Inward Cationic Diffusion and Percolation Transition inGlass–Ceramics

Morten M. Smedskjaer,z Yuanzheng Yue,*,w,z and Steen M^rupy

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

yDepartment of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

We show the quantitative correlation between the degree ofcrystallization and the cationic diffusion extent in iron-contain-ing diopside glass–ceramics at the glass transition temperature.We find a critical degree of crystallization, above which thediffusion extent sharply drops with the degree of crystallization.Below the critical value, the diffusion extent decreases onlyslightly with the degree of crystallization. No cationic diffusionis observed in the fully crystalline materials. The critical valuemight be associated with a percolation transition from an inter-connected to a disconnected glass phase.

I. Introduction

GLASS is formed when crystallization is avoided upon coolingof a melt. Controlled crystallization of a glass can result in

a partially crystallized material, i.e., a so-called glass–ceramic,which possesses superior physical and chemical properties, andhence enables various technical applications ranging from cook-ware to architectural materials and bone implants.1 Diffusion ofmobile ions (normally network modifiers) is an important pro-cess in glasses because it has strong impact on electrical conduc-tivity, thermal expansion, dielectric loss, and chemical durability.However, we expect that ions migrate in a more complicatedmanner in a glass–ceramic than in a glass. Therefore, the extentand manner of ionic diffusion should differ in the two types ofmaterials.2–5 In this paper, we explore how the diffusion of al-kaline earth ions6,7 in iron-bearing diopside (CaMgSi2O6) sys-tems depends on the degree of crystallization. We chose diopsideas the object of this study for the following reasons. First, whenthe diopside glass crystallizes partly or totally, the resulting crys-talline phase will have the same composition as the original glass.This allows us to compare the diffusion extent of glass–ceramicswith different degrees of crystallization. If the crystalline phaseremoves certain ions from the residual glass, the ionic diffusionin the glass will be affected.8–10 Second, the simple system allowsus to obtain more clear information about the diffusion of singleelements without influences from other elements.

We study the diffusion by using the reduction-inward diffu-sion approach.6,7 This approach is based on a reduction of apolyvalent element (e.g., Fe31 to Fe21) at temperatures aroundTg (glass transition temperature). Such a reduction causes aninward diffusion (from the surface toward the interior) of mod-ifying ions, which in turn leads to the formation of an SiO2-richsurface layer. The reduction of the polyvalent element proceeds

via two simultaneous processes: gaseous permeation and out-ward flux of electron holes. To maintain charge neutrality, thelatter process requires an inward diffusion of mobile cations.Hence, in this study, the glasses first crystallize to various extentsand the crystallized samples are then heat treated in a reducingatmosphere to induce the diffusion. Finally, the diffusion profilesare measured and compared with the degree of crystallization.

II. Experimental Procedure

The glass compositions used in this work are mentioned inTable I. Mixtures of reagent-grade SiO2, CaCO3, MgO, andFe2O3 powders were melted in a Pt90Rh10 crucible at 1803 K for3 h. The glass samples were obtained by quenching the melts ona brass plate and they were then annealed at 998 K for 15 min.Cylindrical glass samples (diameter: B8 cm; height: B5 mm)were prepared and glass–ceramic samples were obtained by heattreating the cylindrical samples for 30 min at various tempera-tures in argon. These samples were polished according to theprocedure described elsewhere.12 Tg, degrees of crystallization(a), and onset and peak temperatures of crystallization (Tc andTp, respectively) were measured using a differential scanningcalorimeter (DSC) (STA 449C Jupiter, Netzsch, Selb, Germany)in argon at 20 K/min.11,13 A homemade constant accelerationtransmission 57Fe Mossbauer spectrometer was used to deter-mine the iron redox state in the fully amorphous and fully crys-talline Diop-Fe1 samples, respectively. In selected samples, theidentities of the crystalline phases were determined using anX-ray diffractometer (XRD) (Siemens D5000, Karlsruhe,Germany) at the CuKa line. The inward diffusion was inducedby treating the glasses, glass–ceramics, and crystalline samples ina reducing H2/N2 (1/99 v/v) atmosphere at 995 K (BTg) for 2 h.Diffusion profiles were measured using secondary neutral massspectroscopy (SNMS) as described in detail elsewhere.6,7,12

Table I. Chemical Composition, Glass TransitionTemperature (Tg), and CrystallizationOnset (Tc) and Peak (Tp)

Temperatures of the Glasses

Glass ID

Chemical composition (mol%)

Tg (K) Tc (K) Tp (K)SiO2 CaO MgO Fe2O3w

Diopside 49.8 24.9 25.1 0.0 994 1261 1302Diop-Fe0.1 50.0 24.8 25.0 0.1 997 1258 1299Diop-Fe0.3 49.9 24.9 24.8 0.3 995 1257 1299Diop-Fe0.6 49.8 24.8 24.6 0.6 994 1250 1295Diop-Fe1 49.8 24.4 24.6 1.0 991 1243 1292

The chemical compositions are measured by X-ray fluorescence. Tg is deter-

mined by differential scanning calorimeter (DSC) according to the method de-

scribed by Yue.11 Tc and Tp are determined by DSC at a rate of 20 K/min. wAll

iron reported as Fe2O3.

J. Mauro—contributing editor

This work was supported by the International Doctoral School of Technology and Sci-ence at Aalborg University under Ph.D. stipend No. 562/06-FS-28045.

*Member, The American Ceramic Society.wAuthor to whom correspondence should be addressed. e-mail: yy@bio.aau.dk

Manuscript No. 27425. Received January 21, 2010; approved January 29, 2010.

Journal

J. Am. Ceram. Soc., 93 [8] 2161–2163 (2010)

DOI: 10.1111/j.1551-2916.2010.03701.x

r 2010 The American Ceramic Society

2161

III. Results and Discussion

The XRD analyses show the fully amorphous nature of the as-prepared glasses (inset of Fig. 1). Table I shows the Tg, Tc, andTp values of the glass samples with different iron content. Asshown in Table I, the iron-containing glasses exhibit lower Tc

and Tp values than the iron-free glass. The identity of the crys-talline phase is revealed by the XRD results. When thefive glasses are treated at 1223 K for 30 min in argon, theybecome fully crystallized. Diopside (CaMgSi2O6) forms in theiron-free glasses, whereas augite (Ca(Mg,Fe)(Si,Fe)2O6) formsin the iron-bearing glasses (inset of Fig. 1).

To quantify the degree of crystallization (a) in the glass–ceramics, a calorimetric method is used, which has beenestablished elsewhere.13 a is determined from the area of thecrystallization peak in the DSC scan, i.e. the enthalpy ofcrystallization (DH). The maximum enthalpy is obtained froman untreated glass sample (DHuntreated). a is calculated invol% using Eq. (1)13:

a ¼ DHuntreated � DHsample

� �=DHuntreated � 100% (1)

Figure 1 shows the crystallization peaks of the Diop-Fe1samples that have been treated at various temperatures (Th) for30 min before the DSC scan. The DHsample decreases with anincreasing Th, and hence a increases with Th. No exothermicpeak is observed for the sample heat treated at Th 5 1223 K,indicating that the maximum degree of crystallization isachieved. This is verified by the XRD results (inset of Fig. 1).

The Mossbauer analyses of the Diop-Fe1 systems with a5 0and 100 vol% show that the [Fe21]/[Fetot] ratio, where[Fetot]5 [Fe21]1[Fe31], is 0.3470.03 and 0.3170.03, respec-tively. Hence, the crystallization of the glass does not change theoxidation state of iron. This is important for the analysis ofthe diffusion experiments because the initial content of Fe31

affects the extent of diffusion.7 The Mossbauer analysis also re-veals that Fe31 is both octahedrally and tetrahedrally coordi-nated in the crystallized sample. According to earlier findings,14

the two types of Fe31 coordination are attributed to thepresence of CaFe2

31SiO6 in which MgSi of diopside has beenreplaced by two Fe31.

Figure 2 shows SNMS depth profiles of four different sam-ples. No inward diffusion is observed when the iron-free glass isheat treated in H2/N2 (1/99) (Fig. 2(a)). This is natural becauseno Fe31 ions are available for the reduction process to occur,which is a prerequisite for the inward diffusion. In contrast,surface depletion of calcium, magnesium, and iron is observed in

the reduced Diop-Fe1 glass, meaning that the inward diffusionoccurs (Fig. 2(b)), which in turn leads to the formation of a sil-ica-rich surface layer. When the iron-bearing glass has partlycrystallized, i.e., the glass–ceramic is generated, the extent of theinward diffusion in this glass–ceramic is lower than that in thepure glass. For the sample containing only 7 vol% glass phase, adepletion of cations is still detectable, but the depleted layer israther thin (B100 nm) (Fig. 2(c)). No diffusion is observed inthe time window of the experiments when the sample becomesfully crystalline (Fig. 2(d)).

Figure 3 shows the quantitative link between the extent ofdiffusion and the degree of crystallization. The extent of diffu-sion is quantified by the diffusion depth of the Mg21 ions(DxMg), which is calculated as the first depth at whichc/cbulk � 1. Similar results are obtained for the diffusion of cal-cium and iron ions. It is seen in Fig. 3 that DxMg decreases withan increasing a. As shown by the linear fits (dashed lines) inFig. 3, the decrease of DxMg is especially pronounced in therange of a from 80 to 100 vol%. No diffusion is observed inthe fully crystalline samples. These tendencies may be explainedas follows. First, the diffusing ions are more strongly bound tooxygen ions in the crystalline state than in the glassy state. Thus,a larger potential energy barrier needs to be overcome for the

Fig. 1. Heat flow (f) as a function of temperature (T) for the Diop-Fe1glass in the temperature range of crystallization. The samples have beencrystallized for 30 min in argon at various temperatures (Th) before thedifferential scanning calorimeter scan. Inset: X-ray diffraction patternsfor two Diop-Fe1 samples: untreated (A) and heat treated at 1223 K for30 min in argon (H). The peaks in the pattern of the heat-treated samplehave all been assigned to augite.

Fig. 2. Secondary neutral mass spectroscopy depth profiles of glassesand glass–ceramics heat treated in H2/N2 (1/99) at 995 K for 2 h. Thecurves are plotted as the concentration of the element at a given depthdivided by the concentration of the same element in the bulk of the glass(c/cbulk). (a) Diopside glass (a50.0 vol%). (b) Diop-Fe1 glass (a50.0vol%). (c) Diop-Fe1 sample crystallized at 1210 K for 30 min in argon(a5 93.3 vol%). (d) Diop-Fe1 sample crystallized at 1223 K for 30 minin argon (a5 100 vol%).

Fig. 3. Diffusion depth ofMg21 ions (DxMg) as a function of the degreeof crystallization (a) in the five systems. The dashed lines represent linearfits to the data. For the Diop-Fe1 system, R2 of the linear fit is 0.995 and0.986 in the range of a of 0–60 vol% and 80–100 vol%, respectively.

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cationic diffusion to occur. Second, the more ordered structureof crystals causes the free volume of a glass to be larger than thatof the corresponding crystal. This is macroscopically observedas an increase in density when a glass crystallizes.8,15–17 Third, toinduce the inward cationic diffusion, the reducing H2 gas mustfirst penetrate into the uppermost surface layer, subsequently bedissolved in the structure, and simultaneously contact and re-duce Fe31 ions to Fe21 in the glass structure. The penetration,and hence reduction process is easier in the more open glassstructure than in the crystalline structure.18

The existence of a critical value (a B80 vol%), above whichDxMg drastically drops to zero with a, indicates that a suddendrop in the degree of interconnection of the glass phase occurs.The diffusion occurs much faster in the glassy phase than in thecrystalline phase because no diffusion is observed when the ma-terial is fully crystallized. At low degrees of crystallization, theglassy phase might consist of interconnected channels allowing arelatively fast cationic diffusion. At a certain degree of crystal-lization, the glassy phase starts to be disconnected, graduallybecomes isolated domains, and finally disappears. The discon-nection of the glassy channels significantly lowers the cationicdiffusion extent until it drops to zero at a5 100 vol%.

The existence of the critical value may be described in termsof a percolation transition4,19 because there are both easy anddifficult paths through which the cations diffuse. At low degreesof crystallization, the crystals prevent the mobile ions fromcrossing their domains. At high degrees of crystallization, thecrystals block the diffusion pathways in the glassy matrix, andthereby slow down the ionic transport. At the critical value, theamount of glassy paths for diffusion dramatically decreases dueto a sharp drop of the degree of the channel interconnection.Despite this, the diffusion does not stop until the sample is fullycrystallized. This implies that a limited number of the intercon-nected paths still remain. The critical value may therefore beassociated with a percolation threshold value for the beginningof the interruption of the diffusion pathways.

In earlier studies,4,5 a similar behavior has been reported forionic conductivity in glass–ceramics with respect to the correla-tion between the extent of transport and the degree of crystal-lization. However, in comparison with the earlier studies, thisstudy focuses on the inward diffusion of alkaline earth ions inglass–ceramics, which is induced by the redox reaction of atransition metal, and occurs in the surface layer. In addition, thiswork makes it possible to modify the surface chemistry of theglass–ceramic in favor of glass–ceramic properties such as hard-ness and chemical durability.6,7

IV. Conclusions

The inward diffusion of divalent cations decreases with an in-creasing degree of crystallization in diopside glass–ceramics, es-pecially when the degree of crystallization is above 80 vol%. Theexistence of this critical value might be associated with a perco-lation transition from an interconnected to a disconnected glass

phase. Using this diffusion approach, a highly silica-rich glassphase is obtained on the glass–ceramic surface. These new find-ings could be used in designing glass–ceramics with improvedsurface properties, i.e. by first making the glass crystallize to adegree below the critical value, and then making the inwarddiffusion occur via a reduction of polyvalent elements.

Acknowledgments

We thank T. Peter and M. Zellmann for SNMS and XRD measurements, re-spectively, and M. Jensen for assistance with glass preparation. We also thankJ. Deubener for supporting experiments and for the useful discussions.

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