A new method for controlling structural, electrical and optical properties of phosphate glasses, containing transition metal ions (TMIs)

Journal of Non-Crystalline Solids 525 (2019) 119693

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A new method for controlling structural, electrical and optical properties of phosphate glasses, containing transition metal ions (TMIs) ⁎

T

⁎

Majid Karimi, Ali Mehdizadeh , Mohammad Hossein Hekmatshoar , Samira Vafaei Faculty of Basic Sciences, Sahand University of Technology, Sahand New Town 51335-1996, Tabriz, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Mixed alkali effect Phosphate glasses Glass modifiers FT-IR and UV–vis spectroscopy Dc conductivity

In this study, glassy samples with a composition of 40P2O5–10V2O5–(50−x) Li2O–xNa2O, (x = 5–45 mol%), were prepared and their structural, electrical, and optical properties were investigated for the mixed alkali effect (MAE). The density of the samples displayed nonlinear variation with Na2O content (x mol%), which confirmed the existence of the MAE. It was found that the conductivity in the present glassy system is more ionic rather than electronic, and the minimum dc conductivity at x = 25 mol% is due to the MAE on ionic conductivity. Some optical parameters such as indirect allowed optical band gap, Urbach energy, refractive index, dielectric constant, reflection loss, molar refraction, and electronic polarizability were evaluated from the absorption and reflection spectra. The values of the optical band gap showed nonlinear behavior upon substitution of Li2O by Na2O with a maximum at x = 25 mol%, which supported the existence of the MAE in the optical properties.

1. Introduction Glassy materials have some unique properties that are not found in other materials [1,2]. Hardness and transparency at room temperature in addition to strength and excellent corrosion resistance make them useful for many practical applications [3–6]. P2O5 is one of the four classic Zachariasen glass forming oxides (along with SiO2, GeO2 and B2O3) [7,8]. Phosphate based glasses have attracted much more attention than other oxide glasses. This attraction is due to their technological and biological applications as well as unique physical properties such as semiconducting properties, simple structure, strong glassforming characteristic, UV transmission and optical features, low melting point and glass transition temperatures, large thermal expansion coefficients, and biomedical compatibility [9–14]. These glasses are being used as host materials for lasers, as potential cathode materials in Li-ion batteries, optical filters, and also to store nuclear waste [15–17]. Although pure phosphate glasses are highly hygroscopic, investigations have shown that the addition of transition metal ions (TMIs) or alkali and alkaline earth ions to the glass networks as modifiers, can solve the issue of low chemical durability of pure phosphate glasses [18–20]. Obviously, research on phosphate glasses can lead to a deep understanding of these useful materials and to finding ways of controlling their properties for different applications. The network modifiers induce defects in glass structure and further doping has a substantial effect on physical and chemical properties.

⁎

Glasses containing high concentration TMIs are known to be electronically semiconducting. Generally, these glasses have electronic conductivity. Moreover, upon adding alkali oxides to their composition, the conductivity of these glasses can be either of electronic, ionic or mixed electronic-ionic nature, depending on the ratio of their constituent oxides [21,22]. The glasses exhibiting mixed electronic–ionic conduction can be used as cathode materials whereas purely ionic conducting glasses can be employed as solid electrolytes in electrochemical devices [23]. Previous studies have shown that in glasses containing more than one alkali ion type, Previous studies have shown that in glasses containing more than one alkali ion type, when one alkali is gradually replaced with another alkali ion, most of the physical properties exhibit remarkable deviation from the linearity while maintaining the total concentration of alkali ions constant. This behavior is well known as mixed alkali effect [24,25]. This effect in glasses gives rise to large changes in properties that are associated with ionic transport, such as ionic conductivity and dielectric relaxation, as well as mechanical loss and internal friction. Moreover, macroscopic properties such as molar volume, density, refractive index, thermal expansion coefficient, and elastic moduli usually change linearly or have small deviations from linearity [24,25]. In general, the MAE becomes stronger with an increase of total alkali elements concentration and mismatch of alkali elements size [26–30]; it becomes weaker at higher temperatures [24,25,31–39]. Mixed alkali effect can be useful in tuning favorable properties in technology and industry. Throughout the years, several

Corresponding authors. E-mail addresses: [email protected] (A. Mehdizadeh), [email protected] (M.H. Hekmatshoar).

https://doi.org/10.1016/j.jnoncrysol.2019.119693 Received 28 June 2019; Received in revised form 29 August 2019; Accepted 14 September 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.

Journal of Non-Crystalline Solids 525 (2019) 119693

M. Karimi, et al.

Table 1 CAS registry number, supplier and purity of the chemicals. component

CAS reg. no.

supplier

purity

Ammonium dihydrogen phosphate Divanadium pentaoxide Lithium carbonate Sodium carbonate

7722-76-1 1314-62-1 554–13-2 497–19-8

Merck Merck Merck Merck

99% 99.9% 99.5% 99.9%

theories and models have been proposed in order to explain the origin of the MAE. Most of the studies in this field have been focused on the mixed alkali glasses that don't have TMIs. There has been little work done on mixed alkali glasses containing TMIs. The present work was undertaken to study various properties of mixed alkali phosphate glasses containing a transition metal oxide in order to give an insight into this intriguing effect. 2. Experimental Fig. 1. XRD patterns of glassy 40P2O5–10V2O5–(50−x) Li2O–xNa2O, (a) x = 5 mol%, (b) x = 15 mol%, (c) x = 25 mol%, (d) x = 35 mol%, (e) x = 45 mol%. amorphous peak shown with dashed wine lines.

The melt quenching technique was used to prepare the glassy samples with a general formula of 40P2O5–10V2O5–(50−x) Li2O– xNa2O, where x = 5, 15, 25, 35 and 45 mol%. V2O5, Li2CO3, Na2CO3 and NH4H2PO4, were taken as starting materials. Table 1 represents CAS registry number, supplier and purity of these chemicals. Stoichiometric amounts of the initial materials were weighed and mixed finely in a mortar to form a homogeneous mixture. The mixture was poured into alumina crucibles and transported to an electrical furnace and were it was kept at a temperature of 423 K for 2 h so to accomplish initial reactions and exiting of volatile elements from the composition. Then, the furnace temperature was slowly increased and the melting point of each glass combination was achieved at a temperature range from 983 K to 1003 K. After an hour, the acquired melt was poured on a preheated thick stainless-steel plate into an annealing furnace in order to prepare bulk samples. The melt was immediately quenched to vitrify it, and the samples were annealed for 3 h. Thin blown films were prepared by immersing the end of an alumina tube into the molten material in the crucible and steadily blowing through the alumina tube. To confirm the amorphous nature of the samples, X-ray patterns were recorded at room temperature by a Bruker, and the scanning angle (2θ) was varied from 10° to 120°. Density measurements were carried out at room temperature using the Archimedes method with ethylmethyl-ketone as an immersion fluid. The uncertainty in the density measurement is ± 0.004. The FT-IR absorption spectrum was achieved using the KBr pellet technique with a FTIR spectrometer (Bruker Tensor 27) in the frequency range of 400–4000 cm−1. To measure the electrical conductivity, glass samples were polished with several grads of polishing papers and a silver paste coating was applied to both sides of the samples to serve as electrodes. Dc electrical conductivity was measured by means of the two Probe method, and Current – Voltage characteristics of the sample were investigated in the temperature range of 290–383 K. The electrical conductivity was calculated as a function of temperature. The error in measurement of the dc electrical conductivity is ± 0.01. The optical absorption and reflectance spectra of samples in the form of thin blown films with a thickness of about 4 μm were recorded at room temperature using a UV–Vis spectrophotometer, manufactured by Scinco, in the wavelength region of 200900 nm.

lines). This is the clear indication of amorphous nature of the prepared glasses [40,41]. Fig. 2 (a, b and c) schematically displays the structure of the glassy samples with x = 20, 25, 30 mol% respectively. As is evident, substitution of Li2O by Na2O leads to a change in ionic interactions in the structure of the amorphous materials considered in this work. The measured values of density (D) are given in Table 2. It is clear that the density varies nonlinearly with Na2O molar percentage, which proves the existence of the mixed alkali effect. Sodium, lithium, and vanadium ion concentrations of the samples in the composition were determined by using the following expression [42];

N=

D × NA × P , M

(1)

where M is the average molecular weight and NA is Avogadro number. P = nx, where x is the mole fraction in glass composition and n is the number of ions atom in a given oxide, n = 1 for oxides like CdO, ZnO, etc. and n = 2 for oxides like Li2O, V2O5, etc. The calculated values of ion concentrations are provided in Table 2. As is evident, lithium ion concentration (NL) decreases with increasing of sodium ion concentration (NS) in the glass network. Vanadium ion concentration (NV) has a nonlinear variation with Na2O content which is due to the MAE. The values of molar volume (Vm), was determined by using the following equation and are listed in Table 2;

Vm =

M , D

(2)

The density of a glass is explained in terms of competition between the masses and sizes of the various structural groups present in its composition. Accordingly, the density depends on how tightly the ions and ionic groups are packed together in the substructure. The density of single-alkali glasses typically change linearly, however, in the mixed alkali glasses the density displays a deviation from linearity. Stevels [43] visualized the glass structure as containing interstices of varying diameter so that alkali ions with the different sizes are more easily accommodated than when the alkali ions are the same (Fig. 3, inset image: zoomed area). Therefore, in Stevels' theory, the higher density of mixed-alkali glasses is due to more efficient ionic packing. Inaba and Fujino reported an empirical equation for the ionic packing ratio (Vp), which is expressed as [44,45];

3. Results and discussion 3.1. Electrical properties

Vp = (D / M )

Fig. 1 illustrates the XRD patterns of all the samples. As is clear, there is no distinct and sharp Bragg's peak except for short range-related broad peak at small angles (amorphous peak shown with dashed wine

∑ Vi xi , i

(3)

where M is the molar weight, D is the density, xi is the molar fraction 2

Journal of Non-Crystalline Solids 525 (2019) 119693

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Fig. 2. Amorphous structure of the glassy samples: (a) x = 20 mol% (30Li2O and 20Na2O), (b) x = 25 mol% (25Li2O and 25Na2O), (c) x = 30 mol% (20Li2O and 30Na2O). Table 2 Physical parameters of the 40P2O5–10V2O5–(50−x) Li2O–xNa2O glasses. Parameters

M (g/mol) D (g/cm3) ( ± 0.004) Vm (cm3/mol) Vp OPD (g-atm/l) NS (1022 ion/cm3) NL (1022 ion/cm3) NV (1022 ion/cm3)

Glass composition x=5

x = 15

x = 25

x = 35

x = 45

91.498 2.118 43.191 0.503 69.459 0.139 1.255 0.279

94.708 2.210 42.848 0.599 70.015 0.422 0.984 0.281

97.878 2.374 41.228 0.632 72.766 0.730 0.730 0.292

101.139 2.220 45.553 0.582 65.858 0.925 0.397 0.264

104.348 2.144 48.665 0.545 61.646 1.114 0.124 0.247

and Vi is the packing factor obtained from the following equation for oxide MXOY;

Vi =

4 3 πNA [(XrM + YrO3 )], 3

(4)

where NA is Avogadro's number and rM and rO are the Paulings ionic radius of element A and oxygen O, respectively. The calculated values of the ionic packing ratio Vp are presented in Table 2. As can be seen, the prepared samples have values, Vp, between 0.503 and 0.632, which are typical values for oxide glasses [46]. The oxygen packing density (OPD) of the samples was evaluated by using the following equation [47];

OPD =

D × (O) , M

(5)

Fig. 3. Density variation, Ionic packing ratio and Oxygen packing density. Zoomed inset image shows accommodation of alkali ions in the structure of the glassy samples.

where (O) is the number of oxygen atoms in the composition. Fig. 3 represents the density, molar volume and ionic packing ratio variation as a function of Na2O content. It is clear that these parameters have similar variation with Na2O content. When Li2O is gradually replaced with Na2O, the glass structure changes to accommodate the sodium ions. From x = 5 to x = 25 mol% the accommodation of the alkali ions in the structure of the glassy system, gradually increases and reaches the maximum at x = 25 mol%, where the confrontation of two type of alkali ions with different size reaches the maximum. Therefore, according to the Stevels' theory, it results in the max value of the ionic

packing ratio and subsequently the max value of the density at x = 25 mol% (dashed black lines). Then, by further increasing of the Na2O, the confrontation of the different alkali ions in the structure of the glassy system decreases and so the ionic packing ratio and density values decrease. Fitted results provided in the SI. The FTIR spectrum provided a significant amount of information about the molecular vibrations and rotations associated with a covalent 3

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M. Karimi, et al.

samples (refer to Fig. 4), which means that V2O5 act as a network modifier in our glassy samples [48]. The presence of V2O5 as a Modifiers in glass network causes depolymerization of the network and shortens the long chains by converting PeOeP to PeOeV bonds. In our studied glasses the peaks in ~ 900–1000 cm−1 range are due to the cation-oxygen attraction of PeOeV bonds(dashed red lines), [54,57]. Since care was taken during the preparation of the samples, no bond due to PeOH is observed. From Fig. 4 it is found that by substitution of lithium ions with sodium ions, PeOeP and PeOeV bonds shift to lower frequency. This degradation is accompanied by the formation of weak links such as Na+…O– bonds and a change in the formation of NBOs. It should be noted that the vibration modes of mobile ions occur in low frequencies, thus, far-infrared spectroscopy is suitable in detecting such peaks. As can be seen in Fig. 5 and Figs. 1S, 2S, 3S, 4S, 5S, the I–V characteristic of the samples display ohmic behavior within the voltage range of 10–300 V (all temperature 306–396 K). Fig. 6 (a and b) displays the temperature dependence of dc electrical conductivity in the temperature range of 306-396 K. Lnσ increases with rising temperature, which confirms the semiconducting nature of the samples. Fitted results provided in the SI. Activation energy values (Eg), were determined by using the Arrhenius equation;

Fig. 4. FTIR spectra of glassy samples: (a) x = 5 mol%, (b) x = 15 mol%, (c) x = 25 mol%, (d) x = 35 mol%, (e) x = 45 mol%. The bonds in composition of the samples are Shown in dashed black, green, red, blue and orange lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

−Eg ⎞ σ = σ0 exp ⎛ , ⎝ kB T ⎠

Table 3 Bond assignments of 40P2O5–10V2O5–(50−x) Li2O–xNa2O glasses in FTIR spectra. Bond assignment

[PO3−]2− Symmetric stretching of PeOeP Cation-oxygen attraction of PeOeV Symmetric stretching of OePeO Stretching modes of P]O

⎜

x = 15

x = 25

x = 35

x = 45

569 767 931 1112 1198

575 765 926 1110 1200

562 763 919 1111 1202

566 761 916 1110 1202

559 756 913 1109 1203

(6)

where σ is conductivity, σ0 is a constant and kB is the Boltzmann constant. The values of Lnσ and Eg are provided in Table 4. Figs. 7 and 8 represent the compositional dependence of the Lnσ and Eg, respectively. Activation energy and dc conductivity display a nonlinear behavior due to the existence of the MAE. As is seen in Fig. 7 (a and b) dc conductivity initially decreases with increasing mole percent of Na2O and reaches a minimum value at intermediate composition (x = 25%mol, shown with dashed black lines), after which, it increases again (increase dc conductivity & increase temperature, shown green arrows). As we expected activation energy varies in reverse order. It first increases and reaches a maximum at x = 25%mol and then decreases (refer to Fig. 8). Fitted results provided in the SI. The electrical properties of vitreous/crystalline materials depend on their structures. Although the glass former P2O5 does not play a major role in electrical conduction, the structure of phosphate units, play a major role in deciding the nature of the conduction in the glass matrices. In our studied glasses, V/P and O/(V + P) ratios are constant, clearly, it can be assumed that the variation of their electrical properties is not influenced by the structural units of V2O5 in their vitreous networks. However, vanadium, as a transition element in oxide glasses might exist in more than one valence state, depending on host glass composition and preparation conditions [58]. In this case, electron transfer between vanadium ions with two different Oxidation is permitted, and the electronic conductivity can occur by small polaron hopping between two valance states. However, previous works have proved that the electronic conductivity arising by the inter-valence transfer process between TIMs is omitted for the mixed alkali glasses corresponding to high total alkali concentration [59]. The argument is that as the glasses become increasingly oxygen-donor, the formation of the higher oxidation valence state is favored. So, it can be said that conductivity in the present glassy system is more ionic rather than electronic, and the minimum of dc conductivity is linked to the MAE on ionic conductivity. Two descriptions of the MAE in ionic conductivity that are currently more accepted are the dynamic structure model (DSM) [38,60–62] and the random ion distribution model (RIDM) [63–68]. The DSM assumes that A and B ions in a mixed alkali glass create their own local environments, which are different for different ions and the result is a site energy mismatch. The possibility for an A ion to hop into a B site is lowered, compared to A-A or B-B hops.

Glass composition x=5

⎟

bond. The FTIR spectra of all samples are shown in Fig. 4; the assignments of peaks are summarized in Table 3. Phosphate glasses have various structures. The structure that is composed of three bridging oxygen (BO) and one binary bond of P]O is called ultra-phosphate. When P2O5 mixed with network modifiers, the bridging oxygen bonds break to form nonbridging oxygen atoms (NBOs) and gradually ultraphosphate units convert to metaphosphate, pyrophosphate and orthophosphate units depending on the type and amount of modifiers [48]. In an ultra-phosphate structure the peak at 1.378 cm−1 is characteristic of the P]O bonds [49]. Adding modifier oxides to the glass network causes a position shift of the P]O bond to a lower frequency of ~1260 cm−1 (dashed orange lines). We can attribute the observed peaks at ~1200 cm−1 to stretching modes of P]O in metaphosphate units [50]. The bonds around ~560 cm−1 (dashed black lines) are due to the fundamental frequency of [PO3−]2− group creating OePeO bending (the formation of metaphosphate glasses) [51,52]. The bonds observed at ~ 1110 cm−1 (dashed blue lines) are related to the symmetric stretching vibrations of OePeO and are characteristic of pyrophosphate units [53,54]. Also, the peaks obtained in the region ~ 760 cm−1 (dashed green lines) are due to symmetric stretching vibrations of PeOeP in pyrophosphate units [55,56]. So, it can be said that the structure of the prepared samples is constituted of the metaphosphate and pyrophosphate units. V2O5 has a dual role in glass networks, it partly behaves as a glass former and partly as a modifier. Herein P2O5 is a dominate glass former and V2O5 is a glass modifier. Furthermore, V2O5 can play a dual role in glass networks. If it acts as a glass former, it may reduce or eliminate the P]O bond, depending on the glass composition. Complete reduction of the P]O bond was not observed in the

4

Journal of Non-Crystalline Solids 525 (2019) 119693

M. Karimi, et al.

Fig. 5. A representative plot of Log (I) versus Log (V) for: (a1) x = 5 mol% (316 K), (a2) x = 5 mol% (376 K), (b1) x = 15 mol% (316 K), (b2) x = 15 mol% (376 K), (c1) x = 25 mol% (316 K), (c2) x = 25 mol% (376 K), (e1) x = 35 mol% (316 K), (e2) x = 35 mol% (376 K), (f1) x = 45 mol% (316 K), (f2) x = 45 mol% (376 K).

Fig. 6. Variation of dc conductivity as a function of inverse temperature: (a) x = 5, 15, 25 mol%, (b) x = 25, 35, 45 mol%.

composition invariant environments. The alkali ions are randomly dispersed between the phosphate chains in low dimensional pathways. Assuming that the different local environments of the two types of alkali ions make hops to dissimilar sites unlikely to occur, the MAE can be understood as a natural result of this structural arrangement. The random mixture of alkali ions in low dimensional pathways and the site

Therefore, diffusion predominantly occurs in some preferred paths, and this is proposed to account for the reduced ionic conductivity. Swenson et al. suggested that the principal origin of the MAE can be understood directly from static structural models of real glasses. Diffraction studies and reverse Monte Carlo simulations of mixed alkali phosphate glasses showed that the different alkali ion types have different local and 5

Journal of Non-Crystalline Solids 525 (2019) 119693

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Table 4 Electrical parameters for 40P2O5–10V2O5–(50−x) Li2O–xNa2O glasses. Parameters

Glass composition

−1

Ln σ at 316 K (Ω.m) ( ± 0. 01) Ln σ at 376 K (Ω.m)−1 ( ± 0.01) Eg (eV) ( ± 0. 01)

x=5

x = 15

x = 25

x = 35

x = 45

−14.45

−16.774

−19.394

−18.542

−15.88

−11.575

−12.514

−14.732

−14.299

−11.925

0.608

0.691

0.833

0.754

0.642

mismatch lead to partial blocking of preferred diffusion paths in the structure of a static glass. This is the essence of the random distribution model RIDM. This model is the first model, based on real glass systems, that provides a complete structural picture of mixed alkali glasses [66]. Ionic conduction in the prepared samples is due to existence of lithium and sodium alkali ions. According to the RIDM model, these two types of alkali ions are randomly mixed and each ion has distinctly different conduction pathways of low dimensionality. This implies that the lithium ions tend to block the pathways for the sodium ions and vice versa. Due to the energy mismatch between dissimilar sites, the hoping possibility of lithium ions into sodium sites and sodium ions into lithium sites reduce, as compare to lithium–lithium and sodium–sodium hops. The blocking of ion hopping to a neighboring site adapted for a dissimilar ion starts with the gradual displacement of lithium ions by sodium ions in the structure of the samples, and reaches the maximum at x = 25 mol%. Consequently, the activation energy reaches its maximum and ionic conductivity reaches its minimum at x = 25 mol%. This is the reason of the minimum observed in the dc conductivity of the prepared samples. The temperature dependence of the mixed alkali effect on the dc conductivity, shown in Fig. 7, indicates that the magnitude of MAE diminishes as the temperature increases. This decrease is a direct consequence of the activation energies of the mixed alkali glasses. As the temperature is increased, the energy mismatch between different ionic sites is decreased; Finally, it becomes comparable to kBT at high temperature; as a result, the MAE is decreased. Also, as the temperature decreases, the average hopping rate in mixed alkali glasses reduces much more rapidly than in single alkali glasses. The increase in activation energy in mixed alkali glasses can be primarily understood from the partial blocking effect of preferred diffusion pathways, which forces the ions to move along pathways with higher energy barriers.

Fig. 8. Variation of activation energy. Zoomed inset image shows maximum activation energy at x = 25 mol%.

3.2. Optical properties The analysis of the optical absorption spectrum and particularly the absorption edge in the ultraviolet and visible regions is one of the most productive tools for investigation of band structure and band gap energy in crystalline and non-crystalline systems. Fig. 9 shows the optical absorption spectra of all samples. The absence of sharp absorption edges in the Figure clearly indicates the amorphous nature of the samples [69]. The optical absorption coefficient (α(ν)), was determined from the relation;

α (v ) =

1 I log ⎛ 0 ⎞, d ⎝ It ⎠ ⎜

⎟

(7)

where d is the thickness of the glass sample and I0 and It are the intensities of the incident and transmitted beams, respectively. The factor log(I0/It) is absorbance. For amorphous materials, the absorption coefficient as a function of the incident photon energy, according to Mott and Davis [70], is given by;

α (v ) = β

(hv − Eopt )n hv

,

(8)

where β is a constant, called the band tailing parameter and hν is the

Fig. 7. Variation of dc conductivity as a function of Na2O content: for temperatures (a) 306 K, 316 K, 326 K, 336 K, 346 K, (b) 356 K, 366 K, 376 K, 386 K, 396 K. minimum of dc conductivity x = 25% mol, shown with dashed black lines. Increase dc conductivity & increase temperature shown with green arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 6

Journal of Non-Crystalline Solids 525 (2019) 119693

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Fig. 11. Linear portion of Lnα versus hν curve for all samples. Fig. 9. Absorbance spectra of glassy samples.

Fig. 12. Reflectance spectra of glassy samples. Fig. 10. Linear portion of (αhν)1/2 versus hν curve for all samples.

incident photon energy. Eopt is the optical band gap and index n determines the type of electronic transitions in k-space and takes the values 2, 1/2 for indirect allowed and direct allowed transitions, respectively. By plotting (αhν)n as a function of photon energy and careful analysis of its linear portion, one can find Eopt for all transitions. Fig. 10 represents the linear portion of (αhν)1/2 versus the hν curve for all samples. The values of Eopt were estimated by extrapolation this portion of the curves to (αhν)1/2 = 0, and are also presented in Table 5. As is evident, the indirect allowed optical band gap values vary from 2.165 eV to 2.741 eV when Li2O is replaced by Na2O. This nonlinear variation in Eopt with the Na2O content indicates the existence of the MAE in the optical properties of the present glassy system. As mentioned, (in FTIR studies), addition of network modifiers into glass network leads to the modification of the glass network and creating NBOs. In single alkali glasses, optical band gap decreases with alkali content, which has been attributed to an increase in the formation of nonbridging oxygens [71]. However, the nonlinear variation of Eopt in our glass system could be due to a change in the formation of NBOs as Li ions are replaced by Na ions. Accordingly, the maximum of Eopt at x = 25 mol% may be related to the formation of a low number of NBOs. There is usually an Urbach tail for the absorption, when α(ν) lying between 102 and 104 cm−1; in which α(ν) depends exponentially on the photon energy as [72,73]:

Table 5 Optical parameters of 40P2O5–10V2O5–(50−x) Li2O–xNa2O glasses. Parameters

Glass composition x=5

x = 15

x = 25

x = 35

x = 45

Eopt (eV) EU (eV)

2.410 0.400

2.165 0.730

2.741 0.368

2.178 0.465

2.225 0.416

n at λ = 450 nm at λ = 700 nm

2.2428 2.1657

2.3100 2.2952

2.0446 2.0363

2.3464 2.2046

2.2200 2.1499

ε at λ = 450 nm at λ = 700 nm

5.030 4.690

5.336 5.268

4.180 4.146

5.506 4.860

4.928 4.622

R at λ = 450 nm at λ = 700 nm

0.0858 0.0783

0.0924 0.0909

0.0667 0.0659

0.0960 0.0821

0.0836 0.0768

Rm (cm3/mol) at λ = 450 nm at λ = 750 nm

24.760 23.824

27.159 26.984

21.216 21.105

27.345 25.632

27.592 26.618

αe (10−24 ion/cm3) at λ = 450 nm 49.073 at λ = 750 nm 47.216

54.319 53.968

42.094 41.875

54.207 50.812

54.750 52.817

hv α (v ) = α 0 exp ⎛ ⎞, E ⎝ U⎠ ⎜

7

⎟

(9)

Journal of Non-Crystalline Solids 525 (2019) 119693

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Fig. 13. (a) Refractive index variation as a function of Na2O content (for λ = 450 and 700 nm), (b) Dielectric constant variation as a function of Na2O content (for λ = 450 and 700 nm).

where hν is the incident photon energy, α0 is a constant and EU is the Urbach energy, which represents the width of localized states tailing in the band gap. Indeed, this quantity can be considered as a measure of disorder in amorphous and crystalline materials [74]. Fig. 11 shows the linear portion of Lnα versus the hν curve for all samples. EU values, were determined from the slopes of this portion of the curves, which are listed in Table 5. It is observed that the value of EU lies between 0.4 eV and 0.73 eV, and these results are in accordance with those reported for inorganic glasses. The nonlinear variation of the Urbach energy with the mole percent of Na2O also shows the existence of the MAE. Fig. 12 shows the reflectance spectra of samples. The refractive index (n) of blown thin films was computed using the following equation [71];

1+R ⎞+ n=⎛ ⎝1 − R ⎠

4R − k2 , (1 − R)2

the values of reflection loss, molar refraction and electronic polarizability vary nonlinearly with the Na2O content, which is due to the MAE. 4. Conclusion The FTIR spectra showed that vanadium oxide acts as a glass modifier that enters the glass network by breaking up other linkages and creating nonbridging oxygens in the network. Substitution of Li2O by Na2O leads to degradation of PeOeP and PeOeV bonds and a change in the formation of NBOs. This is the main reason of the mixed alkali effect in the optical properties. The MAE also appeared as a deep minimum in the dc conductivity. The reason of this minimum was explained within the framework of the RIDM, where the alkali ions are randomly mixed between the phosphate chains. Influence of the MAE in several properties of the glassy systems can play an important role in controlling properties for various applications (such as Thermometer glass and Low-loss electrical glasses).

(10)

where R is the reflectance and k = αλ/4πis the extinction coefficient. The optical dielectric constant (ε) of all samples was calculated from the refractive index of each sample by using;

ε = n2,

Declaration of Competing Interest

(11)

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The variation of refractive index and dielectric constants with Na2O content, is presented in Fig. 13 a and b, respectively. It is found that the refractive index and dielectric constants, varies nonlinear with the Na2O content, which supports the mixed alkali effect in optical properties. Fitted results provided in the SI. The reflection loss from the glass surface (R), was evaluated from the refractive index of samples by using the Fresnel's formula [75];

Acknowledgement Amorphous structure of the glassy samples was visualized with VESTA.

2

n − 1⎞ , R=⎛ ⎝n + 2⎠

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Appendix A. Supplementary data

The molar refractivity of each sample (Rm), was computed using the formula [76];

Rm =

M ⎡ n2 − 1 ⎤ , 2 D⎢ ⎣n + 2⎥ ⎦

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jnoncrysol.2019.119693. References

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where M is Average molecular weight and D is density. The electronic polarizability (αe), was calculated by using the following equation [75];

αe =

3 ⎡ n2 − 1 ⎤ , 2 ⎥ 4πNV ⎢ ⎣n + 2⎦

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where NV is the number of vanadium ions per unit volume. The values obtained for the parameters above are given in Table 5. As is evident, 8

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