Journal of Non-Crystalline Solids 357 (2011) 3744–3750

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Journal of Non-Crystalline Solids

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Sodium diffusion in boroaluminosilicate glasses

Morten M. Smedskjaer a,1, Qiuju Zheng a,b, John C. Mauro b,⁎, Marcel Potuzak b,Steen Mørup c, Yuanzheng Yue a,⁎⁎a Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmarkb Science and Technology Division, Corning Incorporated, Corning, NY 14831, USAc Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

⁎ Corresponding author. Tel.: +1 607 974 2185; fax:⁎⁎ Corresponding author. Tel.: +45 99408522; fax: +

E-mail addresses: mauroj@corning.com (J.C. Mauro)1 Now at Science and Technology Division, Corning Inc

USA.

0022-3093/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.jnoncrysol.2011.07.008

a b s t r a c t

a r t i c l e i n f o

Article history:Received 25 March 2011Received in revised form 5 July 2011Available online 19 August 2011

Keywords:Sodium diffusion;Boroaluminosilicate glass;Ion exchange;Tracer diffusion;Inward diffusion

Understanding the fundamentals of alkali diffusion in boroaluminosilicate (BAS) glasses is of criticalimportance for advanced glass applications, e.g., the production of chemically strengthened glass covers forpersonal electronic devices. Here, we investigate the composition dependence of isothermal sodium diffusionin BAS glasses by ion exchange, inward diffusion, and tracer diffusion experiments. By varying the [SiO2]/[Al2O3] ratio of the glasses, different structural regimes of sodium behavior are accessed. We show that themobility of the sodium ions decreases with increasing [SiO2]/[Al2O3] ratio, revealing that sodium is moremobile when it acts as a charge compensator to stabilize network formers than when it acts as a creator ofnon-bridging oxygens on tetrahedrally-coordinated silicon and trigonal boron. The impacts of both theaddition of iron and its redox state on the sodium diffusivity are explored in terms of the structural role offerric and ferrous ions. By comparing the results obtained by the three approaches, we observe that both thetracer Na diffusion and the Na–K interdiffusion are significantly faster than the Na inward diffusion. The originof this discrepancy could be attributed to the fact that for sodium inward diffusion, the charge compensationfor electron holes is a rather slow process that limits the rate of diffusion.

+1 607 974 2410.45 96350 558., yy@bio.aau.dk (Y. Yue).orporated, Corning, NY 14831,

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Boroaluminosilicate (BAS) glasses are widely applied in technologiessuch as active matrix liquid crystal display substrates [1], photochromicglass [2], fiberglass [3], and radioactive waste glass [4]. Understandingthe fundamentals of alkali diffusion in BAS glasses is crucial for recenthigh-tech applications of BAS glasses such as high strength ionexchanged glass [5,6] and substrate glass for solar energy conversion[7,8]. Chemical strengthening of glass occurs by an ion exchange processof large alkali ions (e.g., K+) from a molten salt bath with smaller alkaliions (e.g., Na+) in the host glass. This process results in the formation of asurface compressive stress that greatly enhances the strength anddamage resistance of these glasses. Many chemically strengthened glassproducts are commercially available, e.g., as cover glass for personalelectronic devices and televisions [9] or aircraft cockpitwindshields [5,6].Alkali diffusion is also important for photovoltaic cells employing a CIGS(copper–indium–gallium–selenide) semiconductor. Alkali ions such assodium are used as dopants to enhance the hole carrier concentrationand open circuit voltage, and alkali-containing glasses may be used as

the alkali source material [7,8]. However, this requires control of theamount of alkali ions incorporated into the CIGS absorbing layer, i.e.,control of the alkali diffusivity in the glass.

Understanding the sodium diffusion in BAS glasses requires that thestructural role of sodium in those glasses is clarified. Addition of anetwork modifier oxide such as Na2O to pure SiO2 glass results indepolymerization of the silicate network by formation of non-bridgingoxygens (NBOs), whereas addition of Na2O to B2O3 glass initially resultsin the boron anomaly, i.e., conversion of trigonal boron to tetrahedralboron without NBO formation. Further addition of Na2O will cause theformation of asymmetric trigonal boron groups with one NBO and twobridging oxygens (BOs) [10,11]. Aluminum is predominantly present intetrahedral configuration provided that sufficient Na+ is available forcharge-balancing, since there is preference in the formation oftetrahedral Al3+ over that of tetrahedral B3+[12,13]. It is expectedthat the sodiumdiffusivity depends on its structural role in the network.Therefore, it is important to study the diffusion in the three differentregimes of the sodium content: 1) Na+ to stabilize aluminum intetrahedral configuration; 2) Na+ to convert boron from trigonal totetrahedral coordination; and 3) Na+ to form NBOs on tetrahedralsilicon and/or trigonal boron. We approach this problem using aquaternary Na2O–B2O3–Al2O3–SiO2 system, changing the [SiO2]/[Al2O3]ratio to access these different regimes (see Table 1). In a parallel study,we have investigated the structure of this system [14]. These findingswill be reviewed when the diffusion data are discussed.

Table 1Chemical composition, homogenization temperature (Th), density (ρ), glass transition temperature (Tg), fraction of tetrahedral to total boron (N4), iron redox ratio ([Fe3+]/[Fe]tot),and atomic packing factor (APF) of the investigated iron-free and iron-containing glasses.

GlassID

Chemical composition (mol%)a Th ρb Tgc N4

d [Fe3+]/[Fe]tote APFf

SiO2 Al2O3 B2O3 Na2O Fe2O3 (°C) (g/cm3) (°C) (at.%) (at.%) (−)

Al2.5 78.8 2.0 4.7 14.4 – 1450 2.409 549 90 – 0.498Al5 78.1 4.0 4.2 13.6 – 1500 2.406 564 87 – 0.496Al7.5 76.9 5.7 4.3 13.0 – 1550 2.402 578 77 – 0.494Al10 75.9 7.5 4.3 12.3 – 1600 2.392 598 68 – 0.491Al12.5 72.0 10.4 4.4 13.1 – 1650 2.398 614 39 – 0.489Al15 69.2 12.7 4.6 13.5 – 1650 2.384 626 17 – 0.485Al2.5* 77.4 2.2 4.9 14.6 0.9 1450 2.448 543 – 95 –

Al5* 74.7 4.7 5.0 14.6 1.0 1500 2.449 551 – 93 –

Al7.5* 71.8 7.6 4.9 14.7 1.0 1550 2.449 573 – 91 –

Al10* 68.9 10.3 5.0 14.8 1.0 1600 2.433 577 – 87 –

Al12.5* 67.1 12.6 5.0 14.3 1.0 1650 2.419 591 – 83 –

Al15* 64.1 15.6 5.0 14.3 1.0 1650 2.413 631 – 78 –

a Chemical compositions were determined using wet chemistry methods. Besides the listed oxides, the iron-free glasses contain 0.06–0.10 mol% As2O3 as fining agent.b Density at room temperature [14]. The errors of the reported density values do not exceed ±1%.c Glass transition temperature defined as temperature at which equilibrium viscosity is 1012 Pa s [14]. The error in Tg associated with this method is generally 2–3 K.d Boron speciation as determined by 11B MAS NMR spectroscopy [14].e Iron redox ratio as determined by 57Fe Mössbauer spectroscopy. Uncertainty: ±5%.f APF is calculated using Eq. (1).

3745M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 357 (2011) 3744–3750

We compare the sodium diffusion data obtained by three differentapproaches in order to clarify the mechanisms of the alkali diffusionencountered in the three different approaches. The first one is basedon the Na+ and K+ exchange between the Na2O–B2O3–Al2O3–SiO2

glass and a molten KNO3 bath [5,15]. The second one is based on thetraditional 22Na tracer diffusion [16–18]. The 22Na tracer data used inthe present paper are provided byWu et al. [19]. The third approach isbased on the so-called inward diffusion of sodium induced byreduction of Fe3+ to Fe2+[20–22]. While the first two approachesare well established for obtaining diffusivity data, the last one has onlyrecently been established, and therefore has not yet been fullyunderstood. In this study, we aim at getting further insights into theinward diffusionmechanism by comparisonwithmechanisms of boththe ion exchange and tracer diffusion. The inward diffusion of cations(such as Na+) occurs when a polyvalent element (such as iron)containing glass is subjected to a reducing atmosphere at elevatedtemperatures. To charge balance the outward flux (from interiortowards surface) of electron holes [23], an inward diffusion of mobilecations is required [20–22]. The degree of the inward diffusion can bequantified by profiling the elemental concentrations as a function ofdistance from the surface. To study the inward diffusion, we prepareboth iron-containing and iron-free glasses for comparison (Table 1).

2. Experimental procedure

2.1. Sample preparation and characterization

All glasses were prepared by conventional melt quenching method.The batch materials used in glass melting were SiO2, Al2O3, H3BO3,Na2CO3, Fe2O3, and As2O3 powders. 0.1 mol% As2O3 was added as finingagent in the iron-free compositions. The batch materials were mixedand then melted in a covered Pt crucible at different homogenizationtemperatures Th (see Table 1) for 6 h in air. Themelts were quenched inwater, and the resulting glass shards were remelted for another 6 h attheir respective homogenization temperature to ensure chemicalhomogeneity, and finally poured in air. The glasses were annealed for2 h at different temperatures depending on chemical composition. Thechemical compositions of the glasses as reported in Table 1 weredetermined by wet chemistry methods.

The iron redox state in the iron-containing glasseswas determined bytransmission 57FeMössbauer spectroscopy. The spectra were recorded atroom temperature using a conventional constant acceleration spectrom-eter with a source of 57Co in rhodium. Data were acquired for around10 days for each glass due to the relatively low iron content of the

samples. Measurements were performed in the range ±24 mm/s usingthe 14.4 keV radiation. The isomer shifts were recorded relative to α-Femetal at room temperature. A spectrumobtained at 20 Kwas recorded ina closed cycle helium refrigerator. In addition, optical absorption spectraof ~0.79 mm thick samples weremeasured to get further information onthe iron redox state in the glasses. Spectra were recorded in the 300–2500 nm region using a PE 950 (Perkin Elmer) spectrophotometer.

2.2. Diffusion experiments

Ion exchange experiments were conducted to obtain the effectiveinterdiffusion coefficient DNa−K between Na+ and K+. This was done byimmersing polished 25×25×1mm3 samples in a molten salt bath oftechnical grade KNO3 at 410 °C for 8 h. Afterwards, the penetration depthof the potassium ions was measured using an FSM-6000 instrument(Frontier Semiconductor). The K+-for-Na+ ion exchange gives the glasssurface a higher refractive index than the interior, i.e., the surface can actas a waveguide. This is utilized in the FSM instrument to measure thesaturation depth of the refractive index profile, which corresponds to thediffusion depth of potassium [24]. A total of eight FSM measurementswere performed on each sample (using four 90° rotations per face).

Tracer diffusion coefficients of the radioactive isotope 22Na wereobtained by Wu et al. [19] by measuring residual radioactivities as afunction of the distance (A(x)) from the surface of as-prepared samples.The tracer was in the form of an aqueous chloride solution and applied toone large surface of a sample by using a syringe. After drying at roomtemperature, the glass sample was transferred into a tube furnace fordiffusion-annealing at a preset temperature (300 °C) in dry air at 1 atmtotal pressure. After diffusion-annealing, about 1 mm of sample materialwas groundoff fromeachedgeof the sampleperpendicular to the surface,where the tracer had been applied. This was done in order to eliminateany influence of surface diffusion on the experimental results. A highresolution high-purity Ge detector (EG&G Ortec) was used to measureresidual radioactivities related to the two energies (0.51 and 1.28 MeV)associated with the γ-radiation resulting from the decay of 22Na [25].Residual radioactivity profiles, A(x)/A(x=0), were obtained by measur-ing the initial radioactivity of a sample, A(x=0), and residual radioac-tivities of the sample, A(x), after stepwise removing material with thethickness xparallel to the surface,where the tracerwas originally applied.More details of this procedure can be found elsewhere [19].

Finally, we also studied the inward diffusion of sodium in the iron-containing glasses. To do so, we first subjected cylindrical samples(10 mm diameter; 3 mm thickness) with one polished surface to heat-treatment in a H2/N2 (1/99 v/v) atmosphere for 16 h at 575 °C. Then the

-24 -18 -12 -6 0 6 12 18 24

Velocity (mm/s)

Rel

ativ

e ab

sorp

tion

Al2.5*

Al5*

Al7.5*

Al10*

Al12.5*

Al15*

Fig. 1. 57Fe Mössbauer spectra of the iron-containing glasses obtained at roomtemperature. The narrow Fe2+ (green curves) and Fe3+ (red curves) doublets as well asthe broad Fe3+ singlets (blue curves) are shown. The black curve represents the sum ofthe three components.

3746 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 357 (2011) 3744–3750

change in chemical composition of the surface region due to inwarddiffusion was determined by means of secondary neutral massspectroscopy (SNMS). SNMS measurements were carried out on anINA-X (SPECS) instrument equipped with a QMG 422 (Balzers In-struments) quadrupole mass spectrometer and a SEM SEV18 (Phillips)amplifier. The analyzed area had a diameter of 8 mmandwas sputteredusing Kr plasma with energy of 350 eV. The time dependence of thesputter profileswas converted into depthdependence bymeasuring thedepth of the sputtered crater at 12 different directions on the samesamplewith a P1 (Tencor) profilometer. From the surface concentrationprofiles, the sodium inward diffusion depth can be determined as thedepletion depth of sodium in the surface region.

3. Results

3.1. Network structure and atomic packing

The structural role of sodium depends on the [SiO2]/[Al2O3] ratio.Since all of the glasses under study are peralkaline, there is sufficientNa+ available to stabilize all aluminum in 4-fold coordination in all ofthe glasses (besides Al15*, which contains 14.3 mol% Na2O and15.6 mol% Al2O3). Hence, aluminum speciation is essentially unaffectedby glass composition as evidenced by 27Al MAS NMR spectroscopy onthe iron-free glasses, i.e., aluminum is four-coordinated in all glasses[14]. The additional Na+ ions not used for stabilizing aluminum intetrahedral configuration are either used for varying the boroncoordination change or for forming NBOs on tetrahedral silicon ortrigonal boron. By using 11B MAS NMR spectroscopy, we have foundthat the fraction of tetrahedral to total boron (N4) depends on the[SiO2]/[Al2O3] ratio [14]. In the low Al2O3 region, most of the boron ispresent in 4-fold coordination, and N4 then gradually decreases withdecreasing [SiO2]/[Al2O3] ratio (Table 1).

Besides the impact of the structural role of sodium on its diffusivity,the openness of the glass network should also be considered wheninterpreting the sodium diffusion data. For high atomic packingfractions, a highmechanical strainwill be imposed upon ionic transport,which will lower the diffusivity. To characterize the openness of thenetwork, we calculate the atomic packing factor (APF), i.e., the ratiobetween theminimum theoretical volume occupied by the ions and thecorresponding molar volume of the glass, as [26]

APF = ρ∑fiVi

∑fiMið1Þ

for the ith constituentwith the formula AxBy.ρ is thedensity, fi themolarfraction,Mi themolarmass, and Vi=(4/3)πNa(xrA3+yrB

3) the theoreticalvolume,where rA and rB are the ionic radii andNa is Avogadro's number.APF can then be calculated from the measured densities (see Table 1)and by using the effective ionic radii given by Shannon [27] for theappropriate coordination number. The composition dependence of APFis calculated and given in Table 1 for the iron-free glasses, since we onlyknow the boron speciation in those glasses. APF slightly increases withincreasing [SiO2]/[Al2O3] ratio.

3.2. Iron redox state

Iron exists primarily as Fe2+ and Fe3+ in glasses and can be present in4-, 5-, or 6-fold coordination. To compare the three processes involvingsodium diffusion, we must determine the [Fe3+]/[Fe2+] ratio in the as-prepared iron-containingglasses, since it is a crucial factor influencing theextent of Fe3+ reduction, and hence, that of the sodium inward diffusion[20]. To obtain this ratio, 57Fe Mössbauer spectra of the as-preparedsamples were obtained as shown in Fig. 1. The spectrum of each glasscontains an Fe2+ doublet and an Fe3+ doublet, both with narrow lines,and a very broad Fe3+ component. Similar broad Fe3+ components havebeen observed in earlier room temperature Mössbauer studies of silicate

glasses with low concentrations (≤5 mol%) of Fe [e.g., 28–31], and havebeen attributed to paramagnetic Fe3+ ions with relaxation time (τ) onthe order of a few nanoseconds. In general, the paramagnetic relaxationtime is determined by the combined effects of concentration-dependentspin–spin relaxation and temperature-dependent spin–lattice relaxation[29,32]. At 4.2 K, the broad Fe3+ components are transformed to sextets[29,30]. This indicates that the room temperature spectra are influencedby spin–lattice relaxation, which becomes slow (τ≥10−8 s) at 4.2 K. Therelative area of the broad Fe3+ component decreaseswith increasing ironconcentration [29,31]. It is noteworthy that spectra obtained at 4.2 K,where the spin–lattice relaxation is expected to be slow, still contain anFe3+ doublet with narrow lines. This suggests that some of the Fe3+ ionshave fast spin–spin relaxation,which can be explained by the presence ofiron-rich clusters. Electron spin resonance studies have in fact indicated atendency for clustering of Fe3+ ions in alkali-containing silicate glasses[e.g., 33,34]. In accordance with this, Weigel et al. [35] found by high-resolution neutron diffraction combined with structural modeling thatfive-coordinated iron atoms in such glasses tend to form clusters,whereas four-coordinated iron atoms are randomly distributed.

The presence of the broad component complicates the fitting of thespectra and hence, the determination of the [Fe3+]/[Fe]tot ratio, where[Fe]tot=[Fe2+]+[Fe3+]. If spectra are obtained in a small velocity range,the estimated [Fe3+]/[Fe]tot ratios may be erroneous [29,31]. Therefore,we recorded Mössbauer spectra in a large velocity range (±24 mm/s)although this gives a limited resolution of the components with narrowlines in thecentralpart of the spectra. Eachof the spectra arefitted to twodoublets with narrow Lorentzian lines with pairwise identical linewidths and line intensities. The Fe2+ components have isomer shiftsaround 1.0 mm/s and quadrupole splittings around 2.1 mm/s, whereasthe Fe3+ components have isomer shifts around 0.40 mm/s andquadrupole splittings around 0.80 mm/s. The broad component is fittedto a single Lorentzian line with line width around 15 mm/s and isomershift around 0.30 mm/s. A spectrum of Al5* obtained at 20 K shows thatthe broad Fe3+ component has transformed to a magnetically split

0 50 100 150 200 250

x /(

0.0

0.5

1.0

1.5

2.0

erfi[

1-A

(x)/

A(x

=0)

]

0.51MeV

1.28MeV

22Na in glass Al10*

T=300 oCair,1 atm

t=90,741s

0 140 280 420 560 7000.2

0.4

0.6

0.8

1.0

1.2B

Na

Al

O

c/c

bulk

Depth (nm)

Si

a

b

Fig. 3. Determination of diffusivity. (a) Inverse of the error function (erfi) of theargument 1-A(x)/A(x=0) as a function of the thickness of removed layers (x) for a 22Natracer diffusion experiment of the Al10* glass [19]. (b) SNMS concentration profile atthe surface of the heat-treated Al12.5* glass used to determine the sodium inwarddiffusion depth. The curves are plotted as concentration of a given element at givendepth divided by the concentration of that element in the bulk of the glass (c/cbulk) as afunction of depth.

3747M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 357 (2011) 3744–3750

component, but the spectrum still contains a Fe3+ component withnarrow lines as in earlier Mössbauer studies of alkali-containing silicateglasses with low iron concentrations [29,30]. This indicates that some ofthe Fe3+ ions have formed clusters with fast spin–spin relaxation. OurMössbauer measurements were performed at lower temperatures thanour alkali diffusivity measurements. Hence, such clustering of iron ionsmay have occurred during the cooling of the glass-forming liquids, i.e.,they may not be present at elevated temperatures.

We find that the narrow Fe3+ component constitutes ~25% in allsamples, whereas the broad component constitutes ~70% in Al2.5* andthen gradually decreases to ~50% in Al15*. Consequently, the [Fe3+]/[Fe]tot ratio increases with increasing [SiO2]/[Al2O3] ratio (Table 1).This composition dependence of the iron redox state is supported byoptical absorption spectroscopy measurements (Fig. 2). The intensity ofthe absorption band in the near infra-red region due to a d–d transitionof Fe2+ (between 600 and 1700 nm) decreases with increasing [SiO2]/[Al2O3] ratio. Only the Al15* sample does not follow this trend. However,it should be mentioned that iron absorption coefficients may differ fromone composition to another, i.e., peak intensities may not be directlyproportional to ionic concentrations.

The optical basicity parameter (Λm) describes the negative chargedonating ability of oxygen in oxide glasses. The concept is commonlyapplied for explaining the composition dependence of redox states ofpolyvalent elements in oxide glasses [36–38]. Glasses with highervalues of Λm generally favor the higher charged cations. However, Λm

decreases with increasing [SiO2]/[Al2O3] ratio [38]. Instead, theincrease of [Fe3+]/[Fe]tot ratio with increasing [SiO2]/[Al2O3] ratiomay be explained by the decrease in the employed melt homogeni-zation temperature Th with increasing [SiO2]/[Al2O3] ratio (seeTable 1).

3.3. Determination of diffusivity

The tracer diffusion coefficient of sodium DNa* is determined bydepth profiling the radioactivity A(x) of the sample. The normalizedresidual radioactivity as a function of depth can be described as [39],

A xð ÞA x = 0ð Þ = 1−erf

Δx2

ffiffiffiffiffiffiffiffiffiffiD�Nat

p !

; ð2Þ

where t is the diffusion time. DNa* can then be calculated from the slopein a plot of the inverse function of the error function (erfi) of theargument 1-A(x)/A(x=0) as a function of thicknessΔx (when a=erf(b),b=erfi(a)). For example, Fig. 3(a) shows this plot for theAl10* glass. Thisprocedure for determiningDNa* is described inmore detail elsewhere [19].In Fig. 4(a), the sodium tracer diffusion coefficient is plotted as a function

300 800 1300 1800 23000.0

0.2

0.4

0.6

0.8

Al15*

Al12.5*

Al10*

Al7.5*

Al5*

Abs

orba

nce

Wavelength (nm)

Al2.5*

Fig. 2. UV–VIS–NIR absorption spectra of the iron-containing glasses of ~0.79 mmthickness. The broad peak between 600 and 1700 nm is due to a d–d transition of Fe2+.

of [SiO2]/∑[Oxi],where∑[Oxi]=[SiO2]+[Al2O3]+[B2O3]+[Fe2O3]+[As2O3]. Theerrors of the tracerdiffusioncoefficients values are estimatedto be around 5% [40].

In the classical description of mutual diffusivity during an ionexchange process, the interdiffusion coefficient DNa−K is given by theNernst–Planck equation,

DNa−K =DNaDK

DNaNNa + DKNK; ð3Þ

where Ni and Di are the fractional concentration and self-diffusioncoefficient of alkali ion i, respectively. This equation is only valid underthe assumption of thermodynamic ideality, i.e., ∂ ln ai/∂ ln ci=1,where ai and ci are the thermodynamic activity and concentration ofalkali ion i, respectively. It is necessary to define the interdiffusioncoefficient since the larger potassium ions diffuse at a slower rate thanthe smaller sodium ions, i.e., DNa−K is different from the sodium self-diffusion coefficient (unlessNNa=0). Furthermore, DNa−K varies withlocal composition (i.e., position of the diffusion profile), temperature,and time [41].We therefore define an average or effective interdiffusioncoefficient (DNa−K) as a constant for a given diffusion profile. DNa−K iscalculated based on the potassium diffusion depth combined with theion exchange time and temperature. The FSM measurements providethe diffusion depth of the potassium ions as a result of the K+-for-Na+

ion exchange process. The determined composition dependence ofDNa−K is illustrated in Fig. 4(b). The error bars ofDNa−K correspond to the

a

b

c

Fig. 4. Composition dependence of isothermal diffusivity. (a) Sodium tracer diffusioncoefficient (DNa) at 300 °C [19]. The errors are estimated to be ~5% [40]. (b) K+-for-Na+

effective interdiffusion coefficient (DNa−K) as determined by ion exchange experimentsat 410 °C. (c) Apparent sodium inward diffusivity at 575 °C. The secondary axis depictsthe composition dependence of the iron redox ratio ([Fe3+]/[Fe]tot) of the as-preparediron-containing glasses as determined by 57Fe Mössbauer spectroscopy. The errors ofthe reported diffusivities and iron redox ratios are estimated not to exceed 15% and 5%,respectively.

3748 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 357 (2011) 3744–3750

standard deviation of the eight measurements of the potassium diffusiondepth for the same ion exchanged sample.

The apparent sodium inward diffusivity is obtained by determiningconcentration profiles in the glass surface layers after exposure to thereducing gas at high temperature. For example, Fig. 3(b) shows theconcentrationprofiles of theAl12.5* glass. The inwarddiffusionof sodiumions has caused the increased concentrations of silicon, boron, andaluminum at the surface. Furthermore, the sodium ions are found inhigher concentrations in the interior of the samples than at the surface. Bycalculating the amounts of depleted and enriched Na+ ions, respectively,wefind that there is amass balance between them. This indicates that the

sodium ions arenot depleted at the surfacedue to evaporation loss duringthe heat-treatment. This is further substantiated by the fact that sodiumions are not depleted in the heat-treated iron-free glasses. From thesurface depletion depth of sodium and the reduction time, the apparentsodium inwarddiffusivity is calculated [20]. The compositiondependenceof the apparent sodium inward diffusivity is illustrated in Fig. 4(c). Theerrors associated with the sodium diffusion depths are typically ±10 nm[42], i.e., the errors of the data points in Fig. 4(c) do not exceed ±15%.

4. Discussion

All three methods reveal a decreasing alkali diffusivity withincreasing [SiO2]/[Al2O3] or [SiO2]/Σ[Oxi] ratios for both iron-containingand iron-free glasses (Fig. 4). We ascribe this trend to two factors. First,the structural role of sodium in influencing the sodium diffusiondepends on the [SiO2]/[Al2O3] ratio. For the high Al2O3 content, Na+ isused for charge compensation of AlO4

− and BO4−. In this case, the

diffusion ofNa+ is relatively fast (see Fig. 4). Thismay be becauseNa+ isnot a rigid part of the network. In the low Al2O3 region, some of thesodium ions create NBOs bonded with Si\O or B\O, and these sodiumions are less mobile. Second, the differences in boron speciation andchemical composition lead to differences in atomic packing of the glassnetworks. The network becomes more densely packed with increasing[SiO2]/[Al2O3] ratio (Table 1), and this contributes to the lowering of thealkali diffusivity. These findings agree well with previous studies byother scientists. For example, Frischat & Kirchmeyer [43] havedemonstrated good agreement between tracer diffusion coefficientmeasurements and interdiffusion coefficients calculated using Eq. (3)for sodium rubidium silicate glasses. Furthermore, Terai [44] has shownthat for aluminosilicate glasses the sodium diffusivity reaches itsmaximum value when all AlO4 tetrahedra are fully charge balanced byNa+ ions and essentially no non-bridging oxygens exist in the glassnetwork.

Fig. 4(a–b) also reveals that the alkali diffusivity is larger in theiron-free glasses than in the iron-containing glasses. Furthermore, thedifference in alkali diffusivity between iron-free and iron-containingglasses decreases with increasing [SiO2]/[Al2O3] ratio and at the sametime the [Fe3+]/[Fe]tot ratio increases (see second y-axis in Fig. 4(c)).Therefore, Fe2+ has larger hindrance to alkali diffusivity than Fe3+. Inother words, there is little or no decrease in alkali diffusivity wheniron is present as Fe3+. We ascribe the impact of iron on alkalidiffusivity to two factors. First, there is competition between cationsfor the charge compensation of AlO4

− and BO4−units. It has been shown

that Fe2+ can charge compensate AlO4− units in aluminosilicate

glasses, even though alkali ions are more efficient charge compensa-tors than Fe2+[45,46]. Hence, it is possible that some Fe2+ ions cancompete with Na+ ions for charge compensating AlO4

− (and possiblyalso BO4

−), which could cause some of the sodium ions to create NBOson tetrahedral silicon or trigonal boron. According to the discussionabove, this will lower the alkali diffusivity. Second, the presence ofrelatively slowly moving divalent cations lowers the mobility of thefast moving monovalent alkali cations. Fe2+ ions play a network-modifying role in the network, and therefore theymay be blocking thediffusion paths of the fast moving Na+ ions (similar to the impact ofalkaline earth ions on alkali diffusivity [47]). On the other hand, Fe3+

ions play a more network-forming role in the network, and they aretherefore not occupying sites that Na+ ions would use for diffusion.

Ion exchange and tracer diffusion experiments are well-establishedmethods for studying cationic diffusion in glasses. The results presentedhere show that the inward diffusion approach may be used as a simplealternative method to assess compositional trends, since the alkalidiffusivity reveals the same composition dependence for all threemethods (Fig. 4). However, the extent of sodium inward diffusiondepends on the iron redox ratio [20]. Hence, if the iron redox ratio variessignificantly in a studied series of glasses, it may be difficult to extractthe true composition dependence of the diffusion. For these glasses, the

3749M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 357 (2011) 3744–3750

ratio of sodium diffusivity of Al15* to that of Al2.5* is 8.7 and 3.0 fortracer diffusion and inward diffusion, respectively. This may be ascribedto the fact that the [Fe3+]/[Fe]tot ratio is 94% and 76% for Al2.5* andAl15*, respectively (Fig. 4(c)). Thus, the driving force for sodium inwarddiffusion is largest for theAl2.5* sample,which causes a less pronounceddependence of the apparent sodium inward diffusivity on compositionin comparison to that of the sodium tracer diffusion coefficient.However, it is possible that this could also be ascribed to the differencein diffusion temperature. Due to the experimental differences betweenthe three applied methods, the alkali diffusivity has been studied atthree different temperatures. If the activation energy of alkali diffusiondepends on the [SiO2]/[Al2O3] ratio, it can cause an apparent differencein the composition dependence of the alkali diffusivity for the threemethods.

As shown in Fig. 4, the apparent sodium inward diffusivity is fiveorders of magnitude smaller than the sodium tracer diffusion coefficient.Note that the diffusion experiments were carried out at 575 and 300 °C,respectively. This means that if both types of experiments wereconducted at same temperature, the difference of the diffusivity wouldbe even larger. Now the question arises: what is the source of this hugedifference?Wehavepreviously foundgoodagreementbetweendiffusioncoefficients of alkaline earth ions derived from inward diffusionexperiments and tracer diffusion experiments in literature [20]. Bothfollow the Arrhenius temperature dependence. In contrast, alkali ionsbehave significantly differently from alkaline earth ions concerning theability of charge compensating electron holes during the inwarddiffusion. As described in a recentwork [42], due to the charge difference,alkaline earth ions have higher degree of the ease of the joint motion ofthe cations with the electron holes than alkali ions. This is because analkaline earth ion is capable of neutralizing two electron holes, whereasan alkali ion can neutralize only one electron hole. To charge balance thesame amount of the electron holes, half the number of alkaline earth ionsis demanded than the alkali ions. Thus, the alkali ions are more crowdedand hence, more easily block each other during transport. The alkalineearth ions should thereforediffuse faster thanalkali ions. This implies thatfor alkali inward diffusion, the charge compensation is the rate-limitingprocess and hence a governing factor for determining the absolute valueof thediffusivity. Thismight be themain source of thedifference betweensodium inward diffusivity and the sodium tracer diffusion coefficient.

This explanation is also supported by the fact that the inwarddiffusivity of Fe2+ is larger than that of Na+[42]. The reduction of Fe3+ toFe2+ creates an electron hole. The newly reduced Fe2+ ions arecompeting with the existing Na+ ions for charge compensation ofelectronholes.Hence, theremaynotbeenoughelectronholes available tobe neutralized by Na+, since Fe2+ can neutralize two electron holes, i.e.,the apparent sodium inward diffusivity becomes low. Furthermore, thereduction of Fe3+ to Fe2+ during the inward experiments could alsocontribute to the difference in sodium inward and tracer diffusivity, sincethe presence of Fe2+ lowers the apparent sodium inward diffusivity.

Finally, we note that slow alkali diffusion observed during thermalreduction is also observed during thermal oxidation. During heat-treatment of Fe2+-containing glasses in air, oxidation of Fe2+ to Fe3+

occurs, which results in outward diffusion of alkali and alkaline earthions [48,49]. Diffusion of divalent alkaline earth ions is the dominantmechanism at sub-liquidus temperatures [50].

5. Conclusions

Three kinds of sodium diffusion processes (inter-, tracer and inwarddiffusion) have been compared for boroaluminosilicate glasses withvarious [SiO2]/[Al2O3] ratios. The results of comparison reveal adecreasing mobility of the sodium ions with increasing [SiO2]/[Al2O3]ratio. This is ascribed to the fact that the structural role of sodium ininfluencing its diffusivity changes with varying [SiO2]/[Al2O3] ratio. Indetail, Na+ diffuses faster when it acts as a charge compensator to Al3+

or B3+ than when it acts as a creator of non-bridging oxygen. These

results could be useful for optimizing basic compositions of boroalumi-nosilicate glasses concerning the efficiency of ion exchange strength-ening. Furthermore, Fe2+ lowers the alkali diffusivity, whereas Fe3+ hasa negligible effect. Both the tracer Na diffusion and the Na–Kinterdiffusion are significantly faster than the Na inward diffusion. Theorigin of this discrepancy could be attributed to the fact that for sodiuminward diffusion, the charge compensation for electron holes is a ratherslow process, and this limits the rate of diffusion.

Acknowledgements

We thank Xinwei Wu and Rüdiger Dieckmann (Cornell University)for supplying information and results of tracer diffusion experiments.Furthermore, we thank Adam J. Ellison (Corning Incorporated) forhelpful discussions, Thomas Peter and Joachim Deubener (ClausthalUniversity of Technology) for SNMS measurements, Dennis Barney,Leilani Burdick, and Corey Solsky (Corning Incorporated) for assistancewith sample preparation, Derek Webb (Corning Incorporated) for saltbath preparation, Scott Aldrich (Corning Incorporated) for UV–VISmeasurements, Douglas C. Allan and Sinué Gómez (Corning Incorpo-rated) for assistance with the FSM-6000 instrument, and Helge K.Rasmussen and Cathrine Frandsen (Technical University of Denmark)for assistance with the Mössbauer measurements.

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