Alkali Ionic Conductivity in Inorganic Glassy Electrolytes

Ram Krishna Hona¹, Mandy Guinn¹, Uttam S. Phuyal², S’Nya Sanchez¹, Gurjot S. Dhaliwal³

¹Department of Environmental Science, United Tribes Technical College, Bismarck, USA.
²School of Arts and Science, University of Mount Olive, Mount Olive, USA.
³Intertribal Research and Resource Center, United Tribes Technical College, Bismarck, USA.

DOI: 10.4236/msce.2023.117004                

Abstract

Glassy electrolytes could be a potential candidate for all-solid-state batteries that are considered new-generation energy storage devices. As glasses are one of the potential fast ion-conducting electrolytes, progressive advances in glassy electrolytes have been undergoing to get commercial attention. However, the challenges offered by ionic conductivity at room temperature (10⁻⁵ - 10⁻³ S∙cm⁻¹) in comparison to those of organic liquid electrolytes (10⁻² S∙cm⁻¹) hindered the applicability of such electrolytes. To enhance the research development on ionic conductivity, the overall picture of the ionic conductivity of glassy electrolytes is reviewed in this article with a focus on alkali oxide and sulfide glasses. We portray here the techniques applied for alkali ion conductivity enhancement, such as methods of glass preparation, host optimization, doping, and salt addition for enhancing alkali ionic conductivity in the glasses.

Keywords

Glass Electrolyte, Solid State, Ionic Glass, Battery, Charge, Antiperovskite, Ionic Conductivity

1. Introduction

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.

Figure 1. Flow chart for alkali ion conducting oxide and sulfide glasses.

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

Figure 2. Silicate network cleaved by Na₂O (former) to form nonbonding oxygens (brown, red and green spheres represent Si, O and Na atoms, respectively).

Figure 3. Schematic two dimensional representations of (a) tetrahedrally coordinated silica glass and (b) tetrahedrally and trigonally coordinated borate glass.

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] .

Figure 4. Schematic reaction for Li⁺ ion arrangement in borate glass. Defect is created around the second B when Li₂SO₄ is added.

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.

1.1. The Strong-Electrolyte Model

According to this model, the effective carrier density is independent of temperature and ion concentration. All ions are mobile while the strain (mobility) energy dominates the direct current (DC) conductivity. This model, also called the Anderson-Stuart model, is based on a thermally activated charge hopping process for DC conductivity in the glass. This involves the activation energy required for the migration of cations as studied in alkali silicate glasses. According to this model, a cation hops from an occupied site close to a negatively charged counter ion (such as a non-bridging oxygen (NBO) site in an oxide glass) to a vacancy near another NBO site. To accomplish the hopping, the ion needs to pass through a gateway formed by bridging oxygen (BO) atoms (Figure 5) [33] . Here, activation energy (E_σ) is related to an electrostatic binding energy (E_b) required to remove a cation from an NBO site and a strain energy (E_s) of long-range mobility or gate-passing.

E_σ = E_b + E_s (1)

where E_σ is the difference between the maxima of the energy where the cation is located halfway between neighboring sites and the bottom of the energy well, where the cation normally resides without conduction activity.

1.2. The Weak-Electrolyte Model

This approach relates to correlations between thermodynamic activity and ionic conductivity of fast ion-conducting glasses. According to this model, mobility is independent of temperature and ion concentration while the coulomb energy is dominant in the DC conductivity. This approach is widely used to describe the conductivity in silica-based glass. The large increases in conductivity in Na₂O-SiO₂ glasses are associated with large increases in Na₂O activity.

2. Common Characterization Techniques

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

Figure 5. Energy diagram for ion hopping from one site to other in Anderson-Stuart model. Red, green and brown sphares represent oxygen (negatively charged), Lithium (or sodium) and silicon (or boron) atoms, respectively.

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.

2.1. XRD

X-ray diffraction (XRD) is the chief tool generally used for the identification of glassy/amorphous phase formation for a solid-state material. The molecules or the ions in glass or amorphous solids are arranged in disordered manner lacking 3-D periodicity. Due to the absence of long range ordered arrangements in glasses or amorphous solids, their X-ray diffraction patterns normally contain diffused broad peaks or do not show any peaks in contrast to those of polycrystalline solids which show well-defined sharp diffraction peaks [34] due to the existence of 3-D regular periodic lattice and long-range ordered structural arrangements. Since pure glassy/amorphous solids contain only a few broad/diffused patterns, the presence of broad-diffused peak in the XRD pattern confirms the formation of the glassy/amorphous phase. If a material contains mixed glassy/amorphous solids, XRD pattern contains sharp peaks along with the broad diffused peaks [35] [36] [37] [38] . Figure 6 shows the distinction between the X-ray diffraction patterns of glassy or amorphous state and crystalline solid.

2.2. DSC

Glasses show transition from hard brittle to softer rubbery state over a narrow temperature range referred to as a glass transition temperature (T_g). The

Figure 6. X-ray diffraction for a) diffused peak (upper) representing the formation of glass or amorphous phase and b) sharp peaks (lower, rietveld refined) representing the formation of the crystalline phase.

temperature (T_g) is a characteristic of a glass or amorphous material. Differential scanning calorimetry (DSC) is generally used to characterize the T_g of a glass. T_g can be differentiated from the other two thermal transition temperatures: melting temperature T_m and crystallization temperature (T_c) of a glass or amorphous material in DSC plot. During the T_g measurement in DSC, we may get different curves as shown in Figure 7; a dip for melting temperature T_m where a material absorbs heat and melts, a peak for crystallization (T_c) where a material releases heat and crystallizes. For glass transition, there is neither a dip nor a peak, but a slow slope as shown in Figure 7. T_g is specific to a particular glass for a particular composition. Sometimes, differential thermal analysis (DTA) is used instead of DSC.

2.3. FTIR and Raman Spectroscopy

Infrared spectroscopy (IR) is used to study the structure and dynamics of amorphous materials [39] [40] . Since glasses lack long range order, the vibrational spectroscopy has strong impact on their structural studies than that of crystalline solids which have long range order and for which diffraction method is probably more informative.

Glass structure can also be studied by Raman spectroscopy [40] [41] . It is also used to study the structural changes like crystallization during the fabrication of glass ceramic materials. This technique involves the comparison of peaks (Raman shift) to probe the vibrational levels of specific groups of atoms or ions.

2.4. Solid State NMR

NMR has been used for structural investigation of glassy solids [41] [42] . For example, it has been applied to figure out the relative concentration of three- and four-coordinate boron atoms in alkali borate glasses [43] . Many factors are

Figure 7. Representative DSC plot of a glassy material.

to be considered during the NMR spectra analysis. In general, the range of chemical shift for different coordination numbers of most commonly studied nuclei are defined based on the comparison with the NMR peaks of known crystalline compounds.

3. Oxide Glasses

3.1. Binary Oxide Glasses

As mentioned above, alkali ion conducting oxide glasses may be prepared from silicate, borate, phosphate and germanate. There are studies of other oxide glass systems as well. Nassau and Grasso in 1979 studied the binary glass system in Li₂O-Al₂O₃ and Li₂O-Ga₂O₃ [44] . The ionic conductivity is different for different glasses and it is dependent on different factors. Steve W, Martin, 1991 collected some data from previous reports to review the composition dependence of the conductivity and activation energy for binary oxide glasses such as Li₂O + P₂O₅ [45] [46] , Li₂O + B₂O₃ [47] and Li₂O+SiO₂ [13] . For the same amount of Li₂O composition, the conductivity was found to increase from Li₂O-P₂O₅ to Li₂O-B₂O₃ to Li₂O-SiO₂ [13] [29] [45] . The reason behind the conductivity trend was attributed to the fraction of Li⁺ cation to oxygen with full negative charge (0.5 for SiO₂ > 0.33 for B₂O₃ > 0.25 for P₂O₅) [13] [45] . R. F. Bartholomew [48] reported the ionic conductivity of phosphate groups in xNa₂O + (1 − x) P₂O₅ systems. It was reported that the energy barrier to ion migration in the Na₂O-P₂O₅ glass (18.8 kcal/mole) is higher than that for the Na₂O-SiO₂ glass, (13 - 14 kcal/mole) [48] . At room temperature, Na₂O-SiO₂ glass has resistivity of 3.5 × 10⁷ Ω/cm which is two order less than that of the Na₂O-P₂O₅ glass (7.7 × 10⁹ Ω/cm) [48] . Li-based phosphate series were discussed for xLi₂O + (1 − x) P₂O₅ series [29] [45] . Some research groups have also studied lithium germanate glasses xLi₂O-(1 − x)GeO₂ [x = 0.002 - 0.25] [49] [50] . In the case of Li-borate glass, M.R.S. Abouzari, in 2007 (Thesis) [51] , reported that the conductivity of lithium borate thin films of composition 0.20 Li₂O-0.80 B₂O₃ depended strongly on the film thickness [51] . Table 1 shows the highest ionic conductivities of Li and Na-based

Table 1. Ionic conductivities of Li₂O-P₂O₅ to Li₂O-B₂O₃ to Li₂O-SiO₂ glass systems at 25˚C.

binary glasses.

The pseudo binary system, ortho-oxo salt compositions were found to contain high Li ion concentration and exhibit high conductivities. Some research groups studied a series of lithium ortho-oxo salt such as Li₄SiO₄-Li₃BO₃ and Li₃BO₃-Li₂SO₄ glasses for Li ion conduction [57] [58] [59] . The conductivity for different (mol%) compositions of x = 0, 5, 10, 15, 25, 50, 60 in glassy samples of (100 − x)Li₃BO₃-xLi₂SO₄ was reported. The conductivity was nearly 10⁻⁶ S∙cm⁻¹ at room temperature for x =10 [57] [58] . The increase of conductivity is observed with the addition of small amounts of Li₂SO₄. This is considered to be due to the so-called anion mixing of the glasses and/or the improvement of packing density of the pellet after cold press [57] . Some researchers reported in 1977 that large amounts of LiX, (X = I-, Br-, and CI-) were dissolved into LiPO₃ glass [60] [61] . The conductivity increases in the order from I > Br > Cl addition in LiPO₃ as shown in Figure 8. Martin and Angell compared the effect of addition of Li₂O and LiI to LiPO₃ and reported that LiI increases the conductivity and decreases the activation energy than when Li₂O is added. It is also suggested that substituting the larger I⁻ ion for O²⁻ produces a wide range of compositional effect on the conductivity as in the case with other halides [29] [45] . J.P. Malugani et al. suggested that when Li⁺ cation is associated with a larger singly charged anion and an oxygen anion, the dissociation energy of the Li⁺ cation from halide anion would be less than that from oxygen anion. Hence, the LiX-doped glasses are found with much higher conductivities (see Figure 8). They prepared glasses in the Li₂SO₄ + LiPO₃ series and reported that addition of Li₂SO₄ in place of LiX (X = Cl, Br, I) and Li₂O increased conductivity [62] . A report suggested that the electrical conductivity in glasses of the Li₂SO₄-LiPO₃ system increases upon introduction of lithium sulfate into lithium metaphosphate due to the change in the mechanism of charge carrier migration. It reported that S ions are incorporated into polyphosphate structural fragments as terminal groups (Figure 9(a)), while in lithium metaphosphates, the lithium ions are found migrating through the interstitial mechanism. Li₂SO₄ addition increased charge carrier concentration that was reported to migrate through vacancy mechanism leading to enhancement in conductivity [63] . Another report suggests that the higher

Figure 8. Order of conductivity as an effect of LiX (X = F, Cl, Br and I) addition to (a) LiPO₃ and (b) Li₂S-SiS₂ glass systems.

Figure 9. Five different possible structural positions of sulfate in sulfate–polyphosphate chains.

conductivity after Li₂SO₄ introduction is due to the relative weaker columbic force of oxygen in ${\text{SO}}_4^{2-}$ (−0.5 partial formal charge of oxygen) to Li ion compared to that of the oxygen of P-O⁻ entities on the phosphate chains (single negative charge on oxygen) [54] . Different structural arrangements of ${\text{PO}}_4^{\text{3}-}$ and ${\text{SO}}_4^{2-}$ groups have been discussed such as ${\text{SO}}_4^{2-}$ group attached terminally to the ${\text{PO}}_4^{\text{3}-}$ chains [63] [64] , inserted in between ${\text{PO}}_4^{\text{3}-}$ groups forming long chain of ${\text{PO}}_4^{\text{3}-}$ and ${\text{SO}}_4^{2-}$ groups [65] or sulfate groups are not incorporated into phosphorus–oxygen chains of the initial glass but form an independent sulfur–oxygen network [66] . Even it is hypothesized that sulfur can occupy five different structural positions in sulfate-polyphosphate chains [67] (Figure 9). It is also reported that the ortho-oxosalt compositions contain high Li ion concentration and exhibit high conductivities. Thus, the ortho-oxosalt compositions can show improved conductivities. Since, it is difficult to synthesize ortho-oxosalt compositions by melt quenching technique, Hayashi et al. studied the systems Li₂O-M_xO_y (M = B, Si, P, Ge or Al), by mechanical milling which exhibited the glass forming region wider than that by rapid quenching [59] . Similarly, Glasses of Li₃BO₃ and Li₄SiO₄ compositions were also reported for the fabrication by mechanical milling [57] .

Compared to Li-glasses, fewer studies can be found for ionic conductivity of binary system of sodium-based glass. Sodium ion conductivity was reported for binary system in Na₂O-B₂O₃ which was prepared by melting borax at temperatures sufficiently high for dehydration without significant volatilization. The resistivity at 300˚C was reported to be ~ 6 × 10⁴ Ω/cm [68] . A report mentions the conductivity of ~10⁻⁹ S∙cm⁻¹ for Na₂O-B₂O₃ glass [69] . Na₂O-GeO₂, Na₂O-SiO₂ and Na₂O-P₂O₅ glasses were reported to exhibit the conductivity of 2.3 × 10⁻⁵, 2.0 × 10⁻⁷ and 5.6 × 10⁻¹¹ S∙cm⁻¹, respectively [15] . Sodium-based Ortho-oxo salts were also studied, on (100 − x)Na₃BO₃-xNa₂SO₄ (0 ≤ x (mol%) ≤ 50). The glasses were fabricated by mechanical milling [10] . 50Na₃BO₃·50Na₂SO₄ glass were reported for the highest conductivity of 5.9 × 10⁻⁸ S∙cm⁻¹ at 25˚C.

3.2. Ternary and Quaternary Oxide Glasses

In the attempts to improve the ionic conductivity of glassy electrolytes, the studies were not limited to binary systems. Ternary or quaternary glass systems were also studied and were found to improve ionic conductivity. The conductivity of Li-glass can be improved by increasing the amount of Li⁺ ions [44] . The Li ion can be increased by incorporating more Li ion into oxide glasses in the form of LiX (X = CI, Br, I). A number of studies have been reported on such systems [70] . The conductivity increases with the increase of ionic size of the added halide as shown in Table 2. However, the introduction of LiF has the opposite effect (decrease of Li ion conductivity). This effect was considered to be due to the hindrance of Li⁺ ion motion due to formation of local columbic traps of F⁻ ions [54] [71] [72] . Li-salt addition increased the Li⁺ ion conductivity in Li₂O-P₂O₅, Li₂O-B₂O₃ and Li₂O-SiO₂ glass systems. The conductivity order after Li-ion addition was found to be Li₂O-P₂O₅ < Li₂O-B₂O₃ < Li₂O-SiO₂ similar to the pure binary systems [47] [70] .

Glasses were synthesized with variety of compositions in the systems Li₂O-SiO₂-B₂O₃, Li₂O-B₂O₃-P₂O₅, and Li₂O-P₂O₅-SiO₂ following a rapid quenching technique [74] . Here, network formers are mixed. The widest glass-forming region among these three systems is observed in the system Li₂O-SiO₂-B₂O₃. The two glass-forming oxides SiO₂ and B₂O₃ form glasses easily and give the glasses with high amount of Li₂O. However, for the other glass formers during mixing, the glass-forming window is relatively narrow [71] . In the system Li₂O-P₂O₅-SiO₂, the mixing of two glass formers is difficult because the mixing of P₂O₅ and SiO₂ tends to raise the liquidus temperature [74] [75] . Study on phosphosilicate glass, xLi₂O-yP₂O₅-(1 − x − y)SiO₂ [76] [77] reported larger activation barriers compared to even the binary glasses [78] . The mixed silicate–phosphate system

Table 2. Effect of LiX (X = F, Cl, Br) on the conductivity of B₂O₆-0.56Li₂O-0.08LiX [73] .

36Li₂O-63SiO₂-1P₂O₅ was reported to exhibit the activation energy of 0.23 eV [79] . S. Chatterjee et al. in 2018 fabricated the nanocomposites of silicophosphate glasses found the electrical conductivity of ~3 × 10⁻⁴ S∙cm⁻¹ at near room temperature with 35 mole % Li₂O. The activation energy for Li⁺ ion migration was reported as 0.078 eV [80] . The mixed former effect is seen in the case of borophosphate glasses as well. A report mentioned the effect of B₂O₃ addition in the 50Li₂O-xB₂O₃-(50 − x)P₂O₅ glasses. The room temperature conductivity of the glasses was found to increase with boron addition up to 20 mol % B₂O₃ [81] . Another research group prepared, by melt quench technique, the xLi₂O-(1 − x)(yB₂O₃-(1 − y)P₂O₅) glasses with wide range of composition, i.e. x = 0.35 - 0.5 and y = 0.17 - 0.67. The ionic conductivity of the electrolyte at room temperature was found to increase with x and y. The maximum conductivity of the glass system was reported as 1.6 × 10⁻⁷ Ω⁻¹∙cm⁻¹ for 0.45Li₂O-0.275B₂O₃-0.275P₂O₅ at room temperature [82] . The conductivity of borophosphate glass has been reported of 1 × 10⁻⁶ (ohm∙cm)⁻¹ at 30˚C corresponding to a Li/P ratio of unity [83] . Similar conductivity was reported by other group for the glass prepared by twin roller quenching technique [84] . Spectroscopic studies reveal that the glass matrix consisting of B₂O₃ and P₂O₅ undergoes structural modification with the formation of borophosphate structural units during the mixed former effect [16] [85] [86] [87] . The BPO₄ was found to be formed in tri- and pyrophosphate, but not in orthophosphate. The formation of BPO₄ makes the glass heterogeneous and could produce a weak binding area around the strong structure of BPO₄, where a conduction path of electricity is formed [85] [86] [88] . The enhancement of conductivity to 1.8 × 10⁻⁵ S∙cm⁻¹ in the glass composition 50Li₂O: 30P₂O₅:20B₂O₃, from 8.4 × 10⁻⁷ S∙cm⁻¹ of 50Li₂O: 50P₂O₅ at 110˚C also shows the evidence of the effect of BPO₄ formation [85] . In this report, ball milling technique shows better conductivity than melt quench technique. Table 3 shows the highest conductivities for ternary mixed former oxide glasses.

${\text{SO}}_4^{2-}$ anion has also been used for ternary and quaternary systems such as Li₂SO₄-Li₂O-P₂O₅ [54] . For a glass system, xLi₂SO₄-(100 − x)(0.5Li₂O-0.5P₂O₅), the conductivity of ~10⁻⁶ Ω⁻¹∙cm⁻¹ at 100˚C has been reported for x = 60. The ionic conductivity is found to increase with the addition of Li₂SO₄ content [90] . The conductivity enhancement is reported in borate glass also. The conductivity increases at 200˚C from 5.3 × 10⁻⁶ S∙cm⁻¹ for Li₂O-B₂O₃ to 2.66 × 10⁻³ S∙cm⁻¹ 15Li₂SO₄-42.5Li₂O-42.5B₂O₃ [25] . Spectroscopic studies show that ${\text{SO}}_4^{2-}$ ions occupy interstitial positions and interact ionically with surrounding in the glass network. Increasing Li₂SO₄ content induces small structural changes to the

Table 3. Highest conductivities for mixed former effect in the oxide glasses.

depolymerized pyroborate glasses but has a larger effect on the structure of metaborate network where small addition of Li₂SO₄ induces the transformation of metaborate triangles into their isomeric tetrahedra [91] . Similarly, the effect of Li₂SO₄ addition in ionic conductivity was studied in Li₂O-B₂O₃-P₂O₅-Li₂SO₄. The high ionic conductivity was found at the composition of 20 and 35 mol% Li₂SO₄ containing glasses (such as 30Li₂O-25B₂O₃-25P₂O₅-20Li₂SO₄ and 30Li₂O-17.5 B₂O₃-17.5 P₂O₅-35Li₂SO₄). The conductivities were 9.78 × 10⁻⁴ and 1.65 × 10⁻³ S∙cm⁻¹ respectively at 473 K [92] . S.S. Gundale et al. reported the conductivity of 4.08 × 10⁻⁴ S∙cm⁻¹ at 523 K for Li₂O-B₂O₃-SiO₂-Li₂SO₄ [89] . The report states that the glass transition temperature and density decrease with the addition of Li₂SO₄ indicating weakening of the glass structure and expansion of the network, leading to increase in conductivity [89] . NMR and spectroscopic results revealed the retainment of boron atoms four-coordinated more in sulfate-containing glasses than in pure lithium borate glasses. Some sulfoborate-type units were also reported [93] . P. Kluvanek, R. Klement and M. Karáčoň [71] reported the correlation of oxides ratio (network former) with the properties of the glasses (Li₂O)_0.4(B₂O₃)_0.6x(Si₂O₄)_{0.6(1 − x)} [75] . Generally, the mixed glass former effect increases the conductivity. However, the mixed glass-former effect (positive) was not observed on some samples studied (see Figure 10). For example, the conductivity of lithium borosilicate system (Li₂O)_0.4(B₂O₃)_0.6x(Si₂O₄)_{0.6(1 − x)}) with x = 0, 0.2, 0.3, 0.4, 0.6, and 0.8 was investigated. The conductivity of the investigated glass samples was found to increase from silica rich (x = 0) to the boron rich (x = 0.8) samples. Activation energy of 0.65 eV was reported for high conducting sample and 0.8 eV for low conducting sample, respectively [71] .

The ionic conductivity of a glass improves with the increase of network modifier concentration such as Li₂O and Na₂O [13] . The effect of Li₂O concentration was reported in ternary systems such as in Li₂O-(1 − х)(yB₂O₃-(1 − y)P₂O₅) glass system [74] . C.E. Kim et al. [94] reported study of the electrical conductivity of Li₂O-B₂O₃-SiO₂ glasses with the lithium ion concentration range of 35 - 50 mol%. They reported influence of the variation of SiO₂-B₂O₃ ratio in the range of 0.1 - 0.2 on the lithium ionic conductivity [75] . Lithium ion conducting glasses in xLi₂O-(1 − х)(0.75B₂O₃-0.25SiO₂) system were also reported with the x range from 50 to 67.5 mol%. The highest conductivity at room temperature was 3.6 × 10⁻⁶ S/cm for the glass containing 65.0 mol% of lithium oxide [75] . M. Neyret et al. [95] reported the effect of the alkali cation on the structure and the transport properties of R₂O-SiO₂-B₂O₃ glasses, (R = Li, Na, K or Cs). They reported that larger alkali cation causes the expansion of glass network leading to weaker binding forces between non-bridging oxygen and alkali cations [75] . The volume of the ion diffusion pathway correlates with reduced activation energy and enhanced ionic conductivity [5] [96] . The effect of the alkali ion size in the ionic conductivity has been reported for sulfide glasses as well, which we will discuss below.

The effect of glass former mixing has been studied on Na-based ternary glasses as well. For example, the ionic conductivity of 0.35Na₂O + 0.65 [xB₂O₃ + (1 − x)P₂O₅] glasses changes with varying compositions [56] . The highest conductivity was reported in the order of 10⁻⁹ S∙cm⁻¹. 1) Anderson-Stuart model was used to explain the composition dependence of the activation energy in these ternary glasses. According to this, the strain energy is smaller than the columbic binding energy [56] . Two extreme assumptions have been made for glass conduction theory; Anderson-Stuart model that assumes the independent nature of carrier density with temperature but mobile nature of all ions while the strain (mobility) energy dominates the d.c. conductivity [52] [56] [97] [98] . 2) The weak-electrolyte nature which assumes that mobility is independent of ion concentration or temperature while the Coulomb energy dominates the d.c. conductivity [52] [56] [97] [98] . Bruce et al. studied the conductivity in Na₂O-based borosilicate glasses and explained the conductivity on the basis of weak electrolyte theory. The conductivities of two different compositions are shown in Table 4 [99] .

Christensen et al. explains the sodium borophosphate 0.35Na₂O + 0.65 [xB₂O₃ + (1 − x)P₂O₅] glass, where 0.0 ≤ x ≤ 1.0, and sodium borosilicate glass 0.2Na₂O + 0.8 [xB₂O₃ + (1 − x)SiO₂], where 0.0 ≤ x ≤ 1.0. They reported an ionic conductivity of 10⁻⁸ S/cm [69] [100] [101] . The “mixed network former effect”, was also studied on the sodium borophosphate glass system (Na₂O)_0.4 [(B₂O₃)_x(P₂O₅)_{1 − x}]_0.6 (0.0 ≤ x ≤ 1.0) which reported high conductivity and low E_a at a range of compositions 0.4 ≤ x ≤ 0.9 [102] . Another report was on the influence of partial replacement of phosphate by borate in 50Na₂O-50 [xB₂O₃-(1 − x)P₂O₅] glasses. There was conductivity variation with composition change. When x = 0, σ₂₀₀ = 2.38 × 10⁻⁶ S∙cm⁻¹ and Ea = 0.79 eV but for x = 0.6, σ₂₀₀ = 1.6 × 10⁻⁵ S∙cm⁻¹ and Ea = 0.68 eV [103] .

4. Sulfide Glasses

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

Table 4. Conductivity comparision [99] .

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⁺, ${\text{PS}}_4^{\text{3}-}$ ,  ${\text{P}}_{\text{2}}{\text{S}}_7^{\text{4}-}$ 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.

Ternary and Quaternary Sulfide Glasses

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]

Table 5. Ionic conductivity of binary sulfide glasses.

[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

Table 6. Enhancement of room temperature ionic conductivities by LiI substitution on binary sulfide glasses.

Table 7. Comparative room temperature conductivities of LiX substitution on binary sulfide glasses.

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

Figure 10. The highest conductivities (in S∙cm⁻¹) of Li and Na ternary glasses. The glass systems above red line (diagonal) are the oxide systems with Li₂O or Na₂O and below the red line are the sulfide glass systems with Li₂S or Na₂S.

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.

5. Alumina-Based 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

Figure 11. The highest conductivities of different glass systems.

Table 8. Highly ion conductive glasses.

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] .

6. Unconventional Glasses

6.1. Nitrogen Doped Glasses

Oxynitride phosphate glasses of xLi₂O-(1 − x)P₂O₅ (x = 0.5, 0.55, 0.575) glasses exhibited the conductivity of 10⁻⁸ S∙cm⁻¹ [180] . However, LIPON exhibited an average conductivity of 2.3 × 10⁻⁶ S/cm at 25˚C and an average activation energy of Ea = 0.55 eV [181] . Metaphosphate glasses such as LiPO₃ and NaPO₃ prepared by the reaction: (Li/Na)PO₃ + xNH₃ → (Li/Na)PO_3−(3x/2)N_x + (3x/2)H₂O, reported partial replacement of two-coordinated oxygen with two- and three-coordinated nitrogen. Ionic conductivity of the glasses improved after nitridation. Conventional melting and casting methods can be used to synthesize LiPO₃ and NaPO₃ glasses. These glasses are used as base glasses for the ammonolysis procedure to introduce nitrogen in the glasses. The nitridation processes were performed by remelting the base glasses under NH₃ environment at 780˚C [182] . Fast lithium ion conducting glasses such as Li₂S-SiS₂-Li₃N were synthesized by a melt-quenching with compositions of (60-3x/2)Li₂S-40SiS₂-xLi₃N (x = 0, 3, 5). The highest room temperature conductivity and activation energy were reported as 1.5 × 10⁻³ S/cm for x = 3 and 27 kJ/mo, respectively. The conductivity at the maximum x = 5 is 9.6 × 10⁻⁴ S/cm [183] . Boron containing nitride glass was also studied for alkali ionic conductivity. Li₃BN₂ glass was prepared from Li₃N and BN by planetary ball milling. Li₃BN₂ glass showed conductivity higher than that of oxide-based glass electrolytes such as Li₃BO₃ glass and LiPON thin films [184] . The reported conductivity was 1.3  ×  10⁻⁵ S∙cm⁻¹ at 25 ˚C. Na ion conductivity was studied in NASICON-based NCAP glasses. Na⁺ ion conductivity was different when boron and gallium substitutes phosphorus in NASICON-based NCAP glass (Na_2.8Ca_0.1Al₂P₃O₁₂) to get (NCABP: Na_2.8Ca_0.1Al₂B_0.5P_2.7O₁₂) and (NCAGP: Na_2.8Ca_0.1Al₂Ga_0.5P_2.7O₁₂), respectively. The dc conductivity were reported as (∼3.13 × 10⁻⁸ S∙cm⁻¹) for NCAP glass, (∼2.27 × 10⁻⁸ S∙cm⁻¹) for NCAGP and (∼1.46 × 10⁻⁸ S∙cm⁻¹) for NCABP. High lithium ion conducting Li₂S-P₂S₅-Li₃N glasses were reported with the composition of (75 – 1.5x)Li₂S-25P₂S₅-xLi₃N (mol%) where 0 ≤ x ≤ 20. The glass conductivity increased with more Li₃N concentration. The highest conductivity was reported as 5.8 × 10⁻⁴ S∙cm⁻¹ for 20 mol% of Li₃N at room temperature [185] .

6.2. Antiperovskite-Based Glasses

For the first time, M.H. Braga et al., in 2014, developed a novel type of glasses based on antiperovskite with super ionic conduction [186] . They were inspired from Li₃ClO antiperovskite crystals for formation of these glasses. The glass preparation technique is different from conventional melt-quenching, twin roller quenching or mechanical milling techniques. They synthesized the glasses with the composition of Li_{3 − 2x}M_xHalO where Hal = halides like Cl⁻ or I⁻ or a mixture and x = 0 for Li3ClO, x = 0.002, 0.005, 0.007 and 0.01 for M = Mg and Ca and x = 0.005 For M = Ba). They prepared the glasses from LiCl and hydroxides of Li, Ca, Mg and Ba by paste formation with deionized water. The process used Teflon reactor, heat up to 240 C for several days and cold. The samples needed to be dried at certain temperature for certain duration. Glassy samples could not be obtained if the drying of the powders were too long. They claim that Li_2:99Ba_0:005ClO and Li_2:99Ba_0:005Cl_0:5I_0:5O exhibit conductivities of 25 and 121 mS∙cm⁻¹ at 25˚C, respectively in the glassy or supercooled liquid state establishing the highest ionic conductivity ever reported in glassy electrolytes. Two years later, Braga et al. published another paper stating that dry, glass/amorphous solid electrolytes can be obtained from A₃OCl (A = Li or Na) by the addition of water where a small amount of Ba(OH)₂ or another oxide or hydroxide may or may not be added [187] . The activation energy of the Li⁺ or Na⁺ ionic conductivities were reported as 0.1 eV with the room-temperature conductivity comparable to that of the best organic liquid electrolytes.

Recently, H.H. Hennen et al. in 2019 published a theoretical report on the ionic conductivity of antiperovskite-based glass produced from Li₃ClO by density functional theory-based on energies, forces, and stresses [188] . In the study, the theoretical Li₃OCl glass was created by conventional melt-quench procedures. The study also found high ionic conductivity for the material in the agreement with the Braga’s experiment but Cl⁻ ion mobility was also found in the material showing that the Li₃OCl glass is not a single-ion conductor. However, the Li⁺ ion conduction is dominant with transference number t⁺ ≈ 0.84. The study also did not see the evidence for the dipole alignment in the bulk of the glass in simulations even in the presence of electric fields comparable to those present in a battery as suggested by Braga et al.

7. Prospective of K⁺ Ion Conductive Glass

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] .

8. Summary

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.

Acknowledgements

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.

Conflicts of Interest

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

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