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Effect of thermal history and chemical composition on hardness of silicate glasses
Journal of Non-Crystalline Solids 356 (2010) 893–897
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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 2009 Received in revised form 16 December 2009 Available online 18 January 2010 Keywords: Hardness Silicates Structural relaxation
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 the present paper, we describe and discuss several important factors that should be used for predicting the hardness of glasses. To do so, we have studied the influences of thermal history and chemical composition on hardness of silicate glasses. By subjecting E-glasses of different compositions to various degrees of annealing, it is found that hardness decreases with the fictive temperature. Addition of Na2O to a SiO2–Al2O3–Na2O glass system causes a decrease in hardness. However, the number of non-bridging oxygen per tetrahedron (NBO/T) is not the only parameter determining hardness. In addition, it is found that the effect of ionic radius on hardness is opposite for alkali and alkaline earth ions. Hence, changes of the structural network occurring at the atomic scale must be taken into account when predicting the effect of composition on hardness. The principles used in the calculation of hardness of crystalline materials are only partly valid for glasses. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Silicate glasses are used in numerous applications where hardness is an important property since it affects abrasiveness and wear resistance. From an industrial point of view, it would be desirable if the hardness of a glass could be predicted from its composition and manufacturing conditions. It has been investigated whether other mechanical properties such as bulk and shear modulus could be used for predicting the hardness of oxide glasses and crystals [1–4]. However, such prediction has not yet been possible [1,2,5,6]. Recently, a semiempirical method for calculating hardness of crystals has been developed by considering the strength of each individual bond and the bond density per area [7,8]. The method has experimentally been proven to be valid for various types of crystalline materials [9–12]. However, this method does not apply to glasses due to their high degree of disorder (e.g., broad distribution of bond angles and lengths). In spite of this, some attempts have been made by scientists to predict the hardness of glasses. For instance, it has been suggested that structural parameters such as the number of non-bridging oxygen per tetrahedron (NBO/T) and structural density could be used for predicting hardness of glasses [5]. In this work, density is distinguished between structural density and glass density referring to atomic packing and macroscopic density, respectively. The aim of this study is to discuss the factors that should be taken into account in the calculation of hardness of glass. This is done
* Corresponding author. Tel.: +45 99408522; fax: +45 96350558. E-mail address: [email protected] (Y.Z. Yue). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.12.030
by conducting new experiments and by using literature data on hardness of different silicate glass systems. In order to evaluate the contribution of each type of element to glass hardness, only simple glass systems with 3 or 4 components are used for this purpose. Properties of glasses do not only depend on their composition, but also on their thermal history as a glass is in a non-equilibrium state. The structural density of glass depends on fictive temperature, i.e., on thermal history. Normal silicate glass shows decreasing density with increasing fictive temperature [13], whereas anomalous glass, such as highly silica containing glass (SiO2-content > 95 mol%), shows increasing density with fictive temperature [13,14]. In addition, an earlier study indicates that hardness of alkali–alkaline earth-silicate glasses increases with increasing glass density [5]. In this work, we attempt to explore the direct relationship between thermal history and hardness for silicate glasses. Thereby, the effect of structural density on hardness can be distinguished from that of glass density. 2. Experimental Two different commercial E-glasses (iron-bearing boroaluminosilicate system) were obtained from PPG Industries. They are denoted E1 and E2. The isobaric heat capacity (Cp) of the glass samples was measured using a Netzsch STA 449C differential scanning calorimeter (DSC). The samples were placed in a platinum crucible situated on a sample holder of the DSC at room temperature. The samples were held 5 min at an initial temperature of 333 K, and then heated at a rate of 20 K/min to 1073 K, and then
M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897
Table 1 Chemical composition of the SiO2–Al2O3–Na2O glasses. The chemical composition was determined by wet chemistry analysis. The excess Na2O was calculated as the amount of Na2O that does not participate in AlO4 charge balancing. Glass
Na1 Na2 Na3 Na4
Glass composition (mol%)
Excess Na2O (mol%)
Na2O
Al2O3
SiO2
27.0 29.1 30.9 36.4
17.3 16.5 16.6 15.4
55.7 54.4 52.4 48.2
ment as stated above. A load of 0.98 N was applied for 5 s and 30 indentations were performed on each glass. To investigate the effect of network-modifying cations on hardness, 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., Sigma–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 raw materials. The mixed batch materials were melted in an electric furnace (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 obtain cylindrical glasses of 7–10 cm diameter and 5 mm height. The prepared glasses were annealed 10 K above their respective glass transition temperatures for 10 min and then cooled naturally down to room temperature. The samples for hardness measurements were ground flat on one surface to a thickness of 2 mm by a six-step procedure with SiC paper under ethanol. Afterwards, the surfaces were carefully polished with 3 lm diamond paste. Vickers microhardness of the seven glasses was measured using the same instrument as stated above. A load of 0.25 N was applied for 5 s and 25 indentations were performed on each glass.
3. Results To study the annealing effect of the E1 glass on the fictive temperature Tf, the heat capacity (Cp) has been measured as a function of temperature for the glasses annealed for various durations (ta) at Tg = 984 K (Fig. 1). The endothermic event corresponds to the glass transition. From each of the DSC curves, Tf can be determined by employing the enthalpy-matching approach [16]. In the inset of Fig. 1, Tf is plotted as a function of ta and it is seen that Tf decreases with increasing ta. Fig. 2 shows the compositional changes in the surface layer of the E1 glass annealed at 984 K for 100 h. Annealing of iron-bearing glasses under atmospheric conditions can cause an oxidation of ferrous (Fe2+) to ferric (Fe3+) iron, which induces the formation of a nano-crystalline surface layer [19–22]. A slight depletion of aluminum 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-
1.8
990
-1
Tf (K)
1.6
-1
cooled back at 20 K/min to 573 K. After natural cooling to room temperature, the second upscan was performed using the same procedure as for the first to ensure a uniform thermal history of the glasses [15]. To determine Cp of the samples, both the baseline (blank) and the reference sample (Sapphire) were measured. Measurements were carried out in a purged Ar atmosphere. The glass transition temperature (Tg) was determined as the onset temperature of the glass transition peak on the second upscan Cp curve, i.e., the temperature of the intersection between the extrapolated line of 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 samples were heated to their respective Tg in air at a rate of 700 K/h and kept at this temperature for different durations ta (5 min, 20 h, 64 h, and 100 h). The enthalpy overshoot at the glass transition of the annealed samples was determined by DSC in order to determine the fictive temperature Tf [16]. This was done by heating the samples in argon at 10 K/min to 1123 K. The method for determining Tf is described in detail elsewhere [17,18]. To measure the hardness of the annealed glasses, the samples were ground flat on one surface by a seven-step procedure with SiC paper under water using a grit size of P4000 at the final step. Vickers microhardness (Hv) was measured using a Duramin 5 indenter (Struers, Denmark). All indentations were performed at a load of 0.49 N for a duration of 5 s. The hardness of each sample was measured at 25 different locations. The chemical composition of the E-glass surfaces may be modified as a result of the annealing process in air [19–22]. To know whether or not this has happened, secondary neutral mass spectroscopy (SNMS) was employed to determine the elemental concentrations as a function of the depth within the E1 glass annealed at its Tg for 100 h. The measurements were performed by using an INA3 (Leybold AG) instrument equipped with a Balzers QMH511 quadrupole mass spectrometer and a Photonics SEM XP1600/14 amplifier. The details of the method are described elsewhere [23]. To explore the effect of sodium content on the hardness, four glasses were prepared by gradually substituting SiO2 with Na2O (Table 1). The glasses were prepared from SiO2 (purum p.a., Sigma–Aldrich), Al2O3 (P99.5%, Merck), and Na2CO3 (P99.9%, Merck) powders. The batches were mixed and melted in an electric furnace (SF6/17, Entech) in a Pt90Rh10 crucible at 1798 K for Na1 and Na2 and at 1773 K for Na3 and Na4. The glass melt was then quenched on a brass plate and the samples were immediately transferred to a pre-heated annealing furnace that was allowed to cool naturally down to room temperature after insertion of the samples. The glasses Na1, Na2, and Na3 were annealed at 993 K, whereas Na4 was annealed at 923 K. The cooled samples were then ground flat on one surface by an eight-step procedure with SiC paper under water using a grit size of P4000 at the final step. The surfaces were afterwards carefully polished using 3 lm diamond paste and finally cleaned with toluene. Vickers microhardness of the four glasses was measured using the same instru-
Cp (J K g )
894
1.4
985 980 975
0
25
50
ta (h)
75
100
1.2
5 min 20 h 64 h 100 h
1.0 600
800
1000
1200
T (K) 9.7 12.6 14.3 21.0
Fig. 1. Heat capacity (Cp) as a function of temperature for the E1 glass annealed at various durations (ta) at Tg = 984 K. All Cp curves were measured at a DSC upscan rate of 10 K/min in argon. Inset: The corresponding fictive temperatures (Tf) as a function of ta determined by a previously proposed method [16].
895
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Intensity (-)
10000
Al Ca
Mg
1000
Na
B
100
0
Fe
20
40
60
80
100
Depth (nm) Fig. 2. SNMS depth profile of the E1 glass annealed for 100 h at at Tg = 984 K. The intensities of the various elements are plotted as a function of the depth within the sample.
face should have been observed [19–22]. Instead, the depletion of aluminum and calcium is most likely due to their leaching from the surface 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 to increase with duration of annealing for the two compositions. However, the dependence of hardness on the thermal history is stronger for the E1 glass than for the E2 glass. For the E1 glass, the quantitative link between thermal history in terms of Tf and hardness is established (see inset of Fig. 3). As there is an inverse relationship between Tf and ta, Hv is found to decrease with increasing Tf. The trend is confirmed by nanoindentation measurements on hyperquenched E-glass fibers [24]. Compared to the glasses studied in this work, the E-glass fibers have significantly higher Tf values (i.e., 1166 K) and considerably lower hardness (6.6 GPa) at a load of 0.3–1.2 mN. The hardness measurements conducted 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 than 6.6 GPa at a load of 0.49 N. The highest Tf of the E-glasses studied in this work is 988 K, which corresponds to a Hv value of 7.3 ± 0.2 GPa. Hence, the hardness measurements of the E-glass fibers are in qualitative agreement with those of the glasses studied in this work.
9.5
6.1
Hv (GPa)
8
8.5 8.0 7.5 7.0 980
985
Tf (K)
990
8.0
16
20
excess Na2O (mol%) Fig. 4. Vickers hardness (Hv) of four Na2O–Al2O3–SiO2 glasses of varying excess Na2O (see Table 1). The excess Na2O was calculated as the amount of Na2O that does not participate in AlO4 charge balancing.
9.0
8.0 7.5 7.0
7.5
E1 E2
7.0 0
12
8.5
9.0
975
5.7
5.3
9.5
8.5
5.9
5.5
Hv (GPa)
Hv (GPa)
9.0
The four SiO2–Al2O3–Na2O glasses contain different amounts of sodium. Aluminum is tetrahedrally coordinated in SiO2–Al2O3– Na2O glasses when Na/Al P 1 [27], i.e., one Na+ ion is coordinated to one Al3+ ion to maintain charge neutrality. In Table 1, the Na2O excess is calculated as the amount of Na2O that does not participate in AlO4 charge balancing. The excess Na2O acts as network-modifying oxides. The hardness of the four SiO2–Al2O3–Na2O glasses is plotted as a function of the excess Na2O in Fig. 4. Hv decreases with an increasing excess amount of Na2O, i.e., with increase of the number of non-bridging oxygen per tetrahedron (NBO/T). The effect of the type of network-modifying cation on hardness has been investigated by comparing the hardness of 68SiO2– 8Na2O–1Fe2O3–23RO glasses (R = Mg, Ca, Sr, and Ba) with that of 68SiO2–23CaO–1Fe2O3–8M2O glasses (M = Na, K, Rb, and Cs). The iron redox ratio (Fe3+/Fe2+) of the glasses has been found not to vary from one glass to another within the two series [28,29]. A plot of the hardness of the two glass series against the radius of R2+ or M+ (r) is shown in Fig. 5. For the alkaline earth glass series, Hv decreases with increasing radius, whereas the opposite is found for the alkali series.
Hv (GPa)
Si
20
40
60
80
100
ta (h) Fig. 3. Vickers hardness (Hv) of two different E-glasses (E1 and E2) as a function of the annealing duration (ta) at Tg = 984 K for E1 and Tg = 937 K for E2. Inset: Hv as a function of the fictive temperature (Tf) for E1.
6.5 0.6
Alkaline earth series Alkali series 0.8
1.0
1.2
1.4
1.6
1.8
r (Å) Fig. 5. Vickers hardness (Hv) of (mol%) 68SiO2–8Na2O–1Fe2O3–23RO glasses with R = 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 earth series, r increases in the order Mg, Ca, Sr, and Ba. For the alkali series, r increases in the order Na, K, Rb, and Cs. Notice that the glasses with R = Ca and M = Na are identical, but due to the different ionic radiuses of Ca2+ and Na+, Hv of this glass is shown twice.
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4. Discussion The fictive temperature Tf is a monitor of the energy landscape of a glass [30–32] and the configuration of a glass corresponds to the frozen-in structure at Tf [17,33]. Re-heating of a glass at a temperature around Tg (i.e., annealing) causes a decrease of Tf (see inset of Fig. 1) and thereby affects the atomic configurations of the glass. At temperatures below Tg, structural relaxation times are too long to allow such configurational rearrangements. At higher temperature, the larger number of configurations available to the glass allows such rearrangements [34]. This microscopic rearrangement has a consequence to macroscopic properties since structural density increases with increasing degree of annealing for normal silicate glasses [13,14]. For crystalline solids, an increase in crystal density is accompanied by an increase in bond density (structural density). On the other hand, the atomic coordination will be higher and this elongates the chemical bonds. Thus, the increasing crystal density leads to two counteracting effects on hardness for the same chemical composition [35]. Annealing of the glasses increases the structural density without affecting the glass density and therefore, annealing results in increased hardness as confirmed by the results shown in Fig. 3. Since the E-glasses studied in this work contain ferrous iron (about 0.2 wt%), the increasing hardness could be attributed to the formation of an oxidation induced nanocrystalline layer. However, the SNMS measurement of the E1 glass annealed for 100 h at Tg does not show the formation of such layer (Fig. 2). Compositional changes only occur in the surface layer of about 20 nm of the glass. The ratio of the indentation diagonal length to the depth for a Vickers diamond is 7:1 [36]. As the length of the indentation diagonal is 10 lm for the E-glasses annealed for 100 h at Tg, the indentation depth is 1.4 lm. Hence, the indenter penetrates the modified layer and reaches into the original glass. Since the effect of surface modification can be neglected and the chemical composition does not change during annealing, the increase in hardness with annealing duration (Fig. 3) must arise from the increasing structural density. In other words, the thermal history of glasses plays an important role in influencing their hardness. This suggests that thermal history must be taken into account when establishing a model for predicting the hardness of glasses. This also means that comparison of hardness of different glass compositions is only meaningful, if their thermal histories or fictive temperatures are similar. The hardness measurements presented in Fig. 4 indicate that NBO/T is a useful parameter for a qualitative prediction of the hardness of silicate glasses. Addition of network-modifying oxides into glass increases NBO/T, i.e., decreases the polymerization degree of the glass network due to the breakage of Si–O–Si bonds. Since the Si–O–Si covalent bonds constitute the strongest bonds in silicate glasses, the average bond strength decreases when NBO/T increases. Therefore, NBOs provide shear paths in the glass network, which explains the trend presented in Fig. 4. However, this correlation between NBO/T and Hv is not valid for all silicate glass systems. It has been shown for basaltic glasses that an increase in NBO/T can cause both an increase and a decrease of hardness. The same study found that addition of MgO to the glass increases the hardness, whereas addition of Na2O has the opposite effect [37]. To further explore the effect of network-modifying cations on hardness, the hardness of both 68SiO2–8Na2O–1Fe2O3–23RO glasses 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 effect of NBO/T on hardness. The decrease in Hv with increasing radius of R2+ ions is explained by a weakening of the overall
network structure because an increase of radius leads to a decrease in the field strength of the R2+ ions. Hence, the attraction of R2+ ions to their surrounding structural groups of [SiO4] tetrahedra is reduced. Therefore, it seems that the R–O bond strength plays a decisive role in controlling hardness in the alkaline earth glass series. The alkali ions are not as strongly associated with the glass network as the alkaline earth ions. With increasing radius of M+ ions, a strengthening of the Si–O bonds occurs, which is caused by a weakening of the M–O bonds. Besides affecting the chemical bonding, the alkali ion also affects the structural density. It has been found that the glass densities of the glasses containing Na and K are identical even though a potassium ion weighs almost doubly as much as a sodium ion [29]. The reason for the identical glass densities must be that the structural density increases with decreasing radius of the alkali ion, and thereby, compensates the decreased mass of the alkali ion. Hence, the increase in Hv with increasing radius of M+ ions is attributed to the strengthening of Si–O bonds. This finding is in contradiction to the calculation approach of the hardness of crystalline materials. In the crystalline materials, the weak bonds are of greater importance to Hv than the strong bonds since the former ones break before the latter ones during load [7,12]. Thus, the principles of the calculation of hardness of crystalline materials cannot be transferred to amorphous materials. The evaluation of hardness of glasses is complex due to a broader distribution of bond lengths and in particular bond angles compared to crystals. As demonstrated in this work, the principles of the hardness calculation method developed for crystals only partly hold for glasses. As shown in Fig. 3, annealing (and hence, Tf and structural density) leads to a pronounced increase of the hardness of glasses for a given composition. However, an increase in sodium content increases the glass density because sodium ions occupy interstitial positions within the network. Therefore, sodium could be believed to increase the hardness, but in fact, the hardness decreases due to the weakening of bond strength as a result of the change in composition (Fig. 4). This again indicates the complexity of evaluation of hardness as different factors (degree of polymerization, bond strength, fictive temperature, etc.) may counter one another. Even though NBO/T is a valuable parameter for describing the glass network connectivity, it cannot be used for the prediction of hardness and hence, the development of a universal hardness calculation method is a challenge. However, within a given glass system, the effect of compositional change of glasses with similar thermal history on hardness can be qualitatively predicted.
5. Conclusion Both thermal history and chemical composition affect the hardness of silicate glasses. Annealing lowers the fictive temperature and thereby improves the structural density of glasses. This leads to an increase of hardness. The effect of network-modifying ions on hardness differs between alkali and alkaline earth ions. For alkali ions, hardness increases with increasing ionic radius, whereas the opposite trend is observed for alkaline earth ions. Therefore, the structural changes of the network occurring at the atomic scale must be taken into consideration when predicting the effect of composition on hardness.
Acknowledgements The authors thank J. Holm, T.R. Andersen, T. Madsen, K.H. Nielsen, and E.M. Nielsen for experimental assistance. They also thank X.J. Guo for useful discussions.
M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897
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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 2009 Received in revised form 16 December 2009 Available online 18 January 2010 Keywords: Hardness Silicates Structural relaxation
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 the present paper, we describe and discuss several important factors that should be used for predicting the hardness of glasses. To do so, we have studied the influences of thermal history and chemical composition on hardness of silicate glasses. By subjecting E-glasses of different compositions to various degrees of annealing, it is found that hardness decreases with the fictive temperature. Addition of Na2O to a SiO2–Al2O3–Na2O glass system causes a decrease in hardness. However, the number of non-bridging oxygen per tetrahedron (NBO/T) is not the only parameter determining hardness. In addition, it is found that the effect of ionic radius on hardness is opposite for alkali and alkaline earth ions. Hence, changes of the structural network occurring at the atomic scale must be taken into account when predicting the effect of composition on hardness. The principles used in the calculation of hardness of crystalline materials are only partly valid for glasses. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Silicate glasses are used in numerous applications where hardness is an important property since it affects abrasiveness and wear resistance. From an industrial point of view, it would be desirable if the hardness of a glass could be predicted from its composition and manufacturing conditions. It has been investigated whether other mechanical properties such as bulk and shear modulus could be used for predicting the hardness of oxide glasses and crystals [1–4]. However, such prediction has not yet been possible [1,2,5,6]. Recently, a semiempirical method for calculating hardness of crystals has been developed by considering the strength of each individual bond and the bond density per area [7,8]. The method has experimentally been proven to be valid for various types of crystalline materials [9–12]. However, this method does not apply to glasses due to their high degree of disorder (e.g., broad distribution of bond angles and lengths). In spite of this, some attempts have been made by scientists to predict the hardness of glasses. For instance, it has been suggested that structural parameters such as the number of non-bridging oxygen per tetrahedron (NBO/T) and structural density could be used for predicting hardness of glasses [5]. In this work, density is distinguished between structural density and glass density referring to atomic packing and macroscopic density, respectively. The aim of this study is to discuss the factors that should be taken into account in the calculation of hardness of glass. This is done
* Corresponding author. Tel.: +45 99408522; fax: +45 96350558. E-mail address: [email protected] (Y.Z. Yue). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.12.030
by conducting new experiments and by using literature data on hardness of different silicate glass systems. In order to evaluate the contribution of each type of element to glass hardness, only simple glass systems with 3 or 4 components are used for this purpose. Properties of glasses do not only depend on their composition, but also on their thermal history as a glass is in a non-equilibrium state. The structural density of glass depends on fictive temperature, i.e., on thermal history. Normal silicate glass shows decreasing density with increasing fictive temperature [13], whereas anomalous glass, such as highly silica containing glass (SiO2-content > 95 mol%), shows increasing density with fictive temperature [13,14]. In addition, an earlier study indicates that hardness of alkali–alkaline earth-silicate glasses increases with increasing glass density [5]. In this work, we attempt to explore the direct relationship between thermal history and hardness for silicate glasses. Thereby, the effect of structural density on hardness can be distinguished from that of glass density. 2. Experimental Two different commercial E-glasses (iron-bearing boroaluminosilicate system) were obtained from PPG Industries. They are denoted E1 and E2. The isobaric heat capacity (Cp) of the glass samples was measured using a Netzsch STA 449C differential scanning calorimeter (DSC). The samples were placed in a platinum crucible situated on a sample holder of the DSC at room temperature. The samples were held 5 min at an initial temperature of 333 K, and then heated at a rate of 20 K/min to 1073 K, and then
M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 893–897
Table 1 Chemical composition of the SiO2–Al2O3–Na2O glasses. The chemical composition was determined by wet chemistry analysis. The excess Na2O was calculated as the amount of Na2O that does not participate in AlO4 charge balancing. Glass
Na1 Na2 Na3 Na4
Glass composition (mol%)
Excess Na2O (mol%)
Na2O
Al2O3
SiO2
27.0 29.1 30.9 36.4
17.3 16.5 16.6 15.4
55.7 54.4 52.4 48.2
ment as stated above. A load of 0.98 N was applied for 5 s and 30 indentations were performed on each glass. To investigate the effect of network-modifying cations on hardness, 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., Sigma–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 raw materials. The mixed batch materials were melted in an electric furnace (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 obtain cylindrical glasses of 7–10 cm diameter and 5 mm height. The prepared glasses were annealed 10 K above their respective glass transition temperatures for 10 min and then cooled naturally down to room temperature. The samples for hardness measurements were ground flat on one surface to a thickness of 2 mm by a six-step procedure with SiC paper under ethanol. Afterwards, the surfaces were carefully polished with 3 lm diamond paste. Vickers microhardness of the seven glasses was measured using the same instrument as stated above. A load of 0.25 N was applied for 5 s and 25 indentations were performed on each glass.
3. Results To study the annealing effect of the E1 glass on the fictive temperature Tf, the heat capacity (Cp) has been measured as a function of temperature for the glasses annealed for various durations (ta) at Tg = 984 K (Fig. 1). The endothermic event corresponds to the glass transition. From each of the DSC curves, Tf can be determined by employing the enthalpy-matching approach [16]. In the inset of Fig. 1, Tf is plotted as a function of ta and it is seen that Tf decreases with increasing ta. Fig. 2 shows the compositional changes in the surface layer of the E1 glass annealed at 984 K for 100 h. Annealing of iron-bearing glasses under atmospheric conditions can cause an oxidation of ferrous (Fe2+) to ferric (Fe3+) iron, which induces the formation of a nano-crystalline surface layer [19–22]. A slight depletion of aluminum 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-
1.8
990
-1
Tf (K)
1.6
-1
cooled back at 20 K/min to 573 K. After natural cooling to room temperature, the second upscan was performed using the same procedure as for the first to ensure a uniform thermal history of the glasses [15]. To determine Cp of the samples, both the baseline (blank) and the reference sample (Sapphire) were measured. Measurements were carried out in a purged Ar atmosphere. The glass transition temperature (Tg) was determined as the onset temperature of the glass transition peak on the second upscan Cp curve, i.e., the temperature of the intersection between the extrapolated line of 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 samples were heated to their respective Tg in air at a rate of 700 K/h and kept at this temperature for different durations ta (5 min, 20 h, 64 h, and 100 h). The enthalpy overshoot at the glass transition of the annealed samples was determined by DSC in order to determine the fictive temperature Tf [16]. This was done by heating the samples in argon at 10 K/min to 1123 K. The method for determining Tf is described in detail elsewhere [17,18]. To measure the hardness of the annealed glasses, the samples were ground flat on one surface by a seven-step procedure with SiC paper under water using a grit size of P4000 at the final step. Vickers microhardness (Hv) was measured using a Duramin 5 indenter (Struers, Denmark). All indentations were performed at a load of 0.49 N for a duration of 5 s. The hardness of each sample was measured at 25 different locations. The chemical composition of the E-glass surfaces may be modified as a result of the annealing process in air [19–22]. To know whether or not this has happened, secondary neutral mass spectroscopy (SNMS) was employed to determine the elemental concentrations as a function of the depth within the E1 glass annealed at its Tg for 100 h. The measurements were performed by using an INA3 (Leybold AG) instrument equipped with a Balzers QMH511 quadrupole mass spectrometer and a Photonics SEM XP1600/14 amplifier. The details of the method are described elsewhere [23]. To explore the effect of sodium content on the hardness, four glasses were prepared by gradually substituting SiO2 with Na2O (Table 1). The glasses were prepared from SiO2 (purum p.a., Sigma–Aldrich), Al2O3 (P99.5%, Merck), and Na2CO3 (P99.9%, Merck) powders. The batches were mixed and melted in an electric furnace (SF6/17, Entech) in a Pt90Rh10 crucible at 1798 K for Na1 and Na2 and at 1773 K for Na3 and Na4. The glass melt was then quenched on a brass plate and the samples were immediately transferred to a pre-heated annealing furnace that was allowed to cool naturally down to room temperature after insertion of the samples. The glasses Na1, Na2, and Na3 were annealed at 993 K, whereas Na4 was annealed at 923 K. The cooled samples were then ground flat on one surface by an eight-step procedure with SiC paper under water using a grit size of P4000 at the final step. The surfaces were afterwards carefully polished using 3 lm diamond paste and finally cleaned with toluene. Vickers microhardness of the four glasses was measured using the same instru-
Cp (J K g )
894
1.4
985 980 975
0
25
50
ta (h)
75
100
1.2
5 min 20 h 64 h 100 h
1.0 600
800
1000
1200
T (K) 9.7 12.6 14.3 21.0
Fig. 1. Heat capacity (Cp) as a function of temperature for the E1 glass annealed at various durations (ta) at Tg = 984 K. All Cp curves were measured at a DSC upscan rate of 10 K/min in argon. Inset: The corresponding fictive temperatures (Tf) as a function of ta determined by a previously proposed method [16].
895
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Intensity (-)
10000
Al Ca
Mg
1000
Na
B
100
0
Fe
20
40
60
80
100
Depth (nm) Fig. 2. SNMS depth profile of the E1 glass annealed for 100 h at at Tg = 984 K. The intensities of the various elements are plotted as a function of the depth within the sample.
face should have been observed [19–22]. Instead, the depletion of aluminum and calcium is most likely due to their leaching from the surface 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 to increase with duration of annealing for the two compositions. However, the dependence of hardness on the thermal history is stronger for the E1 glass than for the E2 glass. For the E1 glass, the quantitative link between thermal history in terms of Tf and hardness is established (see inset of Fig. 3). As there is an inverse relationship between Tf and ta, Hv is found to decrease with increasing Tf. The trend is confirmed by nanoindentation measurements on hyperquenched E-glass fibers [24]. Compared to the glasses studied in this work, the E-glass fibers have significantly higher Tf values (i.e., 1166 K) and considerably lower hardness (6.6 GPa) at a load of 0.3–1.2 mN. The hardness measurements conducted 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 than 6.6 GPa at a load of 0.49 N. The highest Tf of the E-glasses studied in this work is 988 K, which corresponds to a Hv value of 7.3 ± 0.2 GPa. Hence, the hardness measurements of the E-glass fibers are in qualitative agreement with those of the glasses studied in this work.
9.5
6.1
Hv (GPa)
8
8.5 8.0 7.5 7.0 980
985
Tf (K)
990
8.0
16
20
excess Na2O (mol%) Fig. 4. Vickers hardness (Hv) of four Na2O–Al2O3–SiO2 glasses of varying excess Na2O (see Table 1). The excess Na2O was calculated as the amount of Na2O that does not participate in AlO4 charge balancing.
9.0
8.0 7.5 7.0
7.5
E1 E2
7.0 0
12
8.5
9.0
975
5.7
5.3
9.5
8.5
5.9
5.5
Hv (GPa)
Hv (GPa)
9.0
The four SiO2–Al2O3–Na2O glasses contain different amounts of sodium. Aluminum is tetrahedrally coordinated in SiO2–Al2O3– Na2O glasses when Na/Al P 1 [27], i.e., one Na+ ion is coordinated to one Al3+ ion to maintain charge neutrality. In Table 1, the Na2O excess is calculated as the amount of Na2O that does not participate in AlO4 charge balancing. The excess Na2O acts as network-modifying oxides. The hardness of the four SiO2–Al2O3–Na2O glasses is plotted as a function of the excess Na2O in Fig. 4. Hv decreases with an increasing excess amount of Na2O, i.e., with increase of the number of non-bridging oxygen per tetrahedron (NBO/T). The effect of the type of network-modifying cation on hardness has been investigated by comparing the hardness of 68SiO2– 8Na2O–1Fe2O3–23RO glasses (R = Mg, Ca, Sr, and Ba) with that of 68SiO2–23CaO–1Fe2O3–8M2O glasses (M = Na, K, Rb, and Cs). The iron redox ratio (Fe3+/Fe2+) of the glasses has been found not to vary from one glass to another within the two series [28,29]. A plot of the hardness of the two glass series against the radius of R2+ or M+ (r) is shown in Fig. 5. For the alkaline earth glass series, Hv decreases with increasing radius, whereas the opposite is found for the alkali series.
Hv (GPa)
Si
20
40
60
80
100
ta (h) Fig. 3. Vickers hardness (Hv) of two different E-glasses (E1 and E2) as a function of the annealing duration (ta) at Tg = 984 K for E1 and Tg = 937 K for E2. Inset: Hv as a function of the fictive temperature (Tf) for E1.
6.5 0.6
Alkaline earth series Alkali series 0.8
1.0
1.2
1.4
1.6
1.8
r (Å) Fig. 5. Vickers hardness (Hv) of (mol%) 68SiO2–8Na2O–1Fe2O3–23RO glasses with R = 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 earth series, r increases in the order Mg, Ca, Sr, and Ba. For the alkali series, r increases in the order Na, K, Rb, and Cs. Notice that the glasses with R = Ca and M = Na are identical, but due to the different ionic radiuses of Ca2+ and Na+, Hv of this glass is shown twice.
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4. Discussion The fictive temperature Tf is a monitor of the energy landscape of a glass [30–32] and the configuration of a glass corresponds to the frozen-in structure at Tf [17,33]. Re-heating of a glass at a temperature around Tg (i.e., annealing) causes a decrease of Tf (see inset of Fig. 1) and thereby affects the atomic configurations of the glass. At temperatures below Tg, structural relaxation times are too long to allow such configurational rearrangements. At higher temperature, the larger number of configurations available to the glass allows such rearrangements [34]. This microscopic rearrangement has a consequence to macroscopic properties since structural density increases with increasing degree of annealing for normal silicate glasses [13,14]. For crystalline solids, an increase in crystal density is accompanied by an increase in bond density (structural density). On the other hand, the atomic coordination will be higher and this elongates the chemical bonds. Thus, the increasing crystal density leads to two counteracting effects on hardness for the same chemical composition [35]. Annealing of the glasses increases the structural density without affecting the glass density and therefore, annealing results in increased hardness as confirmed by the results shown in Fig. 3. Since the E-glasses studied in this work contain ferrous iron (about 0.2 wt%), the increasing hardness could be attributed to the formation of an oxidation induced nanocrystalline layer. However, the SNMS measurement of the E1 glass annealed for 100 h at Tg does not show the formation of such layer (Fig. 2). Compositional changes only occur in the surface layer of about 20 nm of the glass. The ratio of the indentation diagonal length to the depth for a Vickers diamond is 7:1 [36]. As the length of the indentation diagonal is 10 lm for the E-glasses annealed for 100 h at Tg, the indentation depth is 1.4 lm. Hence, the indenter penetrates the modified layer and reaches into the original glass. Since the effect of surface modification can be neglected and the chemical composition does not change during annealing, the increase in hardness with annealing duration (Fig. 3) must arise from the increasing structural density. In other words, the thermal history of glasses plays an important role in influencing their hardness. This suggests that thermal history must be taken into account when establishing a model for predicting the hardness of glasses. This also means that comparison of hardness of different glass compositions is only meaningful, if their thermal histories or fictive temperatures are similar. The hardness measurements presented in Fig. 4 indicate that NBO/T is a useful parameter for a qualitative prediction of the hardness of silicate glasses. Addition of network-modifying oxides into glass increases NBO/T, i.e., decreases the polymerization degree of the glass network due to the breakage of Si–O–Si bonds. Since the Si–O–Si covalent bonds constitute the strongest bonds in silicate glasses, the average bond strength decreases when NBO/T increases. Therefore, NBOs provide shear paths in the glass network, which explains the trend presented in Fig. 4. However, this correlation between NBO/T and Hv is not valid for all silicate glass systems. It has been shown for basaltic glasses that an increase in NBO/T can cause both an increase and a decrease of hardness. The same study found that addition of MgO to the glass increases the hardness, whereas addition of Na2O has the opposite effect [37]. To further explore the effect of network-modifying cations on hardness, the hardness of both 68SiO2–8Na2O–1Fe2O3–23RO glasses 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 effect of NBO/T on hardness. The decrease in Hv with increasing radius of R2+ ions is explained by a weakening of the overall
network structure because an increase of radius leads to a decrease in the field strength of the R2+ ions. Hence, the attraction of R2+ ions to their surrounding structural groups of [SiO4] tetrahedra is reduced. Therefore, it seems that the R–O bond strength plays a decisive role in controlling hardness in the alkaline earth glass series. The alkali ions are not as strongly associated with the glass network as the alkaline earth ions. With increasing radius of M+ ions, a strengthening of the Si–O bonds occurs, which is caused by a weakening of the M–O bonds. Besides affecting the chemical bonding, the alkali ion also affects the structural density. It has been found that the glass densities of the glasses containing Na and K are identical even though a potassium ion weighs almost doubly as much as a sodium ion [29]. The reason for the identical glass densities must be that the structural density increases with decreasing radius of the alkali ion, and thereby, compensates the decreased mass of the alkali ion. Hence, the increase in Hv with increasing radius of M+ ions is attributed to the strengthening of Si–O bonds. This finding is in contradiction to the calculation approach of the hardness of crystalline materials. In the crystalline materials, the weak bonds are of greater importance to Hv than the strong bonds since the former ones break before the latter ones during load [7,12]. Thus, the principles of the calculation of hardness of crystalline materials cannot be transferred to amorphous materials. The evaluation of hardness of glasses is complex due to a broader distribution of bond lengths and in particular bond angles compared to crystals. As demonstrated in this work, the principles of the hardness calculation method developed for crystals only partly hold for glasses. As shown in Fig. 3, annealing (and hence, Tf and structural density) leads to a pronounced increase of the hardness of glasses for a given composition. However, an increase in sodium content increases the glass density because sodium ions occupy interstitial positions within the network. Therefore, sodium could be believed to increase the hardness, but in fact, the hardness decreases due to the weakening of bond strength as a result of the change in composition (Fig. 4). This again indicates the complexity of evaluation of hardness as different factors (degree of polymerization, bond strength, fictive temperature, etc.) may counter one another. Even though NBO/T is a valuable parameter for describing the glass network connectivity, it cannot be used for the prediction of hardness and hence, the development of a universal hardness calculation method is a challenge. However, within a given glass system, the effect of compositional change of glasses with similar thermal history on hardness can be qualitatively predicted.
5. Conclusion Both thermal history and chemical composition affect the hardness of silicate glasses. Annealing lowers the fictive temperature and thereby improves the structural density of glasses. This leads to an increase of hardness. The effect of network-modifying ions on hardness differs between alkali and alkaline earth ions. For alkali ions, hardness increases with increasing ionic radius, whereas the opposite trend is observed for alkaline earth ions. Therefore, the structural changes of the network occurring at the atomic scale must be taken into consideration when predicting the effect of composition on hardness.
Acknowledgements The authors thank J. Holm, T.R. Andersen, T. Madsen, K.H. Nielsen, and E.M. Nielsen for experimental assistance. They also thank X.J. Guo for useful discussions.
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