Journal of Non-Crystalline Solids 356 (2010) 893–897

Contents lists available at ScienceDirect

Journal of Non-Crystalline Solids

journal homepage: www.elsevier .com/ locate/ jnoncrysol

Effect of thermal history and chemical composition on hardness of silicate glasses

Morten M. Smedskjaer, Martin Jensen, Yuanzheng Yue *

Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark

a r t i c l e i n f o

Article history:Received 27 May 2009Received in revised form 16 December 2009Available online 18 January 2010

Keywords:HardnessSilicatesStructural relaxation

0022-3093/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.jnoncrysol.2009.12.030

* Corresponding author. Tel.: +45 99408522; fax: +E-mail address: yy@bio.aau.dk (Y.Z. Yue).

a b s t r a c t

The prediction of hardness is possible for crystalline materials, but not possible for glasses so far. In thepresent paper, we describe and discuss several important factors that should be used for predicting thehardness of glasses. To do so, we have studied the influences of thermal history and chemical compositionon hardness of silicate glasses. By subjecting E-glasses of different compositions to various degrees ofannealing, it is found that hardness decreases with the fictive temperature. Addition of Na2O to aSiO2–Al2O3–Na2O glass system causes a decrease in hardness. However, the number of non-bridging oxy-gen per tetrahedron (NBO/T) is not the only parameter determining hardness. In addition, it is found thatthe effect of ionic radius on hardness is opposite for alkali and alkaline earth ions. Hence, changes of thestructural network occurring at the atomic scale must be taken into account when predicting the effect ofcomposition on hardness. The principles used in the calculation of hardness of crystalline materials areonly partly valid for glasses.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Silicate glasses are used in numerous applications where hard-ness is an important property since it affects abrasiveness andwear resistance. From an industrial point of view, it would bedesirable if the hardness of a glass could be predicted from its com-position and manufacturing conditions. It has been investigatedwhether other mechanical properties such as bulk and shear mod-ulus could be used for predicting the hardness of oxide glasses andcrystals [1–4]. However, such prediction has not yet been possible[1,2,5,6]. Recently, a semiempirical method for calculating hard-ness of crystals has been developed by considering the strengthof each individual bond and the bond density per area [7,8]. Themethod has experimentally been proven to be valid for varioustypes of crystalline materials [9–12]. However, this method doesnot apply to glasses due to their high degree of disorder (e.g., broaddistribution of bond angles and lengths). In spite of this, some at-tempts have been made by scientists to predict the hardness ofglasses. For instance, it has been suggested that structural param-eters such as the number of non-bridging oxygen per tetrahedron(NBO/T) and structural density could be used for predicting hard-ness of glasses [5]. In this work, density is distinguished betweenstructural density and glass density referring to atomic packingand macroscopic density, respectively.

The aim of this study is to discuss the factors that should be ta-ken into account in the calculation of hardness of glass. This is done

ll rights reserved.

45 96350558.

by conducting new experiments and by using literature data onhardness of different silicate glass systems. In order to evaluatethe contribution of each type of element to glass hardness, onlysimple glass systems with 3 or 4 components are used for thispurpose.

Properties of glasses do not only depend on their composition,but also on their thermal history as a glass is in a non-equilibriumstate. The structural density of glass depends on fictive tempera-ture, i.e., on thermal history. Normal silicate glass shows decreas-ing density with increasing fictive temperature [13], whereasanomalous glass, such as highly silica containing glass (SiO2-con-tent > 95 mol%), shows increasing density with fictive temperature[13,14]. In addition, an earlier study indicates that hardness of al-kali–alkaline earth-silicate glasses increases with increasing glassdensity [5]. In this work, we attempt to explore the direct relation-ship between thermal history and hardness for silicate glasses.Thereby, the effect of structural density on hardness can be distin-guished from that of glass density.

2. Experimental

Two different commercial E-glasses (iron-bearing boroalumi-nosilicate system) were obtained from PPG Industries. They are de-noted E1 and E2. The isobaric heat capacity (Cp) of the glasssamples was measured using a Netzsch STA 449C differential scan-ning calorimeter (DSC). The samples were placed in a platinumcrucible situated on a sample holder of the DSC at room tempera-ture. The samples were held 5 min at an initial temperature of333 K, and then heated at a rate of 20 K/min to 1073 K, and then

1.4

1.6

1.8

0 25 50 75 100975

980

985

990

(J K

-1 g

-1)

ta (h)

T f (K)

894 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897

cooled back at 20 K/min to 573 K. After natural cooling to roomtemperature, the second upscan was performed using the sameprocedure as for the first to ensure a uniform thermal history ofthe glasses [15]. To determine Cp of the samples, both the baseline(blank) and the reference sample (Sapphire) were measured. Mea-surements were carried out in a purged Ar atmosphere. The glasstransition temperature (Tg) was determined as the onset tempera-ture of the glass transition peak on the second upscan Cp curve, i.e.,the temperature of the intersection between the extrapolated lineof the glass Cp and the extrapolated line of the rapidly rising Cp. Tg

of the E1 and E2 glasses was found to be 984 and 937 K,respectively.

In order to obtain different thermal histories, the glass sampleswere heated to their respective Tg in air at a rate of 700 K/h andkept at this temperature for different durations ta (5 min, 20 h,64 h, and 100 h). The enthalpy overshoot at the glass transitionof the annealed samples was determined by DSC in order to deter-mine the fictive temperature Tf [16]. This was done by heating thesamples in argon at 10 K/min to 1123 K. The method for determin-ing Tf is described in detail elsewhere [17,18]. To measure thehardness of the annealed glasses, the samples were ground flaton one surface by a seven-step procedure with SiC paper underwater using a grit size of P4000 at the final step. Vickers microh-ardness (Hv) was measured using a Duramin 5 indenter (Struers,Denmark). All indentations were performed at a load of 0.49 Nfor a duration of 5 s. The hardness of each sample was measuredat 25 different locations.

The chemical composition of the E-glass surfaces may be mod-ified as a result of the annealing process in air [19–22]. To knowwhether or not this has happened, secondary neutral mass spec-troscopy (SNMS) was employed to determine the elemental con-centrations as a function of the depth within the E1 glassannealed at its Tg for 100 h. The measurements were performedby using an INA3 (Leybold AG) instrument equipped with a BalzersQMH511 quadrupole mass spectrometer and a Photonics SEMXP1600/14 amplifier. The details of the method are described else-where [23].

To explore the effect of sodium content on the hardness, fourglasses were prepared by gradually substituting SiO2 with Na2O(Table 1). The glasses were prepared from SiO2 (purum p.a., Sig-ma–Aldrich), Al2O3 (P99.5%, Merck), and Na2CO3 (P99.9%, Merck)powders. The batches were mixed and melted in an electric fur-nace (SF6/17, Entech) in a Pt90Rh10 crucible at 1798 K for Na1and Na2 and at 1773 K for Na3 and Na4. The glass melt was thenquenched on a brass plate and the samples were immediatelytransferred to a pre-heated annealing furnace that was allowedto cool naturally down to room temperature after insertion ofthe samples. The glasses Na1, Na2, and Na3 were annealed at993 K, whereas Na4 was annealed at 923 K. The cooled sampleswere then ground flat on one surface by an eight-step procedurewith SiC paper under water using a grit size of P4000 at the finalstep. The surfaces were afterwards carefully polished using 3 lmdiamond paste and finally cleaned with toluene. Vickers microh-ardness of the four glasses was measured using the same instru-

Table 1Chemical composition of the SiO2–Al2O3–Na2O glasses. The chemical compositionwas determined by wet chemistry analysis. The excess Na2O was calculated as theamount of Na2O that does not participate in AlO�4 charge balancing.

Glass Glass composition (mol%) Excess Na2O (mol%)

Na2O Al2O3 SiO2

Na1 27.0 17.3 55.7 9.7Na2 29.1 16.5 54.4 12.6Na3 30.9 16.6 52.4 14.3Na4 36.4 15.4 48.2 21.0

ment as stated above. A load of 0.98 N was applied for 5 s and 30indentations were performed on each glass.

To investigate the effect of network-modifying cations on hard-ness, the following seven glasses were prepared (in mol%): 68SiO2–8Na2O–1Fe2O3–23RO with R = Mg, Ca, Sr, and Ba and 68SiO2–23CaO–1Fe2O3–8M2O with M = K, Rb, and Cs. SiO2 (purum p.a., Sig-ma–Aldrich), Na2CO3 (P99.9%, Merck), MgO (P98%, Merck), CaCO3

(P99%, Merck), SrCO3 (P99.9%, Aldrich), BaCO3 (P99%, Chempur),K2CO3 (P99.5%, Merck), Rb2O3 (>99%, Chempur), Cs2CO3 (P99%,Aldrich), and Fe2O3 (P99%, Merck) powders were used as rawmaterials. The mixed batch materials were melted in an electricfurnace (SF6/17, Entech) at 1773 K in a Pt90Rh10 crucible for 3 h.The melt was then cast onto a brass plate and pressed to obtaincylindrical glasses of 7–10 cm diameter and �5 mm height. Theprepared glasses were annealed 10 K above their respective glasstransition temperatures for 10 min and then cooled naturally downto room temperature. The samples for hardness measurementswere ground flat on one surface to a thickness of �2 mm by asix-step procedure with SiC paper under ethanol. Afterwards, thesurfaces were carefully polished with 3 lm diamond paste. Vickersmicrohardness of the seven glasses was measured using the sameinstrument as stated above. A load of 0.25 N was applied for 5 s and25 indentations were performed on each glass.

3. Results

To study the annealing effect of the E1 glass on the fictive tem-perature Tf, the heat capacity (Cp) has been measured as a functionof temperature for the glasses annealed for various durations (ta) atTg = 984 K (Fig. 1). The endothermic event corresponds to the glasstransition. From each of the DSC curves, Tf can be determined byemploying the enthalpy-matching approach [16]. In the inset ofFig. 1, Tf is plotted as a function of ta and it is seen that Tf decreaseswith increasing ta.

Fig. 2 shows the compositional changes in the surface layer ofthe E1 glass annealed at 984 K for 100 h. Annealing of iron-bearingglasses under atmospheric conditions can cause an oxidation offerrous (Fe2+) to ferric (Fe3+) iron, which induces the formation ofa nano-crystalline surface layer [19–22]. A slight depletion of alu-minum and calcium is observed in the outer layer of �20 nm(Fig. 2). But this cannot be attributed to oxidation of Fe2+ to Fe3+.Otherwise, an enrichment of calcium and magnesium at the sur-

600 800 1000 1200

1.0

1.2Cp

T (K)

5 min 20 h 64 h 100 h

Fig. 1. Heat capacity (Cp) as a function of temperature for the E1 glass annealed atvarious durations (ta) at Tg = 984 K. All Cp curves were measured at a DSC upscanrate of 10 K/min in argon. Inset: The corresponding fictive temperatures (Tf) as afunction of ta determined by a previously proposed method [16].

0 20 40 60 80 100100

1000

10000

Ca

Fe

Si

Al

Mg

NaInte

nsity

(-)

Depth (nm)

B

Fig. 2. SNMS depth profile of the E1 glass annealed for 100 h at at Tg = 984 K. Theintensities of the various elements are plotted as a function of the depth within thesample.

8 12 16 205.3

5.5

5.7

5.9

6.1

Hv (G

Pa)

excess Na2O (mol%)

Fig. 4. Vickers hardness (Hv) of four Na2O–Al2O3–SiO2 glasses of varying excessNa2O (see Table 1). The excess Na2O was calculated as the amount of Na2O that doesnot participate in AlO�4 charge balancing.

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897 895

face should have been observed [19–22]. Instead, the depletion ofaluminum and calcium is most likely due to their leaching from thesurface during the sample grinding and polishing procedures.

Fig. 3 shows Vickers hardness of the two commercial E-glasses(E1 and E2) as a function of the annealing time at Tg. Hv is found toincrease with duration of annealing for the two compositions.However, the dependence of hardness on the thermal history isstronger for the E1 glass than for the E2 glass. For the E1 glass,the quantitative link between thermal history in terms of Tf andhardness is established (see inset of Fig. 3). As there is an inverserelationship between Tf and ta, Hv is found to decrease withincreasing Tf. The trend is confirmed by nanoindentation measure-ments on hyperquenched E-glass fibers [24]. Compared to theglasses studied in this work, the E-glass fibers have significantlyhigher Tf values (i.e., 1166 K) and considerably lower hardness(�6.6 GPa) at a load of 0.3–1.2 mN. The hardness measurementsconducted in this work have been performed at a load of 0.49 N.Normally, hardness of glasses decreases with increasing load[25,26], i.e., the hardness of the glass fibers should be lower than6.6 GPa at a load of 0.49 N. The highest Tf of the E-glasses studiedin this work is 988 K, which corresponds to a Hv value of7.3 ± 0.2 GPa. Hence, the hardness measurements of the E-glass fi-bers are in qualitative agreement with those of the glasses studiedin this work.

0 20 40 60 80 100

7.0

7.5

8.0

8.5

9.0

9.5

975 980 985 9907.07.58.08.59.09.5

Hv (G

Pa)

ta (h)

E1 E2

Hv (G

Pa)

Tf (K)

Fig. 3. Vickers hardness (Hv) of two different E-glasses (E1 and E2) as a function ofthe annealing duration (ta) at Tg = 984 K for E1 and Tg = 937 K for E2. Inset: Hv as afunction of the fictive temperature (Tf) for E1.

The four SiO2–Al2O3–Na2O glasses contain different amounts ofsodium. Aluminum is tetrahedrally coordinated in SiO2–Al2O3–Na2O glasses when Na/Al P 1 [27], i.e., one Na+ ion is coordinatedto one Al3+ ion to maintain charge neutrality. In Table 1, the Na2O ex-cess is calculated as the amount of Na2O that does not participate inAlO�4 charge balancing. The excess Na2O acts as network-modifyingoxides. The hardness of the four SiO2–Al2O3–Na2O glasses is plottedas a function of the excess Na2O in Fig. 4. Hv decreases with anincreasing excess amount of Na2O, i.e., with increase of the numberof non-bridging oxygen per tetrahedron (NBO/T).

The effect of the type of network-modifying cation on hardnesshas been investigated by comparing the hardness of 68SiO2–8Na2O–1Fe2O3–23RO glasses (R = Mg, Ca, Sr, and Ba) with that of68SiO2–23CaO–1Fe2O3–8M2O glasses (M = Na, K, Rb, and Cs). Theiron redox ratio (Fe3+/Fe2+) of the glasses has been found not tovary from one glass to another within the two series [28,29]. A plotof the hardness of the two glass series against the radius of R2+ orM+ (r) is shown in Fig. 5. For the alkaline earth glass series, Hv

decreases with increasing radius, whereas the opposite is foundfor the alkali series.

0.6 0.8 1.0 1.2 1.4 1.6 1.86.5

7.0

7.5

8.0

8.5

9.0

Hv (G

Pa)

r (Å)

Alkaline earth series Alkali series

Fig. 5. Vickers hardness (Hv) of (mol%) 68SiO2–8Na2O–1Fe2O3–23RO glasses withR = Mg, Ca, Sr, and Ba (j) and 68SiO2–23CaO–1Fe2O3–8M2O glasses with M = Na, K,Rb, and Cs (h) as a function of the radius of R2+ or M+ (r). For the alkaline earthseries, r increases in the order Mg, Ca, Sr, and Ba. For the alkali series, r increases inthe order Na, K, Rb, and Cs. Notice that the glasses with R = Ca and M = Na areidentical, but due to the different ionic radiuses of Ca2+ and Na+, Hv of this glass isshown twice.

896 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897

4. Discussion

The fictive temperature Tf is a monitor of the energy landscapeof a glass [30–32] and the configuration of a glass corresponds tothe frozen-in structure at Tf [17,33]. Re-heating of a glass at atemperature around Tg (i.e., annealing) causes a decrease of Tf

(see inset of Fig. 1) and thereby affects the atomic configurationsof the glass. At temperatures below Tg, structural relaxation timesare too long to allow such configurational rearrangements. At high-er temperature, the larger number of configurations available tothe glass allows such rearrangements [34]. This microscopic rear-rangement has a consequence to macroscopic properties sincestructural density increases with increasing degree of annealingfor normal silicate glasses [13,14].

For crystalline solids, an increase in crystal density is accompa-nied by an increase in bond density (structural density). On theother hand, the atomic coordination will be higher and this elon-gates the chemical bonds. Thus, the increasing crystal density leadsto two counteracting effects on hardness for the same chemicalcomposition [35]. Annealing of the glasses increases the structuraldensity without affecting the glass density and therefore, anneal-ing results in increased hardness as confirmed by the resultsshown in Fig. 3. Since the E-glasses studied in this work containferrous iron (about 0.2 wt%), the increasing hardness could beattributed to the formation of an oxidation induced nanocrystallinelayer. However, the SNMS measurement of the E1 glass annealedfor 100 h at Tg does not show the formation of such layer (Fig. 2).Compositional changes only occur in the surface layer of about20 nm of the glass. The ratio of the indentation diagonal lengthto the depth for a Vickers diamond is 7:1 [36]. As the length ofthe indentation diagonal is �10 lm for the E-glasses annealed for100 h at Tg, the indentation depth is �1.4 lm. Hence, the indenterpenetrates the modified layer and reaches into the original glass.

Since the effect of surface modification can be neglected and thechemical composition does not change during annealing, the in-crease in hardness with annealing duration (Fig. 3) must arise fromthe increasing structural density. In other words, the thermal his-tory of glasses plays an important role in influencing their hard-ness. This suggests that thermal history must be taken intoaccount when establishing a model for predicting the hardness ofglasses. This also means that comparison of hardness of differentglass compositions is only meaningful, if their thermal historiesor fictive temperatures are similar.

The hardness measurements presented in Fig. 4 indicate thatNBO/T is a useful parameter for a qualitative prediction of thehardness of silicate glasses. Addition of network-modifying oxidesinto glass increases NBO/T, i.e., decreases the polymerization de-gree of the glass network due to the breakage of Si–O–Si bonds.Since the Si–O–Si covalent bonds constitute the strongest bondsin silicate glasses, the average bond strength decreases whenNBO/T increases. Therefore, NBOs provide shear paths in the glassnetwork, which explains the trend presented in Fig. 4. However,this correlation between NBO/T and Hv is not valid for all silicateglass systems. It has been shown for basaltic glasses that an in-crease in NBO/T can cause both an increase and a decrease of hard-ness. The same study found that addition of MgO to the glassincreases the hardness, whereas addition of Na2O has the oppositeeffect [37].

To further explore the effect of network-modifying cations onhardness, the hardness of both 68SiO2–8Na2O–1Fe2O3–23ROglasses with R = Mg, Ca, Sr, and Ba and 68SiO2–23CaO–1Fe2O3–8M2O glasses with M = Na, K, Rb, and Cs has been measured(Fig. 5). Hence, the NBO/T is fixed for these series to exclude the ef-fect of NBO/T on hardness. The decrease in Hv with increasing ra-dius of R2+ ions is explained by a weakening of the overall

network structure because an increase of radius leads to a decreasein the field strength of the R2+ ions. Hence, the attraction of R2+ ionsto their surrounding structural groups of [SiO4] tetrahedra is re-duced. Therefore, it seems that the R–O bond strength plays a deci-sive role in controlling hardness in the alkaline earth glass series.The alkali ions are not as strongly associated with the glass net-work as the alkaline earth ions. With increasing radius of M+ ions,a strengthening of the Si–O bonds occurs, which is caused by aweakening of the M–O bonds. Besides affecting the chemical bond-ing, the alkali ion also affects the structural density. It has beenfound that the glass densities of the glasses containing Na and Kare identical even though a potassium ion weighs almost doublyas much as a sodium ion [29]. The reason for the identical glassdensities must be that the structural density increases withdecreasing radius of the alkali ion, and thereby, compensates thedecreased mass of the alkali ion. Hence, the increase in Hv withincreasing radius of M+ ions is attributed to the strengthening ofSi–O bonds. This finding is in contradiction to the calculation ap-proach of the hardness of crystalline materials. In the crystallinematerials, the weak bonds are of greater importance to Hv thanthe strong bonds since the former ones break before the latter onesduring load [7,12]. Thus, the principles of the calculation of hard-ness of crystalline materials cannot be transferred to amorphousmaterials.

The evaluation of hardness of glasses is complex due to a broad-er distribution of bond lengths and in particular bond angles com-pared to crystals. As demonstrated in this work, the principles ofthe hardness calculation method developed for crystals only partlyhold for glasses. As shown in Fig. 3, annealing (and hence, Tf andstructural density) leads to a pronounced increase of the hardnessof glasses for a given composition. However, an increase in sodiumcontent increases the glass density because sodium ions occupyinterstitial positions within the network. Therefore, sodium couldbe believed to increase the hardness, but in fact, the hardness de-creases due to the weakening of bond strength as a result of thechange in composition (Fig. 4). This again indicates the complexityof evaluation of hardness as different factors (degree of polymeri-zation, bond strength, fictive temperature, etc.) may counter oneanother. Even though NBO/T is a valuable parameter for describingthe glass network connectivity, it cannot be used for the predictionof hardness and hence, the development of a universal hardnesscalculation method is a challenge. However, within a given glasssystem, the effect of compositional change of glasses with similarthermal history on hardness can be qualitatively predicted.

5. Conclusion

Both thermal history and chemical composition affect the hard-ness of silicate glasses. Annealing lowers the fictive temperatureand thereby improves the structural density of glasses. This leadsto an increase of hardness. The effect of network-modifying ionson hardness differs between alkali and alkaline earth ions. For alka-li ions, hardness increases with increasing ionic radius, whereasthe opposite trend is observed for alkaline earth ions. Therefore,the structural changes of the network occurring at the atomic scalemust be taken into consideration when predicting the effect ofcomposition on hardness.

Acknowledgements

The authors thank J. Holm, T.R. Andersen, T. Madsen, K.H. Niel-sen, and E.M. Nielsen for experimental assistance. They also thankX.J. Guo for useful discussions.

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897 897

References

[1] D.M. Teter, Mater. Res. Soc. Bull. 23 (1998) 22.[2] A.Y. Liu, M.L. Cohen, Science 245 (1989) 841.[3] A. Makishima, J.D. Mackenzie, J. Non-Cryst. Solids 12 (1973) 35.[4] M. Yamane, J.D. Mackenzie, J. Non-Cryst. Solids 15 (1974) 153.[5] S. Deriano, T. Rouxel, M. LeFloch, B. Beuneu, Phys. Chem. Glasses 45 (2004) 37.[6] D.J.M. Burkhard, Phys. Chem. Glasses 39 (1998) 1.[7] F.M. Gao, J.L. He, E.D. Wu, S.M. Liu, D.L. Yu, D.C. Li, S.Y. Zhang, Y.J. Tian, Phys.

Rev. Lett. 91 (2003) 015502.[8] F.M. Gao, Phys. Rev. B 69 (2004) 094113.[9] A. Šimunek, J. Vackár, Phys. Rev. Lett. 96 (2006) 085501.

[10] X.J. Guo, J.L. He, B. Xu, Z.Y. Liu, D.L. Yu, Y.J. Tian, J. Phys. Chem. C 111 (2007)13679.

[11] X.J. Guo, L. Li, Z.Y. Liu, D.L. Yu, J.L. He, R.P. Liu, B. Xu, Y.J. Tian, H.T. Wang, J. Appl.Phys. 104 (2008) 023503.

[12] M.M. Smedskjaer, M. Jensen, Y.Z. Yue, J. Am. Ceram. Soc. 91 (2008) 514.[13] T.M. Gross, M. Tomozawa, J. Appl. Phys. 104 (2008) 063529.[14] R. Le Parc, C. Levelut, J. Pelous, V. Martinez, B. Champagnon, J. Phys.: Condens.

Matter 18 (2006) 7507.[15] Y.Z. Yue, J. Non-Cryst. Solids 354 (2008) 1112.[16] C.T. Moynihan, A.J. Easteal, M.A. Debolt, J. Tucker, J. Am. Ceram. Soc. 59 (1976)

12.[17] Y.Z. Yue, L. Wondraczek, H. Behrens, J. Deubener, J. Chem. Phys. 126 (2007)

144902.[18] L. Wondraczek, H. Behrens, Y.Z. Yue, J. Deubener, G.W. Scherer, J. Am. Ceram.

Soc. 90 (2007) 1556.

[19] G.B. Cook, R.F. Cooper, T. Wu, J. Non-Cryst. Solids 120 (1990) 207.[20] R.F. Cooper, J.B. Fanselow, D.B. Poker, Geochim. Cosmochim. Acta 60 (1996)

3253.[21] Y.Z. Yue, M. Korsgaard, L.F. Kirkegaard, G. Heide, J. Am. Ceram. Soc. 92 (2009)

62.[22] D.J.M. Burkhard, J. Petrol. 42 (2001) 507.[23] M.M. Smedskjaer, Y.Z. Yue, J. Non-Cryst. Solids 355 (2009) 908.[24] N. Lonnroth, C.L. Muhlstein, C. Pantano, Y.Z. Yue, J. Non-Cryst. Solids 354

(2008) 3887.[25] H. Li, R.C. Bradt, J. Non-Cryst. Solids 146 (1992) 197.[26] R. Roesky, J.R. Varner, J. Am. Ceram. Soc. 74 (1991) 1129.[27] A.K. Varshneya, Fundamentals of Inorganic Glasses, Society of Glass

Technology, Sheffield, 2006.[28] M.M. Smedskjaer, Y.Z. Yue, J. Deubener, H.P. Gunnlaugsson, J. Phys. Chem. B

113 (2009) 11194.[29] M.M. Smedskjaer, J.C. Mauro, Y.Z. Yue, J. Chem. Phys. 131 (2009) 244514.[30] C.A. Angell, Y.Z. Yue, L.M. Wang, J.R.D. Copley, S. Borick, S. Mossa, J. Phys.:

Condens. Matter 15 (2003) S1051.[31] G. Parisi, J. Phys.: Condens. Matter 15 (2003) S765.[32] T.S. Grigera, V. Martin-Mayor, G. Parisi, P. Verocchio, Nature 422 (2003) 289.[33] A. Monaco, A.I. Chumakov, Y.Z. Yue, G. Monaco, L. Comez, D. Fioretto, W.A.

Crichton, R. Rüffer, Phys. Rev. Lett. 96 (2006) 205502.[34] G. Adam, J.H. Gibbs, J. Chem. Phys. 43 (1965) 139.[35] J.L. He, L.C. Guo, D.L. Yu, R.P. Liu, Y.J. Tian, H.T. Wang, Appl. Phys. Lett. 85 (2004)

5571.[36] M.M. Smedskjaer, J. Deubener, Y.Z. Yue, Chem. Mater. 21 (2009) 1242.[37] N. Lonnroth, Y.Z. Yue, Glass Technol.: Eur. J. Glass Sci. Technol. A 50 (2009) 165.