surface and bulk structural relaxation kinetics of silica glass

Ž .Journal of Non-Crystalline Solids 209 1997 264–272

Surface and bulk structural relaxation kinetics of silica glass

Anand Agarwal 1, Minoru Tomozawa )

Materials Science and Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA

Received 18 April 1996; revised 20 June 1996; accepted 5 July 1996

Abstract

The structural relaxation kinetics of a silica glass were measured by following the IR structural band positions, which aredirectly correlated with the average Si–O–Si bond angle as well as with the fictive temperature of the glass, as a function ofheat-treatment time, temperature and the water vapor pressure. Both surface relaxation and bulk relaxation kinetics weredetermined by measuring the IR reflection and absorption band positions, respectively. The surface relaxation was muchfaster than the bulk relaxation and had a smaller activation energy. Also, both relaxation kinetics were faster in the presenceof water vapor. The apparent bulk relaxation time determined from the IR absorption band shift was a composite relaxationtime consisting of both the relaxation time of the water-catalyzed near surface layer and the true bulk relaxation time of theglass interior which is unaffected by water vapor. The true bulk relaxation time was evaluated and found to have anactivation energy consistent with that of the viscous flow.

1. Introduction

Recently, a method to measure the fictive temper-ature of silica and silicate glasses by IR spectroscopy

w xwas reported 1–3 . The method consisted of deter-mining the band position of IR structural bandscorresponding to the average Si–O–Si bond anglewhich assumes a unique value at a given fictivetemperature. In particular, for silica glass it waspossible to determine the fictive temperature of thesample by using both IR absorption and reflectionspectroscopy. Traditionally the fictive temperature ofglasses has been determined by differential scanning

Ž . w xcalorimetry DSC measurements 4 but this method

) Corresponding author. Tel.: q1-518 276 6659; fax: q1-518276 8554; e-mail: [email protected].

1 Now at Sterlite Communications Limited, Maharashtra, India.

is not applicable to silica glasses which exhibit asmall change of specific heat with temperature.

By following the time dependence of the fictivetemperature using the IR method, the kinetics ofstructural relaxation can be investigated. Since manyglass properties vary with the fictive temperature,kinetics of the fictive temperature variation can pro-vide a measure of property changes of glasses due toheat treatment. Furthermore, since some propertiessuch as chemical durability and mechanical strengthare sensitive to the surface structure of the glass,relaxation kinetics of the glass surface are particu-larly useful for estimating changes in these proper-

w xties 5 . By using the IR reflection band shift, surfacestructural relaxation can be monitored separately fromthe bulk structural relaxation. In this study, bothsurface and bulk relaxation kinetics of a silica glasswere measured by following the time dependence of

0022-3093r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved.Ž .PII S0022-3093 96 00570-4

( )A. Agarwal, M. TomozawarJournal of Non-Crystalline Solids 209 1997 264–272 265

the IR reflection and absorption band positions atvarious temperatures.

2. Experimental

A silica glass made by Furukawa using a vaporŽ .axial deposition VAD method was used. The glass

is identical to those used as cladding glasses foroptical communication fiber. This glass has ex-

Ž .tremely low hydroxyl less than 0.1 ppm and alkaliŽ .0.04 ppm Na impurities but a high chlorine contentŽ .1000 ppm . However, since a variety of silica glassesexhibit a nearly identical relationship between theequilibrium IR band position and the heat-treatment

Ž . y1 Ž .Fig. 1. IR structural band changes during hydration measured by a IR reflection band shift at ;1122 cm and b IR absorption bandy1 Ž . y1shift at 2260 cm and c the corresponding IR 3672 cm absorbance representing water uptake, all at 9508C under water vapor pressure

355 Torr and 0.3 Torr.

( )A. Agarwal, M. TomozawarJournal of Non-Crystalline Solids 209 1997 264–272266

w xtemperature or fictive temperature 1 the same anal-ysis can be applied to any type of silica glass.

Glass samples for this relaxation study were pre-pared by cutting and polishing in the same manner as

w xdescribed earlier for the fictive temperature study 1 .Silica glass plate samples measuring ;10=10 mm2

and ;1 mm thick were heat-treated at varioustemperatures in the presence of water vapor. In some

cases, the specimen thickness was varied from 0.2 to5.5 mm to examine the thickness effect on relaxationkinetics. Water vapor, e.g., 355 Torr from the waterbath held at 808C, was introduced through a heatedtube into the furnace where the specimen was heat-

Ž .treated. Low water vapor pressure ;0.3 Torr wasproduced by passing dry air through a liquid nitrogencold trap. Other specimens were heat-treated in a dry

Ž .Fig. 2. IR structural band changes during hydration at 355 Torr followed by dehydration in dry nitrogen measured by a IR reflection bandy1 Ž . y1 Ž . y1shift at ;1122 cm and b IR absorption band shift at ;2260 cm and c the corresponding IR 3672 cm absorbance representing

water uptake, all at 9508C.


nitrogen atmosphere. Specimens were taken out ofthe furnace periodically to measure IR spectra. IRstructural bands at ;1122 cmy1 reflection band,;2260 cmy1 absorption band as well as hydroxylband at 3672 cmy1 absorption band were monitored.It is estimated that IR reflection at ;1122 cmy1

w xprobes approximately 0.5 mm 6 of the glass surfacewhile ;2260 cmy1 absorbance gives the averagestructural information of the entire specimen thick-ness.

3. Results

The IR structural band position variations with theheat-treatment time at 9508C under two differentwater vapor pressures are shown in Fig. 1, togetherwith the hydroxyl absorbance change. Two datapoints for 1122 cmy1 reflection at each heat-treat-

Ž .ment time in Fig. 1 a come from the two sides ofthe specimen surface. The slight difference betweenthese two data points is due to different stages ofrelaxation of each side and indicates the maximumrange of error in the measurement. When data wereobtained from the same location of the sample, theerror range of the sample was smaller than thesymbol size shown. Under a high water vapor pres-sure of 355 Torr, water uptake by the glass specimen

Ž Ž ..is clearly detected cf. Fig. 1 c while under lowwater vapor pressure of 0.3 Torr, water uptake wasnegligible. The corresponding relaxation kinetics of

Ž Ž .. Ž Ž ..both surface Fig. 1 a and bulk Fig. 1 b werefaster under higher water vapor pressure. Also, relax-ation kinetics of the surface were faster than the bulkrelaxation under the same water vapor pressure.

After 138 h of hydration at 9508C, water vaporfrom the water bath was stopped and dry nitrogengas was passed through the furnace. Fig. 2 shows theIR signal change during dehydration for specimensafter hydration in 355 Torr water vapor as reportedin Fig. 1. It can be seen, consistent with our previous

w xstudies 1,3 , that the water content in glass is re-duced but the structural bands remain practicallyunchanged during dehydration, indicating that theobserved structural change during hydration is irre-versible, relaxational in nature and that the water issimply promoting the relaxation.

Fig. 3 compares the kinetics of the surface relax-ation in terms of the IR structural reflection bandshift at various heat-treatment temperatures under aconstant water vapor pressure of 355 Torr. Naturallythe relaxation is faster at higher temperature. Asimilar study was also performed under low watervapor pressure, 0.3 Torr. The relaxation kineticswere represented by the relaxation function,

w x1yf t s n t yn r n yn , 1Ž . Ž . Ž .e 0 e

Ž .where n is the initial band position, n t is the0

band position at time t and n is the equilibriumew xband position. It was found 3 that the IR structural

band shift is accompanied by a change in bandheight and that they are proportional to each other.Thus the same relaxation function can be obtained

Fig. 3. IR reflection band shift at ;1122 cmy1 for silica glassheat-treated at various temperature under 355 Torr water vaporpressure.


Ž .Fig. 4. Relaxation function according to Eq. 1 evaluated from IRreflection band shift measured at 9508C under 355 Torr water

Ž . Ž .vapor pressure, in comparison with theoretical Eq. 2 and Eq. 3 .

by following IR absorption band height instead ofthe band position. For band height analysis, n s in

Ž .Eq. 1 are replaced by the corresponding bandheights.

The 1122 cmy1 reflection band shift data ob-tained at 9508C under 355 Torr water vapor pressureshown in Fig. 3 were curve-fitted with both a simpleexponential function

f t sexp ytrt 2Ž . Ž . Ž .and the KWW function

bf t sexp ytrt . 3Ž . Ž . Ž .The results compared in Fig. 4 indicate that either ofthese functions is satisfactory within experimentalerror. Consequently all of the subsequent analyseswere made using a simple exponential function. Fig.5 compiles the relaxation times obtained in thismanner from the surface relaxation under two differ-ent water vapor pressures. It is clear that underhigher water vapor pressure, the relaxation time isshorter and its activation energy is smaller.

The kinetics of bulk relaxation at 10008C under355 Torr of water vapor pressure determined fromthe IR absorption band at ;2260 cmy1 are shownin Fig. 6 in terms of band height per unit thicknessfor specimens with different thicknesses. Unlike theIR reflection band change, there is a clear effect ofthe thickness of the specimen at this temperature,with the thicker specimen relaxing more slowly. Therelaxation time evaluated from this type of data areplotted against the sample thickness in Fig. 7 bothfor 355 Torr and 0.3 Torr water vapor pressure. The

Fig. 5. Temperature dependence of surface structural relaxationtime under water vapor pressure 355 Torr and 0.3 Torr.

relaxation times become longer for thicker speci-mens approaching a finite value and the effect ofwater vapor on the relaxation time appears to dimin-ish for thicker specimens at this temperature. Whenthe specimens were heat-treated at high temperature,e.g., 12508C, the relaxation time was independent ofspecimen thickness as well as water vapor pressurewithin experimental error as can be seen in Fig. 8.

The observed thickness dependence of the relax-ation time was believed to originate from the factthat the water entry into the specimen surface pro-motes the relaxation process. The relative contribu-

Fig. 6. IR absorption band height change at ;2260 cmy1 at10008C under water vapor pressure, 355 Torr for samples withdifferent thicknesses.


Fig. 7. The apparent bulk relaxation time as a function of speci-men thickness measured at 10008C under water vapor pressures,355 Torr and 0.3 Torr.

tion of the fast-relaxing surface layer diminishes forthicker specimens. In this process, therefore, thereshould be a non-uniform relaxation with the fastestrelaxation occurring at the specimen surface layeraffected by water diffusion. In order to demonstratethe presence of the non-uniform relaxation, IR reflec-tion band measurement was combined with succes-sive etching with a dilute HF–H SO solution for a2 4

specimen heat-treated for 1.5 h at 10008C under 355Torr water vapor to obtain the relaxation depth pro-file. Weight loss by etching, surface area and densitywere used to estimate the thickness removed fromboth sides of the surface by etching. IR reflectionfrom both sides of the specimen was measured aftereach etching. Fig. 9 shows the resulting IR reflectionband profile as a function of depth. As expected, the

Fig. 8. The apparent bulk relaxation time as a function of speci-men thickness measured at 12508C under water vapor pressures,355 Torr and dry nitrogen atmosphere.

Fig. 9. Depth profile of IR reflection band after heat-treatment at10008C for 1.5 h under 355 Torr water vapor pressure.

surface of ;200 mm relaxed faster with the interiorof the specimen hardly exhibiting a detectable relax-ation after a time of 1.5 h at 10008C. The corre-sponding hydroxyl concentration profile showed thatthe water diffusion was limited to a surface layer of;20 mm. The smaller depth of hydroxyl waterdiffusion than the depth of the relaxed surface layerat this temperature is consistent with our previous

w xobservations 7 .

4. Discussion

It is clear that water entry into silica glass pro-motes structural relaxation. Even under a low watervapor pressure of 0.3 Torr, where negligible wateruptake occurred, the relaxation kinetics appeared tobe accelerated by water vapor. The water is believedto exist predominantly in the form of hydroxyl andthe amount of water which enters into silica glassunder this low water vapor pressure is expected to beless than 3% of that which enters under 355 Torrwater vapor pressure assuming that water solubilityis proportional to the square root of the water vaporpressure. It appears that a small concentration ofwater can promote the structural relaxation. It isunlikely, however, that a small quantity of hydroxylis promoting the glass structural relaxation since

w xhydroxyl are immobile 8 and cannot influence alarge volume of glass structure beyond the vicinityof the hydroxyl. We speculate that a small quantityof molecular water which can move around in thesilica glass network is promoting the structural relax-ation.

The faster surface relaxation probed by the IR


reflection, compared to bulk relaxation is also at-tributable to the effect of water, with water readilyentering a glass surface layer of ;0.5 mm.

The bulk relaxation kinetics determined by IRabsorption are results of a composite effect involvingboth the relaxation of the water-catalyzed surface

Ž .layer and the true bulk relaxation by viscous flowunaffected by water. The apparent bulk relaxationtime, t , can be expressed in terms of the water-rel

catalyzed relaxation time, t , and the true bulk relax-1

ation time, t , by0

1rt s1rt q1rt . 4Ž .rel 0 1

The true bulk relaxation time, t , should be similar0

to the relaxation time commonly determined by vis-cosity and shear modulus while the water-catalyzedsurface relaxation time, t , should be related to1

water entry. This water-catalyzed relaxation time, t ,1

is different from the relaxation time observed in thesurface relaxation kinetics using IR reflection, whichwas related to the relaxation of the thin surface layerof 0.5 mm. The water-catalyzed relaxation time, t ,1

may be estimated as follows: in the low temperaturerange where the true bulk relaxation is negligible, therelaxation is solely caused by water diffusion. In thiscase the relaxation time is expected to be approxi-mately equal to the time in which diffusion proceedshalf way through the specimen. When the thicknessof the specimen is x with diffusion taking placefrom both sides, this indicates Dt fxr4, i.e.,( 1

t fx 2r16 D, where D is the water diffusion coeffi-1

cient. When the exponential relaxation function wasfitted to the diffusion uptake function, i.e.,

2 21yexp ytrt f1y 8r 2nq1 pŽ . Ž .Ý1ns0

=2 2 2exp yD 2nq1 p trx ,Ž .� 4

5Ž .the best fit was obtained when t sx 2r12 D. Thus1

the apparent bulk relaxation time determined by theIR absorption band shift can be expressed as

1rt s1rt q12 Drx 2 . 6Ž .rel 0

The water diffusion coefficient, D, estimated fromthe structural relaxation depth profile was greaterthan the hydroxyl diffusion coefficient. This differ-

w xence was attributed 7 to the presence of a smallquantity of mobile molecular water diffusing farther

than the hydroxyl concentration front detectable byIR spectroscopy, and promoting the structural relax-ation. Furthermore, the value of the diffusion coeffi-cient evaluated from the relaxation profile can betime dependent since the related hydroxyl waterdiffusion of glass is known to vary with the fictive

w xtemperature 9 .The expected apparent bulk relaxation time, t ,rel

is schematically shown in Fig. 10 as a function of thespecimen thickness. As observed experimentally therelaxation time becomes thickness independent forthick specimens. The experimental data shown inFig. 7 resembles the theoretical curve shown in Fig.10.

It is possible to extract the true bulk relaxationtime, t , and the diffusion coefficient from the ex-0

perimentally determined apparent bulk relaxationŽ .time, t . According to Eq. 6 , when the reciprocalrel

of the observed relaxation time, 1rt , is plottedrel

against the reciprocal of the sample thicknesssquared, 1rx 2, the reciprocal of the true bulk relax-

Ž .ation time 1rt is obtained as the intercept corre-02 Ž .sponding to 1rx ™0. Eq. 6 predicts a straight line

in the plot with the slope being proportional to thediffusion coefficient, D, provided that D is a con-

w xstant. In reality, D is not a constant 3 during thestructural relaxation. Examples of such an analysis toobtain the true bulk relaxation time and the long timediffusion coefficient are shown in Figs. 11 and 12 forsamples treated at 10008C under two different water

Fig. 10. Schematic representation of theoretical apparent bulkŽ .relaxation time according to Eq. 6 as a function of sample

thickness. Dotted lines represent limiting cases for low tempera-ture or thin sample and high temperature or thick specimen.


Fig. 11. The reciprocal apparent bulk relaxation time versusreciprocal of specimen thickness square for specimen heat-treatedat 10008C under water vapor pressure 355 Torr. The true bulkrelaxation time and diffusion coefficient were obtained from the

Žintercept and limiting slope, respectively, for thick samples x)2.mm .

vapor pressures. In these figures, t and D values0

were obtained by using a least square fit of a straightŽ . Ž .line through t x data for thick samples x)2 mm

for which thermal relaxation is the dominant mecha-nism. The resulting true bulk relaxation time isplotted in Fig. 13 as a function of reciprocal tempera-ture. The same relaxation time was obtained, withinexperimental error, from two other sets of data ob-tained under different water vapor pressures. Theresulting activation energy of 410 kJrmol may ap-pear to be slightly smaller than the common activa-tion energy for viscous flow of silica glasses. But it

w xis known 10 that the activation energy of viscousflow decreases drastically with increasing hydroxylor chlorine content. In view of the high chlorine

Ž .content 1000 ppm of the present samples the ob-tained activation energy appears reasonable.

Fig. 12. The reciprocal apparent bulk relaxation time versusreciprocal of specimen thickness square for specimen heat-treatedat 10008C under water vapor pressure 0.3 Torr. The true bulkrelaxation time and diffusion coefficient were obtained from the

Žintercept and limiting slope, respectively, for thick samples x)2.mm .

Fig. 13. The true bulk relaxation time versus temperature.


5. Conclusion

It was possible to measure the structural relax-ation kinetics by following the IR structural band

Ž .position or intensity as a function of heat-treatmenttime at various temperatures and water vapor pres-sures. By monitoring IR reflection and absorptionbands both surface and bulk relaxation kinetics werestudied. The surface relaxation time was much shorterthan the bulk relaxation time. The apparent bulkrelaxation time consisted of two parts; a water-cata-lyzed relaxation time of the sample surface which iscontrolled by water diffusion and the true bulk relax-ation time which is unaffected by water vapor. Sincesome of the glass properties are surface sensitive andare affected by the fictive temperature, the surfacerelaxation kinetics measurement will be particularlyuseful for evaluating the change of these propertiesby heat treatment.

Acknowledgements

This research was supported by the US Depart-ment of Energy under Grant No. DE-FG02-

85ER45217. The authors thank Dr Steve Crichton ofRensselaer for careful reading of the manuscript.

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surface and bulk structural relaxation kinetics of silica glass

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