The effect of adding CsCl content on physicochemical properties of (GeS2–Sb2S3)100-x(CsCl)x (0 ≤ x ≤ 40 mol%) chalcohalide glasses


 The physico-chemical properties of (GeS2–Sb2S3)100-x(CsCl)x (0 ≤ x ≤ 40 mol%) chalcohalide glasses were theoretically studied. The band gap (Eg) of the studied glass system was estimated and was found to increase by adding the CsCl content. Furthermore, the positions of the valence band and conduction band edges was determined. The results reveal that the molar volume (Vm) of the studied samples increased while the density (ρ) and the number of atoms per unit volume (N) decreased with increasing the CsCl content. The overall coordination number (CN), constraints number (Ns) and overall mean bond energy () were computed using the chemical bond approach and were found to decrease. In contrast, the number of lone-pair electrons (LP) and cohesive energy (CE) increased. Finally, the glass-transition temperature (Tg) was also estimated based on the overall mean bond energy, and was found to decrease with increasing the CsCl content.


Introduction
Chalcogenide glasses (ChGs) are attractive research subjects owing to their exceptional properties like high refractive index, wide transparency and low photon energy, and are used in various applications, including in the radiation shielding field, infrared optics, optical amplifiers, optical sensors, and nonlinear optics [1][2][3][4]. The properties of these ChGs were frequently investigated. Dahshan et al. [5] studied the optical constants of Ge-Sb-Se-I chalcogenide glasses via a single reflectance spectrum. They proved that the refractive index and the Urbach energy increase while the optical band gap decreases by adding the iodine content. Aly et al. [6] studied the ternary Cux(Ge30Se70)100-x thin films in terms of optical constants. The main result showed that the optical band gap decreases whereas Urbach energy increases by increasing Cu content. Mehta et al [7] investigated the effect of tellurium addition on the physicochemical properties of Ge10Se90−xTex glassy alloy. The authors showed that the density, molar volume and compactness of the samples increase whereas the optical band gap decreases with the addition of Te amount.
Nevertheless, ChGs have some drawbacks, such as their reduced thermal and mechanical properties, which limit their uses [8]. Hence, it is crucial to improve these properties for better applications by making compositional changes. Many recent studies have shown that adding metal halides to the glass matrices overcomes the high coefficient of thermal expansion as well as low fracture toughness of glasses, which eliminate the drawbacks that prevent the intensive use of ChGs in infrared (IR) optical and photonic fields [9,10]. Therefore, ChGs containing metal halides, named chalcohalide glasses, have become a very attractive research topic in many domains.
They not only retain the exceptional IR optical properties and are low cost to synthesise, but also enhance the chemical stability and thermomechanical properties of glasses [12][13][14]. These properties are highly dependent on the glass matrix composition and the amount and kind of metal halide existing in the glass matrix [15]. In this context, many researchers have investigated the impact of adding CsCl metal halide to Ge-Sb-S ChGs and extracted results for various aspects. Yang et al. investigated the impact of annealing temperature on the properties of Ge-Sb-S-CsCl ChGs [16]. Their results indicate that rigorous control of the annealing process is crucial for creating chalcohalides with enhanced mechanical properties and reduced optical loss. Hao et al. described the fabrication and microstructure of Ge-Sb-S-CsCl ChGs [17]. The principal result was that these glasses had higher transmittance in the far and mid IR spectral region. Delaisir et al. synthesised GeS2-Sb2S3-CsCl chalcohalide glasses with finely porous surfaces [10]. They showed that porous ChGs can be used as optical elements in an attenuated total reflectance (ATR) configuration.
For better applying chalcohalide glasses, one of the main points is to investigate their physico-chemical properties in terms of overall coordination number, overall cohesive energy, overall mean bond energy, distribution and strength of chemical bonds, etc.
Indeed, properties of glasses are highly affected by these characteristics. However, the above-mentioned researches show that no study has been published to date on the physical and chemical properties of GeS2-Sb2S3-CsCl chalcohalide glasses. Therefore, the present study focuses on a detailed investigation of the physico-chemical properties of chalcohalide glasses with the composition (GeS2-Sb2S3)100-x(CsCl)x. In particular, the effect of adding CsCl on the physico-chemical, optical and thermal properties of this glassy system was investigated. The distribution and strength of the chemical bonds in the studied system were determined with the help of the chemical bond approach (CBA) [18]. These data were then used to compute the average coordination number, constraints number, cohesive energy, lone-pair electrons and mean bond energy.
Furthermore, different estimations of the band gap and positions of the conduction band and valence band edges were presented. An estimation of the glass-transition temperature was also presented.

Results and discussion
To elucidate the correlation between optical and physico-chemical properties, the optical band gap energy (Eg) of (GeS2-Sb2S3)100-x(CsCl)x (x = 0, 5, 10, 15, 20, 25, 30, 35 and 40 mol%) chalcohalide glasses has to be estimated first. For this system, Eg can be estimated theoretically by different methods.
The first estimation expressed Eg as a function of the density (ρ) of the chalcohalide glass system by a simple empirical equation [19]: where E0 = 4.5 ± 0.1eV and a = 0.65 ± 0.01eV.cm 3 /g. The densities used were measured by Zhao et al. for the same (GeS2-Sb2S3)100-x(CsCl)x glassy system [20]. The calculated values of Eg1 and measured densities are listed in Table 1.
Using the EEA and EION of the elements (see Table 2), we obtained XGe, XS, XSb, XCs, XCl and X. Table 3 regroups the computed values for X, ECB and EVB.  Figure 2 shows the plots of ECB and EVB. Although both ECB and EVB increased with increasing CsCl content in the (GeS2-Sb2S3)100-x(CsCl)x system, the increase in ECB was more pronounced, which explains the increase in Eg previously observed.  Table 1 shows that increasing the CsCl content led to a decrease in density which accounts for the increase in the optical band gap. To confirm this result, we calculated molar volume from the density values cited in Table 1 as: where xi and Awi are the atomic percent and the atomic weight of the i th element listed in Table 2. Vm values are listed in Table 4. The variation in Vm with composition is plotted in Figure 3 which clearly shows that Vm increased from 15.46 to 19.99 cm 3 /mol as the CsCl content increased from 0 to 40%. We note that Eg (see Fig. 1) and Vm had the same increasing trend. This effect was also shown in previous studies [36].
where Na and M are Avogadro's number and molecular weight, respectively. Calculated PD values are cited in Table 4.  The molecular weight of CsCl is greater than those of GeS2 and Sb2S3; due to this, PD decreased while Vm increased as the proportion of CsCl in the glassy system increased (see Fig. 3) [38].
The increase in Vm and the decrease in PD led to a rise in the energy of the conduction band edge, which corresponded to an increase in the optical gap [37]. All the aforementioned results confirm the increase in Eg and the variation in ECB and EVB positions shown in Figure 1 and Figure 2, respectively, and highlight the very close correlation between optical and physico-chemical properties.
Using the coordination numbers of the elements listed in Table 2 where MFGe, MFS, MFSb, MFCs, and MFCl are the mole fractions for Ge, S, Sb, Cs and Cl, respectively.
The constraints number (Ns), which represents the rigidity of glasses, was computed using the CN values [39]: The computed CN and Ns values for the (GeS2-Sb2S3)100-x(CsCl)x glassy system are given in Table 4. Figure 4 shows the variation in CN and Ns with increasing the CsCl content. Indeed, when there was no added CsCl content, the first composition was stressed-rigid or over-coordinated since CN > 2.4 and Ns > 3 (these two values are known as the rigidity percolation threshold) according to constraint theory [40]. The  = -− 2 (11) where Ns represents the number of constraints which must be broken to attain fluidity. GeS2-Sb2S3-CsCl can effectively inhibit the propagation of glass cracks [45].
where VE represents valence electrons.
LP values are cited in Table 4 and graphically depicted in Figure 6. It is clear that LP increased gradually with increasing CsCl content. This is caused by the rise in interaction between Ge, S and Sb atoms and lone-pair electrons of Cs and Cl atoms. The increase in LP raises bond angles flexibility which causes a decrease in the strain energy of the system [47,48] and, consequently, leads to stable glass formation [46].  Table 4), we conclude that the first composition is stoichiometric glass (r = 1), while the other compositions are chalcogen-poor glasses (r < 1) [46,50].
Using the homopolar bond energies (BE(i − i) and BE(j − j)) listed in Table 2, the heteropolar bond energy BE(i − j) could be estimated with the equation below [51,52]: where χi and χj are the electronegativities for i and j atoms, respectively.
Values for cohesive energy (CE) were obtained by summing the bond energies and are given in Table 4 [33]: = ∑ X ⋅ X X /100 (15) where Ci and BEi are the number and the energy of the bond, respectively. The chemical bond distribution was estimated using CBA and is summarised in Table 1.  kcal/mol, BE(Ge-S) = 53.49 kcal/mol, and BE(Sb-S) = 47.64 kcal/mol (calculated using eq. 14).
The increase in Eg with increasing CsCl content (see Fig. 1) was most probably due to the higher stabilisation energy. Increased CE denotes higher bonding strength, i.e. low defect bonds. In fact, Eg is a bond-sensitive property [53]. Therefore, the increase in Eg caused by the addition of CsCl may be attributed to the increase in CE.
The majority of glassy network properties are strongly linked to the bonds formed.
Therefore, the overall degree of ionicity (Ion) can be estimated according to Pauling for simple bonds [51]: where Dcth is the calculated overall electronegativity difference of the whole compound given as [21]: The electronegativities of all elements are listed in Table 2 and the estimated values of Δχth are grouped in Table 4. The variation in Ion and Dc against the CsCl content is shown in Figure 7; both Dc and Ion increased with increasing the CsCl content. This behaviour can be attributed to the increase in excess Sb-Sb homopolar bonds (see Table   1), which decreases the degree of covalency of the compound ( ).
Consequently, the degree of iconicity increases as well as Dc. The glass-transition temperature, Tg, is the most important parameter for characterisation of the glassy state. Indeed, in terms of physical properties, Tg represents the temperature range across which the material passes from a rubbery (floppy) to a glassy (rigid) state. It is thus reasonable to suppose that the glass-transition temperature must be linked to the magnitude of cohesive forces in the network, since these forces should be surmounted to enable atom movement. Therefore, it is not surprising that predictions of Tg are generally based on simple models assuming that Tg is proportional to the mean bond energy <E>.
Tichy and Tichá, using a series of 186 glassy systems, illustrated an impressive relationship between Tg and <E> as follows [49,50]: <E> is calculated as in ref. [50]: A detailed discussion relating to the calculation of <E> is provided elsewhere [50]. The computed values of <E> are listed in Table 4. Ionicity strongly correlated with the overall mean bond energy <E>. Indeed, the system was stoichiometric (r = 1) and completely cross-linked in the first composition (0% of CsCl), which thus had the highest Tg. When the CsCl content decreased, the system mean bond energy (<E>) decreased linearly leading to poor system chalcogen (r < 1), as seen in inset of figure 8. Hence, Tg diminishes due to the decreasing average bond strength. This aspect is similar in other glassy systems previously published [46].
In addition, the decrease in Tg was in perfect agreement with decreasing CN, Ns, PD and CD on the one hand and increasing Vm, LP and F on the other. Indeed, it is well known that rigidity is closely associated with Tg. These aspects were previously considered by Bocker et al. who showed that adding the CsCl metal halide into the glass matrix can cut the glass network and then decrease its rigidity [54,55].

Conclusion
The optical band gap of the (GeS2-Sb2S3)100-x(CsCl)x chalcohalide glasses was theoretically estimated. All estimations showed an increase in the band gap from 2.08 eV to 2.42 eV, making these glasses suitable for improvement of relevant materials operating at a wavelength between 0.51 and 0.59 µm. Thus, all compounds may be suitable for a very wide range of applications such as solar cells. Furthermore, the positions of the valence band and the conduction band edges were theoretically determined. Using CBA, the average coordination number, constraints number and mean bond energy were computed and were found to decrease when the CsCl content increased. On the other hand, the number of lone-pair electrons and cohesive energy increased. Finally, the glass-transition temperature was estimated based on mean bond energy and was found to decrease with increasing the CsCl content.