Effect of Al2O3 content on the mechanical and interdiffusional properties of ion-exchanged Na-aluminosilicate glasses

Journal of Non-Crystalline Solids 458 (2017) 129–136

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Effect of Al2O3 content on the mechanical and interdiffusional properties of ion-exchanged Na-aluminosilicate glasses C. Ragoen a,⁎, S. Sen b, T. Lambricht c, S. Godet a a b c

Université Libre de Bruxelles, 4MAT Department, CP165/63, Avenue F. Roosevelt 50, B-1050 Brussels, Belgium University of California at Davis, Dept. of Materials Science & Engineering, Davis, CA 95616, USA AGC Glass Europe, Technovation Centre, Rue Louis Blériot 12, B-6041 Gosselies, Belgium

a r t i c l e

i n f o

Article history: Received 9 September 2016 Received in revised form 14 December 2016 Accepted 18 December 2016 Available online xxxx Keywords: Glass Aluminosilicate Diffusion Chemical tempering Structure Ion exchange

a b s t r a c t The effect of the variation in the Al2O3 content on select physical properties of pristine and ion-exchanged glasses in the systems: (75 − x)SiO2mol%-25Na2O-xAl2O3 and (75 − x)SiO2-15Na2O-10CaO-xAl2O3, are reported. The surface compressive stress, surface hardness and K+/Na+ exchange ratio increase, while the depth of the interdiffusion distance decreases, with increasing Al2O3 content. These trends are shown to be consistent with the compositional variation of the glass transition temperature and the molar volume, and their atomistic and thermodynamic bases are discussed. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Chemical strengthening via ion exchange is commonly used in the industry to improve both the mechanical strength and the scratch resistance of glasses. The ion exchange process involves replacing smaller host alkali ions such as Na+ in the glass with larger ions such as K +, in a molten salt bath at a temperature below the glass transition temperature Tg. This process results in the formation of an ion-exchanged region near the glass surface that is under significant compressive stress, which tremendously improves the mechanical resistance of the glass [1,2]. Over the last decade, the increasing demand of highly damage resistant touch-screens has renewed the interest in the chemical strengthening process. However, the major drawback of this process is the high production cost due to the long timescale associated with the ion-exchange step. Nevertheless, a compromise between the production cost and the product quality can be struck by suitable adaptation of the bulk glass composition, which has led to the introduction of mechanically resistant commercial products such as the Asahi Dragontrail™, Corning Gorilla Glass™ and Schott Xensation™ [3]. All these products are based on alkali aluminosilicate glasses. It is well known that the alkali oxide: alumina ratio R is an important compositional parameter that controls the structure⁎ Corresponding author. E-mail address: [email protected] (C. Ragoen).

http://dx.doi.org/10.1016/j.jnoncrysol.2016.12.019 0022-3093/© 2016 Elsevier B.V. All rights reserved.

properties relationship in these glasses. Therefore, an understanding of the effect of R on the ion-exchange process parameters will allow optimization of the mechanical properties of these glasses. Previous studies in the literature primarily focused on the effect of R on self-diffusion of Na+ in silicate glasses [4,5,6]. However, little is known regarding the effect of R on the Na+-K+ ion-exchange in alumino-silicate glasses with the exception of the study of Burggraaf and Cornelissen [7], which was based on a rather limited set of compositions and R values. Na diffusion and Na +-K+ interdiffusions have been already studied in glasses with two network formers in the Na2O-B2O3-SiO2 glass system [8,9]. In (Na2O)0.2-(B2O3)y-(SiO2)0.8 − y glasses and at constant temperature, the Na tracer diffusion coefficient decreases as the B2O3 content (y) increases [8]. According to Wu et al. [8], the change in the glass structure may be one explanation of this decrease. In the present study, we report the results of a systematic investigation of the effect of R on the properties of ion-exchanged glasses in the systems (75 − x)SiO 2 mol%-25Na2 O-xAl2 O 3 (0 ≤ x ≤ 25) and (75 − x)SiO2-15Na2O-10CaO-xAl2O3 (5 ≤ x ≤ 15). In particular, this study focuses on the compositional dependence of the interdiffusional properties of Na + and K + and of the mechanical properties of the ion-exchanged glasses, such as the surface compressive stress and the surface hardness to establish the corresponding relationships between these properties and the atomic structure of these glasses.

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2. Experimental methods 2.1. Glass synthesis The nominal glass compositions investigated in the present study are shown in Fig. 1. These glasses are characterized by different R = [Na2O] / [Al2O3] or ([Na2O] + [CaO]) / [Al2O3] ratios and were synthesized from constituent oxide and carbonate precursors: SiO2 (Alpha products 99.5%), Al2O3 (Ceram Tm incorporated 99.5%), Na2CO3 (VWR 99.7%), CaCO3 (Merck 99.5%). Approximately 300 g batches were melted in platinum/rhodium crucible between 1450 °C and 1650 °C for 2 h depending on the composition. The melt was then quenched and the resulting glass was crushed and remixed followed by remelting for two additional hours to facilitate homogenization. The final melts were subsequently quenched on a graphite plate and annealed for 12 h at the respective Tg, in order to release the internal stresses. The resulting glass compositions were analyzed by inductively coupled plasma mass spectrometry (ICP OES, Varian Vista MPX). The analyzed compositions are observed to be within ±1 mol% of the target compositions (see Table 1 and Fig. 1). 2.2. Density measurements

Table 1 Nominal compositions (mol%) and non-bridging oxygen per Si + Al atoms (NBO/T) for all glasses synthesized in this study. Glass

SiO2

Na2O

1 2 3 4 5 6 7 8 9 10 11

75 72 70 68 65 60 55 50 70 65 60

25 25 25 25 25 25 25 25 15 15 15

CaO

Al2O3

NBO/T

10 10 10

0 3 5 7 10 15 20 25 5 10 15

0.666 0.564 0.500 0.439 0.353 0.222 0.105 0.000 0.500 0.353 0.222

constant thickness (4.1 mm) and widths and lengths varying between 12 and 15 mm and 36 and 38 mm, respectively, were used. The IET technique consists in measuring the resonant frequency and the damping or internal friction of the glass samples [12]. The Young's and shear moduli are calculated using the relation [12]: 2 3

E ¼ 0:9465

mf f l wt3

T

The densities of the glasses were determined at ambient temperature using the Archimedes' method with ethanol as the immersion medium. Reported densities are averages of three consecutive measurements on 3–5 g samples and are determined to within ±0.02 g/cm3. The free molar volume was evaluated by the difference between the corresponding molar volume of the glass and the minimum theoretical volume occupied by the ions (ionic volume) [10]. Shannon's ionic radii were used to calculate the ionic volume [11]. The coordination number of Na was assumed to be 6, 2 for O and 4 for Al and Si.

where E and G are Young's modulus and shear modulus, respectively, m is the mass, l is the length of the sample, w = width, t is the thickness, ff and ft are, respectively, the flexural and torsion frequencies and T, A, B are all correction coefficients as defined in [12]. The measurements were performed at room temperature and the moduli were determined to within ±0.7 GPa.

2.3. Thermal analysis

2.5. Surface hardness

Thermal analysis (DTA, Netzch STA 409 PC) was carried out to determine the glass transition temperature. Measurements were performed under helium atmosphere on 40–50 mg of glass powder taken in alumina crucibles. The Tg was determined to within ±2 °C, as the inflection of the glass transition region, using a heating rate of 25 °C/min.

The surface hardness of the pristine and the ion-exchanged glasses was measured by nanoindentation. Patterns consisting of 25 indents separated by 5 μm were recorded on the glass surfaces. The measurements were conducted with a Hysitron TriboIndentor equipped with a Berkovitch diamond tip. The load cycle consisted in loading from 0 to 3000 μN in 10 s, maintaining the load for 5 s before unloading over a period of 10 s. The surface hardness was calculated using the Olivier and Pharr method [13]:

2.4. Young's and shear modulus measurements The Young's modulus and the shear modulus of the Na-aluminosilicate pristine glasses were determined using the impulse excitation technique (IET, IMCE RFDA professional). Rectangular samples with

2

G¼

H¼

4lm f t B wt 1 þ A

P max A

Fig. 1. Glass compositions (mol fraction) in the SiO2-Na2O-Al2O3 ternary system (a) and in the SiO2-Na2O-CaO-Al2O3 quaternary system (b), synthesized in the present study.

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with Pmax corresponding to the peak indentation load and A is the projected area of the hardness impression, as described in [13]. The surface hardness is determined to within ±0.15 GPa. 2.6. Ion-exchange and related measurements 2.6.1. Ion-exchange process Polished glass samples of dimension 4 cm × 4 cm × 4.1 mm were taken in a stainless steel rack and pre-heated from room temperature to 370 °C over a period of 1.5 h. Subsequently, the rack with the samples was immersed for up to 8 h in the molten salt tank that contained 2.2 tons of KNO3 at the desired temperature. In this study, the glasses were ion-exchanged at three temperatures: 400 °C, 430 °C and 460 °C. At the end of ion-exchange, the samples were removed from the bath and cooled to room temperature and then washed in water. 2.6.2. Interdiffusion characterization The ion-exchanged samples were cut and the cross section was embedded in resin, polished down to 3 μm using abrasive polishing pads and cerium oxide. In order to avoid charging effect, these samples were coated with a thin carbon coating. The K profiles (atom%) were determined by Energy Dispersive X-ray spectroscopy in a scanning electron microscope (FEG-SEM, Hitachi SU 70). The K profiles were obtained by performing line scans from the surface to a desired depth in the material. The measurements were performed with an accelerating voltage of 15 kV and a dwell time of 2 s. Based on the K profiles, the depth of layer values (DOL) and the interdiffusion coefficients for the glasses belonging to the SiO2-Na2O-Al2O3 glass system were calculated. At the DOL value, the potassium content is constant and within the detection limit of the measurements system. The alkali interdiffusion coefficients as a function of local composition were computed using the Boltzmann-Matano expression [14]: 3 2
C t 4 ∫ 0 xdC 5 dC DðcÞ ¼ − 2 dx C

2.6.3. The differential surface refractometry measurements The DOL and the surface compressive stress for the glasses belonging to the SiO2-Na2O-CaO-Al2O3 system were evaluated by photoelasticimetry (differential surface refractometry, Toshiba FSM7000H). This technique is a non-destructive method that takes advantage of the stress induced optical birefringeance of the chemically tempered glasses. The compressive stress and the DOL were obtained from the fringe patterns according to [15,16]: σ¼

Fig. 2. Glass transition temperature as a function of mol% Al2O3 for pristine Na (filled triangles) and Na, Ca (open diamonds) – aluminosilicate glasses. Errors are smaller than symbol size.

in [17] for the ternary system. The Tg increases monotonically with Al2O3 content, for both composition series. The substitution of a part of the Na2O content by CaO in the second composition series induces an increase in Tg by about 100 °C (Fig. 2). The molar volume of the pristine glasses also increases with the Al2O3 content, nearly linearly for both composition series, (Fig. 3). For a fixed Al2O3 content, the partial substitution of Na2O by CaO in the second composition series results in a decrease in the molar volume by ~0.8 cm3/mol. The Young's modulus E of the pristine Na-aluminosilicate glasses increases linearly with the Al2O3 content from ~60 GPa in the 75SiO225Na 2 O glass to ~ 71 GPa for the glass 60SiO 2-25Na 2O-15 Al2 O 3 (Fig. 4(a)). Yoshida et al. obtained results in the same order of magnitude [17]. The shear modulus of these Na-aluminosilicate glasses increases with the alumina content (Fig. 4(d)). As shown in Fig. 4(b, c), E of these glasses also increases linearly with the molar volume and the average bond strength ΣGi *x i . The average bond strength is estimated by the sum of Gi*xi for all the oxides present in the glass where, Gi is the dissociation energy of a given oxide per unit volume [18] and xi is mole fraction of the ith oxide in the glass.

3.2. Interdiffusion behavior The K concentration profiles for Na-aluminosilicate glasses, that were ion-exchanged for 8 h at 460 °C, are shown in Fig. 5. It is clear from Fig. 5 that the rate of decay of the K profile with depth in these

Δn0 C

DOL ¼

0:26N Δn

with Δ n0 being the birefringeance very close to the surface, C is the photoelastic constant of glass at the surface, N is the number of fringes counted in the part of the fringe pattern with the widest area of fringe distribution and Δ n is the difference in refractive index between the surface and the interior of the sample. The constant value of 2.69 TPa−1 was used for the whole set of samples [16]. The surface compressive stress was determined to within ±40 MPa. 3. Results 3.1. Thermophysical and elastic properties of pristine glass The compositional variation of Tg of the pristine glasses is shown in Fig. 2. It is worth mentioning that similar results have been observed

Fig. 3. Molar volume as a function of mol% Al2O3 for pristine Na (filled squares) and Na,Ca (open diamonds) – aluminosilicate glasses.

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Fig. 4. Young's modulus of pristine Na-aluminosilicate glasses as a function of mol% Al2O3 (a), average bond strength (b), molar volume (c) and shear modulus as a function of mol% Al2O3 (d).

glasses increases rapidly with the Al2O3 content. Moreover, the atomic fraction of K+ at the glass surface increases with the Al2O3 content. The evolution of the DOL in these glasses with the Al2O3 content is shown in Fig. 6 for different ion exchange temperatures. As expected, for a given composition, the DOL increases with temperature. On the other hand, for a given temperature, the DOL decreases with increasing Al2O3 content of these glasses. Moreover, the temperature dependence of the DOL increases with decreasing Al2O3 content. The effect of the addition of CaO in the glass composition on the DOL is shown in Fig. 7. In comparison to the SiO2-Na2O-Al2O3 glass system, the DOLs are drastically reduced when CaO is introduced and no significant effect of the alumina content on the DOL values can be observed. Fig. 8 shows the variation of the concentration dependent interdiffusion coefficients calculated using the Boltzmann-Matano equation, for the glasses belonging to the SiO2-Al2O3-Na2O glass system that were ion-exchanged at 460 °C. It is clear that the interdiffusion coefficients in these glasses decrease with increasing Al2O3 content, a result that is

consistent with the data presented in Fig. 6 that shows a corresponding decrease of the DOL.

3.3. Mechanical properties The composition dependence of the surface compressive stress in ion-exchanged Na-Ca-aluminosilicate glasses is presented in Fig. 9 for the three tempering temperatures. The surface compressive stress increases with the alumina content and with the decrease in the ion-exchange temperature. It is interesting to note that the temperature dependence of the compressive stress decreases monotonically with increasing Al2O3 content. Indeed, there is a 466 MPa difference in the compressive stress for ion exchange at 400 °C and 460 °C for the 5 mol% Al2O3 glass while this difference decreases to about 90 MPa for the 15 mol% Al2O3 glass.

Exchange rate=CK/CK+CNa

1 0.9 0.8 0.7 0.6

0% Al2O3

0.5

7% Al2O3

0.4

15% Al2O3

0.3 0.2 0.1 0 0

50

100 150 200 250 Interdiffusion distance (µm)

300

350

Fig. 5. Exchange rate vs. interdiffusion distance for the glasses 75SiO2-25Na2O, 68SiO225Na2O-7Al2O3 and 60SiO2-25Na2O-15Al2O3 after ion exchange for 8 h at 460 °C.

Fig. 6. Depth of the interdiffusion layer as a function of mol% Al2O3 for SiO2-Na2O-Al2O3 glasses ion exchanged for 8 h at 400 (crosses), 430 (open squares) and 460 °C (filled circles). Errors are smaller than symbol size.

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Fig. 7. Depth of the interdiffusion layer as a function of mol% Al2O3 for SiO2-Na2O-CaOAl2O3 glasses ion exchanged at 400 (crosses), 430 (open squares) and 460 °C (filled circles) for 8 h.

Fig. 9. Surface compressive stress vs. mol% Al2O3for SiO2-Na2O-CaO-Al2O3 glasses ion exchanged at 400 (crosses), 430 (open squares) and 460 °C (filled circles) for 8 h. Errors are smaller than symbol size.

The surface hardness of the Na-aluminosilicate glasses before and after ion exchange is compared in Fig. 10. It is clear that the surface hardness increases upon ion exchange but this effect becomes progressively weaker with increasing Al2O3 content. It is noteworthy that the hardness of the pristine glasses does not change significantly with increasing Al2O3 content to up to 5 mol%, while at 7 mol% of Al2O3, there is a sudden increase in the hardness. A progressive increase of the Vickers hardness together with the Al2O3 content of the pristine glasses was also observed in the literature [10,17]. The effect of the addition of CaO on the surface hardness of ion-exchanged glasses is shown in Fig. 11. Similar to the Na-aluminosilicates, there is an increase in the surface hardness with increasing Al2O3 content. The hardness of the ion-exchanged glasses increases with increasing temperature of treatment but this difference is more pronounced for the glass containing 5 mol% of Al2O3 than for the other two compositions with higher Al2O3 content.

in the R value lowers the number of non-bridging oxygen atoms (NBO) and thereby, increases the network connectivity. On the other hand, for a fixed Al2O3 content, Tg increases with the substitution of Na2O by CaO (Fig. 2), which can be ascribed to the increase in the average bond strength of the network. This effect results from the fact that the bonding between Ca2 + and NBO is stronger than that between Na+ and NBO, owing to the higher field strength of Ca2+ compared to that of Na+ [19]. The decrease in the R value leads to an increase in the free volume available and hence, to an opening of the glass framework (cf. Fig. 12). Indeed, increasing connectivity of a tetrahedral aluminosilicate network is expected to result in an open framework structure consisting of interconnected rings made of corner-sharing AlO4 and SiO4 tetrahedra. On the other hand, the observed decrease in the molar volume of these glasses upon substitution of Na2O by CaO (cf. Fig. 3) can be attributed to the higher field strength of Ca2 + ions that leads to average Ca\\O bond distances that are shorter than Na\\O bond distances [19]. According to Makishima and Mackenzie [18] and Veit and Rüssel [20], Young's modulus depend both on the atomic packing density and the average strength of the chemical bonds in the glass (ΣGi*xi). Rouxel [21] adds that the coordination and the glass connectivity also influence Young's modulus. As shown in Fig. 4(a), Young's modulus increases with increasing Al2O3 content as the NBO concentration decreases. These results are consistent with the effect of the glass connectivity on Young's modulus. Indeed, the higher the NBO

4. Discussion 4.1. Pristine glasses

Interdiffusion coefficients (cm 2/s)

There are two main compositional parameters that influence the Tg. The first one is the R ratio and the second is the substitution of Na2O by CaO. The Tg is known to be controlled by the overall bond strength and by the network connectivity [19]. Hence, the observed increase of the Tg values with the Al2O3 content (Fig. 2) can be immediately explained by the increase of the network connectivity, as it is well known that addition of Al2O3 to an alkali or alkaline-earth silicate glass i.e. a decrease 1.4E-09 1.2E-09 1E-09 0% Al2O3

8E-10

7% Al2O3

6E-10

15% Al2O3

4E-10 2E-10 0

0

0.2

0.4 0.6 0.8 Exchange rate= CK/(CK+CNa )

1

Fig. 8. Dependence of interdiffusion coefficient on exchange rate for SiO2-Al2O3-Na2O glasses with 0, 7 and 15 mol% Al2O3, ion exchanged at 460 °C. Corresponding symbols are shown in the inset.

Fig. 10. Surface hardness of pristine (short dashes) and ion-exchanged (crosses and circles) SiO2-Na2O-Al2O3 glasses as a function of mol% Al2O3. Ion exchange was carried out for 8 h at 400 °C (crosses) and at 460 °C (circles).

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Fig. 11. Surface hardness of ion-exchanged (crosses and circles) SiO2-Na2O-CaO-Al2O3 glasses, as a function of mol% Al2O3. Ion exchange was carried out for 8 h at 400 °C (crosses) and at 460 °C (circles).

Fig. 13. Surface compressive stress in SiO2-Na2O-CaO-Al2O3 glasses, as a function of ΔT. Ion exchange was carried out for 8 h at 400 °C (crosses), 430 °C (filled diamonds) and 460 °C (open squares). Errors are smaller than symbol size. The dashed line is a guide for the eye.

concentration, the lower the network connectivity will be and consequently, the weaker the network. Fig. 4(b), on the other hand, highlights the effect of the average bond strength of the glass on Young's modulus as the latter increases monotonically with increasing average bond strength. Another parameter that according to Veit and Rüssel and Makishima and Mackenzie must influence the Young's modulus is the atomic packing density [18,20]. It is considered that the higher is the packing density, the higher will the elastic modulus and, as the packing density is inversely proportional to the molar volume, the elastic modulus should decrease with an increase of the molar volume. However, in this study, the opposite trend is observed (see Fig. 4(c)), indicating that the network connectivity and average bond strength play a dominant role in controlling the Young's modulus.

process. This effect is highlighted in Fig. 13, where the surface compressive stress is plotted as a function of the difference between the Tg and Tex, denoted as ΔT = Tg − Tex. It is clear from Fig. 13, that higher the ΔT, the higher is the surface compressive stress, since stress relaxation is increasingly hindered as the system moves further from equilibrium at the transition point. As an increase in the Al2O3 content leads to an increase in Tg and hence in ΔT for a fixed Tex, it explains the corresponding increase in the compressive stress. The surface hardness of the pristine glasses shows an increase with increasing Al2O3 content (Fig. 10), consistent with a concomitant increase in the network connectivity and in the average bond strength [23]. The ion exchange treatment is also responsible for an increase in the glass hardness. According to Koike et al. this effect can be explained by both the increase in density due to the ion-exchange and the developed compressive stress [24]. However, according to them the compressive stress has a small effect on the hardness. As shown in Figs. 10 and 11, the hardness of the glasses ion-exchanged at 460 °C is higher than the one at 400 °C, however, compressive stress measurements indicate that the latter glasses have a higher compressive stress because there is less relaxation (see Fig. 9). Thus, the trend in hardness is likely due to the densification of the surface structure resulting from the structural relaxation during ion exchange. Therefore, although the salt bath is below the glass transition temperature, small rearrangements of the glass structure are possible. Moreover, the ion-exchange process appears to influence the hardness values to a lesser extent when the alumina content increases (see Figs. 10, 11) and the surface compressive stresses are at their maximum. This result could indicate that the glass hardness is influenced more by the average bond strength and the number of rigid bonding constraints associated with the network forming species [23] than by the compressive stress.

4.2. Ion-exchanged glasses 4.2.1. Mechanical properties The observation of an increase in the surface compressive stress with Al2O3 content, in ion-exchanged SiO2-Na2O-CaO-Al2O3 glasses (Fig. 9), can be explained by considering temperature dependent relaxation processes in glasses. Some stress relaxation in glass may occur well below Tg, that involves small rearrangements of the glass structure [22]. The compressive stress results indicate that these structural rearrangements appear more easily in glasses with low Al2O3 content and at higher ion exchange temperatures. The difference between the Tg value of the glass and the ion-exchange temperature Tex is a good indicator of the extent of stress relaxation that can be obtained during the ion-exchange

Fig. 12. Free molar volume for SiO2-Na2O-Al2O3 glasses as a function of mol% Al2O3.

4.2.2. Ion exchange rate Fig. 5 highlights a difference in the extent of Na+ replacement on the surface as a function of the alumina content. For glasses containing 15 mol% of Al2O3 the Na/K exchange ratio is nearly equal to 1, while this rate is close to 0.3 for the glasses without alumina and ion-exchanged at 460 °C. As reported in previous studies [14,25,26], the exchange rate at the surface depends on the thermodynamic activity of the molten salt at the surface. This activity is a function of different parameters such as the temperature, the salt and glass compositions [14]. Since the temperature and the molten salt composition were the same for the different glasses presented in Fig. 5, the glass composition must be responsible for the observed difference in the exchange rates. As the molar volume increases with the Al2O3 content, it is possible that the chemical potential for K+ in the glass decreases with the

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Fig. 14. Depth of layer for the glasses ion exchanged for 8 h at 460 °C, as a function of the alumina content (a), the NBO/T ratio (b), the shear modulus (c), and the Young's modulus (d). Errors are smaller than symbol size.

alumina content as more free volume becomes available for its larger size compared to Na+. 4.3. Structural origin of interdiffusion properties For the glasses belonging to the SiO2-Na2O-Al2O3 glass system, the higher the Al2O3 content or lower the R ratio, the lower is the interdiffusion coefficient (cf. Fig. 5). These results can be contrasted with the known effect of the R ratio on the Na+ self-diffusion in the SiO2-Na2OAl2O3 glass system [6] and on the ionic conductivity of Na+ [4]. Indeed, according to Frischat [6], the addition of small amount of alumina to Nasilicate glass decreases the Na+ self-diffusion coefficient but further addition of alumina leads to an increase of this coefficient until the R ratio is equal to one [6]. It is important to keep in mind that the Na+ and K+ ions exchange with each other to minimize the local build up of electric charge and so the interdiffusion coefficients can be expressed for ideal solution as [6,14,27]: DðC Þ ¼

DNa DK γ Na DNa þ γK DK

glass system. As the R ratio decreases upon addition of Al2O3, the sodium sites near non-bridging oxygens are replaced by those near the AlO4 tetrahedra and the sodium cations present in these two different sites, owing to their different site energies, interact and hinder each other's motion to lower the diffusion coefficient, similar to the mixedalkali effect [4]. When Na+ and K+ are both present, as in the ion-exchanged glasses, there can be four different kinds of alkali sites available and the interaction between these sites should be much more important. Finally, the compressive stress resulting from ion exchange may also influence the interdiffusion [14,28]. In fact, the developed compressive stress will have an effect on the free volume available for ionic motion in the glass and on the energies of the sites available for the diffusion jump [14]. The higher K+ content at the surface of the ion-exchanged glasses with high Al2O3 content (see Fig. 5), gives rise to higher compressive stress at the surface, which could potentially lower the interdiffusion coefficient further for these glasses compared to the ones with lower Al2O3 content.

5. Summary where γNa (γK) is the mole fraction of Na+ (K+) and DNa (DK) is the corresponding self-diffusion coefficient [6,14,27,28]. Therefore, the observed interdiffusion properties can differ from the Na+ self-diffusion and there are several hypotheses that are consistent with the observed variation of the interdiffusion coefficient with the R ratio. The first hypothesis is based on the effect of the elastic modulus on the interdiffusion values. As shown in Fig. 14(c and d), the glasses with the higher values of the elastic moduli are also the one with the lower values of the DOL, which could be a manifestation of the effect of the elastic moduli on the strain energy part of the migration energy for ionic diffusion [29]. Hence, the lower these moduli, the easier it would be for small structural rearrangement required to allow for the migration of mobile ions through the glass structure. As the K+ ions are bigger than the Na+ cations, it is possible that the strain energy becomes the predominant factor controlling the migration of K+. An alternative hypothesis involves the mixed-site effect, originally proposed by Lacourse [4] to explain that the composition dependence of electrical conductivity due to Na+ diffusion in the SiO2-Na2O-Al2O3

The compositional variation of the physical properties such as Tg, molar volume and elastic modulus of the Na and Na,Ca –aluminosilicate glasses can be related to the effect of the Al2O3 content and hence, the R ratio on the network connectivity and the average bond strength. Increasing surface compressive stress of the ion-exchanged glasses with increasing Al2O3 content is shown to be a manifestation of the degree of stress relaxation, which decreases with increasing difference between Tg and Tex. On the other hand, the surface hardness of pristine Na-aluminosilicate glasses increases with the Al2O3 content, consistent with a concomitant increase in the network connectivity and the average bond strength. The ion-exchange is also shown to be responsible of an increase of the surface hardness. High exchange rates were obtained for glasses with high alumina content. Since, the molar volume of these glasses increases with increasing alumina content, the high exchange rates are likely related to a lowering of the chemical potential of K+ in the glass as more free volume becomes available for this large cation.

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