Since the first commercialization of Li-ion batteries in 1991 [1] , many attempts have been made for the revolutionary improvement in safety, efficiency, and durability of batteries that have powered today’s essential mobile electronic devices, such as laptops, mobile phones, and electric vehicles all over the world. As the demand for high-performance energy storage and conversion technologies for portable electronic equipment, electric vehicles, and large-scale energy consumption increases, a new type of battery is needed to be developed [2] . Though the Li-ion technology plays a key role in the transport sector, it could not fulfill the demand for the stationary storage sector because of its limited source of availability related to high cost [2] . As an alternative, Sodium-ion battery technology has recently been under study because it is relatively more environmentally friendly and more abundant on the planet [2] . Commercially, available all these batteries consist of two electrodes connected by a liquid electrolyte. The performance of a battery is basically rooted in the efficiency of its electrodes and electrolyte [3] . Most sodium and lithium-based batteries currently in use still depend on liquid-organic electrolytes, which pose restrictions on cyclability due to electrode corrosion, high flammability, and highly resistive solid electrolyte interphase (SEI) formation at the electrodes leading to capacity loss, and risk of leakage [4] . Extensive research works are being conducted for developing solid electrolytes that can be potential candidates to replace liquid electrolytes [5] . All-solid-state batteries (ASSBs), where the electrolyte is also solid, are the safest batteries with no leakage, no volatilization, or no flammability. Generally, solid-state electrolytes can be categorized into inorganic glass/ceramic electrolytes, organic polymer electrolytes, and ceramic-polymer composite electrolytes. The inorganic electrolyte is essential for rigid battery design for its good thermal/chemical stability, wide electrochemical window, high ionic conductivity and low electronic conductivity [6] . Toyota Motor Corp, Japan, for the first time, revealed the prototype of its ASSB on 18 November 2010, in Japan. The battery used a sulfide solid electrolyte of the system Li₂S-P₂S [7] . The same company presented a new prototype of ASSB with five times higher output density after two years. The main improvement in the battery was focused on sulfide-based solid electrolyte, Li₁₀GeP₂S₁₂ which showed an ionic conductivity of lithium (Li) ions as high as 1 × 10⁻² S∙cm⁻¹ [7] . Thus, inorganic solid-state electrolytes drew much attention in research. Inorganic solid electrolytes can be crystalline, glassy and glass ceramic electrolytes [5] . Glassy electrolytes are one of the promising candidates as inorganic solid electrolytes, applicable to all-solid-state battery systems. Such systems offer enhanced safety, simplified cell design and environmental sustainability.

Glasses are amorphous solids that can be distinguished by their unique property known as glass transition temperature. Glasses exhibit variations of thermal expansivity, heat capacity, entropy, viscosity, and entropy. Glassy electrolytes are more attractive compared to their crystalline counterparts in electrochemical applications because they are cheaper, without grain boundaries, easy to fabricate into complex shapes and resistant to environmental effects [8] [9] . They have a wide range of compositional adjustment and isotropic conductivity [8] . Glass electrolytes are considered to exhibit higher ionic conductivity than that corresponding crystalline ones [10] [11] [12] . Depending on the type of ions taking part in conduction and chemical composition, the glasses are classified as shown in the following flow chart (Figure 1) [9] .

Ionic glasses are generally formed by mixing network modifier, network former and dopant salt in different proportions [13] . Sometimes, intermediates (Al₂O₃, Ge₂O₃, etc.) are also used. Usually, glass network formers are oxide/sulfide materials of covalent nature (e.g. SiO₂, B₂O₃, P₂O₅, SiS₂, P₂S₅, etc.). These oxides and sulfides, when quenched, facilitate glass formation by forming cross-linked macromolecular chains. In general, alkali metal oxides or sulfides (e.g. Li₂O, Na₂O, K₂O, etc.) are used as a modifier, which is ionic in nature [14] . The modifier interacts strongly with the structural units of the network formers leading to the progressive breaking of oxygen or sulfur bridges to result in the maximum number of non-bridging oxygen or sulfur atoms. It reduces the average length of the macro-molecular chain, as shown in Figure 2. This lacks long-range order and creates more disorder in the material leading to the formation of interconnected “open channels” or sites, which act as conduction pathways for the charge carriers in the glass matrix [14] [15] . For example, when Li₂O or Na₂O is added as network modifiers to vitreous silica, it results in the chain breaking of the network. It transforms bridging oxygen atoms into non-bridging oxygens, but the silicon atoms remain tetrahedrally coordinated.

The positive cations are situated near the anionic sites of the non-bridging oxygens for providing local charge neutrality (see Figure 2). Non-bridging oxygen sites offer the hopping site for ionic conduction in an oxide glass network. Cations such as Li⁺ jump into or out of these hopping sites easily due to relatively weak bonding or shallow energy well [16] [17] (see Figure 3). The formation of non-bridging oxygen also contributes to the open network structure with increased free volume for ion conduction [16] . Thus, the increase in alkali-ion (such as Li⁺) mobility is due to the formation of the non-bridging oxygens or broken bonds within the glass network. In principle, the positively charged cations are localized in interstitial sites by insertion of the modifier anions into the network chains. It develops ionic bonds between the modifier cations and network anions. With the increase in modifier concentration, adjacent negative anion sites come closer decreasing the depth of the potential well in the energy profile. The ionic transport path becomes favorable when such wells are densely interconnected in the glass. Thus, increasing modifier concentration enhances the ionic conductivity of glasses [18] . However, increasing modifier concentration may cause the glass less stable and with low glass transition temperature. Some

examples can be discussed here for the effect of modifier addition on glass networks. In borate glasses, alkali oxides addition to B₂O₃ limits the glass network for a certain boron atoms concentration. In such a case, the added alkali oxide molecules form four-coordinated boron atoms. They form tetrahedral BO₄ units that provide anionic sites for the alkali ions with relatively small binding energy [19] . BO₄ tetrahedra have larger molecular diameters and its oxygens provide relatively weaker ionic field strength to alkali ions (such as Li⁺) compared to the field offered by nonbridging oxygen in a 3-coordinated boron structure. The 3-coordinated non-bridging oxygens (negative sites) have binding energies different from those of localized BO₄ units [18] . Thioborate glasses xLi₂S-(1 − x)B₂S₃ have also been reported to change four-coordinated boron atoms to three-coordinated with the rise of modifier concentration. Here also, the formation of non-bridging sulfur atoms causes the depolymerization in the thioborate matrix [18] [20] .

Ionic salts or dopant salts can be added to a glassy matrix because the addition can significantly enhance the ionic conductivity by several orders of magnitude compared to the one without the salts. In most cases, these additives are halides, phosphates or sulfates which contain the common cation of the network modifier. For these salts, the glass matrix acts as a solvent. When salt is added to the glass matrix, it affects the bonding network between the network former and the glass modifier influencing the network rigidity of the glassy material which leads to reduced activation energy and enhanced conductivity. When lithium salts LiX (X = F. CI. Br or I) were added to lithium borate glasses B₂O₃-Li₂O, the local structural modifications were found which were attributed to interactions between the network and the anions of the doping salt [18] [21] . Though the cations play a dominant role in ionic conductivity, both cations and anions are adjusted interstitially into the glass [22] [23] . Spectroscopic studies revealed that halogenide ions, Cl⁻ and Br⁻, when doped in borate glasses distribute in interstitial positions in the glass matrix [24] but sulfate tetrahedra are incorporated in macromolecular chains [25] . Li₂SO₄ addition forms six-membered rings with BO₄ tetrahedra. However, sulfate anions are completely dispersed in the B-O network for high Li₂O-containing ternary glasses, and increase the concentration of non-bridging oxygen atoms [26] . There is evidence of spectroscopic study for the accumulation of sulfate in the glass network without changing the structure of the B-O matrix by the addition of Li₂SO₄ [27] [28] . Li₂SO₄ can also be added like Li₂O in borate glasses. When Li₂SO₄ is added to lithium borate glass, it can create defects through the modification of the macro-molecular chain as shown below in Figure 4 [9] [25] .

Here, the conduction in glass is considered to take place through a defect type of mechanism [9] . A report mentions that the dopants (salts) do not react with the network former but their dissolution is only due to electrostatic interactions. The addition of ionic salts also rises the amount of charge carriers [14] . Thus, two contributions assist in the increase in ionic conductivity: high mobile cations concentration and redistribution of the sites suitable for ionic motion [18] .

It is believed that binding energies and migration energy barriers control the magnitude of the glass conductivity as will be discussed below. Binding energy is associated with the degree of the mobile ions at their equilibrium (metastable) sites while the migration energy barrier is associated with the volume requirements for their movement [29] . However, a recently published theoretical study reports a new possible mechanism, the paddle wheel mechanism, for cation mobility in glasses with complex anions. The glasses with complex anions and short-range covalent networks are expected to accelerate cation mobility at low temperatures due to paddlewheel dynamics [30] .

The glassy solid electrolyte system, AgIAg₂SeO₄, had conductivities of approximately 10⁻² S∙cm⁻¹ at room temperature [31] . Though the first study of a glassy solid electrolyte system, AgIAg₂SeO₄, had been reported by Kunze in 1973, Oxide-based materials, in lithium silicate, borate, phosphate or germanate glasses, such as Li₂O-SiO₂-Al₂O₃ [32] had already been studied. We discuss the practice of improving room temperature conductivity of alkali ion conductivity in oxide and sulfide glasses based on the following 4 methods [29] :

1) By adding alkali halide or alkali oxysalt;

2) By adding other glass networks former (mixed glass former effect);

3) By anion mixing effect;

4) By synthesis technique.

These methods are believed to follow the following conduction behaviors in glasses.

Some common characterization techniques are mentioned here for general information. Glasses pose relatively more challenges to structural elucidation than crystalline solids do. Diffraction techniques can only be used to identify the

formation of the glassy state but not to resolve structural details of the glassy state owing to the absence of long-range periodicity. Generally, the structural analysis of glassy state emerges from the joint interpretation of numerous complementary spectroscopic experiments. Some of the widely used common techniques for ion conductive glass characterization are:

1) XRD;

2) DSC;

3) FTIR;

4) Raman spectra;

5) Solid state NMR.

In the decade, 1970s, it was demonstrated that improvement in ionic conductivity in glasses could be achieved by replacing oxygen by larger, more polarizable and glass forming S²⁻ ion [15] . The study of ion conducting sulfide glass system can be found to start with simple binary systems such as Li₂S-SiS₂ [104] , Li₂S-P₂S₅ [105] , Li₂S-B₂S₃ [106] and Li₂S-GeS₂ glass systems [107] [108] . The most studied sulfide system in the ion conductive glasses is Li₂S-P₂S₅. In the early 1980s, R. Mercier et al. initiated research on the binary system Li₂S-P₂S₅ [105] . Later, A. Hayashi et al. followed the study on the Li₂S-P₂S₅ system [109] [110] . The sulfide electrolytes in the simple Li₂S-P₂S₅ binary system (LPS system) are interesting as they possess high conductivities without the addition of any extra element (e.g. Si, Ge, Al) [111] . The highest conductivity reported at room temperature

for Li₂S-P₂S₅ binary system is 0.160 mS∙cm⁻¹ with activation energy of 0.40 eV [112] [113] . Several crystalline and amorphous materials in the LPS family were reported using different synthesis methods [114] . In 1999, Morimoto et al. used the mechanical milling technique instead of the traditional synthesis based on the melt quenching [115] [116] . The new technique is found to give good conductivity. For example, the new technique used the reactants Li₂S, SiS₂ and Li₄SiO₄ and the mixture was placed in an alumina container with alumina balls in a high-energy ball-mill for 10 hours. The glass formed by this technique exhibited the same conductivity as a glass obtained by quenching from a melt. The conductivity of a mechanochemically prepared sample 60Li₂S-40SiS₂ (mol%) after a milling for 20 h was around 10⁻⁴ S∙cm⁻¹ at room temperature [115] . Like in oxide glasses, increasing the amount of charge carriers and their mobility lead to higher ion conductivity in sulfide glasses [117] . By using mechanical milling techniques [115] as well as twin-roller rapid quenching [104] , glasses with higher Li ion concentrations could be obtained compared to the process of traditional melt quenching as it is easy to crystallization during cooling process. The Li₂S-P₂S₅ glasses can be prepared by quenching method. The optimization of the synthesis of the Li₂S-P₂S₅ glass obtained by mechanochemical milling gave a conductivity of 10⁻⁴ S∙cm⁻¹ for the composition 75Li₂S-25P₂S₅ (wt%) [110] [107] . The compound 0:66Li₂S-0:33P₂S₅ (in wt%), obtained by melting and quenching in a silica tube, exhibited a conductivity of 10⁻⁴ S∙cm⁻¹ at 298 K [118] . The similar conductivity (σ₂₅ = 10⁻⁴ S∙cm⁻¹)) has been reported for another composition of the 60Li₂S-40PS_2.5 (mol%) glass prepared by mechanical milling [113] . In all the systems, the conductivities at 25 ºC values increase with an increase in Li₂S content [113] . Baba and Kawamura reported a study of modeling the glass structures in ab initio fashion. They created the structures of xLi₂S-(100 − x)P₂S₅ (x = 67, 70, 75, and 80) with the compositions of Li⁺, PS 4 3 − ,  P 2 S 7 4 − and S²⁻. They used DFT-MD calculations. They reported the ionic conductivity of 10⁻⁵ S/cm [119] . The ionic conductivity x = 75 was the highest [119] . Si and Ge-based binary sulfide glasses were also reported for high conductivity. A report mentioned the conductivity of σ₂₅ = 10⁻⁴ S∙cm⁻¹ for the 60Li₂S-40SiS₂ glass [113] . The glass was prepared by mechanical milling. Other synthetic methods have also been reported to obtain better conductivity. For example, glasses with the composition xLi₂S-(1 − x)SiS₂ (x ≤ 0.6) were prepared by twin roller quenching [104] . The highest conductivity reported was 5 × 10⁻⁴ S∙cm⁻¹ at 25˚C [104] . By dissolving a halide salt (LiI) in the matrix, this value was improved to 8.2 × 10⁻⁴ S∙cm⁻¹ [104] . K. Mori et al. followed computing/modeling the three-dimensional atomic configurations and conduction pathways for Li ions in (Li₂S)_x-(SiS₂)_{100 − x} glasses [120] . They found that (Li₂S)_x-(SiS₂)_{100 − x} glass frameworks facilitate high mobility of Li ion conduction relative to those of (Li₂S)_x-(GeS₂)_{100 − x} glasses and (Li₂S)_x-(P₂S₅)_{100 − x} glasses [120] . M. Ribes et al. reported good conductivity of the GeS₂-based glass, 0.5Li₂S-0.5GeS₂, at 25˚C which was 4 × 10⁻⁵ S∙cm⁻¹ [107] .

Comparative study of P₂O₅ and GeS₂-based glasses was also accomplished. xLi₂O(1 − x)P₂O₅ and xLi₂S(1 − x)GeS₂ glasses were prepared in a twin roller apparatus [121] . The effect of cooling rate on the electrical properties of glasses was studied for rapidly quenched and conventional glasses. The results were found to be different for oxide and sulfide glasses. Rapid quenching did not affect ionic conductivity of oxide glasses much whereas pre-exponential factors and activation energies of sulfide glasses [121] . Compositional adjustment exhibited the good conductivity of 4 × 10⁻⁵ S∙cm⁻¹ at 20˚C for 0.5Li₂S-0.5GeS₂ glass [107] . Replacement of the oxygen atom by a sulfur atom improved the ionic conductivity of glasses noticeably. This may be due to the great polarizability of sulfur. The conductivity can be enhanced by changing the composition to 0.63Li₂S-0.37GeS₂ which gives the conductivity of 1.5 × 10⁻⁴ S∙cm⁻¹ at room temperature.

A study on (1 − x)B₂S₃-xLi₂S (0.5 < x < 0.75) glasses containing B₂S₃ as a part of glass reports the composition dependence of ionic conductivity where the result shows the conductivity in contrast to the expectation. The conductivity decreases with the increase of Li₂S composition. Generally, conductivity increases with higher concentration of glass modifier. However, the maximum conductivity was reported for 0.31B₂S₃-0.69Li₂S glass among all of the studied compositions. The materials were made by melt quenching method [122] . Glasses obtained in the B₂S₃-Li₂S binary system was reported to have a conductivity of about 10⁻⁴ S∙cm⁻¹ at 25˚C [106] [122] .

Sodium-based sulfide glasses were also studied but to a less extent compared to Li-based sulfide glasses. Steve Martin (ISU, MSE) has reported vast majority of Na-based glasses. The very first investigations are related with the Na₂S-GeS₂, Na₂S-XS₂ (X = Si, Ge), Na₂S-P₂S₅ [123] . Na₂S forms stable glasses with GeS₂, SiS₂ and P₂S₅ to form Na₂S-XS₂ (X = Si, Ge), Na₂S-P₂S₅ and Na₂S-GeS₂ with a large range of composition [107] [124] . The comparative trend of conductivity at room temperature revealed that 0.5Na₂S-0.5SiS₂ (1.2 × 10⁻⁵ S∙cm⁻¹) > 0.5Na₂S-0.5P₂S₅ (3.9 × 10⁻⁶ S∙cm⁻¹) > 0.5Na₂S-0.5GeS₂ (1 × 10⁻⁶ S∙cm⁻¹) [107] . The electrical conductivities of these glasses were measured over a range of compositions and temperature (−20˚C, 150˚C). They reported the effect of electronegativity on the ionic conductivity. The ionic conductivity was found to enhance with decreasing electronegativity of the network forming sulfide [107] . Ab initio molecular dynamics (MD) simulations study was performed for sodium thiophosphates [xNa₂S-(100 − x)P₂S₅] for potential glassy solid electrolytes (GSEs). The highest Na⁺ ion conductivity of ~10⁻⁵ S∙cm⁻¹ was reported for the x  =  75 composition [125] . Mechanochemical synthetic method was used to prepare xNa₂S-(100 − x)P₂S₅ (mol%; x = 67, 70, 75 and 80) glasses. Composition dependence of electrical conductivity study demonstrated the higher ionic conductivity with more Na₂S content reaching the highest for x = 80 composition. The highest conductivity is 1 × 10⁻⁵ S∙cm⁻¹ [126] . A comparative study of conductivities of GeS₂-based stable glasses with Li₂S and Na₂S in a large range of composition (from 1 - 0.5 in molar ratio of GeS₂) over a wide range of temperature (−20˚C - 150˚C) exhibited a higher ionic conductivity 10⁻⁵ (Ω∙cm)⁻¹ for Li glasses than 10⁻⁶ (Ω∙cm)⁻¹ for Na glasses at high alkali sulfide concentration [127] . There are studies on Na₂S-B₂S₃ system as well. For example, wide compositions and temperature range conductivity measurements have been reported on the fast ion conducting glass series, xNa₂S + (1 − x)B₂S₃. Among the reports between x = 0 and 0.15, the conductivity was reported highest for the composition x = 0.005 [128] . Some high ionic conductivity of binary oxide glasses are given below in Table 5.

As in oxide glass systems, sulfide glasses also show improved ionic conductivity in ternary and quaternary systems. Here we first discuss the ternary systems with improved conductivity. Different approaches have been proposed for improving the conductivity of glassy electrolytes, one of them is the addition of Li halide salts. The addition of a lithium halide salt (e.g. LiI or LiCl) can increase the lithium concentration and it increases the ionic conductivities of the glasses. R. Mercier et al. (1981) demonstrated that the lithium ion conductivity of 67Li₂S-33P₂S₅ glass increased from 10⁻⁴ S∙cm⁻¹ to 10⁻³ S∙cm⁻¹ when 45 mol% of LiI were added [105] . J.P. Malugani et al. (1983) also mentioned LiI doping in Li₂S-P₂S₅ system which improved ionic conductivity to 10⁻³ S∙cm⁻¹ at room temperature [132] . Studies on glass formation, structure and electrical conductivity in the Li₂S-P₂S₅-LiI system with the ratio Li₂S/P₂S₅ = 2 revealed that the addition of LiI did not break the P₂S₇⁻⁴ units [105] . Table 6 shows the effect of LiI addition on some sulfide glasses.

The studies of addition of Li halide salt to the glass systems with SiS₂, B₂S₃ and GeS₂ can also be found. In the 1980s, Ménétrier et al. studied the system Li₂S-B₂S₃-LiI, which exhibited a conductivity equal to 10⁻³ S∙cm⁻¹ at 298 K [106] [133] , while Ribes and Pradel worked on the system Li₂S-(Ge,Si)S₂-LiI [107] [133] with a conductivity a little bit less, around 8 × 10⁻⁴ S∙cm⁻¹. The conductivities of some glasses, 30Li₂S-26B₂S₃-44LiI (Wada et al., 1983), and 63Li₂S-36SiS₂-Li₃PO₄ (Aotani et al., 1994), have been reported to be as high as 1.7 × 10⁻³ S/cm, an order of magnitude increase from the Li₂S–B₂S₃ system (10⁻⁴ S∙cm⁻¹) [106] [134] . Another report discussed the system Li₂S-SiS₂-LiX (X = Br, Cl, or I) [133]

[135] [136] [137] . The SiS₂-Li₂S-Lil glasses reach room temperature conductivities of nearly 1.8 × 10⁻³ S∙cm^−l. This high temperature synthesis can lead to an oxidation of iodide by SiS₂ [135] [138] . So, the systems of the SiS₂-Li₂S-LiBr and SiS₂-Li₂S-LiCl were also studied [139] . Ionically, conductive glasses have been synthesized using a 1:1 SiS₂-Li₂S base glass and doping with lithium halides. Conductivity of the glass system SiS₂-Li₂S-LiCl was 1.2 × 10⁻⁴ S∙cm⁻¹ at 25˚C [139] and with the glass system SiS₂-Li₂S-LiBr, the highest conductivity was reported as 3.2 × 10⁻⁴ S∙cm⁻¹ at 25˚C [137] . The conductivity trend in SiS₂-Li₂S-LiX system is SiS₂-Li₂S-LiI > SiS₂-Li₂S-LiBr > SiS₂-Li₂S-LiCl (see Table 7). The conductivity of SiS₂-Li₂S-LiI glass system is further increased, though slightly, when B₂S₃ is added to form the composition of 30Li₂S-25B₂S₃-45LiI-25SiO₂. It gives the conductivity of 2.1 × 10⁻³ S∙cm⁻¹ [8] .

The mixed glass former effect (MGFE) has also been investigated for ionic conductivity in different glass systems, such as Li₂S-P₂S₅-SiS₂ [140] , Li₂S-SiS₂-GeS₂ [129] or Li₂S-P₂S₅-B₂S₃ [112] [133] . The activation energy for Li₂S-P₂S₅-SiS₂ is reported 0.37 eV [140] . A glass processing method using a carbon-coated quartz container was employed for the investigation of B₂S₃ containing glasses such as (1 − x) B₂S₃−xLi₂S and 0.33 [(1 − y)B₂S₃-yP₂S₅]-0.67Li₂S. This technique expanded the glass forming region from 0.66 ≤ x ≤ 0.68 for (1 − x)P₂S₅-xLi₂S to 0.5 ≤ x ≤ 0.7 for (1 − x)B₂S₃-xLi₂S. Higher Li⁺ ionic conductivity was found for the conformer sulfide glasses of the 0.33 [(1 − y)B₂S₃-yP₂S₅]-0.67Li₂S system than for single sulfide network former glasses. The room temperature conductivity of

the glass was 0.141 mS/cm [112] . Glasses belonging to the 0.33 [(1 − x)P₂S₅-xAl₂S₃]-0.67Li₂S system for 0 ≤ x ≤ 0.5 prepared by classical quenching techniques showed improved conductivity (0.267 mS∙cm⁻¹) [141] . The system Li₂S-GeS₂-P₂S₅ prepared by a high-energy ball-milling process showed the lithium-ion conductivity of 4.0 × 10⁻⁴ S∙cm⁻¹ [142] . This conductivity was higher than that of the Li₂S-P₂S₅ system prepared by the same method. The enhancement of conductivity was attributed to the mixed former effect by mixing two kinds of network-forming sulfides GeS₂ and P₂S₅. The region of glass formation by the ball-milling process was found wider than a method by a conventional melt-quenching [142] .

Glasses with GeS₂ such as 0.3Li₂S-0.7[(1 − x)SiS₂-xGeS₂] were prepared by the twin roller quenching technique. Here, the composition range is 0 ≤ x ≥ 1. A large enhancement of ionic conductivity of about 2 orders of magnitude was reported for glasses at around x = 6.5 which was attributed to the mixed glass former effect. The conductivity was in the order of 10⁻⁴ S∙cm⁻¹ for 0.3Li₂S-0.7 [(1 − x)SiS₂-xGeS₂] [129] [143] [144] but the conductivities of binary systems were 1.5 × 10⁻⁶ and 9.3 × 10⁻⁷ S∙cm⁻¹ for 30Li₂S-70SiS₂ and 30Li₂S-70GeS₂, respectively [129] [144] . However, 60Li₂S-40SiS₂ and 63Li₂S-37GeS₂ glass compositions were reported to have conductivity of 10⁻⁴ S∙cm⁻¹ [129] . The enhancement of conductivity by adding GeS₂ is the mixed former effect [144] . The electrical conductivity of 30Li₂S-(70 − x)SiS₂-xGeS₂ (0 < x < 70) glasses has also been studied. The conductivity and activation energy for 30:25:45 for Li₂S:SiS₂:GeS₂ were reported as 1.7 × 10⁻³ S∙cm⁻¹ and 0.33 eV, respectively. The enhancement in the conductivity has been attributed to mixed glass former effect [129] . Generally, LiX addition to a binary system increases the conductivity. The addition of LiI in Li₂S-GeS₂ glass composition did not exhibit difference. The conductivity of 0.24 Li₂S-0.36 GeS₂-0.40 LiI is 1.2 × 10⁻⁴ S∙cm⁻¹. Sometimes, quaternary systems also work for ionic conductivity enhancement. LiBr addition to the ternary system gives higher ionic conductivity of 2 × 10⁻⁴ S∙cm⁻¹ at the composition of 0.24Li₂S-0.36GeS₂-0.36LiI-0.04LiBr [145] . Ionic conductivity of GeS₂-Ga₂S₃-Li₂S-LiI glass powders prepared by ball milling is 9.0 ×10⁻⁴ S∙cm⁻¹ at the composition of 0.4LiI-0.24GeS₂-0.06Ga₂S₃-0.3Li₂S [146] . Similarly, Ga₂S₃ addition to the ternary system shows better enhancement in the conductivity. The 0.225Li₂S-0.225GeS₂-0.5LiI-0.05Ga₂S₃ glass system gives the conductivity of 1.7 ×10⁻³ S∙cm⁻¹ at room temperature [147] . When SiS₂ is added instead of LiI, the conductivity becomes 1.7 ×10⁻⁴ S∙cm⁻¹ for the composition, 0.3Li₂S-0.45GeS₂-0.25SiS₂. When Li₃PO₄ is added instead of LiI or SiS₂, the conductivity increases to 3.0 × 10⁻⁴ S∙cm⁻¹ for the composition, 0.58Li₂S-0.39GeS₂-0.03Li₃PO₄ [148] . Li₂SiO₄ addition seems the best for the conductivity enhancement in the glass system. The conductivity is 3.4 × 10⁻⁴ S∙cm⁻¹ for the composition 0.48Li₂S-0.48GeS₂-0.04Li₄SiO₄ [130] [149] .

Sometimes, the ionic conductivity can be increased by mixing different types of glass formers (sulfide and oxide) [150] . For example, GeO₂ was added to Li₂S-GeS₂ system to get the glass of the composition GeO₂ was added to Li₂S-GeS₂ system to get the glass of the composition 0.5Li₂S − 0.5 [(1 − x)GeS₂-xGeO₂], and the ionic conductivity increased from 4.5 × 10⁻⁵ (Ω cm)⁻¹ to 1.5 × 10⁻⁴ (Ω cm)⁻¹ and the activation energy was lowered from 0.385 eV to 0.358 eV by the addition of 5 mole % of GeO₂ [130] . When the composition was changed as xLi₂S-(1 − x) [0.6GeS₂-0.4GeO₂], at x = 0.7 the conductivity was improved to 4.36 × 10⁻⁴ S∙cm⁻¹ [151] .

For Na-based ternary glasses, a study for the composition dependence of room temperature ionic conductivity of [Na₂S]_2/3-[(B₂S₃)_x-(P₂S₅)_{1 − x}]_1/3 glasses showed the highest conductivity at x = 0.5 with σ = 10⁻⁵ S∙cm⁻¹ [152] . There are reports of other glass compositions such as 0.5Na₂O-0.5 [xB₂O₃-(1 − x)P₂O₅], 0.5Na₂S-0.5 [xGeS₂-(1 − x)P₂S₅] and 0.67Na₂S-0.33 [xB₂S₃-(1 − x)P₂S₅]. The ionic conductivities of the 0.67Na₂S-0.33 [xSiS₂-(1 − x)P₂S₅] was reported for 30˚C. The x = 0.0 glass has a conductivity of 3.55 × 10⁻⁶ S∙cm⁻¹.The highest conductivity was reported for x = 0.6 as 2.08 × 10⁻⁵ S∙cm⁻¹ [100] . Figure 10 shows the highest conductivities of the ternary glass systems with MGFE.

The strongest positive effects were observed in alkali borosphosphate glasses [56] [83] [84] [88] [103] . Positive MGFE effect shows the enhanced or higher conductivity than the parent binary glass system and negative MGFE shows opposite results. Phosphogermanate [153] , thiogermanosilicate [129] and thioborophosphate glasses [112] [152] were also reported for positive effect. Systems with strongly positive MGFE effects, such as the alkali borosphosphate glasses were found to exhibit non-linear co-relation of composition with physical properties such as glass transition temperatures (Tg), and densities suggesting the effect of structural organization on ionic mobility [102] [154] [155] [156] . The study of negative NFM effects are also reported which are not important for

application but can help understand the structure-property correlation. The sodium thio-germanophosphate glass, 0.5Na₂S-0.5 [xGeS₂-(1 − x)P₂S₅], was reported with a negative MGFE in the ionic conductivity with a minimum of 5 × 10⁻⁷ S/cm at x = 0.5 [157] .

It is also important to learn the effect of alkali ion size on the ionic conductivity of the glasses. In one study, alkali sulfides, M₂S (M = Li, Na, K, Cs) were systematically mixed with the 0.1Ga₂S₃-0.9GeS₂ base glass-forming system [158] . Wide range of compositions were formed in xM₂S-(1 − x)(0.1Ga₂S₃ + 0.9GeS₂) system. The addition of Li₂S and Na₂S enhanced the conductivity. When the same concentration of alkali sulfide (M₂S) was added, the conductivities of the glasses were found to decrease with the increasing alkali metal size. The K₂S and Cs₂S compositions showed limited range of glass formation compared to Li₂S and Na₂S compositions. K₂S and Cs₂S glasses exhibited poor conductivity [158] .

Glassy electrolytes were also prepared by mixing two different anion species, so called “mixed anion effect” [159] . It is also a kind of mixed former effect. One example is the pseudobinary system of Li₃BO₃-Li₂SO₄. The system was prepared by cold press method. The ionic conductivity at room temperature for the cold-pressed Li₃BO₃-Li₂SO₄ glass systems ranges from 10⁻⁷ to 10⁻⁶ S∙cm⁻¹. The conductivity increased with the addition of small amounts of Li₂SO₄ which was considered to be due to the anion mixing in the glasses [58] . The other example is Li₄SiO₄-Li₃BO₃ glasses [58] [159] . M. Tatsumisago et al. showed the highest conductivity of 5.4 × 10⁻² Sm⁻¹ at 400 K for the composition 6:4 for Li₄SiO₄:Li₃BO₃ while the conductivity reported for individual salts Li₄SiO₄ and Li₃BO₃ were 1.9 × 10⁻² and 2.4 × 10⁻³ Sm⁻¹ [159] . Mixed anion effect is studied in thiosulfate systems as well. Here, one report discusses the conductivity in mechanochemically prepared Na₃PS₄-NaI glass system. The conductivity was found to rise with increasing NaI concentration where the highest conductivity of 1.4 × 10⁻⁵ S∙cm⁻¹ was found for 71Na₃PS₄-29NaI glass [160] . (100 − x)Na₃PS₄-xNa₄GeS₄ glass electrolytes were prepared by mechanical-milling. The glasses exhibit conductivities of ~10⁻⁵ S∙cm⁻¹ at room temperature [161] . Na-based borate and sulfate containing glasses such as (100 − x)Na₃BO₃-xNa₂SO₄ (0 ≤ x (mol%) ≤ 50) were fabricated by mechanical milling. In this glass system, the conductivity was found to rise with increasing Na₂SO₄ concentration. The highest conductivity of 5.9 × 10⁻⁸ S∙cm⁻¹ at 25˚C was found for 50Na₃BO₃·50Na₂SO₄ composirion [10] .

The addition of ortho-oxosalts to binary sulfide glasses enhances conductivity. For example, doping small amounts of lithium oxy salts, Li_xMO_y (where Li_xMO_y = Li₃PO₄, Li₄SiO₄, Li₃BO₃, and Li₄GeO₄), into the Li₂S-SiS₂ glass system increased the conductivity [130] [162] . The (100 − x)(0.6Li₂S-0.4SiS₂)-xLi_xMO_y (Li_xMO_y = Li₄SiO₄, Li₃PO₄, Li₄GeO₄ and Li₃BO₃) system demonstrates a maximum ionic conductivity of 10⁻³ S∙cm⁻¹ at 5mol% Li_xMO_y [123] [162] [163] . The glass-forming regions of each system were 0 < mol% Li₄GeO₄ <15.0 < mol% Li₄SiO₄ < 20.0 < mol% Li₃BO₃ < 25 and 0 < mol% Li₃PO₄ < 40 [163] . This is also attributed to the “mixed-anion effect” [164] . The Li₃PO₄-Li₂S-SiS₂ and Li₂SO₄-Li₂S-SiS₂ glassy systems present a conductivity somewhat lower than that of their homologs with LiI [134] [165] . The sample (100 − y)(0.6Li₂S-0.4SiS₂)-yLi₄SiO₄ (y = 3) obtained by mechanical milling treatment for 20 h exhibits conductivity of 1.5 × 10⁻⁴ S∙cm⁻¹, at room temperature. The oxysulfide system Li₂S-SiS₂-Li₄SiO₄ was obtained by mechanical milling of crystalline starting materials in a dry N₂ atmosphere at room temperature [116] . The glasses (1 − y)[0.6Li₂S-0.4SiS₂]-yLi₄SiO₄ which were synthesized by a liquid nitrogen quenching method showed glass forming region of 0 ≤ y ≤ 0.075. The maximum ionic conductivity was obtained at y = 0.03 with 1.5 × 10⁻³ S∙cm⁻¹ at 298 K [166] . New Li⁺ ion-conductive glasses Li₂S-B₂S₃-Li₄SiO₄ were prepared by rapid quenching. The heat treatment enhanced the ionic conductivities for Li₄SiO₄-doped glasses leading to the highest ionic conductivity of 1.0 × 10⁻³ S∙cm⁻¹ at room temperature [167] . Another series of glasses, 40Li₂O-(40 − x)B₂O₃-20SiO₂-xLi₂SO₄ have also been studied and the highest conductivity of 1.46 × 10⁻² S/cm at 523 K was found for the composition of 40Li₂O-32.5B₂O₃-20SiO₂-7.5Li₂SO₄.The glasses were prepared by melt quench technique technique [168] . When the Li₃PO₄-Li₂S-SiS₂ glass system with the composition of 0.03Li₃PO₄-0.59Li₂S-0.38SiS₂ was prepared at ambient pressure by quenching in liquid nitrogen, its conductivity was 6.9 × 10⁻⁴ S∙cm⁻¹ at room temperature [165] . The stability of the glass towards electrochemical reduction was dramatically improved when compared with SiS₂-Li₂S-LiI glass. The glass synthesized with Li₂SO₄ instead of Li₃PO₄ also indicated good conductivity and stability against electrochemical reduction [165] . But when another synthesis method called twin roller technique was employed instead of liquid nitrogen quenching, the glass forming region expands and conductivity increases up to 1.4 or 1.5 × 10⁻³ S/cm for Li₃PO₄-Li₂S-SiS₂ glass system [134] [169] . After composition optimization, structural analysis on the glass revealed that Li₃PO₄ doping changes the glass structure of Li₂S-SiS₂, thereby enhancing the electrical conductivity [134] . In 2012, LiBH₄ was also added to the binary system to enhance the conductivity. The (100 − x)(0.75Li₂S-0.25P₂S₅)-xLiBH₄ (0 ≤ x (mol%) ≤ 33) glass electrolytes were synthesized by a mechanical milling [170] . The conductivity was found to rise with increasing LiBH₄ concentration. The glass at the composition of x = 33 showed the highest lithium-ion conductivity of 1.6 × 10⁻³ S∙cm⁻¹ at room temperature [170] . Figure 11 shows the highest conductivities of different glass systems and Table 8 reflects the highly ion conducting glasses.

The impact of Al₂O₃ addition on ionic conductivity improvement has also been studied. Al₂O₃ and Ga₂O₃ are considered as intermediates for glass formation. Li-containing aluminosilicate glasses are fast ion conductors [171] [172] . The glasses of the Li₂O-Al₂O₃-SiO₂ system, where Lithium is the only mobile particle, can be polymerized and depolymerized. Polymerized (compositional join LiAlSiO₄-LiAlSi₄O₁₀) aluminosilicates are faster lithium ion conductors than depolymerized because polymerized glasses have a wider distribution of lithium

percolation paths [173] . J.O. Isard in 1959 studied the composition dependence of activation energy for conductivity in Na₂O-xAl₂O₃-2(4 − x)SiO₂ glass system [174] . The effect of alkaline-earth ions on Na transport in aluminosilicate glasses was studied by measuring ionic conductivity for a systematic compositional series of Na₂O-RO-Al₂O₃-SiO₂ [175] where R is Mg, Ca, Sr or Ba.

For aluminophosphate glasses, the conductivity was investigated in wide range of compositions, (20 + x)Li₂O-(20 − x)Al₂O₃-60P₂O₅ (x = 0, 4, 8, 12, and 16, in mol%). The glasses were prepared by the melt quenching technique. The highest conductivity was observed for the glass containing 28 mol% of Li₂O (x = 8), (σ = 1.23 9 × 10⁻⁷ S/cm, at 403 K) [176] . Aluminoborate glasses exhibit higher conductivities than aluminophosphate glasses. The ionic conductivity in the glass system with composition, xNa₂O-(1 − x)(0.87B₂O₃-0.13Al₂O₃) was studied and the highest conductivity was 10⁻⁵ S∙cm⁻¹ for x = 0.70 [177] . In a comparative study of sodium-based silicate glasses, borate addition exhibited higher ionic conductivity than alumina addition. The highest conductivity observed for borate glass was with the composition of 40Na₂O-10B₂O₃-50SiO₂ and it was 2.69 × 10⁻⁵ S∙cm⁻¹ while for aluminate glass, the best composition was 25Na₂O-5Al₂O₃-70SiO₂ and the conductivity was 8.91 × 10⁻⁷ S∙cm⁻¹ [99] . In some borate glass compositions prepared by melt quenching method, the addition of Al₂O₃ has found negative effect on ionic conductivity. Ion conducting glasses 30Li₂O-(70 − x)B₂O₃-xAl₂O₃ have been prepared over wide range of compositions (x = 0, 5, 10, 15 and 20 mole %). The addition of Al₂O₃ in the series of lithium borate glasses decreases ionic conductivity. The room temperature conductivity is 6.44 × 10⁻⁶ S∙cm⁻¹ for x = 0 [178] . The addition of aluminum oxide influenced positively on the electrical conductivity of 27.5Li₂O-(72.5 − х)B₂O₃–хAl₂O₃ glasses. The conductivity of Li₂O-B₂O₃ system increases with addition of Al₂O₃ up to 2.5 mol% and is 8 × 10⁻⁴ S/cm [179] .

Potassium ion battery has recently attracted much attention for its development because of low reduction potential and low cost of abundant resources for potassium [195] . As the potassium ion has larger mass than those of Na⁺ and Li⁺ ions, it can provide high-density charge storage capacity [195] . Not only the study of K⁺ ion battery, but also the study of K-O2 battery has been reported. Since the interest in these batteries is increasing recently, the demand for the development of their highly conductive and stable solid-state electrolytes lied importance on the research of K⁺ ion conducting glassy electrolytes as in the case of Li⁺ and Na⁺-based batteries. However, less attention has been found on the study for K⁺ ion conducting glassy electrolytes unlike for Li⁺ and Na⁺ ion conducting glassy electrolytes.

The above discussion on the Li⁺ and Na⁺ ion conductivity in glassy electrolytes has shed light on high probability of K⁺ ion conductivity in glassy electrolytes. Since K⁺ ion is larger in size than those of Li⁺ and Na⁺ ions, the transport pathways for K⁺ ion should be wider for its mobility. There are some reports of mixed ion conductivity for K⁺ ions with other cations [196] . As in the Li⁺ and Na⁺ ion conducting glassy electrolytes, K⁺ ion conducting glassy electrolytes may be prepared from oxides, sulfides and phosphates [156] [158] [196] [197] . The introduction of antiperovskite-based glassy electrolyte [186] with unexpectedly high ionic conductivity raised a hope for the invention of new types of alkali ion conductive glasses which throws the message that we should not stick to the synthesis by only traditional methods such as use of only network formers and modifiers and by melt quench technique or mechanical milling. Sol-gel techniques are also used for the preparation of glasses/amorphous solid electrolytes [38] [198] .

The conductivities of oxides and sulfides-based glassy electrolytes can be enhanced by increasing the concentration of glass modifiers. The conductivity can be enhanced by the addition of an alkali halide, MX, where M is an alkali and X is a halide (X = Cl, Br, I) or an alkali oxy salt such as M₂SO₄ to the glass matrix and mixing different salts (anions) such as Na₃BO₃-Na₂SO₄. When ionic salts are added, the ionic conductivity increases because of high mobile cation concentration and the re-establishment of the sites suitable for ionic motion. Mixed glass former effect (MGFE) can also be applied for conductivity enhancement. For example, M₂O-P₂O₅-B₂O₃ (M = Li, Na) glasses exhibit conductivities higher than either the pure phosphate or borate binary glasses with similar alkali content. MGFE is believed to originate from microstructural and topological alterations at the short-range level. The conductivities of sulfide-based glasses show better conductivities than those of oxide-based glasses due to their relatively more polar nature and larger ionic size of the S²⁻ ion. The introduction of alumina and nitrogen has been attempted to improve the conductivity, but there is no significant effect of their introduction to the glass. Finally, a new type of glass that is different from the conventional glasses without a glass modifier and network mixture has been reported to exhibit the highest conductivity ever reported. The new type of glass is antiperovskite-based and is prepared in different ways.

As a conclusion, the traditional synthesis method and compositional method can be reconstructed to get better ionic conductivity. K⁺ ion conducting glasses can be developed from oxides, sulfides, phosphates and antiperovskites.

This work is supported in part by the National Science Foundation Tribal College and University Program Instructional Capacity Excellence in TCUP Institutions (ICE-TI) award # 1561004, and we express gratitude to the program managers and review panels for project support. A part of this work is also supported by NSF grant no. HRD 1839895. Additional support for the work came from ND EPSCOR STEM grants for research. The authors also acknowledge the support of North Dakota EPSCoR for the purchase of thermal conductivity equipment and X-ray diffractometer. Permission was granted by United Tribes Technical Colleges (UTTC) Environmental Science Department to publish this information. The views expressed are those of the authors and do not necessarily represent those of United Tribes Technical College and funding agencies.

The authors declare no conflicts of interest regarding the publication of this paper.

Hona, R.K., Guinn, M., Phuyal, U.S., Sanchez, S. and Dhaliwal, G.S. (2023) Alkali Ionic Conductivity in Inorganic Glassy Electrolytes. Journal of Materials Science and Chemical Engineering, 11, 31-72. https://doi.org/10.4236/msce.2023.117004