Journal of Non-Crystalline Solids 356 (2010) 290–298

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Journal of Non-Crystalline Solids

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

Modifying glass surfaces via internal diffusion

Morten M. Smedskjaer a, Yuanzheng Yue a,*, Joachim Deubener b, Haraldur P. Gunnlaugsson c, Steen Mørup d

a Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmarkb Institute of Non-Metallic Materials, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germanyc Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmarkd Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

a r t i c l e i n f o

Article history:Received 20 February 2009Received in revised form 30 November 2009Available online 6 January 2010

Keywords:Diffusion and transportSurfaces and interfaces

0022-3093/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.jnoncrysol.2009.12.004

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

a b s t r a c t

The surface chemistry and structure of iron-bearing silicate glasses have been modified by means of heat-treatment around the glass transition temperature under different gaseous media at ambient pressure.When the glasses are heat-treated in atmospheric air, oxidation of Fe2+ to Fe3+ occurs, which leads to out-ward diffusion (OD) of divalent cations (primarily Mg2+), i.e., diffusion from the interior of the glass to thesurface, and thereby, to formation of an oxide surface nano-layer. In contrast, when the glasses are heat-treated in H2/N2 gas containing 10 vol.% H2, reduction of Fe3+ to Fe2+ occurs due to both the permeationand reducing ability of H2. In this case, OD of divalent ions also occurs, and hence, an oxide surface layerforms. However, such outward diffusion differs from that induced by the iron oxidation in terms of phys-ical origin. The former is due to incorporation of the N3� ions in the network and their strong attraction tothe modifying ions, whereas the latter is due to the requirement of the charge neutrality. The role of N3�

in driving OD is verified by the composition profile of the surface layer of the glass treated in pure N2 gas.The OD exerts pronounced impacts on some properties such as hardness, chemical durability, and surfacewettability.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

The interplay between a glass and its surroundings is to a largeextent determined by the chemical and structural features of theglass surface [1]. These features can be tailor-made by using a sur-face modification technique, e.g., coating of metal oxides or poly-mers, ion exchange between glass and salt melt, or fire polishing.By using physical or chemical approaches, new functional surfacescan be created and applied in new contexts or in improvements ofexisting materials. In the present work, we attempt to modify thesurface of silicate glasses via new chemical routes, i.e., by heat-treating the glasses at temperatures near Tg (glass transition tem-perature) under different atmospheres.

The surface of basaltic glass systems (iron-bearing aluminosili-cate glasses) can be modified by heat-treatment in atmospheric airat temperatures near Tg for suitable durations [2–4]. The heat-treatment leads to oxidation of ferrous iron (Fe2+) to ferric iron(Fe3+), which causes outward diffusion (OD), i.e., a diffusion ofdivalent cations (such as Mg2+ and Ca2+) from the interior of theglass towards the surface. Surprisingly, the oxidation process doesnot cause oxygen to diffuse into the interior of samples, instead, itcauses the motion of electron holes (h�) into the interior via thereaction Fe2++�=Fe3+ [2–9]. The driving force (Gibbs free energy of

ll rights reserved.

45 96350558.

the redox reaction) is gradually dissipated by the electron holes.To maintain charge neutrality, the inward motion of electron holesis charge-coupled with the motion of network-modifying cationsin the opposite direction. A crystalline layer forms on the glass sur-face as the divalent cations react with ionic oxygen at the surface.This surface layer exhibits excellent thermal performance [4].

The question arises whether the surfaces of iron-bearing glassescan be modified by heat-treatment near Tg in other gases thanatmospheric air, e.g., reducing or inert gases. In other words, howsensitive are the chemical composition and morphology of the sur-face layer to the heat-treatment atmosphere? We have recentlyshown that a silica-rich surface layer can be created in polyvalentelement-bearing silicate glasses by subjecting them to heat-treat-ments in H2/N2 (1/99 v/v). In this case, the network-modifying cat-ions diffuse inward to charge-neutralize the outward movingelectron holes, resulting in formation of the silica-rich layer. Theinward diffusion is reported elsewhere [10,11].

In this paper, we present findings about the outward diffusionand the resulting surface modification in iron-bearing silicateglasses as a consequence of heat-treatments under different atmo-spheres (H2/N2 10/90, air, N2, and argon) near Tg. These findingswill shed light onto the origin of the relation between redox reac-tions and cationic diffusion processes near the glass surface. Wedescribe how the diffused N2 and H2 molecules are incorporatedin the glass surface structure. The effect of the diffusion of gas mol-ecules on the glass structure has been studied for other purposes

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298 291

[12–22]. However, to our best knowledge, the correlation betweenincorporation of gaseous molecules into the surface structure andcationic diffusion processes has not yet been investigated. In thispaper, both diffusion of gaseous molecules and cations are referredto as internal diffusion. Finally, we also demonstrate whether andhow surface modification due to the internal diffusion influencesphysical and chemical properties of the glasses.

2. Experimental methods

2.1. Sample preparation and thermal treatment

The investigated glass compositions belong to simple modelsystems as listed in Table 1, where the density and Tg of the glassesare also given. We chose these model systems in order to more eas-ily find out which types of modifying ions are the most mobileones, Ca2+ or Mg2+, and to more clearly observe the impact of theiron content on the studied diffusion and redox processes. Na2Owas included in the systems to enhance the glass forming abilityof the melts.

The glasses were prepared from analytical reagent-grade SiO2,CaCO3, Na2CO3, Mg(OH)2�(MgCO3)4�(H2O)5, and Fe2O3 powders.The batch materials were melted in air at 1773 K in a Pt–10% Rhcrucible. Quenching of the melts resulted in circular glass plateswhich were immediately annealed in air at 923 K for 1 h. Circularglass samples (diameter 8–10 mm; thickness 3 mm) were pre-pared by cutting a cylinder cored from the larger glass plates usinga diamond studded saw. Afterwards, the samples were polishedusing 1 lm diamond paste at the final step. X-ray diffraction(XRD) measurements confirmed the vitreous nature of the sam-ples. The compositions were measured using X-ray fluorescence(XRF) on a S4-Pioneer X-ray spectrometer (Bruker-AXS, Karlsruhe,Germany). Densities were measured using a He-pycnometer (Poro-tec, Germany). The Tg values of the glasses were determined usingdifferential scanning calorimetry (DSC, Netzsch STA 449C Jupiter)according to the procedure proposed by Yue [23] (see Table 1).

The glasses were heat-treated at three different temperatures(0.95Tg, 1.00Tg, and 1.05Tg, where Tg = 926 K) for various durations(ta) in the following atmospheres (all at 1 atm): H2/N2 (10/90 v/v),air, N2, and argon. H2/N2 (10/90) and N2 treatments of the glasssamples were conducted in an electric furnace placed in a Labmas-ter 130 glovebox (Mbraun, Garching, Germany). The glass sampleswere inserted into the pre-heated furnace, and upon reaching thepre-determined treatment time, the samples were quenched byremoving them from the furnace. As impurities, 3 � 10�5 bar H2Oand 10�5 bar O2 were present in the H2/N2 (10/90) gas and 10�5

bar H2O and 4 � 10�5 bar O2 in N2. Air treatments were performedunder atmospheric conditions using an identical procedure in anelectric furnace (Scandiaovnen A/S, Allerød, Denmark). Argontreatments were conducted in the instrument used for the DSCexperiments by placing the samples in the sample holder. Heatingand cooling were conducted with 40 and 30 K/min, respectively.The partial oxygen pressure of the Ar gas was 10�5 bar.

Table 1Chemical composition, iron redox ratio, density, and glass transition temperature (Tg)of the starting glasses.

Glass Chemical composition (wt.%) Fe3+/Fetot

(at.%)Density(g/cm3)

Tg

(K)SiO2 CaO MgO Na2O Fe2O3

*

0wtFe 74.3 10.8 10.2 4.43 – – 2.501 9171wtFe 72.5 11.4 9.95 4.63 1.09 35–50 2.517 9143wtFe 70.8 11.1 9.59 4.49 3.14 60–75 2.549 9216wtFe 69.4 10.8 9.34 4.41 6.07 69 ± 3 2.600 926

* All iron reported as Fe2O3.

2.2. UV–VIS-NIR spectroscopy

UV–VIS-NIR (ultraviolet–visible-near infrared) spectroscopywas used to determine the redox state of iron in the heat-treatedsamples. The samples used for the spectroscopic analyses wereground to a uniform thickness of 0.2 mm, and subsequently pol-ished to get a smooth surface prior to the heat-treatments. UV–VIS-NIR spectra were recorded over the wavelength range of190 nm (52632 cm�1) to 1100 nm (9091 cm�1) using a UV–VIS-NIR Specord 200 spectrophotometer (Analytik Jena AG) at a resolu-tion of 1 nm. The spectra were recorded with air as reference.

The Fe2+ ion has a maximum absorption peak near 9500 cm�1

[24,25], but the position and intensity of this peak varies with glasscomposition. The absorption coefficients for our glasses were notknown and therefore the absorption coefficient of the Lambert–Beer equation was calculated: A = c e t, where A is absorbance, cthe concentration, e the absorption coefficient, and t the samplethickness. To determine the absorption coefficient, the Fe3+/Fetot

ratio was estimated in the as-prepared glasses using Mössbauerspectroscopy (see Section 2.4 and Table 1). By using this ratioand the total iron content, the concentration of ferrous iron wascalculated. Plotting the absorbance near 9500 cm�1 versus thesample thickness (0.12, 0.20, 0.40, and 0.80 mm) gave a linear rela-tion (R2 = 0.997). From the slope of this plot (c e), the absorptioncoefficient was calculated to be 3.90 L mol�1 mm�1.

2.3. FT-IR spectroscopy

The OH content of glasses was measured using FT-IR (Fouriertransform infrared) absorption spectroscopy. The samples usedfor these analyses were ground to a uniform thickness of 0.2 mm,and subsequently polished to obtain a smooth surface prior tothe heat-treatments. FT-IR spectra were acquired using a BrukerVertex 70 FT-IR spectrometer (Bruker Optics) equipped with KBrbeamsplitter and a DLaTGS detector. The absorption spectra werecollected in the wavenumber region from 2500 to 4000 cm�1 usingair as reference. Data had a resolution of 2 cm�1 and were averagedover 32 scans.

To study the bonding environment of silicon in the glass sur-face, FT-IR reflection spectra were considered. The reflectancespectra were recorded at a glazing incidence angle of 80� and col-lected with a resolution of 2 cm�1. Data were averaged over 32scans. A background spectrum was collected with a gold-coatedreference mirror.

2.4. Mössbauer spectroscopy

Conventional transmission 57Fe Mössbauer spectroscopy mea-surements on powdered samples were used to determine the ironredox state of the untreated iron-containing glasses. A constantacceleration spectrometer with a source of 57Co in rhodium wasused. The spectrometer was calibrated using a foil of a-Fe at roomtemperature. Isomer shifts are given relative to that of the calibra-tion spectrum.

The iron redox state in the surface layer (�200 nm) was ana-lysed in the untreated 6wtFe glass and in the same glass heat-trea-ted in air by using conversion electron Mössbauer spectroscopy(CEMS). The CEMS spectra were recorded using 57Co in rhodiumas source. The source moved relative to the sample on a conven-tional constant acceleration system calibrated with a-Fe. Sampleswere placed on double adhesive conducting tape in a parallel plateavalanche detector. The detector was operated with a plate dis-tance of �2.5 mm in 25 mbar acetone gas and a voltage of 1 kVwas applied. The measurements were conducted at roomtemperature.

-6 -4 -2 0 2 4 60.988

0.992

0.996

1.000

1.004

1.008

Fe2+

Fe3+

Rel

ativ

e tra

nsm

issi

on

Velocity [mm/s]

Data Simulation Fe3+ fit Fe2+ fit

Fig. 1. 57Fe Mössbauer spectrum of the untreated 6wtFe glass obtained at 295 K.The fitted doublets from Fe3+ and Fe2+ are shown.

0 100 200 300 400 5000

1

2

3

4

5

SiNa

OCa

Fe

Mg

c/c bu

lk

Depth [nm]

Fig. 2. SNMS depth profile of the 6wtFe glass heat-treated in air at Tg = 926 K for16 h. The curves are plotted as concentration of the element at a given depthdivided by the concentration of the same element in the bulk of the glass (c/cbulk).

292 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298

2.5. Secondary neutral mass spectroscopy

Compositional analysis of the surface was carried out usingelectron–gas secondary neutral mass spectroscopy (SNMS). Themeasurements were performed using an INA3 (Leybold AG) instru-ment equipped with a Balzers QMH511 quadrupole mass spec-trometer and a Photonics SEM XP1600/14 amplifier. Theanalyzed area had a diameter of 5 mm and was sputtered usingKr plasma with an energy of �500 eV. The time dependence ofthe sputter profiles was converted into depth dependence by mea-suring the depth of the sputtered crater at 10 different directionson the same sample with a Tencor P1 profilometer.

2.6. Atomic force microscopy

The morphology of the glass surfaces were analysed usingatomic force microscopy (AFM). An ULTRAObjective AFM instru-ment from Surface Imaging Systems (Herzogenrath, Germany)was utilized. The microscope was operated in the non-contactmode. All AFM images were collected using a silicon tip and thescan size was 5 � 5 lm2. The root mean square (RMS) roughnessof each surface was calculated [26].

2.7. Vickers indentation

Vickers hardness (Hv) was measured by microindentation (Dur-amin 5, Struers). Twenty five indents were made for each sample atwidely separated locations with a load of 0.25 N and a hold time atthe maximum load of 5 s. The lengths of the indentation diagonalswere measured using an optical microscope (reflection method).

2.8. Chemical durability

The chemical resistance of the samples was examined in 0.25 MHCl and 0.25 M KOH solutions. After immersing a sample in a plas-tic container with the test solution (20 cm3 for 1 cm2 of the glasssurface area), the container was mounted on a thermostatic shak-ing assembly at 90 �C (agitated at 100 rpm). After 12 h, the samplewas removed from the solution. The concentrations of leached Na+

and Mg2+ ions were measured in the test solution using atomicabsorption spectroscopy (AAnalyst 100, Perkin Elmer).

2.9. Contact angle measurements

Contact angle (CA) measurements were performed using thesessile drop method (Contact Angle System OCA 15 plus, Dataphys-ics Instruments) with deionised water as the test liquid (3 lL drop-let). The angle was measured using video capture, and the averageof 10 measurements per sample was reported.

3. Results

3.1. Initial iron redox state

Fig. 1 shows the transmission 57Fe Mössbauer spectrum of theuntreated 6wtFe glass at 295 K. The two doublets, seen in the spec-trum, are caused by Fe3+ (isomer shift of 0.29 mm/s and quadru-pole splitting of 1.03 mm/s) and Fe2+ (isomer shift of 0.99 mm/sand quadrupole splitting of 1.93 mm/s), respectively. By determin-ing the relative areas of the fitted doublets of Fe3+ and Fe2+ for eachof the untreated iron-containing glasses, the Fe3+/Fetot ratio is cal-culated and given in Table 1.

CEMS is used to determine the iron redox state in the �200 nmsurface layer of the 6wtFe glass. However, the CEMS spectra ob-tained within reasonable measurement time are of poor quality.

In order to obtain useful information, they are analysed by usingthe hyperfine parameters determined by transmission Mössbauerspectroscopy. The relative areas of the fitted doublets of Fe3+ andFe2+ from the CEMS spectra are used to calculate the Fe3+/Fetot ra-tio. It is found that about 68% of the ionic iron atoms are present asFe3+ in the surface of the untreated sample in accordance with theresult obtained from transmission Mössbauer spectroscopy(Table 1).

3.2. Treatment in air

The SNMS depth profile of the 6wtFe glass heat-treated in air atTg = 926 K for 16 h exhibits an enrichment of magnesium, calcium,and iron on the surface (Fig. 2). The diffusion of divalent cations isdriven by the oxidation of Fe2+ to Fe3+ as electron holes move fromthe surface towards the interior. The divalent cations react with io-nic oxygen at the surface to create a modified surface layer (com-pare the AFM images in Fig. 3(a) and (b)). XRD measurements haverecently revealed that this oxide surface layer is crystalline [4].Hence, it is assumed that primarily periclase (MgO) crystals areformed at the surface since diffusion of Mg2+ is predominant inthe overall diffusion process. The CEMS data show that about98% of the ionic iron atoms within the 200 nm surface layer arepresent as Fe3+ in the sample heat-treated in air, i.e., the surfaceof this sample has been oxidized.

Fig. 3. Three-dimensional AFM surface images (5 � 5 lm2) of (a) the original 6wtFe glass and of 6wtFe glasses heat-treated at Tg for 16 h under different atmospheres: (b) air,(c) H2/N2 (10/90), and (d) N2. The RMS roughness (R) is stated for each surface.

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298 293

3.3. Treatment in H2/N2 (10/90)

Fig. 4(a) shows UV–VIS-NIR spectra of 6wtFe glasses heat-trea-ted at Tg for different durations in H2/N2 (10/90). The reducingatmosphere causes a reduction of Fe3+ to Fe2+ and the intensityof the Fe2+ band near 9500 cm�1 increases with increasing ta, whilethe intensity of the Fe3+ band near 22 500 cm�1 decreases withincreasing ta. Generally, hydrogen is able to dissolve in intersticesor atomic-sized holes in silicate glasses [27]. Furthermore, hydro-gen is able to reduce polyvalent ions from the higher valence stateto the lower valence state, and itself become a proton in the formof hydroxyl [12–17,28,29]. Fig. 4(b) indicates that the Fe3+ reduc-tion in H2/N2 (10/90) is accompanied by formation of Si–OHgroups. The OH contents of the glasses are measured using infraredabsorption bands at 3550 cm�1 and 2850 cm�1. These bands arecaused by OH stretching vibrations of weakly and strongly hydro-gen-bonded OH species, respectively [30]. Gaseous H2 species mustbe dissolved at the glass surface to account for the incorporation ofOH groups. The mobile H2 species then diffuse and are immobi-lized in the form of OH subsequent to reaction with Fe3+. Usingthe notation of Hess [31], the following reaction is proposed to ac-count for the Fe3+ reduction and the formation of OH groups:

H2þ2½NaFe3þO2� þ4½SiOSi� ! 4½ðFe2þÞ0:5OSi�þ2½SiOH� þ2½NaOSi�;ð1Þ

where [NaFe3+O2] is Fe3+ in tetrahedral coordination charge-bal-anced by Na+, [(Fe2+)0.5OSi] is Fe2+ in octahedral coordination con-nected to a non-bridging oxygen (NBO), and [NaOSi] is Na+

connected to a NBO. According to the proposed reaction, the reduc-tion of Fe3+ results in a depolymerization of the glass network.

Using Scholze’s two-band model in the modified form of Beh-rens and Stuke [30], the OH contents, cOH, can be estimated fromthe background corrected peak heights at 2850 and 3550 cm�1

using the Lambert–Beer law,

cOH ¼MOH

qLDA3550

e3550þ DA2850

e2850

� �; ð2Þ

where MOH is the molar mass of OH, q is the density of the glass, L isthe sample thickness, DAi is the background corrected absorbance,and ei is the molar absorption coefficient, with the subscript i denot-ing the band considered. Molar absorption coefficients of 70 and112.5 L mol�1 cm�1 at 2850 and 3550 cm�1, respectively, for a so-dium silicate glass are used for calculation of the OH content sinceno calibration file is available for the studied composition [30]. Thechanges in OH and Fe2+ content as a result of the treatment are de-noted DcOH and DcFe2þ , respectively. The ratio DcOH/DcFe2þ is calcu-lated for the same heat-treatment conditions. If Fe3+ is solelyreduced to Fe2+ as a result of Reaction (1) and OH is solely formeddue to the same reaction, DcOH=DcFe2þ . For the 6wtFe glasses treatedin H2/N2 (10/90), the average value of DcOH/DcFe2þ is 0.95 ± 0.02.Hence, it is inferred that most (if not all) of the Fe2+ ions are formeddue to Reaction (1), i.e., due to permeation (dissolution and diffu-sion) of H2.

Surprisingly, the SNMS depth profiles of 6wtFe glasses heat-treated in the reducing H2/N2 (10/90) gas reveal an OD of divalentcations similar to that observed as a result of the air treatment(Fig. 5(a)). Mg2+ and Fe2+ diffusion is dominating and as shown inthe inset of Fig. 5(a), the extent of diffusion increases with increas-ing ta. The extent of diffusion also increases with increasing heat-treatment temperature [32]. Fig. 3(c) shows that the diffusion is

10000 15000 20000 250000.0

0.3

0.6

0.9

1.2

0 30 60 90 1200.00

0.15

0.30

0.45120 h

60 h

16 h

2 h

untreated

A[-]

6wtFe3wtFe1wtFe

ta [h]Δ c

(F cce2+

) [m

mol

/g]

2500 3000 3500 40000.0

0.4

0.8

1.2

1.6

0 30 60 90 1200

2

4

6 120 h

60 h

16 h

4 h8 h

2 h

untreated

A

Wavenumber [cm-1]

Wavenumber [cm-1]

6wtFe3wtFe1wtFe

Δ c(O

H) [

103 p

pm w

t]

ta [h]

[-]

a

b

Fig. 4. (a) UV–VIS-NIR spectra of the 0.20 mm thick 6wtFe glass samples heated inH2/N2 (10/90) at Tg for different durations. The band positioned near 9500 cm�1 isdue to a d ? d transition of Fe2+. Inset: the corresponding change in Fe2+

concentration as a function of the heat-treatment duration (ta) for 6wtFe, 3wtFe,and 1wtFe. (b) FT-IR absorption spectra of the 0.20 mm thick 6wtFe glass samplesheated at Tg for various durations in H2/N2 (10/90). The bands at 2850 and3550 cm�1 are caused by OH� stretching vibrations of strongly and weakly H-bonding water species, respectively. Inset: the corresponding change in OH contentas a function of the heat-treatment duration (ta) for 6wtFe, 3wtFe, and 1wtFe.

0

1

2

3

4

5

6

7

8

0 4 8 12 160

100

200

300

400

c/c bu

lkc/

c bulk

Mg in 6wtFeFe in 6wtFeMg in 3wtFeMg in 0wtFe

Na

Ca

Mg

Fe

O Si

ta [h]

Are

a [A

U]

0 100 200 300 4000.0

0.5

1.0

1.5

2.0

Na

Fe

MgCa

OSi

Depth [nm]

0 100 200 300 400

Depth [nm]

a

b

Fig. 5. SNMS elemental concentration profiles over the depth of the 6wtFe glassheat-treated at Tg for 16 h in (a) H2/N2 (10/90) and (b) N2. The concentration of theelement normalized by that of the same element in the bulk of the glass, c/cbulk, isplotted as a function of the depth of the glass. Inset in (a): areas calculated betweenthe curves of Mg and Fe and the horizontal line through c/cbulk = 1 from thecorresponding SNMS profiles. The areas are plotted as a function of heat-treatmentduration (ta) for the 6wtFe, 3wtFe, and 0wtFe glasses heated in H2/N2 (10/90).

900 1000 1100 12000.22

0.24

0.26

0.28

0.30

0.32

960 965 970 975 9800.255

0.260

0.265

0.270

0.275

Ref

lect

ance

[-]

Wavenumber [cm-1]

untreated H

2/N

2 (10/90), 2 h

H2/N

2 (10/90), 4 h

H2/N

2 (10/90), 16 h

N2, 16 h

Fig. 6. FT-IR reflection spectra of the untreated and heat-treated 6wtFe glasses. Theheat-treatments were performed at Tg in different atmospheres and for differentdurations. Inset: enlargement of the region with the Si–N band.

294 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298

accompanied with a change in the surface morphology that is dif-ferent from that of the sample treated in air. If the diffusion of diva-lent cations should be attributed to the Fe3+ reduction, it shouldhave occurred from the surface towards the interior (called inwarddiffusion) as a mirror-image of the oxidation mechanism [10].Therefore, the observed diffusion is not a direct consequence ofFe3+ reduction.

The FT-IR reflection spectra presented in Fig. 6 show the follow-ing spectra features with increasing ta. First, the peak assigned toSi–O–Si antisymmetric stretching at 1100 cm�1 shifts towardslower wavenumbers and its intensity decreases. Second, the for-mation and growth of a peak at 940 cm�1 occurs. Third, the forma-tion and growth of a low-intensity peak near 970 cm�1 is observed.The evolution of the Si–O–Si antisymmetric stretching peak showsthat the surface depletes in silica [33–35]. This confirms the SNMSresults. The peak at 940 cm�1 is assigned to the vibration of Si–OH[36–40] which is in agreement with the FT-IR absorption spectros-copy results as OH groups are created. The weak peak near970 cm�1 is assigned to the vibration of Si–N bonds [41,42]. Hence,the thermal treatment in H2/N2 (10/90) causes partial surfacenitridation (nitrogen incorporation). The latter may refer to partialexchange of 3O2� (bridging and/or non-bridging) for 2N3� ions inthe structural network of the glass surface [43]. ‘Partial’ means that

only a fraction of oxygen ions within the surface layer are replacedby N3�. Previous studies have shown that heat-treatment of a sili-cate glass in N2 [18–20] or NH3 [18,20,35,44–47] can result innitridation.

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298 295

3.4. Treatment in N2 or argon

Treatment in N2 does not change the redox state of iron in thesamples [32]. The variations both in surface morphology(Fig. 3(d)) and in composition of the surface layer (Fig. 5(b)) forthe N2 treated sample are basically similar to those observed forthe H2/N2 (10/90) treated samples. The bumps on the surface havea similar shape for both samples, but the distribution density of thebumps is larger for the H2/N2 (10/90) treated sample than for theN2 treated sample. Furthermore, the diffusion extent of the cationsis more pronounced for the former than for the latter. Partial sur-face nitridation is also observed in the N2 treated sample (Fig. 6).Heat-treatment in argon neither changes the iron redox state northe surface composition and morphology [32].

3.5. Influence of iron content

By comparison of the UV–VIS-NIR and FT-IR spectra of the1wtFe, 3wtFe, and 6wtFe glasses, it is obvious that the amount ofresulting Fe2+ ions and OH groups due to the H2/N2 (10/90) treat-ment increases with increasing iron content of the glass (see insetsof Fig. 4(a) and (b)). When heating the iron-free glass (0wtFe) inH2/N2 (10/90) at Tg for 16 h, the SNMS depth profile reveals migra-tion of Mg2+ and Ca2+ towards the surface, revealing that this OD isnot caused by iron reduction. The extent of the diffusion is muchless than that observed for iron-containing glasses. In fact, the ex-tent of the diffusion processes increases with increasing iron con-tent (inset of Fig. 5(a)).

3.6. Impact on properties

Table 2 shows the changes of Vickers hardness (Hv), chemicaldurability, and water contact angle (CA) as a function of theheat-treatment atmosphere for 6wtFe glasses heated atTg = 926 K for 16 h. Chemical durability is expressed as the concen-trations of leached Na+ and Mg2+ ions after 12 h in 0.25 M aqueousHCl and KOH solutions. In acid solutions, leaching of alkali ions isthe dominant dissolution mechanism. In alkali solutions, the Si-network is dissolved directly into the solution as the OH� ions di-rectly attack the Si–O network bonds, i.e., no selective leaching ofelements occurs in the alkali solution [48].

Treatment in argon neither changes the surface wettability northe hardness. In contrast, treatment in N2 leads to an increase inacid resistance and CA and to a decrease in alkali resistance. Thesurface of the air-treated sample becomes more hydrophobic,harder, and more resistant against the acidic solution as a resultof the treatment, whereas the alkali resistance decreases. Treat-ment in the reducing H2/N2 (10/90) atmosphere causes a decrease

Table 2Effect of the heat-treatment atmosphere on the Vickers hardness (Hv), chemicaldurability, and water contact angle (CA) of the 6wtFe glasses. The heat-treatedsamples have all been heated at Tg for 16 h. Chemical durability is expressed by theleached amount of Na+ (c(Na+)) and Mg2+ (c(Mg2+)) ions after 12 h in the acid (0.25 MHCl) and alkali (0.25 M KOH) solutions. Concentration measurements were done withaccuracies better than ±0.3 mg/L.

Heat-treatmentatmosphere

Hv

(GPa)c(Na+)acid

(mg/L)c(Mg2+)acid

(mg/L)c(Na+)alkali

(mg/L)c(Mg2+)alkali

(mg/L)CA (�)

Untreated 8.9 ± 0.2 8.7 0.2 1.1 2.4 39 ± 4Argon 9.0 ± 0.2 – – – – 40 ± 3N2 8.8 ± 0.2 6.2 0.2 1.1 3.7 53 ± 6Air 9.3 ± 0.1 1.9 0.1 1.0 3.9 56 ± 4H2/N2

(10/90)8.0 ± 0.2 2.4 0.1 1.0 3.5 30 ± 3

in hardness, CA, and alkali resistance, but at the same time, the acidresistance is increased.

4. Discussion

4.1. Influence of redox state on surface modification

4.1.1. In airOxidation of Fe2+ to Fe3+ causes an OD of divalent cations. This

observation agrees with the results of previous studies based onbasaltic glass systems [2–4]. A small enrichment of oxygen is seenwithin the depth of 25 nm. However, there is no enrichment peakof oxygen in the depth range from about 25 to 450 nm, in whichthe enrichment peaks of Mg2+, Ca2+, and Fe3+ appear (Fig. 2). Thisis not contradictory to the oxidation mechanism due to two facts.First, the stoichiometric concentration of oxygen ions in, e.g., MgOcrystals is close to that in the interior of the glass. Second, the con-centration of the external oxygen entering the surface layer isapproximately two orders of magnitude lower than the averageconcentration of oxygen in the sample [4], i.e., the oxygen enrich-ment in the surface layer is not detectable from the c/cbulk curve ofoxygen (Fig. 2). The outward diffusion of Mg2+ is predominant inthe overall diffusion process. This could be attributed to the smal-ler size of Mg2+ compared to Ca2+ and Fe2+. The CEMS measure-ments showed that iron almost exclusively exists as Fe3+ in thedepth range from 0 to �200 nm. Since Fe3+ has higher chargeand hence higher binding strength to its surrounding oxygen ionscompared to Fe2+, it should not diffuse to the surface during thetreatment. First, the Fe2+ ions diffuse to the surface to charge-com-pensate for inward migration of electron holes. Then, the Fe2+ ionsare oxidized and a Fe3+-bearing surface layer is formed.

4.1.2. In H2/N2 (10/90)To understand the reduction mechanism, it is important to

know whether the permeation of H2 rate-limits the Fe3+ reductionprocess during heat-treatment in H2/N2 (10/90). To do so, theexperimental data are fitted to the tarnishing model [13,14,49].The model assumes that the reaction between H2 and Fe3+ is veryfast compared with the diffusion rate and that the concentration ofreaction sites (Fe3+ ions) is independent of temperature and is aconstant throughout the glass. The concentration of Fe2+ ions(cFe2þ ) is then given by [13],

cFe2þ � cFe2þ ;i

cFe2þ ;f � cFe2þ ;i¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi8KPta

L2cx

sð3Þ

where cFe2þ ;i and cFe2þ ;f are the initial and final concentration of Fe2+,respectively, K the permeability of the gas, P the gas pressure, L thesample thickness, and cx the equivalent concentration of dissolvedgas required to fully react with all the potential reaction sites inthe glass. The ratio on the left-hand side of Eq. (3) is calculated fromthe UV–VIS-NIR spectroscopy data and plotted as a function of t0:5

a /L(Fig. 7(a)). The three series of measurements are in excellent agree-ment with Eq. (3). The tarnishing model predicts the temperaturedependence of the reduction process to be included in the perme-ability term in Eq. (3). At each heat-treatment temperature(0.95Tg, 1.00Tg, and 1.05Tg), K is calculated from the slopes of thelines in Fig. 7(a) and the resulting values are fitted to an Arrheniuslaw (see inset of Fig. 7(a)). The linear relationship confirms that thepermeation of H2 is thermally activated and from the parameters ofthe linear regression, the activation energy for H2 permeation (Ea) iscalculated to be 65 kJ/mol by using the Arrhenius law.

The calculated value of Ea is compared to literature data ob-tained for H2 permeation in silicate glasses. It is expected that Ea

of H2 permeation depends on the openness of the glass structureas motion of molecular species in glass occurs by jumping between

0 2000 4000 60000.0

0.2

0.4

0.6

0.8

1.0

1.00 1.08 1.16-24.2

-23.8

-23.4

-23.0975 925 875

(c-c

i)/(c

f-ci)

[-]

t a0.5

/L [s0.5

/mm]

0.95 Tg

1.00 Tg

1.05 Tg

103/T [K-1]

ln K

[K in

mol

s-1 m

-1 b

ar-1]

T [K]

0.46 0.48 0.50 0.5225

40

55

70

85

Ea [k

J/m

ol]

Z [-]

This work Barton and Morain [12] Shelby and Vitko [14] Shelby [43] De Marchi et al. [51]

a

b

Fig. 7. (a) Effect of heat-treatment temperature on the rate of reaction between theH2 gas and the 6wtFe glass. Inset: Arrhenius plot of ln K as a function of thereciprocal absolute temperature. (b) Activation energy for H2 permeation (Ea) as afunction of the ionic porosity (Z) for different silicate glasses. An open glassstructure has a large value of Z and vice versa. (See above-mentioned references forfurther information.)

296 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298

interstitial positions in the structure. The openness of a glass canbe characterized by calculating the ionic porosity (Z) [50]. A largevalue of Z indicates an open structure and vice versa. Fig. 7(b) pre-sents a literature survey in which Ea of H2 is found for differentglasses. The plot reveals that an open glass structure allows an easypermeation of H2. The approximate linear dependence of the acti-vation energy for permeation or diffusion on ionic porosity has pre-viously been reported for other molecular species (H2O and O2)[50]. Obviously, as the size of the molecular species decreases,the permeation becomes less dependent on the ionic porosity[52]. However, the literature survey in Fig. 7(b) confirms that therelationship is also valid for the smallest molecular species. Hence,it is found that the activation energy for the redox reaction corre-sponds to the activation energy for H2 permeation, i.e., when theglass is heated in H2/N2 (10/90), the Fe3+ reduction process occursby dissolution, diffusion, and immobilization (i.e., reaction) of H2

species. The dissolution–diffusion step is rate limiting.

4.2. Influence of partial surface nitridation on surface modification

When treating the 6wtFe glass in H2/N2 (10/90) at Tg, OD of thedivalent cations (Mg2+, Ca2+, and Fe2+) is observed as shown inFig. 5(a). We believe that the observed OD is not induced by a pres-ence of remaining trace oxygen in the H2/N2 (10/90) atmosphere,since the OD does not occur in argon, in which trace oxygen is also

present. The diffusion is also not driven by reduction of Fe3+ to Fe2+

for the following reasons. First, only inward diffusion of divalentcations can be accounted for by the reduction of Fe3+ to Fe2+. Sec-ond, the OD also occurs when heating the iron-free glass (0wtFe) inH2/N2 (10/90) (see the inset of Fig. 5(a)). As discussed in detail else-where [10,11], no inward diffusion occurs because the hydrogenpressure is so high that all Fe3+ ions are reduced to Fe2+ entirelyby H2 molecules before the divalent cations start to diffuse. If thehydrogen content is lowered to 1 vol.%, the inward diffusion takesplace since both H2 permeation and outward flux of electron holesin this case contribute to the reduction of Fe3+ [10,11].

FT-IR reflection spectroscopy data reveal that nitrogen is foundand chemically dissolved in the glass surface when heating theglass in H2/N2 or N2. Treatment in N2 induces the same type ofOD as treatment in H2/N2 (10/90) does. This indicates that the dif-fusion is related to the partial surface nitridation. Hence, an O2�

concentration gradient over the depth of samples is establishedas a consequence of depletion of O2� near the surface due the ex-change of 3O2� for 2N3� ions at the surface. To dissipate the gradi-ent, diffusion of oxygen species (network ions of hydroxyl oroxygen) from the interior towards the surface is required. Tocharge-compensate the oxygen diffusion, diffusion of mobile cat-ions (such as divalent cations) towards the surface must take place.This qualitatively explains the enrichment of divalent cations ob-served in the SNMS depth profiles of glasses treated in H2/N2

(10/90) and N2. It should be noticed that the outward cationic dif-fusion was not observed when Fe2+-bearing glass fibers were heat-treated in N2 in a previous study [4]. This could be related to thefollowing differences between the two samples. First, the fibershave a different composition compared to the samples studied inthis work since the fibers, e.g., contain a high alumina content,whereas the samples studied here do not. Second, the fibers areproduced under reducing conditions, and hence, contain all theiriron as Fe2+. Third, the fibers have a much larger surface to volumeratio than the bulk samples studied in this work. The detailed rea-sons for the discrepancy still need to be explored.

The extent of diffusion is larger for the glass treated in H2/N2

(10/90) than that in N2 and this is attributed to the followingtwo factors. First, the partial surface nitridation is more effectiveunder reducing conditions [43]. When more nitrogen is incorpo-rated into the structural network, more divalent cations diffuse.Second, the reduction of Fe3+ in H2/N2 (10/90) is accompanied byOH formation. According to a three component model [53], forma-tion of OH groups will decrease the glass transition temperaturestrongly, i.e., a surface glass transition temperature of 793 K(�0.86 Tg) for a fully reduced surface layer was calculated. Onthe other hand, nitridation of silicate glasses is in general accompa-nied by a strengthening of the glass network and an increase of Tg

since nitrogen is coordinated to three Si atoms (see e.g., reviews bySakka [21] and Hampshire [22]). Hence, the influences of the H2/N2

(10/90) treatment on the structural polymerization are of a com-plex nature. However, based on the fact that the treatment lowersthe hardness (Table 2), we expect that the net structural change isa decrease of the degree of polymerization. The depolymerizationof the network results in an increase in the diffusion coefficientsof O2� and OH�. This also explains why the extent of diffusion in-creases with increasing iron content.

4.3. Impact of internal diffusion on properties

The hardness measurements were performed by microindenta-tion. It should be mentioned that the Vickers indent provides infor-mation on mechanical behavior of �1 lm depth since the length ofthe indentation diagonal is �7 lm. The applied gas treatmentsmodify a surface layer in the sub-micron range. However, for thinfilm application, the influence of the substrate on the film hardness

M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298 297

becomes evident if the indent depth is more than 10 times largerthan the film thickness. Since the thickness of the surface layersand the depth of the indent involved in this work are about 0.2–0.5 lm and 1 lm, respectively, the influence of the parent glasscomposition on the hardness is relatively small. Thus, the atmo-sphere of heat-treatment is the dominant factor influencing hard-ness (Table 2).

The surface layer created as a result of the oxidation treatmentincreases the Vickers hardness even though the silica surface con-tent of this glass is lower than that of the untreated glass. This isexplained by the formation of primarily MgO (periclase) crystalson the surface as these possess a Vickers hardness between 9.0and 12.5 GPa at a load of 0.491 N depending on the crystal orien-tation [54]. The relatively high CA of the sample heat-treated inair could be ascribed to an increase in surface roughness (seeFig. 3(b)) [55,56]. In addition, the oxide surface layer protectsagainst dissolution in the acid solution since the SNMS experiment(Fig. 2) has revealed a decrease in the Na+ concentration near thesurface of this sample. The low alkali resistance of the air-treatedsample is explained by the low surface concentration of siliconsince few Si–O bonds need to be broken in order to dissolve a rel-atively large amount of Na+ and Mg2+ ions.

When heating the glass in N2, no change in Hv is observed. Thisis because the effect of partial surface nitridation (Fig. 6) has coun-teracted the effect of the outward diffusion of network-modifyingcations (Fig. 5(b)) since the latter process lowers the degree ofpolymerization of the glass network. When the glass is heated inH2/N2 (10/90), Hv decreases since two additional factors counteractthe strengthening effect of partial surface nitridation. First, break-age of Si–O bonds occurs due to permeation of H2. Second, conver-sion of network-forming ions (Fe3+) into network modifying ions(Fe2+) occurs during the reduction.

The CA of the 6wtFe sample heat-treated in N2 is relatively highwhich is expected to be due to incorporation of nitrogen [19] andincreased surface roughness (see Fig. 3(d)) [55,56]. The permeationof H2 results in incorporation of structurally bonded OH groups andthis incorporation has caused the relatively low CA [57] of the sam-ple treated in H2/N2 (10/90) (Table 2). When the 6wtFe glass hasbeen heat-treated in N2 and H2/N2 (10/90), the acid resistance is in-creased and the alkali resistance is decreased compared to the un-treated glass. This can be seen from the leaching measurements(Table 2). The SNMS experiments explain these results as a de-crease in both the sodium and silicon concentration is detectednear the surface of these heat-treated samples.

5. Conclusions

Oxidation of an iron-bearing glass, which is caused by thermaltreatment in atmospheric air, drives the Mg2+, Ca2+, and Fe2+ ionsto diffuse from the interior towards the surface of the glass so asto charge balance inward motion of electron holes. This observa-tion is consistent with the results of previous studies based onbasaltic glass systems. At the surface, the divalent cations ions re-act with external oxygen to form a crystalline nanolayer. The Fe2+

ions that diffuse to the surface are oxidized to Fe3+ at the surface.A striking phenomenon has been observed, i.e., the outward dif-

fusion (OD) of divalent cations does not only occur under an oxi-dizing atmosphere of heat-treatment, but also under N2, evenunder a reducing atmosphere like H2/N2 (10/90). The OD leads tothe formation of an oxide nanolayer on the glass surface. However,the morphology and the concentration profiles of the samples trea-ted in H2/N2 (10/90) or N2 gases are quite different from those ofthe samples treated in air. The OD of divalent cations in glassestreated in N2 and H2/N2 (10/90) is related to partial surface nitrid-ation, i.e., the mechanism of the OD depends on the type of gas

used for the heat-treatment. The reduction of Fe3+ to Fe2+ in H2/N2 (10/90) operates by permeation of H2 into the glass. Thus, OHgroups form and are incorporated into the glass structure. Theexperimental data are in excellent agreement with the tarnishingmodel, confirming the proposed reduction mechanism.

The new chemical routes to modify glass surfaces have an im-pact on physical and chemical glass properties. The hardness in-creases when the glasses are heat-treated in air due to theformation of a crystalline surface layer. Outward diffusion of net-work-modifying cations and formation of OH groups explain thedecrease in hardness of samples heated in H2/N2 (10/90). Surfaceroughness, OH content, and nitridation affect the surface wettabil-ity. The acid resistance of a heat-treated sample is enhanced if thetreatment results in depletion of Na+ ions from the surface. The al-kali resistance is diminished if the treatment results in an enrich-ment of the network-modifying cations on the surface.

Acknowledgements

The authors acknowledge Thomas Peter, Anne Dittmar, and Mi-chael Zellmann for performing SNMS, AFM, and XRF measure-ments, respectively. They also acknowledge Søren Land Jensen,Martin Jensen, Linda Backnäs, Dorthe Lybye, and Hansjörg Bornhöftfor valuable discussions.

References

[1] J.D. Stevenson, P.G. Wolynes, J. Chem. Phys. 129 (2008) 234514.[2] R.F. Cooper, J.B. Fanselow, D.B. Poker, Geochim. Cosmochim. Acta 60 (1996)

3253.[3] D.J.M. Burkhard, J. Petrol. 42 (2001) 507.[4] Y.Z. Yue, M. Korsgaard, L.F. Kirkegaard, G. Heide, J. Am. Ceram. Soc. 92 (2009)

62.[5] G.B. Cook, R.F. Cooper, T. Wu, J. Non-Cryst. Solids 120 (1990) 207.[6] G.B. Cook, R.F. Cooper, Am. Mineral. 85 (2000) 397.[7] D.R. Smith, R.F. Cooper, J. Non-Cryst. Solids 278 (2000) 145.[8] V. Magnien, D.R. Neuville, L. Cormier, J. Roux, J.-L. Hazemann, D. de Ligny, S.

Pascarelli, I. Vickridge, O. Pinet, P. Richet, Geochim. Cosmochim. Acta 72 (2008)2157.

[9] R.F. Cooper, J.B. Fanselow, J.K.R. Weber, D.R. Merkley, D.B. Poker, Science 274(1996) 1173.

[10] M.M. Smedskjaer, Y.Z. Yue, J. Non-Cryst. Solids 355 (2009) 908.[11] M.M. Smedskjaer, J. Deubener, Y.Z. Yue, Chem. Mater. 21 (2009) 1242.[12] J.L. Barton, M. Morain, J. Non-Cryst. Solids 3 (1970) 115.[13] J.E. Shelby, J. Appl. Phys. 51 (1980) 2589.[14] J.E. Shelby, J. Vitko, J. Non-Cryst. Solids 45 (1981) 83.[15] M.R. Tuzzolo, J.E. Shelby, J. Non-Cryst. Solids 143 (1992) 181.[16] C. Estournès, T. Lutz, J.L. Guille, J. Non-Cryst. Solids 197 (1996) 192.[17] F. Gaillard, B. Schmidt, S. Mackwell, C. McCammon, Geochim. Cosmochim. Acta

67 (2003) 2427.[18] R.E. Loehman, J. Non-Cryst. Solids 42 (1980) 433.[19] I.N. Yashchishin, L.V. Zhuk, O.I. Kozii, Glass Phys. Chem. 27 (2001) 470.[20] O.I. Kozii, I.N. Yashchishin, L.O. Bashko, Glass Ceram. 61 (2004) 328.[21] S. Sakka, J. Non-Cryst. Solids 181 (1995) 215.[22] S. Hampshire, J. Eur. Ceram. Soc. 28 (2008) 1475.[23] Y.Z. Yue, J. Non-Cryst. Solids 354 (2008) 1112.[24] A. Montenero, M. Friggeri, D.C. Giori, N. Belkhiria, L.D. Pye, J. Non-Cryst. Solids

84 (1986) 45.[25] C. Ades, T. Toganidis, J.P. Traverse, J. Non-Cryst. Solids 125 (1990) 272.[26] J.D. Kiely, D.A. Bonnell, J. Vac. Sci. Technol. B 15 (1997) 1483.[27] R.H. Doremus, Glass Science, John Wiley and Sons, New York, 1994.[28] H. Maekawa, T. Saito, T. Yokokawa, J. Phys. Chem. B 102 (1998) 7523.[29] X.Y. Xue, M. Kanzaki, J. Phys. Chem. B 105 (2001) 3422.[30] H. Behrens, A. Stuke, Glass. Sci. Technol. 76 (2003) 176.[31] P.C. Hess, in: R.B. Hargraves (Ed.), Physics of Magmatic Processes, Princeton

University Press, Princeton, 1980, p. 3.[32] M.M. Smedskjaer, Master thesis, Aalborg University, Denmark, 2008.[33] A.A. Salem, R. Kellner, M. Grasserbauer, Glass Technol. 35 (1994) 135.[34] S. Dreer, Fresenius J. Anal. Chem. 365 (1999) 85.[35] S. Dériano, T. Rouxel, S. Malherbe, J. Rocherullé, G. Duisit, G. Jézéquel, J. Eur.

Ceram. Soc. 24 (2004) 2803.[36] F. Geotti-Bianchini, M. Preo, M. Guglielmi, C.G. Pantano, J. Non-Cryst. Solids

321 (2003) 110.[37] R.M. Almeida, T.A. Guiton, C.G. Pantano, J. Non-Cryst. Solids 121 (1990) 193.[38] A. Bertoluzza, C. Fagnano, M.A. Morelli, V. Gottardi, M. Guglielmi, J. Non-Cryst.

Solids 48 (1982) 117.[39] A. Duran, C. Serna, V. Fornes, J.M.F. Navarro, J. Non-Cryst. Solids 82 (1986) 69.

298 M.M. Smedskjaer et al. / Journal of Non-Crystalline Solids 356 (2010) 290–298

[40] S.A. MacDonald, C.R. Schardt, D.J. Masiello, J.H. Simmons, J. Non-Cryst. Solids275 (2000) 72.

[41] K. Morita, A. Suganuma, A. Makishima, J. Mater. Sci. 29 (1994) 6587.[42] J.J. Videau, J. Etourneau, C. Garnier, P. Verdier, Y. Laurent, Mater. Sci. Eng. B 15

(1992) 249.[43] J.E. Shelby, Handbook of Gas Diffusion in Solids and Melts, ASM International,

Materials Park, 1996.[44] T. Ito, T. Nozaki, H. Ishikawa, J. Electrochem. Soc. 127 (1980) 2053.[45] M. Guglielmi, P. Colombo, G. Battaglin, P. Mazzoldi, A. De Polo, A. Boscolo-

Boscoletto, G. Granozzi, J. Non-Cryst. Solids 147&148 (1992) 451.[46] R. Marchand, D. Agliz, L. Boukbir, A. Quemerais, J. Non-Cryst. Solids 103 (1988)

35.[47] J. Schroeder, J.J. Jarek, J. Non-Cryst. Solids 102 (1988) 181.[48] A.K. Varshneya, Fundamentals of Inorganic Glasses, Society of Glass

Technology, Sheffield, 2006.

[49] J. Crank, The Mathematics of Diffusion, Clarendon, Oxford, 1975.[50] R.H. Doremus, Diffusion of Reactive Molecules in Solids and Melts, John Wiley

and Sons, New York, 2002.[51] G. De Marchi, F. Caccavale, F. Gonella, G. Mattei, P. Mazzoldi, G. Battaglin, A.

Quaranta, Appl. Phys. A 63 (1996) 403.[52] M.R. Carroll, J.D. Webster, in: M.R. Carroll, J.R. Holloway (Eds.), Volatiles in

Magmas, Reviews in Mineralogy, vol. 30, Mineralogical Society of America,1994, p. 231.

[53] J. Deubener, R. Müller, H. Behrens, G. Heide, J. Non-Cryst. Solids 330 (2003)268.

[54] M.Y. Khan, L.M. Brown, M.M. Chaudhri, J. Phys. D: Appl. Phys. 25 (1992) 257.[55] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40 (1944) 546.[56] X.-M. Li, D. Reinhoudt, M. Crego-Calama, Chem. Soc. Rev. 36 (2007) 1350.[57] M.L. Hair, W. Hertl, J. Phys. Chem. 73 (1969) 4269.