Mixed-Alkali Effect on Thermal Property and Elastic Behavior in Borosilicate Glasses

XIE Xianmao ,ZHOU Hemin ,KE Xuefei ,WANG Xiaowei ,WANG Yadan ,ZHANG Jiayan ,QIAO Ang,3,TAO Haizheng＊

(1. State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Wuhan 430070, China; 2. AVIC Jonhon Optronic Technology Co. Ltd., Luoyang 471003, China; 3. Wuhan University of Technology Advanced Engineering Technology Research Institute of Zhongshan City, Zhongshan 528437, China)

Abstract: We investigated the mixed alkali effect on the thermal properties and elastic response to temperature in the borosilicate glasses system with the composition of 70.65SiO2·21.09B2O3·1.88Al2O3·(6.3 8-x)Li2O·xNa2O glasses,where x=0.00,1.595,3.19,4.785,and 6.38.Except for the expected positive and negative deviations from linearity for the coefficients of thermal expansion,room temperature E and G,we observed a new mixed alkali effect on the response of elastic moduli to temperature.Fourier transform infrared spectra were obtained to elucidate the possible structural origin of the mixed alkali effects.This work provides a valuable insight into the structural and mechanical properties of mixed-alkali borosilicate glasses.

Key words: mixed-alkali effect;borosilicate glass;elastic response to temperature;structural origin

1 Introduction

Mixed alkali effect,or mixed modifier effect,is still one of unsolved basic questions in the glass community,although this effect was firstly discovered in oxide glass by Weber in 1883[1]when investigating the thermometer effect in glasses with more than one alkali modifier.It refers to the phenomenon of nonlinear variation especially in transport properties when a network modifying mobile cation is replaced by a second one[2].These transport properties,also called dynamic properties,include ionic conductivity,diffusion,and viscosity that go through a minimum or maximum when the mixing ratio of two cations changes[3,4].The degree of departure from linearity depends on the compositions,the temperature and frequency of measurement,and especially the discrepancy of size and polarizability of the modifier cations[5].

Despite still lacking a thorough understanding for mixed alkali effect,much progress has been made over the past several decades.Especially,the dynamic structure model,which is based on the energy landscape approach,has helped to establish a more coherent picture[6,7].Based on the idea of a mismatch effect where sites favorable for one type of cation in the glassy network are unfavorable for the other type of cation,this model elucidates the structural origin of mixed alkali effect,and has been further supported by compelling evidences from extended X-ray absorption fine structure (EXAFS),nuclear magnetic resonance(NMR) and Infrared Spectroscopy[8-10].

Contrary to the similar schematic drawings in the previous studies[8,11,12],by constructing a state-of-the art structural model which reproduces both diffraction and NMR data,recently,Koharaet alidentified a highly correlated pair arrangement between K and Na ions around non-bridging oxygen atoms in the 22.7R2O·77.3SiO2(R=Na and/or K) alkali silicate glasses by using a novel topological analysis technique(persistent homology)[13].These facts indicate that the correlated pair arrangement could likely be the intrinsic origin of the mixed alkali effect.However,based on the assumption of identically distributed alkali ion throughout the network,another new structural model based on the topological constraint theory was recently given to elucidate the origin of mixed alkali effect in the 0.30(yNa2O+[1-y]K2O)·0.70SiO2glasses[14].By proposing the composition dependence of constraint energy as a result of network strain due to different cation radii,this model can well explain the experimental observations of the mixed alkali effect in the glass transition temperature,and other performances.Further investigations were conducted on (25-x)Na2O·xK2O·10Al2O3·65SiO2aluminosilicate glasses,where alkali ions act as modifiers forming nonbridging oxygen or as charge compensators to AlO4units.Among the five major interatomic potentials validated in the classical MD simulations,only the polarizable core-shell (CS) force field model was able to well reproduce the mixed alkali effect in both ionic conductivity and glass transition temperature[15].By using the van Hove correlation function,the alkali ion jump analysis clearly indicates that the different alkali ions locate at different local surroundings and obstruct each other in the channel,thus constricting their mobility when mixed.Therefore,much contention also remains about the structural origin of mixed alkali effect in glass community.And although there are many investigations on mixed alkali effects on silicate glasses,less effort has been devoted to study such phenomena in mixed alkali borosilicate glasses.

In this work,based on a batch composition from alkali borosilicate glasses (i e,electronic sealing glass DM308),we prepared a series of mixed lithium-sodium borosilicate glasses with varying molar ratior([Na2O]/([Na2O]+[Li2O])) from 0.00 to 1.00.Coefficient of thermal expansion and room temperature and variable temperature moduli were systematically characterized to investigate their composition dependence.Especially,we observed a new mixed alkali effect on the elastic response to temperature.Further Fourier transform infrared spectroscopy (FTIR) measurements were conducted to investigate the structural origin of mixed alkali effect in this series of mixed lithiumsodium borosilicate glasses.

2 Experimental

2.1 Glass preparation

Alkali borosilicate glasses were prepared using the traditional melt-quenching technique.The glasses had nominal molar compositions of 70.65SiO2·21.09B2O3·1.88Al2O3·(6.38-x) Li2O·xNa2O,wherex=0,1.60,3.19,4.79,6.38 molar percent,which correspond tor=0.00,0.25,0.5,0.75 and 1.00 (ris the molar ratio of[Na2O]/([Na2O]+[Li2O])).The raw materials used in glass melting were SiO2,H3BO3,Al2O3,Li2CO3,and Na2CO3powders.The batches were mixed thoroughly and melted in a Pt90Rh10crucible at 1 873 K for 1-3 hours.Finally,the melts were cast onto a graphite mold and promptly transferred to a preheated annealing furnace,where they were held at their respective glass transition temperatures for 2 hours to eliminate internal stress.By using the wet chemistry method,chemical compositional analysis indicated that the actual chemical compositions are almost the same to the desired compositions.

2.2 Elastic modulus

To monitor the evolution of elastic properties as a function of temperature,the elastic modulus was measured non-destructively by the GrindoSonic HT1200,which is designed to measure the temperature variation of the elastic properties of materials using impulse excitation technique[16].The glasses were heated from room temperature to 520 ℃ for each composition.The Young’s modulus(E) and shear modulus(G) can be calculated using the following equations:

wheremis the weight of the specimen;ffis the fundamental flexure resonant frequency;ftis the fundamental torsional resonant frequency;bis the width of the specimen;Lis the length of the specimen;tis the thickness of the specimen;T,B,andAare the correction factors related to the dimensions of the specimen in calculation.

2.3 Dilatometry properties

By using the thermal dilatometer (type:DIL402PC) made by NETZSCH,coefficients of thermal expansion (CTE,averaged over a temperature range of 50 to 400 ℃) and dilatometric softening temperature (Td,defined as the temperature of maximum expansion,corresponding to the viscosity at about 1010Pa·s),were determined for the polished samples with the size of 5 mm×5 mm×25 mm at an upscan rate of 5 ℃/min.

2.4 Structural analysis

Atomic-scale structure of the as-prepared glasses was obtained from their Fourier transform infrared(FTIR) spectra.By using the KBr pellet technique,FTIR absorption spectra of these glasses were collected by the Bruker INVENIO-S FT-IR spectrometer in the range of 400 to 1 600 cm-1.In order to obtain spectra with high quality,the samples were crushed in an agate mortar to obtain particles of micrometer size.Each sample was mixed with KBr in the proportion of 1:100 and pressed with a pressure of 15 MPa to obtain transparent pallets with an approximate thickness of 1 mm.

3 Results

3.1 Mechanical and thermal properties

Similar to mixed alkali effect on microhardness in borate glasses[17],which is as the positive deviation from linearity,here we also observed a positive deviation onEandGin the present glasses as shown in Fig.1.More concretely,with the substitution of Li by Na,a drop of 5.00 GPa inEoccurs from 58.40 GPa of the Li-containing end member composition to 53.40 GPa of the Na-containing end member composition.And a drop of 2.00 GPa inGappears from 24.20 GPa of Li-containing end member composition to 22.20 GPa of the Na-containing counter-composition.In addition,maximum deviations of 1.35 GPa inEand 0.51 GPa inGfrom linearity come out at about the equal-molar compositionr=0.5.

Fig.1 Composition dependence of Young’s modulus E (a),shear modulus G (b) at room temperature as a function of the molar ratio r (r is equal to the molar ratio of [Na2O]/([Li2O]+[Na2O])) for the 70.65SiO2·21.09B2O3·1.88Al2O3·(6.38-x) Li2O·xNa2O glasses (The uncertainties of E and G are both ± 0.01 GPa)

However,when it comes to the CTE,we observed a negative deviation from linearity (Fig.2).A maximum deviation (0.3×10-6K-1) in CTE from linearity occurs also at aboutr=0.5.And with a gradual increase inr,a big enhancement of about 1.2×10-6K-1turns up from 3.72×10-6K-1of the Li-containing end-member composition to 4.92×10-6K-1of the Na-containing end-member composition.

Fig.2 Composition dependence of coefficients of thermal expansion(CTE) between 50 and 400 ℃ for the 70.65SiO2·21.09B2 O3·1.88Al2O3·(6.38-x) Li2O·xNa2O glasses with different molar ratio r (r is equal to the molar ratio of [Na2O]/([Li2O]+[Na2O]) and the uncertainty of CTE is ± 0.2×10-6 K-1)

Finally,we observed a new mixed alkali effect on temperature dependence ofEandGin the present glasses (Fig.3).For the two end-member compositions,EandGexhibit the similar increase with the step by step rises in temperature up to 440 ℃.For the Li-containing end-member composition,there are increases of 1.27 GPa inEfrom 58.81 GPa at 20 ℃ to 60.08 GPa at 440 ℃ and 0.3 GPa inGfrom 24.12 GPa at 20 ℃ to 24.42 GPa at 440 ℃.Correspondingly,for the Na-containing end-member counterpart,there are increases of 0.94 GPa inEfrom 53.38 GPa at 20 ℃to 54.32 GPa at 440 ℃ and 0.16 GPa inGfrom 22.28 GPa at 20 ℃ to 22.44 GPa at 440 ℃.When it comes to the compositions withr=0.25,0.50,and 0.75,a gradual increase of about 0.60 GPa inEand about 0.10 GPa inGoccurs from 20 to 240 ℃.However,different from the two end-member compositions,the compositions withr=0.25,0.50,and 0.75 exhibit a clear drop inEandGafter 240 ℃.That’s to say,a drop of 0.80,1.01,and 0.87 GPa inEand 0.44,0.50,and 0.79 inGturns up for these compositions withr=0.25,0.50,and 0.75 respectively.This observation indicates that the mixture of Li and Na results in a distinct response ofEandGto temperature.

Fig.3 Young’s modulus E(a),shear modulus G(b) as a function of temperature with different molar ratio r (r is equal to the molar ratio of[Na2O]/([Li2O]+[Na2O])) for the 70.65SiO2·21.09B2O3·1.88Al2O3·(6.38-x)Li2O·xNa2O glasses (The uncertainties of E and G are both± 0.01 GPa)

3.2 Infrared spectra

In order to investigate the atomic-scale structural underpinnings of the above-mentioned mixed alkali effects on mechanical and thermal properties,the FTIR spectra of the prepared 70.65SiO2·21.09B2O3·1.88 Al2O3·(6.38-x)Li2O·xNa2O glasses were obtained and presented in Fig.4(a).The specific attributions of the characteristic peaks are listed in Table 1.As an example,the infrared spectrum with deconvoluted Gaussian bands and their summation curves of the glass atr=0 were shown in Fig.4(b).Composition dependence of the relative fraction (relative to the total integrated area in the region from 400 to 1 600 cm-1) of the infrared band centered at 900 cm-1related to BO4units is shown in Fig.4(c),which indicates a positive deviation from linearity withr.

Table 1 Characteristic bands of infrared spectrum in Fig.4(a)and their attributions

Fig.4 (a) Composition dependence of infrared absorption spectra for 70.65SiO2·21.09B2O3·1.88Al2O3·(6.38-x) Li2O·xNa2O glasses with different molar ratio r (r is equal to the molar ratio of [Na2O]/([Li2O]+[Na2O]));(b) Deconvoluted infrared spectrum in the region of 400 -1 600 cm-1 for the glass at r=0;(c) Composition dependence of the relative fraction (relative to the total integrated area in the region from 400 to 1 600 cm-1) of the infrared band centered at 900 cm-1 related to BO4 units

4 Discussion

4.1 Mechanism for mixed-alkali effects on elastic modulus and CTE

Firstly,the atomic packing density,denoted asCg,was proven by many references to be an important indicator in determining the mechanical properties of oxide glasses,such as elastic modulus,deformation mechanism,and fracture toughness[23-25].This indictor can be calculated using the following formula[26]:

where for theith constituent with chemical formulaAxBy,fiis the molar fraction,Miis the molar mass;Viis the theoretical volume,

whererAandrBare the ionic radii,NAis Avogadro’s number.The coordination numbers of two for O,four for Si,four for Al,and six for Li and Na were assumed.According to the Dell-Bray model[27],the content inN4of boro-oxygen tetrahedra was calculated.For the present glass system,where [R2O]-[Al2O3]＜ [B2O3],N4=([R2O]-[Al2O3])/[B2O3].

A near-linear relationship between the elastic moduli (EandG) and the atomic packing densityCg(Fig.5) with a high goodness of fit (R2values of 0.93 forEand 0.91 forG) was clearly observed,which indicates that the compositions with higher Na2O content have lower packing density and less elastic moduli.This is because alkali metal ions are predominantly present as charge balancing cations in the present alkali borosilicate glasses[28],which serve to balance the negatively charged [AlO4]-and [BO4]-and occupy the interstices in the glass network.When ions have smaller radii and larger field strength,they are packed more closely together,resulting in a higher packing density of atoms.This increased packing density leads to a greater resistance to deformation under the external force and a higher elastic modulus.However,this indicator is not the cause about the above-mentioned mixed alkali effects appeared in the present glass system.

Fig.5 Dependence of Young’s modulus E(a) and shear modulus G(b) on the atomic packing density Cg for the 70.65SiO2·21.09B2O3·1.88Al2 O3·(6.38-x) Li2O·xNa2O glasses

Expect for the atomic packing density,the strength of the chemical bonds is also very important in dominating the elastic modulus of a material[29].This is especially true for glass,where the bond energy significantly impacts its elastic modulus.However,the amorphous nature of glass results in numerous local variations in bond energy,leading to significant differences in bond energy distribution across various regions.Therefore,an index,i e,the average bond energy density (＜U0/V0＞),has been proposed[30].This index can be achieved by calculating the sum of bond energies of all chemical bonds in the glass and dividing it by the volume.It takes into account the enthalpy of dissociation (ΔHai) of the constituent oxides,their molar fraction,molar mass,and the density of the glass:

whereρrepresents the density of the glass;fiis the molar percentage of theicomponentAxBy;Miis the molar mass ofAxBy;ΔHaiis the molar enthalpy of dissociation ofAxBy.

For the present alkali borosilicate glasses,a nearlinear correlation (Fig.6) exists between this index and the mechanical performances (EandG) with a high goodness of fit (R2values of 0.94 inEand 0.92 inG).This near-linear correlation indicates that an increase in the average bond energy density,results in a corresponding increase in bothEandG.A higher average bond energy density generally predicts a larger elastic modulus,as it represents the average energy needed to break bonds between adjacent atoms in the glass.Stronger interatomic bonding is the result of a higher bond energy density,making it more challenging for the material to deform in response to applied stress.However,this index also cannot explain why the nonlinear mixed alkali effects mentioned above occurred in the present glass system.

Fig.6 Dependence of Young’s modulus E(a) and shear modulus G(b) on the mean-field bond energy density ＜U0/V0＞ for the 70.65SiO2·21.09B2O3·1.88Al2O3·(6.38-x) Li2O·xNa2O glasses

According to previous reports[28],due to larger field strength of Li+compared to that of Na+,more fraction of BO4tetrahedra in the B-containing units appears in the Li-containing end-member composition,which can be confirmed by their experimental NMR spectra.This can be explained by the more random distribution of Li ions throughout the glassy network compared to that of Na ions[28].This can also be confirmed by their FTIR spectra (Fig.4) in the present glasses.The relative fraction of the infrared band centered at about 900 cm-1,which is attributed to vibrations of [BO4],is higher for the Li-containing endmember composition than that for the Na-containing counter composition.Therefore,the positive deviation of the relative fraction of this infrared band from linearity (Fig.4(c)) as a function of the molar ratiorcan be considered as a proof about the structural origin of mixed alkali effect onEandGat room temperature.

Coefficient of thermal expansion (CTE) is a vital thermal property for borosilicate glasses,which is influenced by several factors,including cationic field strength,structural symmetry,and non-bridging oxygen(NBO)[31].In the present alkali borosilicate glasses,alkali cations serve as charge balancing cations,which fill into the interstices of the glass network.Based on the bond energy theory,it has been observed that alkali metals with larger atomic numbers tend to have weaker R-O bond strength.This is because of their smaller field strength and weaker network constraints[28].As a result,the pure Na-containing glass exhibits a larger CTE compared to the Li-containing one.Except for SiO4glass former,boron polyhedra,which is also an essential network former,should also play a significant role in the present glass system.The transformation of the coordination environment can alter the symmetry of the structure.It is believed[32]that the Na ions in the present glass series are less effective in promoting the conversion of BIIIto BIVcompared to the Li ions.This decrease in structural symmetry ultimately leads to an increase in CTE.Therefore,the positive deviation of the relative fraction of the infrared band centered at about 900 cm-1related to BO4units from linearity(Fig.4(c)) as a function of the molar ratiorcan be regarded as a proof about the structural origin why the mixed alkali effect on CTE occurs.Certainly,it is worth noting that the relationship between CTE and the structure is complex,and more research is needed to fully understand the mixed alkali effects on thermo-physical properties of borosilicate glasses.Nevertheless,understanding the factors that affect CTE is crucial for the development of new borosilicate glasses with desired thermal properties.

4.2 Understanding the elastic response of borosilicate glass to temperature

Recent studies[33,34]have shown that alloys exhibit the Elinvar effect,wherein their elastic modulus remains constant with increasing in temperature.This discovery has far-reaching implications for the advancement of cutting-edge devices.Moreover,the Elinvar effect has been observed in silicate glass and sodium-boron glass[35,36],similar to alloys.In this paper,we explored the changes ofEandGwith temperature.The response of the elastic moduli of borosilicate glasses to temperature should be closely linked to the effect of temperature on the intermediate-range clusters composed of SiO4,BO4,and BO3polyhedra.On the one hand,the elastic moduli atr=0 andr=1 remain relatively constant with temperature,which could be attributed to the change in silicate ring structure.Specifically,the flexible expansion of theαring to the rigid expansion of theβ-ring may play a role.On the other hand,the variable temperature modulus of boron-containing glass is known to be associated with changes in the intermediate range order (IRO) structure,such as boroxol rings and tetraborate units.In the case of alkali borate glass,the previous investigation suggests that this anomalous behavior may result from a delicate balance between the softening effect of bond weakening in the short-order structure (SRO) and the network hardening effect with temperature in the medium-order structure (IRO)[36].The hardening of the glass network can occur due to a slight distortion in the network topology or a conformational change of the IRO unit.As shown in Fig.3,increasing temperature should decrease the elastic modulus due to the positive coefficient of thermal expansion.The structural distortion is likely caused by the thermal expansion of the glass,which results in the softening of chemical bonds and rotation of the network.

Molecular dynamics (MD) simulations[37]have shown that pure B2O3glass is comprised of two types of rings with different conformations and stiffness:rigidly expandedβ-rings and flexibly expandedα-rings.These rings can undergo transformation into each other under different thermodynamic conditions,which explains why the elastic modulus of pure B2O3glass remains constant with temperature.Based on this hypothesis,we expected that Li-containing (r=0) and Na-containing (r=1) borosilicate glasses might also exhibit similar ring conformation changes.Specifically,as the temperature increases,the flexibly expandedα-ring transforms into the rigidly expandedβ-ring,which counterbalances the softening effect of chemical bonds.

Confirmed by the responses ofEandGto temperature (Fig.3),the mixture of two alkali cations has a detrimental effect on the Elinvar behavior of borosilicate glasses.This is likely due to the mixed alkali effect,which alters the intermediate range structure in the glass.Although theβ-rings provide a strengthening effect,it is not enough to counteract the softening effect of chemical bonds as the temperature increases.As a result,we observed decreases in the elastic moduli of the glasses with increasing temperature.However,more proofs and investigations are needed to elucidate the underlying structural mechanism responsible for this phenomenon.

5 Conclusions

By varying the ratio of Na to Li while maintaining the total alkali content constant,we investigated the impact of mixed modifiers on thermal properties and elastic moduli in borosilicate glasses.The nonlinear evolution of room temperature elastic moduli and CTE withris attributed to the variance of the ratio of BO3and BO4due to the mixture of the alkali ions,evidenced by the positive deviation of the relative fraction of the infrared band centered at about 900 cm-1related to BO4units from linearity as a function of the molar ratior.In addition,we observed a new mixed alkali effect on variable temperature elastic behavior in this glassy system,which could be related to the change in intermediate range structure originated from the mixture of sodium and lithium ions.These findings offer experimental evidence for understanding the temperature dependence behavior of the elastic moduli of alkali borosilicate glasses.

Conflict of interest

All authors declare that there are no competing interests.