑎𝑐 is found to consist of three regions. The low frequency region, region 1 showed weaker frequency dependence followed by stronger frequency dependence regions, region 2 and region 3 as frequency increases. Ironically, region 3 showed a drop in 𝜎𝑎𝑐 followed by a large increase at higher frequency. The dispersion behaviours of the three regions indicate the presence of slightly different conductivity mechanisms [70]. In the present disordered structure containing mixed Na2O and K2O alkali oxides and V2O5 transition metal oxide, the conductivity may be contributed by both mobile Na+ and K+ ions and electron hopping between V4+ and V5+ [71,72]. In region 1, the weak frequency dependence at the low-frequency dispersion may be due to the combined effect of the DC hopping motion of the mobile ions and the short range motion of mobile carriers may be due to slow changing frequency in response to applied electric field. In addition, at low frequency, mobile ions are accumulated at the electrodes because of the slow changing electric field [28]. Mobility of free mobile ions decreased as a result of repulsion between the Na+ and K+ ion due to charges build up close to the electrode interface at low frequency and ultimately decreasing the conductivity [73]. On the other hand, the strong frequency dependence of 𝜎𝑎𝑐 for regions 2 at high frequency showed a dispersion region as the frequency increased and obeyed the power law 𝐴𝜔 𝑠 [73]. The dispersion region (region 2) may be related to the forward-backward hopping of the carrier which is caused by the AC hopping of carriers among potential wells or trap sites separated by energy barriers of various heights. At high frequencies, the mobility of free carriers was restricted to short distances because of the fast-changing frequency where the charge carriers vibrated at their localized sites and contributed to the AC dispersion [74]. Meanwhile, the 𝜎𝑎𝑐 is found to slightly drop at high frequency (region 3) indicating the charge carriers and electronic hopping are unable to respond with fast-changing frequency as charge carriers and electronic hopping become restricted. On 28

the other hand, the large increase in 𝜎𝑎𝑐 at region 3 may associated to electronic polarization involving electronic dipoles. The charge carriers themselves are polarized by an external electric field where positively charged nucleus and negatively charged electrons are displaced opposing the direction of the external electric field, thus causing 𝜎𝑎𝑐 to increase [75]. As revealed by the conductivity plot (Fig. 8a), the width of low-frequency region 1 increased as the temperature increased and shifted towards a higher frequency, indicating the weakening of the bonds that facilitated DC ionic hopping to the frequency in the region. Moreover, as the temperature increased at low frequency, the thermal energy weakened the bond network and facilitated the drifting of ionic charge carriers, thereby increasing the conductivity [68]. Furthermore, the conductivity at higher frequency (Fig. 8b-c) was not temperature-independent but was frequency-dependent. As such, the weakening of bond did not significantly the charge carrier movement and ultimately became almost linear at even higher temperatures. Various models have been proposed to describe the conduction mechanism. These models include quantum mechanical tunneling (QMT), correlated barrier hopping (CBH), and overlapping large polaron tunneling models (OLPT). In the QMT model, the value of frequency exponent (s) is temperature-independent where the carrier motion passed through the tunneling between two localized states near the Fermi level [48]. In the CBH model, s decreases with increasing temperature and is related to the potential barrier to the inter site separation [51]. If s decreases with temperature until a minimum value before increasing back, OLPT is expected. The OLPT model refers to the scenario in which the Coulomb potentials of all neighboring sites overlap, thereby producing overlapping polaron clouds [76]. In this study, in regions 1 (Fig. 9a), 2 (Fig. 10b) and 3 (Fig. 9c), the variation of the frequency exponent (𝑠1 ), (𝑠2 ) and (𝑠3 ) with temperature comfirmed the difference in their conductivity mechanism, respectively. At low frequency region, the 𝑠1 displayed unsystematic variation for all glass samples with temperature which is not in agreement with any single model of conduction mechanism. Furthermore, the variation of the 𝑠2 with temperature at intermediate frequency can be interpreted by the CBH mechanism that was temperaturedependent and composition-dependent for all glass samples [42, 77, 78]. Meanwhile, at high frequency region, the variation of 𝑠3 also displayed the same trend with 𝑠1 which is unsystematic variation for all glass samples. Thus, at intermediate frequencies, the conductivity was dominated by hopping of carriers. Other mixed-alkali oxide glasses has also been reported to display the same conduction mechanism [79].

29

4.5

Dielectric Constant and Loss Studies In dielectric study of solids, the dielectric constant (𝜀 ′ ) is derived through electrical

polarizability, which are space charge, orientation, ionic and electronic polarization due to changing external field [52]. At low frequencies, heavy, medium and light dipoles frequently follow the alternating electric field, thus could contribute to total polarization [52]. In the present work, the values of 𝜀 ′ at low frequencies (f ≤10) (Fig. 10) was mainly affected by Na2O substitution compared to 𝜀 ′ for f >102, where the influence of Na2O was minimal. The large values of 𝜀 ′ at low frequencies (f ≤ 10) could be mainly due to an increased formation of heavy dipoles that contributed to the increase in space charge polarization. In addition, at the low frequency region, ions are able to diffuse along the barriers of varying heights in the field direction, however, some may accumulate at an optimal energy barrier in the field direction causing the formation of medium size dipoles. As frequency was increased, 𝜀 ′ decreased due to decreasing number of dipoles, which were able to respond quickly as the applied field [53, 80]. Meanwhile, the almost constant 𝜀 ′ at high frequencies (f > 102) for all glass samples indicates that heavy dipoles can no longer follow the rapidly changing applied field. Nonetheless, the oscillations of diminutive dipoles were not disrupted in the glass network [81]. An increase in 𝜀 ′ with Na2O doping for 0 ≤ x ≤ 10 mol% (Fig. 11) indicates an increased space charge polarization that caused by the increase in heavy dipoles with an addition of Na2O. This may be caused by the increase of NBO through formation of TeO3 tp and VO4 tp units that are confirmed by FTIR results (Fig. 2). The formation of NBO also indicates the weakening of the glass network, which induced a relative opening of glass network [2, 81]. The relative opening of the glass network caused by NBO created pathways for the migration of Na+ and K+ ions that involved in the build-up of space charge polarization, resulted in the increase in 𝜀 ′ . In addition, the maximum in the 𝜀 ′ value at x = 10 mol% that was in accordance with the conductivity anomaly (Fig. 6) could also be linked to the mixed-alkali effect (MAE). Nevertheless, the decrease in 𝜀 ′ values for 10 < x ≤ 20 mol% may be due to BO that was contributed by the TeO4 and VO5 groups as well as decreased NBO number as indicated by the FTIR results (Fig. 2). The presence of BO enhanced the network linkages, increased the compactness of glass system and limited the movement of Na+ and K+ ions. The strong temperature dependence of 𝜀 ′ at low frequency region (0.01-10 Hz) for x = 10 mol% (Fig. 13) indicates that movement of heavy and medium size dipoles was facilitated with the increase in temperature. As temperature increased, the thermal energy was increased, thereby caused weakening the bonds of the glass network [7, 55, 82] that induced a relative 30

opening of the glass network, which facilitated dipole orientation and ion movement leading to an elevation in space charge polarization that consequently led to rise in 𝜀 ′ . Fig. 12 illustrates the highest increase in 𝜀 ′ for the sample was at 0.01 Hz with increasing temperature indicating an effective delocalization of heavy dipoles. Nevertheless, at greater frequencies (> 1 kHz), the weakening of bonds due to the rise in temperature failed to facilitate dipole rotation at optimal level. The change in dispersion region (Fig. 13) was evident where 𝜀 ′ was decreased with frequency between 1 Hz to 100 Hz due to slower response of heavy and medium dipoles to the fluctuating external field. On the other hand, the relatively constant value of 𝜀 ′ with temperature at higher frequencies (>10 kHz) indicates that light dipoles were not hindered by network bonds. The higher values of dielectric loss at low frequencies can be attributed to the contribution of ion jump, DC conduction loss and electrode polarization loss [52, 83]. The DC conduction losses at the electrodes has resulted in high dielectric loss factor (tan δ) at low frequency region (Fig. 14) for all glass samples [52]. This is indicated by the 1/𝜔 slope of the loss factor plot with frequencies as illustrated by the Fig. 15. At low frequency, DC conductivity elevated currents because charge carrier (Na+ and K+ ions) may jump continuously over large distances with applied voltage, where this current produced conductivity loss. Nevertheless, tan δ decreased with an increased frequency indicating that there was no response from charge carrier due to rapidly changing frequency as charge carrier becomes difficult to travel over large distance. The presence of small peak (Fig. 14) between 0.7 Hz to 2 Hz indicates heavy dipoles relaxation in which dipoles can no longer follow the oscillating electric field as frequency increases and contributes to energy loss. On the other hand, the increase in tan δ at low frequency as temperature increased for x = 10 mol% (Fig. 16) could be characterized by the rise in energy losses due to the electrical leakage. In addition, as the temperature increased at low frequency, tan δ increased and made the orientation of dipoles noncomplex due to an elevated bond weakening with the increase in thermal energy, thus causing higher loss [74]. Meanwhile, the effect of temperature on lighter dipoles was minimal as there was no significant change in tan δ at high frequency region (f >100Hz) as shown in Fig. 17.

4.6

Electrical Modulus Studies The behaviour of real part of electrical modulus (𝑀′ ) at low frequency (Fig. 17)

exhibited insignificant value that nearly reached zero implying the simple nature of migration 31

of conducting ions [84]. As the frequency increased, 𝑀′ was increased and commenced to disperse based on the distribution of relaxation process. Meanwhile, at higher frequencies (f > 100Hz), 𝑀′ reached maximum value with decrease of x ≤ 10 mol% followed by increase of x > 10 mol%. This was at minimal frequency dependent, which indicates high resistance to charge carrier due to the rapid changes in electric field at high frequency region. Thus, the migration of charge carrier was restricted in a potential well [54]. Fig. 17 illustrates the plateau of 𝑀′ at higher frequencies that decreased from x ≤ 10 mol% followed by the increase for x > 10 mol% demonstrating opposite trend to the increase in 𝜎𝑎𝑐 variation with the Na2O content (Fig. 6). For x = 20 mol%, the dispersion at minimal frequency was demonstrated to be comparatively superior compared to other glass samples, thereby indicating higher resistance to ionic carriers. The minimum of 𝑀′ at x = 10 mol% (Fig. 18) was in accordance with 𝜎𝑎𝑐 maxima (Fig. 7) indicating a reverse relationship that may be reflected to the MAE, where the enhancement of NBO induced a relative opening of glass network and resulted in an increase in the carrier pathway. Furthermore, the lower amount of 𝑀′ at x = 10 mol% of Na2O content could be linked with its inferior electrical stiffness in contrast to additional glass samples. On the other hand, the decrease of 𝑀′ as temperature increased at low and intermediate frequency regions (Fig. 19) indicates bond weakening in the glass network. Weakening of bond by increase in thermal energy induced opening of glass network causing charge carrier motion [68]. Meanwhile, at higher frequency region, a relatively constant value of 𝑀′ was observed. This may be due to the high resistance temperature indicating weakening of bond, which had minimal effect on charge carrier mobility, therefore resulting in difficulties for charge carriers to move freely. The shifting of 𝑀′′ peaks (Fig. 20) to higher frequency increased at x < 15 mol% before shifting to lower frequency for x ≥ 15 mol% in conjunction with the increase in 𝜎𝑎𝑐 for x ≤ 15 mol%, followed by the decrease at x ≥ 15 mol%. The relaxation represented by 𝑀′′ peaks indicated relaxation time of charge carriers and non-localized process was dominant [54]. Furthermore, there are two relaxation regions in the imaginary part of the electrical modulus ′′ (𝑀′′ ) in the frequency domain (Fig. 21) including the frequency region below 𝑀𝑚𝑎𝑥 that

determines the range in which charge carriers are mobile over long distances and associated ′′ with hopping conduction, while the frequency region above 𝑀𝑚𝑎𝑥 signifies the range in which

the charge carries are restricted in a potential well, being mobile over short range distances and associated with the relaxation polarization process [54, 65, 77]. The peak frequency (𝑓𝑚 ) (Fig. 21) corresponding to maximum 𝑀′′ (𝜔) typically correlated to the average conductivity 32

relaxation time (𝜏𝑚 ) [85]. Fig.21 illustrates that 𝑀′′ peaks frequency transformed to superior frequency as temperature increased. This implies that the temperature dependent relaxation procedure in which the hopping process charge carriers was influenced by weakening of bonds. Therefore, the relaxation time was decreased and hence increased the relaxation frequency [81]. In addition, the constant height of 𝑀′′ plot might be due to the invariance of 𝜀 ′ and distribution of relaxation times with temperature points [86]. The minimum value in activation energy for relaxation process (𝐸𝜔 ) (Table 3) obtained from the least square fitting of data in Fig. 23 at x = 10 mol% may be related to the conductivity anomaly where maximum value was observed at x = 10 mol% as shown in Fig. 6. ′′ Meanwhile, the perfect overlapping of all curves on a single master curve (𝑀′′ /𝑀𝑚𝑎𝑥

versus log(f/𝑓𝑚𝑎𝑥 )) for 10Na2O-10K2O-30V2O5-50TeO2 glass samples at all temperature points (Fig. 24) nearly merged closely into each other on a single master curve. This reveals that the conductivity relaxation mechanism observed at various frequencies had the similar activation energy, where the distribution of relaxation times could be temperature dependent [86]. On the other hand, the spectra for different compositions at a fixed temperature also merged closely to each other on a single master curve (Fig. 23) implying the similar relaxation dynamic process of charge carriers [86]. The overall weak increase in 𝛽 with the increase in temperature indicates that as the temperature increased, the glass network detached and thus causing a decrease in the interactions between Na+ and K+ and surrounding matrix [86]. Generally, the weak increase in 𝛽 with composition at x ≤ 10 mol% indicates an increased interaction between cations, followed by the decrease at x ≥ 15 mol%. This suggests that a lower value of 𝛽 reveals the cooperative motion of the charge carriers in the glass [87].

5.

Conclusion We have successfully synthesized a new mixed-alkali glass system with composition

xNa2O-(20-x)K2O-30V2O5-50TeO2 (x = 0, 5, 10, 15 and 20 mol%) and found effects which can be related to mixed-alkali effect (MAE). Both AC conductivity and dielectric properties for xNa2O-(20-x)K2O-30V2O5-50TeO2 glasses had been studied. Anomalous AC conductivity (𝜎𝑎𝑐 ) was observed at x = 10 mol% at temperature ≥ 383K was in accordance with the dielectric maximum in which was attributed to the mixing of the two alkali oxides. Notably, transport mechanism was found to be correlated to barrier hopping (CBH) for all glass samples. Evaluation of the conductivity relaxation behaviour of the glass system via electrical modulus

33

plot demonstrated non-Debye type relaxation indicating the presence of dynamic processes, which are both temperature and composition dependent.

Acknowledgement The authors would like to express gratitude to the Institute of Research Management & Innovation (IRMI), Universiti Teknologi MARA for assistance throughout the research. This study was financially supported by the Universiti Teknologi MARA under the BESTARI grant no: 600-IRMI/DANA 5/3/BESTARI (130/2018).

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Highlights    

AC conductivity and dielectric properties of xNa2O-(20-x)K2O-30V2O550TeO2 glasses were studied. AC conductivity and dielectric constant maximum at x=15 mol% were attributed to mixed-alkali effect (MAE). Conduction mechanism of the studied glass samples followed the correlated barrier hopping (CBH) model. Thermal analysis results showed the glass transition temperature (Tg) exhibited a minima at x =10 mol%.

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AUTHORSHIP STATEMENT Manuscript title: Effects of mixed-alkali oxides on AC conductivity and dielectric properties of xNa2O-(20-x)K2O30V2O5-50TeO2 glasses. All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in the Results in Physics. Authorship contributions Conception of study : S. J. Japari, R. Hisam, A. K. Yahya Data curation : S. J. Japari Formal analysis : S. J. Japari, R. Hisam, A. K. Yahya Funding acquisition : R. Hisam Investigation : S. J. Japari Methodology : S. J. Japari, R. Hisam, A. K. Yahya Project administration : S. J. Japari, R. Hisam, A. K. Yahya Resources : S. J. Japari, R. Hisam, A. K. Yahya Software : R. Hisam Supervision : R. Hisam, A. K. Yahya Validation : R. Hisam, A. K. Yahya Visualization : S. J. Japari, R. Hisam, A. K. Yahya Drafting the manuscript : S. J. Japari Revising the manuscript critically for important intellectual content: S. J. Japari, R. Hisam, A. K. Yahya Approval of the version of the manuscript to be published: R. Hisam, A. K. Yahya Acknowledgements All persons who have made substantial contributions to the work reported in the manuscript (e.g., technical help, writing and editing assistance, general support), but who do not meet the criteria for authorship, are named in the Acknowledgements and have given us their written permission to be named. If we have not included an Acknowledgements, then that indicates that we have not received substantial contributions from non-authors. This statement is signed by all the authors

Author’s name

Author’s signature

Date

S. J. Japari

29 September 2019

R. Hisam

29 September 2019

A.K. Yahya

29 September 2019

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