Composition Dependence of the Glass-Transition Temperature and

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The Composition Dependence of the Glass Transition Temperature and Molar Volume in Sodium Thiosilicophosphate Glasses: A Structural Interpretation Using a Real Solution Models Deborah Elizabeth Watson, and Steve W Martin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08603 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 5, 2018

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The Journal of Physical Chemistry

The Composition Dependence of the Glass Transition Temperature and Molar Volume in Sodium Thiosilicophosphate Glasses: A Structural Interpretation Using a Real Solution Model A paper submitted to the Journal of Physical Chemistry B Deborah E. Watson 1, Steve W. Martin * Department of Materials Science and Engineering, Iowa State University Ames, Iowa 50010-2300 ABSTRACT _

The glass transition temperature (Tg) and molar volume, V , are two physical properties known to exhibit the mixed glass former effect (MGFE), a non-linear non-additive increase or decrease from a linear ideal mixing behavior, in ternary glass systems, where the two glass forming species are varied while the glass modifier content remains constant across the system. In the next of our continuing studies of the MGFE in ternary glasses, the Tg and molar volumes of two ternary glass forming series, 0.5Na 2 S + 0.5[xSiS 2 + (1-x) PS 5/2 ], the 0.50 NSP series, and 0.67Na 2 S + 0.33[xSiS 2 + (1-x)PS 5/2 ], the 0.67 NSP series, have been determined across the full glass forming range in both series, 0 ≤ x ≤ 1. The 0.50 NSP glasses were found to have a strongly negative MGFE in the Tg and a weaker MGFE in the molar volume. The 0.67 NSP series of glasses exhibited weak negative and strong positive MGFEs in the Tg and molar volumes, respectively. Using the short range order (SRO) structure model for each glass series that was previously developed, the number of bridging sulfurs (BS) and non-bridging sulfurs (NBS) were determined and analyzed for each of these two series of glasses. A clear linear

1

Author and primary researcher

*

Corresponding author, 515-294-0745, [email protected]

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correlation was observed between the T g and both the fraction of BSs, BS/(BS + NBS), and the number of BS per glass former, BS/GF in both series. The molar volumes of both series of glasses was analyzed using both ideal and real solution models of mixing. The molar volumes of the glasses were best-fit to the molar volumes of all of the individual molar volumes of the various SRO units. In the ideal solution model, the molar volumes of the SRO units were only fit to molar volumes of the end member glasses, x = 0 and 1, respectively. In the real solution model, the molar volumes were best-fit to the full composition dependence of the molar volume of all of the glasses. In both cases, the same molar volumes for the SRO units were used to fit both sets of molar volumes of both glass series. It was found that the best-fit molar volumes of both the P and Si SRO units were essentially the same at the same number of NBS/GF. In this study, therefore, it was observed that the MGFE in the Tg of the glass was linearly correlated with the number of BS per glass former, BS/GF, whereas the MGFE in the molar volumes of the glasses was correlated with the number of NBS per glass former, NBS/GF.


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INTRODUCTION Renewable energy resources and the energy storage systems which accommodate them have gained importance in a society that is becoming ever more dependent on the use of electricity for everyday living1,2. In an initiative going beyond batteries for phones, computers and electric vehicles (eV), advanced battery technologies, like the Li ion battery (LIB), are being explored as energy storage systems for grid level electrical storage applications3. Of the many advanced battery designs being considered, new solid state sodium batteries (SSSBs) have recently gained interest as an alternative to the more expensive LIB. Taking advantage of the similar technology and mechanism of LIB, but capitalizing on its natural abundance4 and equal accessibility in the global community5, SSSBs have the potential to address the needs of this application. In order for the goals to be fully reached and encourage the progression of SSSBs design, research to find new solid electrolyte (SE) materials that can accommodate a sodium metal anode (or similar materials) and cathode materials with the best energy density and capacity is imperative and the field has responded to that demand6. Glassy solid electrolytes (GSEs)7-16 are among the most promising of all kinds of sodium ion conducting SEs due to their wide compositional ranges, their known chemical and electrochemical stabilities, and their known low cost of manufacture. Among the many possible GSEs being studied, those GSEs that contain more than one glass former, mixed glass former (MGF) GSEs, have been shown by us and others to have many advantages such as higher Na+ ion conductivities, higher Tgs, larger mechanical moduli, and improved chemical and electrochemical stability17-34. For these reasons, our research group has being investigating these MGF GSEs for some time.



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The study of the MGFE in ternary glasses is the analysis of the non-linear, non-additive changes in the physical properties as a result of varying two (or more) glass formers (GFs) while holding the alkali (modifier) concentration constant. Strong MGFEs have been observed in the ionic conductivity17-22, Tg23-27, density 28-33, and mechanical moduli34. By controlling the ratio of the modifier to the GFs and varying the ratio of the two GFs, it is possible to link the changes in physical properties with the changes in the atomic short range order (SRO) in the glass. For example, the 0.5Na 2 S + 0.5[xGeS 2 + (1-x)PS 5/2 ], 0.5NGP MGF system, analogous to the 0.50 NSP series studied here, was shown to have a strong and negative MGFE in the Tg, but a weak MGFE in the density28. Bischoff and Martin28 modeled the Tg and molar volumes using the atomic SRO model of these glasses developed from a combination of IR, Raman, and 31P MAS NMR spectroscopies. They showed that the proposed Ge3M SRO units, where the 3 refers to the number of BS bonded to the Ge center and the M refers to these Ge3 SRO units combining to form Ge 4 S 10 4 adamantane-like molecular structures.23,35 These authors showed that the negative MGFE in the Tg and molar volume trends were the direct result of the formation of a large number of Ge3M SRO units in this glass. In our recent paper, the SRO structure of the NSP MGF glass series studied here were reported36. In the 0.50 NSP series, disproportionation reactions, where the SRO units, such as the Si1 and P1 react to form new SRO units with both higher and lower numbers of BS while maintaining overall charge neutrality, were observed in both the phosphorus and silicon SRO units. An example disproportionation reaction is given in Eq. (1). Si2 + P1  Si3 + P0

(1)

These reactions led to a complex diversity of SRO structures at any one composition, x, of the glasses. As suggested by Eq. (1), similar to the results found in the 0.5NGP series35, non-


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equal sharing of Na+ between the Si and P SRO units led to the depolymerization of P1 SRO units to form P0 SRO units and polymerization of the Si2 SRO units to form Si3 SRO units. To conserve charge neutrality, and as evidenced in the 29Si MAS NMR spectra, Na+ required to convert P1 SRO units into P0 SRO units came from the Si2 SRO units which in the process of charge transfer were polymerized into Si3 SRO units. See Fig. 1 and Fig. 2 for a complete list of all of the structures of the SRO units observed in these series of glasses and Fig. 3 and 4 for the composition dependence of these SRO units across both series of glasses. The Raman and 29Si MAS NMR spectra of these glasses further showed the presence of Si3M structures, like the Ge3M proposed in Bischoff and Martin’s work, in addition to the normal network bonded Si3 SRO units35. In the 0.67 NSP series of glasses, the SRO units are nearly completely depolymerized, that is comprising of mostly Si0 and P0 SRO units. However, the 0.67NP binary sodium thiophosphate composition lies above the nominal P0 composition (y = 0.60) and therefore at the x = 0 composition contains both P0 SRO units and ½ mole of free Na 2 S. The number of moles of excess “free” Na 2 S present across this series of glasses coming from the P SRO compositions is therefore (1-x)*0.5. In addition to this, a small population of the defect structure P:0 was also found. At the other compositional extreme, the 0.67NS sodium thiosilicate binary composition lies at the Si0 SRO unit. However, this unit was also found to disproportionate into a small fraction of ESi2 dimers, see Fig. 1, and a corresponding amount of additional “free” Na 2 S required to maintain charge neutrality37. This disproportionation reaction is given in Eq. (2). Note that in this case, a full mole of Na 2 S is released for every mole of ESi2 units formed. Therefore, at this highest modifier concentration, 0.67, there are no new SRO structures



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generated from Na+ exchange between these structures. However, the presence of the P:0 and ESi2 structures lead to the formation of free Na 2 S (and possibly Na 2 S 2 ). Si0  ESi2 + Na 2 S

(2)

The purpose of this work is to examine two important physical properties of glass, Tg and molar volume, in the light of the new SRO structural model recently published on these glasses.37 The Tg of a glass, like the melting point of a crystalline material, is believed to be correlated to the average overall bond strength and glass network connectivity. The molar volume of a glass when connected to the atomic SRO structure can aid in the understanding of the packing behavior and potentially give understanding on the Na+ ion conducting mechanisms in GSEs. These physical properties are very important to GSE design because they provide detailed information on the potential usability of these GSEs in electrochemical applications such as batteries. EXPERIMENTAL METHODS Sample Preparation 0.50 NSP glass system Sodium sulfide (Na 2 S) was synthesized by a low temperature thermal dehydration process of sodium sulfide nona-hydrate (Na 2 S•9H 2 O, 98% Alfa Aesar) under vacuum for 24 hours. After the dehydration process, the product was mechanically milled in a N 2 glove box and then heat treated in a tube furnace for 10 minutes. The sodium sulfide was characterized using mid (MIR) and far (FIR) infrared spectroscopy and powder x-ray diffraction (XRD). 28 gram batches of silicon sulfide (SiS 2 ) were synthesized by combining stoichiometric amounts of silicon (99.999% Alfa Aesar) and sulfur (99.999% Alfa Aesar Puratronics) in a previously flame and vacuumed dried silica glass ampoule (30 mm ID x 300 mm L) which was


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sealed using a 30 mTorr (4 Pa) roughing pump vacuum connected thourgh a liquid nitrogen trap. The reactants were heated to 970oC at 1 oC/min, held with rotation at ~ 5 rpm for 48 hours and then cooled to room temperature at 1oC/min. The ampoule was opened inside a N 2 atmosphere and the extracted product was mechanically milled to produce a powder for glass batching. MIR, Raman and XRD were used confirm the target composition and determine phase purity. P 2 S 5 was used as received from Sigma Aldrich. The ternary 0.50 NSP glasses were prepared by combining stoichiometric amounts of the previously melted and quenched binary end member glasses, 0.5Na 2 S + 0.5SiS 2 and 0.5Na 2 S + 0.5PS 5/2 , ranging from 0 ≤ x ≤ 1. The binary glasses were made by combining stoichiometric amounts of Na 2 S and SiS 2 for the NS and Na 2 S and PS 5/2 for the NP end member glasses. Binary and ternary glass samples were melted in covered vitreous carbon crucibles inside a tube furnace that was hermetically sealed to a nitrogen glove box. Each composition was melted in the temperature ranging from 680° to 795 °C for 3 to 5 minutes. The higher temperatures were used in the thiosilicate rich end, x > 0.5. Weight loss measurements were recorded after the first melt and if a loss of less than 1% was observed, the charge was melted a second time and splat quenched between two room temperature brass plates. The glassy samples were collected and stored in the nitrogen glove box. Powder XRD and SEM EDS compositional analysis was performed on representative samples in this series and it was found that all samples tested were x-ray amorphous and their compositions were as batched to within a few percent. 0.67 NSP glass system Commercial Na 2 S (Alfa Aesar) and PS 5/2 (P 2 S 5 , Sigma Aldrich) was used for the synthesis of these glasses. Silicon sulfide was made via the process described above. The glasses were batched, melted, and quenched in similar manner to the 0.50 NSP glasses. Replicate glasses



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were prepared with the in-house prepared Na 2 S (described above) and the commercial Na 2 S and similar properties and structures were observed for these glasses. Differential Scanning Calorimetry (DSC) Measurements of Tg The Tgs of the glasses were measured using a three point calibrated (In, Sn, and Zn) Perkin Elmer Diamond DSC. Bulk pieces of glass were packed in aluminum pans and cold welded shut using a DSC pan press. Temperature scans at 20°C/min over the range of 50 to 400 °C were done to survey the thermal properties of each sample. After determining the T g and T c from these survey scans, a new glass sample was then cycled at 20 °C/min through and past the T g , but below the T c and then back to Tg – 150oC three times to establish good thermal history for the sample and test the reproducibility of the T g values. To produce glasses with a common thermal history, all of the glasses were cast from the molten state to 50 K below their measured (DSC) Tg and annealed for 1 hour and then slow cooled at 10 K/min to room temperature so that all of the glasses have the same thermal history. Archimedes Measurements of the Density Density measurements were made inside an argon atmosphere glove box using the Archimedes principle. Paraffin oil (ρ = 0.82 g/cc) was used as the immersion fluid. Three or four measurements per composition were done to the determine accuracy and precision of the density measurements. The densities were calculated using Eq. (3) and were corrected for the buoyancy effects due to the (relatively) high density of Ar gas in the glove box used for the density measurements.

ρ glass =

mAr ( ρ0 − ρ Ar ) + ρ Ar mAr − msus


(3)

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Here, ρ glass is the density of the glass, m Ar is the mass of the sample in Ar gas, m sus is the mass of the sample suspended in the immersion liquid, ρ 0 is the density of the immersion liquid, and ρ Ar is the density of argon gas. RESULTS The DSC scans used to determine the Tg and Tc values of the glasses in the 0.67 NSP glass series are shown in Fig. 5. Similar behavior was observed for the 0.50 NSP series of glasses. Figure 5 shows that those glasses rich in Si are extremely stable against crystallization such that for glasses with x ≥ 0.4 showed no crystallization events over the temperature range measured. Tgs of the 0.50 NSP Glasses The composition dependence (x) of the Tgs of both series of glasses are shown in Fig. 6. The x = 0.0 NP glass has a T g of 194 °C while the x = 1.0 NS glass has a T g of 272 °C. The ternary glasses exhibit a negative MFGE in the Tg with the maximum deviation from linear mixing occurring at x = 0.4. Tgs of the 0.67 NSP Glasses The Tgs of the 0.67 NSP glasses series are also shown in Fig. 6. The x = 0 NP glass has a T g 162 °C and the x = 1 NS glass has a Tg of 247 °C. The ternary MGF glasses exhibit a weak negative MGFE, with three local minima at x = 0.1, 0.5 and 0.8. The Tgs of glasses in this compositional series are closer to the Tgs expected for an ideal mixing linear behavior. In the discussion below, these two non-linear compositional behaviors will be shown to be linearized by correlating them to the fraction and total number of BSs in the system.



Densities of the 0.50 NSP and 0.67 NSP Glasses The composition dependence of the densities are shown in Fig. 7. The density of the x = 0 glass is 2.02 g/cm3, while the x = 1 glass has a nearly identical density of 2.03 g/cm3, within the experimental error of ± 0.02 g/cm3. Across the compositional series, the thiophosphate rich x ≤ 0.5 glasses increase in density having a maximum at x ~ 0.2 with a density of 2.07 g/cm3. When x ≥ 0.5, the densities decrease experiencing a minimum at x ~ 0.6 with a density of 1.99 g/cm3. Throughout this series, the average density of this system is 2.02 g/cm3 and therefore the change is ± 0.05 g/cm3. The densities of glasses in the 0.67 NSP series are also shown in Fig. 7. Like the end member glasses of the 0.50 NSP series, the densities of the end member glasses also differ only by ~0.01 g/cm3. The 0.67 NP binary glass has a density of 1.96 g/cm3 and the 0.67 NS glasses has a density of 1.97 g/cm3. An overall negative MGFE is observed in the density for this system. Further, there are two minima in the density at x ~ 0.2 and ~0.6, having densities of 1.89 and 1.85 g/cm3 respectively. Molar Volumes of the 0.50 and 0.67 NSP Glasses Figure 8 shows the composition dependence of the molar volumes for these two series of glasses calculated from the formula weight (FW) of the composition and the density. Due the smaller FW of the NS glass compared to the NP binary glass, the molar volumes in both series decrease with increasing NS content as expected from the nearly identical densities of the end member glasses in each series. Further, the local maxima and minima seen in the density of the two series of glasses produce the opposite behavior in the molar volume. The molar volume of the 0.50 series of glasses has a weak minima at x ~ 0.2 and a broad weak maxima at x ~ 0.6. Similarly, the molar volume of the 0.67 NSP series of glasses has maxima at x ~ 0.2 and x ~ 0.6.


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In the discussion below, these two non-linear behaviors in the molar volumes will be seen to linearly correlated to the molar volumes of the individual SRO units when they are plotted as a function the of the numbers of NBS per GF, NBS/GF. DISCUSSION Glass Transition Temperature While the Tgs of the 0.50 NSP series have a negative MGFE, the overall increase in the Tg from x = 0 (NP glass) to x = 1 (NS glass) is expected. From the 29Si and 31P MAS NMR analysis of these glasses36. The x = 0 NP glass structure consists of P1, small populations of P0 and P2 (which charge balance) and P1P dimer SRO units. Therefore, this glass mainly consists of small molecular anions with very little if any network connectivity. At the other compositional end, x = 1, on the other hand, the NS glass was found to contain Si3 , Si2, ESi2, and Si1 SRO units. The Si3 and Si2 SRO units possess 2 and 3 BS, respectively, and give rise to more network bonding in this glass. In the ternary, 0.50 NSP glasses, as the compositions go from x = 0 to 1, the unequal sharing (disproportionation) of Na+ towards the P and away from the Si SRO units leads to the formation of P0 SRO units from the P1SRO units and to the formation of Si3 SRO units from the Si2 SRO units. This would lead to an overall increase in the network bonding in the glass. It is noted that for the small x glasses, x = 0 to 0.3 for the 0.67 series, the BS/GF does not change from 0 as there is an exchange of NBS between the P and Si SRO units. This network bonding can be further understood by relating it to number of BS per glass former, Si and P, BS/GF. Table 1 lists the SRO structures found in this system with their corresponding number of BS and NBS units. The P1 structure has 0.5 BS, while the Si3, Si2, and Si1 SRO units have 1.5, 1 and 0.5 BS. Using the atomic fractions of the SRO structures, f i (x), from the 29Si and 31P MAS



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NMR results and the number of BS and NBS on each SRO unit, N BSi and N NBSi 37, the number of BS and NBS in each glass composition were calculated using Eq. (4a) and (4b): = (a ) N BS

n

n

= f ( x) N (b) N ∑ ∑ f ( x) N

i BSi NBS =i 1 =i 1

i

NBSi

(4)

Figure 6 shows the composition (x) dependence of the T g along with the N BS across both glass series. The trend of the Tgs in both the 0.50 and 0.67 NSP glass series follows the trends in the increase in BSs. In the 0.50 NSP glass series, this creates a ~ 78 °C increase in T g from x = 0 to 1. Both the BS and Tg weakly increase with x in the region 0 ≤ 0.4 and more strongly increase with x in the region x > 0.4 The BS in the NP rich glasses, 0 ≤ 0.4, are controlled by the P0 formation and perhaps this is what gives rise to the suppression of the T g in these glasses. At x = 0.4, the contribution of BS from P SRO units and Si SRO units are nearly equal (ΔBS = 0.014), but at x = 0.5 the BS from Si increases above P (ΔN BS =0.086). This shift could likely explain the significant increase in the T g . In the 0.67 NSP series, the T g decreases by about 30 °C for each member, x = 0 and x = 1 below that of the Tgs of the end member glasses for the 0.50 NSP series. As in the 0.50 NSP glasses, the T g in the 0.67 NSP glasses increases toward the thiosilicate rich end member, but here in a nominally linear fashion. This suggests no or at most a weak MGFE in the Tg. The increase in Tg overall between the end members is ~ 85 °C. At this high modifier concentration, there is a small concentration of glass formers, consisting of depolymerized P0 and Si0 SRO and weakly polymerized ESi2 SRO units. The NS glass contains P0 and P:0 structures while the NS glass contains Si0 and ESi2 structures. The fractions of P0, Si0, and ESi2 SRO units change in a linear manner across this series with no new SRO units forming. Indeed, the Raman spectra of


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these glasses suggests that there is a simple exchange of P0 for Si0 SRO units as the composition changes, x = 0 to x = 1. As in the 0.50 NSP series, the BS values for the 0.67 NSP series of glasses were calculated from the atomic fractions of SRO structures determined from their fractions given in Figs. 3 and 437. Figures 2 and 3 show the SRO structures of the NP and NS series along with the ratio of Na:Si each SRO units. Figure 6 shows the composition dependence of T g of the 0.67 NSP series of glasses plotted with the calculated values of BS. The trends of these curves behave similarly to those of the 0.50 NSP glass series. Another interesting feature is that BSs, which come only from the ESi2 dimers in both series, change from BS = 0 for the x = 0.0 glass to BS = 0.31 for the x = 1.0 in the 0.67 NSP series glasses. However, in the 0.50 NSP series, the BS goes from 0.5 in the x = 0.0 to 1.0 in the x =1.0 glass. Yet the T g increase across the 0.67 NSP series is larger by 7 °C than the increase in Tg for the 0.50 NSP series of glasses. To examine these correlations of the Tgs of both of these series of glasses with the numbers of BS, Fig. 9 (a) and (b) show the plots of the Tg against the number of BS per glass former, BS/GF (a) and the fraction of BS out of the total S, NBS + BS (b). Both plots show a strikingly linear behavior. For both plots, for the 0.67 series, the Tgs start out at 0 BS/GF and 0 fraction of BS as indicative of the fully ionic depolymerized structure that these glasses exhibit. The Tgs of the 0.67 NSP series of glasses increase faster and are consistently higher than the Tgs of the 0.50 NSP series of glasses. Extrapolating the Tgs of the 0.50 NSP series of glasses back to 0 in both graphs show that the Tgs are higher for the 0.67 series. This suggests that the more ionic character of the glasses in the 0.67 series, on average a -2 charge per GF, compared to a -1 charge per GF for the 0.50 NSP series of glasses, gives rise to a higher Tg. The more rapid increase in the Tgs of the 0.67 NSP series compared to the 0.50 NSP series of glasses may arise



from the greater topological change in the average connectivity of the network in the former series. In the 0.67 series, since the structure begins a BS/GF = 0 there is no net covalent bonding (BS) between the different SRO units. At the end of the 0.67 series, there is ~ 0.3 BS/GF. For the 0.50 NSP glasses, there is a change from ~ 0.5BS/GF to ~ 1BS/GF a change of 100%. The faster increase in the Tgs of the 0.67 glasses may be associated with the onset of the formation of BS, 0 to 0.3, rather than a simple increase in the number of BS, 0.5 to 1 BS/GF, in the 0.50 NSP series of glassesglasses. Density and Molar Volume As seen in Fig. 7, like in the T g of the 0.5NaSP glasses, there is a significant change in the density occurring between the x = 0.4 and 0.5 compositions. While the T g increases from 196 to 217 °C, the density decreases from 2.02 g/cm3 to 1.99 g/cm3. This change in the density is outside the error in the measurements (±0.02 g/cm3) and is expected to arise from changes in the volumes and packing efficiencies of the various SRO structures. To investigate this, the composition dependence of the overall molar volume of the glass and the molar volumes of the individual specific SRO units that are comprised in each glass at each composition are now analyzed. The molar volumes, calculated from the density and the formula weight (FW) of the glass, are shown in Fig. 8. The FW of each composition was determined using the two formulas for the compositions given above, 0.5Na 2 S + 0.5[xSiS 2 + (1-x) PS 5/2 ] for the 0.50 NSP series, and 0.67Na 2 S + 0.33[xSiS 2 + (1-x)PS 5/2 ] for the 0.67 NSP series. Note that at each composition in these series, there is a constant number of 0.5 and 0.33 moles of total glass former, Si + P. In the 0.50 NSP series, the x = 0 NP glass has a molar volume of 46.9 cm3/mol and the x = 1 NS glass has a molar volume of 41.9 cm3/mol. Figure 5 shows the decrease in the molar volumes as


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x  1 is associated with an increase in the BS. This implies that as the Si SRO structures of this glass series increase the networking, through the increase in the ESi2 SRO units, they decrease the molar volume of the glasses. The molar volumes of the NP rich glasses, 0 ≤ x ≤ 0.5, show a negative deviation from the ideal solution model caused by a densification in the glasses. In this region, molar volume behavior is affected by the high concentration P1 SRO units and an increasing concentration of P0 SRO units. In the x = 0 to 0.2 glasses, the P0 concentration is small, but begins to increase after x = 0.2. In the vicinity of x = 0.5, the molar volumes now reach a local maximum over the same region where the number of NBSs created from the formation P0 SRO units also reach a maxima and are almost equal to the number of BS in the system, see Fig. 6. When the population of P0 SRO units decrease in the NS rich region, the number of BS are no longer cancelled out by the NBSs from P0 SRO units. In this same region, the molar volume decreases again as the number of BS increases. The positive deviation in the molar volume in the NS rich glasses is associated with a decrease in the numbers BS. It will be seen below in a more detailed analysis of the molar volumes of the individual SRO units that the number of NBS per glass former (GF) are indeed a dominant factor controlling the molar volumes of the individual SRO units and in turn, the molar volume of the overall glass. The densities of 0.67 NSP glasses are smaller than those of the 0.50 NSP series of glasses, see Fig. 7. These glasses exhibit an average density of 1.93 g/cm3 compared to 2.02 g/cm3 for the 0.50 NSP glasses. The 0.67 NSP glasses exhibit an overall negative MGFE in the density and two local minima at x = 0.2 and 0.6 with densities of 1.89 and 1.85 g/cm3, respectively. The composition dependence of the SRO structure of these glasses may be used to understand this behavior. Initially, the addition of NS decreases the density for compositions x = 0.1 and 0.2, where the P0 SRO unit population decreases proportionally with the increase of Si0



SRO unit population. In the 0.50 NSP glasses, it was shown that the addition of BS results in an increase in the density and a decrease in the molar volume. Conversely, the lack of BSs ,or increase of NBSs, in the 0.67 NSP series of glasses creates an increased depolymerization (NBS formation) in these glasses is associated with a decrease in the density. This can be seen by the molar volume composition dependence in Figure 8. Also at x = 0.2, the population of P:0 SRO units begins at ~3%. As it rises to 9% at x = 0.4, the density also rises from 1.89 g/cm3 to 1.94 g/cm3. The concentration of the ESi2 SRO units increases in the composition region to x = 0 to x = 0.4. Then, as the composition approaches x = 0.6, the density decrease to 1.86 g/cm3, in the same region where the P:0 population decreases to 2.3%. Beyond this composition, the P:0 population decreases as the Si SRO populations become the majority SRO units in the glasses. The density of the x = 0.7 to x = 1.0 glasses increases again ending at 1.97 g/cm3. Here, the densities of these glasses increase where in the same compositional region, the concentration of the ESi2 units increase. Though the number BSs of the ESi2 may not contribute to networking, the ESi2 SRO units is a simple molecular anion specie, the increase in BS does follow the increase in densities as also demonstrated in the 0.50 NSP glass series. Additive Molar Volume Analysis of the Glasses To examine the molar volume of the glasses in more detail, the additive volume method developed by Feller et al.38-40 for oxide borates and used extensive by Martin et al.41-43 for sulfide borate glasses to determine the volumes of the various individual SRO structural units in the glasses was applied simultaneously to the 0.50 and 0.67 NSP glass series studied here. Equation (5) gives the mathematical form of the additive volume method with the ideal solution model. The fractions of the SRO units were taken from Figs. 3 and 4, respectively. The volumes of the individual SRO units were determine by best-fitting the density data to Eqs. (5) and (6) with the


Page 16 of 41

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following constraints. 1. That the molar volume of the SRO unit in the glass must be larger than the corresponding unit in the crystalline form. 2. That the increase in volume of the SRO unit in glassy state could be no more than the increase of the molar volume of the glasses above that of the corresponding crystalline composition. 3. That the molar volume of the SRO units increased with both increasing numbers of Na+ ions and NBS ions. In the latter constraint, for example, the Na 3 PS 4 (P0) unit must be larger in volume than the same unit missing a sulfur atom, the P:0 unit and the Na 4 SiS 4 (Si0) SRO unit must be larger than both the Na 3 SiS 3.5 (Si1) SRO unit and the Na 2 SiS 3 (Si2) SRO units. 4. That the molar volumes for the individual SRO units were the same both series of glasses to obtain a self-consistent set of molar volumes for both series of glasses. 5. The composition dependence of the molar volumes of the individual SRO units was constrained such that Raoultian behavior of the molar volume was obeyed as the solution _

_ 0

becomes pure in the dominant phase, NS  1 and NP1. In this constraint, lim Vi ( x) → Vi . 6. x →1

The composition dependence of the molar volumes of the individual SRO units was constrained such that Henryian behavior was obeyed when the solution becomes infinitely dilute in the second component, NS  0 as NP 1 and NP0 as NS1. In this constraint, _

_ ∞

_ ∞

lim Vi ( x) → constant ≡ Vi , where Vi is the molar volume of the ith SRO unit at infinite x →0

dilution, x i  0. The fitting of the molar volumes of the glasses was performed in two sequential steps. First, the fitting was performed according to an ideal solution model, Eq. (5), where the molar volumes of the individual SRO units are constant across the entire compositional series and equal to the _ 0

molar volumes for the pure end member SRO unit, Vi . Second, using these molar volumes as



Page 18 of 41

starting points and the observed deviation of the experimentally measured molar volumes from the ideal solution model calculated molar volumes, the individual SRO molar volumes were varied with composition so that a better fit to the non-ideal mixing of the molar volume was obtained between experiment and model. _

n

_ 0

V ( x) = ∑ fi ( x) Vi

Ideal solution model (5)

i =1

_

n

_

V ( x) = ∑ fi ( x) Vi ( x)

Real solution model (6)

i =1

_ 0

Table 1 shows the compilation of the molar volumes, Vi , of all of the units used in the fitting of the molar volumes of the 0.50 and 0.67 NSP series of the glasses within the ideal solution model, Eq. (5). In the ideal solution model, the molar volumes of the SRO units were best-fit only to the molar volumes of the end member NP and NS glasses in each series. The volumes are given, where they are available, for both the glassy and crystalline forms. The molar volumes of the glasses were then calculated using Eq. (5) with these best-fit molar volumes of the SRO units and their fractions are plotted on Fig. 8. As expected, the simple ideal solution model of constant molar volumes fits the overall trend of the molar volume, decreasing with increasing Si content in both the 0.50 and 0.67 series. However, the ideal solution model predicts an overly positive trend in the molar volume for the 0.50 series of glass and an overly negative trend in the molar volume for the 0.6 series of glass. Furthermore, the ideal solution model does not predict the local minima at x ~ 0.3 in the 0.50 NSP glass series or the local maxima x ~ 0.4 and 0.7 in the 0.67 NSP glass series in the experimental molar volume.


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The positive deviation in the ideal solution model of the molar volume in the 0.50 NSP series is most pronounced in the phosphorus rich end of the glass series. It is in this region that the P1 SRO structural group is the dominant P SRO group and the Si1, Si2, and Si3 SRO groups are the dominant Si SRO groups. This therefore suggests that these SRO groups may have a negative deviation away from the constant volume ideal solution model. Likewise, the two local maxima in the experimental molar volumes for the 0.67 series of glasses at x ~ 0.4 and x ~ 0.7 are co-located with the dominant P0 SRO group for the former maxima and for the Si0 and ESi2 SRO groups for the latter maxima. These findings suggest that the volumes of these SRO groups must have a positive deviation away from the constant volume ideal solution model. Combined, these two results strongly show that the mixing of the various SRO units in these glasses is highly non-ideal and that the molar volumes of the SRO units are strongly composition dependent. The molar volumes of the P and Si SRO units that were found from the best-fitting of Eq. (6) to the experimental values of the molar volumes of the glasses are shown in Fig. 10. Figure 8 shows the best-fit molar volume of the glasses calculated using the real solution model Eq. (6) and shows very good agreement with the experimental data. It is noted again that the composition dependences of the molar volumes shown in Fig. 10 were determined by simultaneously best-fitting the molar volumes in both the 0.50 and 0.67 NSP series of glasses using the different composition dependence of the fractions of the various SRO units in each series, but the same composition dependence of the molar volumes of the various SRO units. Hence, the negative deviation from ideality of the molar volumes of the glasses in the 0.50 NSP series required some of the SRO molar volumes to exhibit a negative deviation from ideality. Likewise, the positive deviation from ideality in the molar volumes of the glasses in the



0.67 NSP series required some of the SRO molar volumes to exhibit a positive deviation. The hypothesis made here in setting the initial conditions to best-fit the molar volumes of the SRO units was that the SRO units which had the largest concentration among all of the SRO units in the region where the molar volumes deviated from ideality had the greatest influence on the molar volumes and that those SRO molar volumes were allowed to vary in the direction, positive or negative, to best-fit the data. For example, in the 0.50 NSP series, it is the P1 SRO group that has the highest concentration in the region where the molar volume deviates most negatively from the ideal solution model. Therefore, the composition dependence of the molar volume of the P1 SRO units was allowed to initially trend in a negative direction away from the molar volumes used in the ideal solution model. As shown in Fig. 10 and discussed above, the molar volumes of both the P and Si SRO units appear to follow the number of NBS in these glasses. To further examine this observation, Fig. 11 shows the averages of the best-fit molar volumes of both the P and Si SRO units across the series x = 0 to x = 1 shown in Fig. 8 that were used to simultaneously fit the experimentally determined molar volumes of glasses plotted against the number of NBS per GF for each SRO unit. Two observations are immediately apparent in this plot. First, the molar volumes of the P and Si SRO are identical within fitting error at the same number of NBS. This suggests, perhaps as expected, that it is the charged NBS and the accompanying Na+ cations that dominant the volumes of the individual SRO groups and not the small P+5 (r ~ 0.17 Å) and Si+4 (r ~ 0.2 Å) GF cations. Second, consistent with this observation, the molar volumes of both the P and Si SRO units increase with increasing numbers of NBS units. As a further consistency check, it is significant to note that the average molar volume of the P0 and Si0 SRO units in the glassy state for the x = 0 and x = 1 NP and NS glasses are very


Page 20 of 41

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consistent with the molar volumes of the corresponding molar volumes of the same SRO units in the crystalline state, 117 cm3/mole vs. 106 cm3/mole for the former, and 128 cm3/mole vs. 118 cm3/mole, for the latter. In both cases, the molar volumes of the SRO units in the glass state are ~ 8% higher than those in the crystalline state. A value that is often seen when comparing the molar volumes of glasses to the molar volumes of their parent crystalline phases. Finally, as a last consistency check, the average value of 128 cm3/mole molar volume of the Si0 SRO unit (across all 0.50 and 0.67 NSP glasses) gives an average space filling cube of the Na 4 SiS 4 SRO unit of ~ (5.9 Å)3. This compares well with the edge length of a cube created by expected sums of the ionic distances of a tetrahedral Si+4-(S- Na+) 4 unit creating a cube, 2 x sin (35.5o)* (0.2 + 3.6 + 2) = 5.6 Å. Similar consistencies exist for the other P and Si SRO units. The slightly larger edge length of the Na 4 SiS 4 tetrahedron in the glassy state, 5.9 Å, is consistent with the on average larger volume of the glassy state over that of the crystalline state, 5.6Å. CONCLUSIONS The 0.50 NSP and the 0.67 NSP series of glasses exhibit non-linear negative MGFE departures from ideal mixing behavior in their T g s. It was observed for both series of glasses that there is a linear correlation between the Tg of these glasses and the fraction of BSs in their structures. The Tgs of the 0.67 NSP series of glasses increased more rapidly with the fraction of BSs than that for the 0.57 NSP series of glasses. Consistent with this observation is that the overall fraction of BSs were larger in the 0.50 NSP series of glasses compared to the 0.67 NSP series of glasses, with the fraction of BSs beginning at zero for the latter series of glasses. It was hypothesized that the more rapid increase of Tg with fraction of BSs in the 0.67 series was due to the fact that the change in the fraction of BSs was significantly larger in the 0.67 series compared to the 0.50 NSP series of glasses.



The densities of the glasses were converted for analysis to the molar volumes and the molar volumes of both series of glasses overall decreased with increasing x from the NP glasses to the NS glasses. However, in this negative overall trend, the 0.50 NSP series of glasses showed a non-linear negative MGFE in the molar volume for the NP rich glasses, 0 < x ≤ 0.4, but this trend reduced and in the NS rich glasses, 0.4 < x ≤ 1, the densities exhibited only a slight negative MGFE. The densities of the 0.67 NSP series of glasses, on the other hand, exhibited two local maxima in the molar volume for the NP and NS rich glasses. The molar volumes of both series of glasses were modeled with both ideal and a non-ideal solution models. The negative deviation of the molar volume from ideal mixing in the 0.50 NSP series of glasses was primarily correlated to a contraction in the molar volume of the P1 SRO structural groups. The two localized positive deviations in the molar volumes in the 0.67 NSP series of glasses in the NP and NS rich glasses were primarily correlated to expansions in the molar volumes of the P0 SRO for the former and the ESi2 and Si0 SRO units for the latter. This appears to be one of the very first treatments using a non-ideal solution model for the molar volumes for non-oxide glasses and generalized method for modeling the non-ideal solution behavior of such glasses and their properties has been presented.


Page 22 of 41

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ACKNOWLEDGEMENTS This research was supported by the National Science Foundation under DMR grants 1304977 and 0710564. The authors would like to thank the Iowa State University Glass and Optical Materials research group for conversations and the careful proof reading of this manuscript. In particular, Kah Loong Hoh is thanked for his contribution to this project. Professor Gerbrand Ceder and his research group at Lawrence Berkley Laboratory are thanked for their help in providing some of the unit cell volume data for some of the sodium thiosilicate crystalline phases studied in this work. Likewise, Professor Soumik Banerjee and his research group at Washington State University are thanked for their help in providing some of the unit cell volume data for some of the sodium thiophosphate crystalline phases studied in this work.



Page 24 of 41

Table 1 Number of BS and NBS per glass former (GF) in the SRO structures in the NSP glasses and their molar volumes where known.

Pn/Sin

Net

Net Non-

Bridging

Bridging

Sulfur Pn/Sin

Sulfur Pn/Sin

Molar

Molar

Molar

volumes

volumes

volumes

(Crystalline

(Ideal

(Real

phases)

Solution

Solution

(cm3/mole)

Model)

Model)

(cm3/mole)

(cm3/mole)

P2

1

2

85

85

P1

0.5

3

94.0

93.7

P0

0

4

115

117.3

P:0

0

3

95

95

P1P

0.5

3

90

90

Si3

1.5

1

80

70.1

Si2

1

2

75

76

ESi2

1

2

88

89.1

Si1

0.5

3

85

84.9

Si1Si

0

3

90

90

Si0

0

4

118.3

125

128.0

Na 2 S

NA

NA

42.0

46.2

46.2

106.1


Page 25 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Na:P ratio

Connectivity

P SRO Units P3 S

0:1

P S

Branching Network

S S

P2 S

1:1

1-

P S

Branching Network

S S

P1

P1P

S

S

2:1

4-

2-

S

S

P S

P

S

S S

P

S

S

Terminating Unit -orMolecular Anion

P0 S

3:1

3-

Isolated Tetrahedra

P S

S S

P0 S

4:1

3-

P S

S

+

1/2 Na2S

S

Isolated Tetrahedra -andExcess sodium sulfide

Figure 1. Sodium thiophosphate SRO unit structures in the NP glass system.



Na:Si ratio

Si SRO Units

Connectivity E2Si4

Si4 S Si

0:1 S

S

S

S S

S

S

1:1 S-

Si S

S-

-

S-

Si S

Si1 S Si S

S

-orChains 4Branching Network -orAnionic Moleculular Cages

S Si S S Si S Si SS Si S S S

S

Si2 S 2:1

Branching Network

Si-3M S

1S

S Si

Si

Si3B

3:1

Page 26 of 41

E1Si2

2S

Chains -orDimeric Groups

3-

Terminating Unit -orDimeric Groups

S Si

S

2-

Si S

S

Si1Si 3-

S Si

S

S

S

S

Si0 S Si

4:1 -

S

-

S

Si

S S

4-

Isolated Tetrahedra

S

Figure 2. Sodium Thiosilicate SRO unit structures in the NS glass system.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fraction of SRO Units

Page 27 of 41

1.0

0.67 NSP

P0

0.8

Si0 0.6

ESi2

0.4 0.2

P

Si1Si

:0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Composition (x) Figure 3. Composition dependence of the SRO units in the 0.67 NSP series of glasses, redrawn from reference36. x is molar ratio of SiS 2 to PS 5/2 .



1.0

Fraction of SRO unit

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 41

0.50 NSP 0.8

P1

0.6

ESi2

0.4

Si2 Si1

0.2

P1P

P0

P2

Si3

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Composition (x) Figure 4. Composition dependence of the SRO units in the 0.50 NSP series of glasses, redrawn from reference 36. x is molar ratio of SiS 2 to PS 5/2 .


Page 29 of 41

24

x=1.0

20

Heat Flow (W/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.9

16

0.8

Tg

12 0.7

8

0.4

4 0.1

Tc

0.67 NSP

0 0.0 -4 0

50 100 150 200 250 300 350 400 450

Temperature (oC) Figure 5. DSC traces for selected glasses in the 0.67 NSP series of glasses showing the very strong resistance to crystallization for the glasses rich in SiS 2 . Curves have been shifted for clarity. Similar behavior was observed in the 0.50 NSP series of glasses. x is molar ratio of SiS 2 to PS 5/2 .



280

240

Tg Tg BS/GF BS/GF

1.0

0.50 NSP

0.8

220

0.6

200

0.4

BS/GF

260

Tg (oC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 41

180 0.2 160 0.67 NSP 140

0.0

0.0 0.2 0.4 0.6 0.8 1.0 NP Composition (x)

NS

Figure 6. Composition dependence of the T g in the 0.50 and 0.67 NSP series of glasses and the calculated fraction of BSs from the SRO model of the structures of the glasses in this series, see text. x is molar ratio of SiS 2 to PS 5/2 .


Page 31 of 41

2.1 0.50 NSP

Density (g/cm3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.0 0.67 NSP

1.9

1.8

0.0 NP

0.2

0.4

0.6

0.8

Composition (x)

1.0 NS

Figure 7. Composition dependence of the densities in the 0.50 and 0.67 NSP glass series. x is molar ratio of SiS 2 to PS 5/2 .



50

0.50 NSP

Molar Volume (Exp.) Ideal Solution Model Real Solution Model

48

Molar Volume (cm3/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 41

46 44 42 40 50

0.67 NSP

Molar Volume (Exp.) Ideal Solution Model Real Solution Model

48 46 44 42 40

0.0

0.2

0.4

0.6

0.8

1.0

Composition (x) Figure 8. Composition Dependence of the Molar Volume in the 0.50 NSP and 0.67 NSP glass series. x is molar ratio of SiS 2 to PS 5/2 .


Page 33 of 41

300 275

0.50 NS

0.67 NS

250

Tg (oC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


225 200 175 150 125 100

0.50 NP 0.67 NP 0.0

0.67 NSP 0.50 NSP

0.2

0.4

0.6

0.8

1.0

1.2

BS/GF Figure 9 (a). Dependence of the Tgs for the glasses in the 0.50 and 0.67 NSP series of glasses plotted again the numbers of BS per glass former, BS/GF. x is molar ratio of SiS 2 to PS 5/2 .



300 275

0.50 NS 0.67 NS

250

Tg (oC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 41

225 0.50 NSP 0.67 NSP

200 175

0.50 NP

150 125 100

0.67 NP 0.0

0.1

0.2

0.3

0.4

0.5

Fraction of BS Figure 9(b). Dependence of the Tgs for the glasses in the 0.50 and 0.67 NSP series of glasses plotted against the fraction of BS in the glass.


Page 35 of 41

140

Molar Volume (cm3/mole)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P SRO Units

120 100 80 60

P2 P1

140

Si SRO Units

120

Si3 Si1

100

P1P P0

Si2 Si1Si

ESi2 Si0

80 60 0.0

0.2

0.4

0.6

0.8

1.0

Composition (x) Figure 10. Composition dependence of the various molar volumes of the P and Si SRO units in the 0.50 and 0.67 NSP glass series to create a non-ideal mixing model for the solutions. x is molar ratio of SiS 2 to PS 5/2 .



140

Average Molar Volume (cm3/mole)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 41

120

100

80

P SRO Units Si SRO Units

60 1

2

3

4

Non-Bridging Sulfurs/Glass Former

Figure 11. Dependence of the average molar volumes per glass former for the P and Si SRO units in the 0.50 NSP and 0.67 NSP glass series as a function of the NBS/GF.


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Investigated with Neutron Diffraction and Reverse Monte Carlo Modeling. J. Phys. Chem. C 2015, 119, 27275-27284. (21) Christensen, R.; Olson, G.; Martin, S. W. Ionic Conductivity of Mixed Glass Former 0.35na2o + 0.65[Xb2o3 + (1 - X)P2o5] Glasses. J. Phys. Chem. B 2013, 117, 16577-16586. (22) Storek, M.; Boehmer, R.; Martin, S. W.; Larink, D.; Eckert, H. Nmr and Conductivity Studies of the Mixed Glass Former Effect in Lithium Borophosphate Glasses. J. Chem. Phys. 2012, 137, 124507/124501-124507/124512. (23) Bischoff, C.; Schuller, K.; Martin, S. W. Short Range Structural Models of the Glass Transition Temperatures and Densities of 0.5na2s + 0.5[Xges2 + (1 - X)Ps5/2] Mixed Glass Former Glasses. J. Phys. Chem. B 2014, 118, 3710-3719. (24) Larink, D.; Eckert, H.; Reichert, M.; Martin, S. W. Mixed Network Former Effect in IonConducting Alkali Borophosphate Glasses: Structure/Property Correlations in the System [M2o]1/3[(B2o3)X(P2o5)1-X]2/3 (M = Li, K, Cs). J. Phys. Chem. C 2012, 116, 26162-26176. (25) Christensen, R.; Byer, J.; Olson, G.; Martin, S. W. The Glass Transition Temperature of Mixed Glass Former 0.35na2o + 0.65[Xb2o3 + (1 - X)P2o5] Glasses. J. Non-Cryst. Solids 2012, 358, 826-831. (26) Haynes, M. J.; Bischoff, C.; Kaufmann, T.; Martin, S. W. The Mixed Glass Former Effect on the Thermal and Volume Properties of Na2s-B2s3-P2s5 Glasses. Phys.Chem.Glasses: Eur.J.Glass Sci.Technol., Part B 2009, 50, 144-148. (27) Christensen, R.; Byer, J.; Kaufmann, T.; Martin, S. W. Structure-Property Relationships in the Mixed Glass Former System Na2o-B2o3-P2o5. Phys.Chem.Glasses: Eur.J.Glass Sci.Technol., Part B 2009, 50, 237-242. (28) Bischoff, C.; Schuller, K.; Martin, S. W. Short Range Structural Models of the Glass Transition Temperatures and Densities of 0.5na2s + 0.5[Xges2 + (1 - X)Ps5/2] Mixed Glass Former Glasses. J Phys Chem B 2014, 118, 3710-3719. (29) Haynes, M. J.; Bischoff, C.; Kaufmann, T.; Martin, S. W. The Mixed Glass Former Effect on the Thermal and Volume Properties of Na2s-B2s3-P2s5 Glasses. Physics and Chemistry of Glasses-European Journal of Glass Science and Technology Part B 2009, 50, 144-148. (30) Martin, S. W.; Bischoff, C.; Schuller, K. Composition Dependence of the Na+ Ion Conductivity in 0.5na2s + 0.5[Xges2 + (1 – X)Ps5/2] Mixed Glass Former Glasses: A Structural Interpretation of a Negative Mixed Glass Former Effect. J. Phys. Chem. B 2015, 119, 15738. (31) Christensen, R.; Byer, J.; Olson, G.; Martin, S. W. The Densities of Mixed Glass Former 0.35 Na2o + 0.65 [Xb2o3 + (1 – X)P2o5] Glasses Related to the Atomic Fractions and Volumes of Short Range Structures. J. Non-Cryst. Solids 2012, 358, 583. (32) Christensen, R.; Byer, J.; Olson, G.; Martin, S. W. The Glass Transition Temperature of Mixed Glass Former 0.35 Na2o + 0.65 [Xb2o3 + (1-X) P2o5] Glasses. Journal of NonCrystalline Solids 2012, 358, 826-831. (33) Christensen, R.; Olson, G.; Martin, S. W. Ionic Conductivity of Mixed Glass Former 0.35 Na2o + 0.65 [Xb2o3 + (1-X) P2o5] Glasses. Journal of Physical Chemistry B 2013, 117, 1657716586. (34) Wang, W.; Christensen, R.; Curtis, B.; Hynek, D.; Keizer, S.; Wang, J.; Feller, S.; Martin, S. W.; Kieffer, J. Elastic Properties and Short-Range Structural Order in Mixed Network Former Glasses. Phys. Chem. Chem. Phys. 2017, 19, 15942-15952. (35) Bischoff, C.; Schuller, K.; Dunlap, N.; Martin, S. W. Ir, Raman, and Nmr Studies of the Short-Range Structures of 0.5na2s + 0.5[Xges2 + (1-X)Ps5/2] Mixed Glass-Former Glasses. J. Phys. Chem. B 2014, 118, 1943-1953.


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(36) Watson, D. E.; Martin, S. W. Structural Characterization of the Short-Range Order in High Alkali Content Sodium Thiosilicophosphate Glasses. Inorg. Chem. 2018, 57, 72-81. (37) Watson, D. E.; Martin, S. W. Short Range Order Characterization of the Na2s + Sis2 Glass System Using Raman, Infrared and 29si Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopies. J. Non-Cryst. Solids 2017, 471, 39-50. (38) Karki, A.; Feller, S.; Lim, H. P.; Stark, J.; Sanchez, C.; Shibata, M. The Density of Sodium-Borate Glasses Related to Atomic Arrangements. J.Non-Cryst.Solids 1987, 92, 11-19. (39) Lim, H. P.; Karki, A.; Feller, S.; Kasper, J. E.; Sumcad, G. The Density of Potassium Borate Glasses Related to Atomic Arrangements. J.Non-Cryst.Solids 1987, 91, 324-332. (40) Feil, D.; Feller, S. The Density of Sodium Borosilicate Glasses Related to Atomic Arrangements. Journal of Non-Crystalline Solids 1990, 119, 103-111. (41) Martin, S. W.; Cho, J.; Polewik, T.; Bhowmik, S. Density of Xna2s·(1-X)B2s3 (X = 0 to 0.8) Glasses: Correlation with Short-Range Order. J. Am. Ceram. Soc. 1995, 78, 3329-3335. (42) Cho, J.; Martin, S. W. Density Measurements of Xcs2s+(1-X)B2s3 Glasses: Correlation with Short Range Order. Phys.Chem.Glasses 1996, 37, 155-159. (43) Royle, M.; Cho, J.; Martin, S. W. Densities of the Alkali Thioborate Glasses as a Function of Short Range Order. Borate Glasses, Cryst.Melts, [Proc.Int.Conf.], 2nd 1997, 279-286.



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Average Molar Volume (cm3/mole)

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P SRO Units Si SRO Units

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Non-Bridging Sulfurs/Glass Former


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TOC Entry Dependence of the average molar volumes per glass former for the P and Si SRO units in the 0.50 NSP and 0.67 NSP glass series as a function of the NBS/GF.


Composition Dependence of the Glass-Transition Temperature and

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