Correlation of elastic, acoustic and thermodynamic properties in B2O3 glasses

Ž .Journal of Non-Crystalline Solids 221 1997 170–180

Correlation of elastic, acoustic and thermodynamic properties inB O glasses2 3

M.A. Ramos a,), J.A. Moreno a, S. Vieira a, C. Prieto b, J.F. Fernandez c´a Laboratorio de Bajas Temperaturas, Departamento de Fısica de la Materia Condensada, C-III, UniÕersidad Autonoma de Madrid,´ ´

Cantoblanco, 28049 Madrid, Spainb Instituto de Ciencia de Materiales de Madrid, Consejo Superior de InÕestigaciones Cientıficas, Cantoblanco, 28049 Madrid, Spain´

c Departamento de Fısica de Materiales, C-IV, UniÕersidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain´ ´

Received 21 March 1996; revised 6 January 1997

Abstract

Vitreous B O is a model glass whose physical properties may depend on thermal history and hydroxyl ion, OHy,2 3

concentration. A set of different B O glasses has been prepared and their elastic, acoustic and thermodynamic properties2 3

were investigated around the glass-transition temperature T by differential scanning calorimetry and Brillouin-scattering. Ag

noticeable variation of the ‘fictive’ temperature T , sound velocity and elastic constants was found from glass to glass. Massf

density r is a simple and useful parameter to characterize the glassy state of a given B O sample. Correlations among these2 3

physical properties of B O glasses are presented and discussed. q 1997 Elsevier Science B.V.2 3

PACS: 61.43.Fs; 64.70.Pf; 65.20.qw; 62.20.Dc

1. Introduction

Vitreous B O , a well-known oxide glass, has2 3w xbeen studied since the early 1930s 1–4 . Pure boron

oxide is a very good glass-former, covalently bonded,with interesting physico-chemical properties. B O2 3

Žand related binary borate systems especially alkali.borate glasses are also of commercial and techno-

w xlogical interest 1,5 .In a seminal work, Zachariasen proposed a con-

w xtinuous random network model 3 to describe the

) Corresponding author. Tel: q34-1 397 5551; fax: q34-1 3973961; e-mail: [email protected].

structure of glasses, or more specifically, the ideal-ized structure of an amorphous covalent solid. X-raydiffraction experiments a few years later by Warren

w xand co-workers 4 lent support to this model. Theglass structure consists of a three-dimensional net-work built up by molecular-like structural units,lacking symmetry and periodicity, but preserving thenormal valence of atoms. B O is constructed by2 3

corner-sharing of BO planar triangles connected3

together in the network, through a distribution ofdihedral angles characterizing the relative orienta-tions between the triangles. However, diffractionstudies and other structural investigations on glasses

w xhave shown medium-range order 6 , beyond theshort-range order due to chemical bonding within the

0022-3093r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved.Ž .PII S0022-3093 97 00368-2

( )M.A. Ramos et al.rJournal of Non-Crystalline Solids 221 1997 170–180 171

molecular units. In glassy B O , this medium-range2 3

order seems to be governed by the presence of aplanar regular unit, the so-called boroxol ring.Boroxol ring is a hexagonal B O group composed3 3

of three corner-sharing BO triangles forming an3

equilateral triangle. The existence of boroxol rings invitreous B O was first proposed by Goubeau and2 3

w xKeller 7 in 1953, and was later systematized andw xextended by Krogh-Moe 8,9 to binary borate

glasses, where BO triangles are gradually substi-3

tuted by BO tetrahedra, and therefore other ring4

structures such as diborate or tetraborate groups co-exist with boroxol. Nuclear magnetic resonanceŽ .NMR studies of the structure of borate glasses

w xcarried out by Bray and co-workers 10–13 lentstrong support to these structural models of borateglasses. Evidence for the boroxol ring structure inpure B O glasses has been obtained from Raman-2 3

w x w xscattering 7–9,14–20 , neutron-scattering 21,22 ,w xNMR 12,23 , and nuclear quadrupole resonance

Ž . w xNQR 24,25 experiments. Nevertheless, there isstill considerable controversy about the concentration

w xof boroxol rings in B O glasses 21–23,26–34 .2 3

Boron oxide is a very hygroscopic material andw xEversteijn et al. 35 have shown that some basic

properties of vitreous B O depend strongly on glass2 3

stabilization temperature and water content. Thiswide variation of its physical properties is trouble-some and it seems the main cause of the experimen-tal spread of B O data, owing to mixing of data2 3

taken from different B O glasses.2 3

In this work, different samples of glassy B O2 3

were prepared and characterized. Mass-density andwater-content measurements provided the necessarycharacterization of the different methods of prepara-tion and thermal treatments employed. The glasstransition of each sample was investigated throughdifferential scanning calorimetry, obtaining theglass-transition temperature T from the specific heatg

measurements, and the ‘fictive’ temperature T fromf

the corresponding enthalpy variations. Brillouin scat-tering measurements enabled determination of thesound velocities and elastic constants. The aim of

Ž .this work was i to provide a set of some physicaldata depending on the glass preparation, useful for

Ž .further measurements and ii to investigate the cor-relation of elastic, acoustic and thermodynamic prop-erties for different B O glasses.2 3

2. Experimental

The samples were prepared by melting boronŽ .oxide pellets Aldrich, 99.999% purity in a platinum

crucible, placed in a quartz tube inside an electricfurnace. The two wet samples were prepared byheating the material at 3008C in air for 2 h, meltingby heating up to 8008C also in air, holding for 4 h,and pouring into a brass mold. In order to obtain

Ž .samples with lower water content dry samples , adifferent method of preparation was used. First, asimilar procedure as above was employed, but heat-ing more slowly and up to 10508C, until bubblinghad ceased after some 20 h. Then, the material wascooled and the process repeated in vacuum. The finalstep was to keep the melt at 10508C for 24 h, andrapidly pouring the melt into the brass mold. To getappropriate samples for different experimental tech-niques, several pieces were obtained from the samebatch. Planeparallel cutting of samples was donewith a diamond cut-off wheel, using glycerine aslubricant. Samples were carefully polished withoutwater, and stored in dried paraffin oil.

In order to dispose of an extensive set of variableB O glasses, several thermal treatments or anneal-2 3

ing were carried out, following previous workw x16,35,36 . Pyrex tube in an electric furnace wasemployed, and glass temperature was monitored witha NiCr–NiAl thermocouple. The tube was vacuumsealed and a rotary pump was used. Each set ofpieces of the same glass was annealed together in the

Ž y1platinum crucible under moderate vacuum ;10.mbar . To end the annealing, a small amount of

helium gas was admitted into the tube to acceleratecooling to room temperature. A summary of thedifferent samples prepared and studied in the presentwork is given in Table 1.

Mass density of samples was measured by theArchimedes method at 258C using a mineral oilfluid, whose density was determined from three inde-pendent methods. Experimental uncertainty in den-sity measurements is estimated to be "0.1%.

Infrared transmission spectra were obtained with aŽ .Fourier transform spectrometer Bruker IFS66V in

the spectral range 7000–550 cmy1, with a resolutionof about 2 cmy1 using B O plates of 0.2–0.3 mm2 3

thickness.Specific heat measurements were conducted by

( )M.A. Ramos et al.rJournal of Non-Crystalline Solids 221 1997 170–180172

Ž .differential scanning calorimetry DSC in aPerkin–Elmer DSC-4 calorimeter. Measurementsspanned the temperature range from 2008C up to4008C, covering the temperature region around T .g

Ž .Samples 5–25 mg were encapsulated in an alu-minum pan and were heated at a rate of 10 Krmin.All measurements were carried out under a dynamicnitrogen atmosphere. The calorimeter was tempera-

Ž .ture calibrated "1 K by using the melting point ofindium, tin, lead and zinc. The accuracy of theenthalpy measurements is estimated to be "2%.

Brillouin-scattering measurements were per-Ž .formed using a 3q3 tandem Sandercock interfer-

w x Ž .ometer 37 with a free spectral range FSR of 25GHz. The light source used was a Spectra Physics2020 Arq laser with a temperature stabilized intra-cavity etalon. At the selected wavelength, 514.5 nm,the laser provides a single mode output power of 50mW. B O samples were prisms of about 10 mm=2 3

10 mm=4 mm, with optically polished surfaces.Right-angle scattering geometry was used to observeboth longitudinal and transverse acoustic phonons.Additional measurements were carried out withbackscattering geometry, which enabled observationof longitudinal sound waves. Good agreement wasfound for the sound velocities obtained from bothexperimental procedures. For sake of consistency,only right-angle Brillouin scattering results were usedin the present work.

3. Results

It can be seen from Table 1 that the density ofglassy B O depends very strongly on the thermal2 3

Table 1Basic characterization data of the different B O glasses2 3

yw xSample Thermal OH r T Tg f3Ž . Ž . Ž . Ž .treatment mol% kgrm K K

W-1 as quenched 3.4 1818 555 558W-2 490 K, 100 h 5.8 1866 537 497D-1a as quenched 0.27 1804 570 561D-1b as quenched – 1804 572 569D-2 585 K, 48 h – 1806 565 552D-3 530 K, 50 h 0.27 1826 570 550D-4 525 K, 92 h 0.32 1823 569 534D-5 480 K, 170 h 0.40 1834 568 530

Fig. 1. Hydroxyl absorption bands measured by infrared spec-troscopy for different B O glasses. Spectra have been shifted2 3

vertically in steps of 25 cmy1 , ordered as indicated by the labelsat the right side.

history and water content. Combining both, the vari-ation in the density of B O glasses is about 3.5%.2 3

w xIn agreement with previous experiments 16,35,36 ,sub-T structural relaxations produced by annealingg

tend to increase mass density noticeably. The amountof water in the network plays a role in the same way.

The water content was determined by infraredspectroscopy. The amount of structurally bound wa-ter can be deduced from the hydroxyl absorption

Ž y1 .band at 2.8 mm ,3570 cm . Another absorptionŽ y1 .band observed at 3.1 mm ,3220 cm is due to

superficial water produced by atmospheric moisture,and depends on sample surface quality. Fig. 1 showsthe infrared spectra of different B O glasses. For a2 3

quantitative calculation of the water content, it isnecessary to convert the transmission spectra intoextinction spectra using the Lambert–Beer equation:

1 1Esces log , 1Ž .

d T

where d is the sample thickness and T the transmis-sion coefficient. The desired OHy concentration c isobtained by making use of the extinction coefficientes141 lrmol cm for the hydroxyl absorption band

y1 w xat 3570 cm , found by Franz 38 . After subtracting


Žthe absorption band due to superficial water 3220y1 . ycm from the extinction spectra of Fig. 1, OH

concentration is obtained as shown in Table 1. Accu-

racy in these measurements is mainly limited by theuncertainty in plate thickness, giving a relative errorin water-content of about 10%. Although dry sam-

Ž . Ž .Fig. 2. Specific heat measurements in the glass-transition temperature range for wet top curves and dry lower curves B O glasses. The2 3

latter is ordered, in increasing maximum specific-heat value, as follows: D-1b, D-1a, D-2, D-3, D-4, and D-5. Solid lines indicate theŽ .average constant value in the liquid state C , and the vibrational-contribution C curve extrapolated from data down to 420 K, afterp,liquid p

w x Ž .Chen and Kurkjian 40 C .p,glass


ples of B O with lower OHy concentrations have2 3w xbeen reported 27,35 , the water content of most ofŽ .our dry samples about 0.07 wt% can be regarded as

representative. It may be seen from Table 1 that thehighest water contents are found in annealed glasses,both for wet and dry ones. The same effect was

w x Ž .observed by Eversteijn et al. 35 in their drysamples.

DSC specific-heat measurement results around theglass transition in B O are shown in Fig. 2. Calori-2 3

metric glass-transition temperatures T , given ing

Table 1, have been determined as the temperature

where the experimental curve reaches the midpointof the specific-heat jump to the liquid-state value,

w xfollowing Uhlmann et al. 39 . Well below T , allg

B O glasses tend to a common curve, dominated by2 3

the vibrational excitations of the solid state. The Cp

curve extrapolated from data down to 420 K, ob-w xtained by Chen and Kurkjian 40 , is shown in Fig. 2

Ž .C solid lines .p,glass

As can be seen in Fig. 2 and in Table 1, all dryglasses exhibit similar T values about 570 K, ing

good agreement with others previously reported inw xthe literature 39–41 . T clearly decreases with in-g

Ž . Ž . Ž . Ž .Fig. 3. Configurational enthalpy variations D H T of wet above and dry below B O glasses of Fig. 2, calculated via Eq. 2 . Theconf 2 3

construction employed to determine the ‘fictive’ temperature T is shown. See text for further details.f


creasing OHy concentration and further annealing.In the liquid state, an approximately constant specificheat of C s1.89"0.03 Jrg K is found for allp

glasses, in agreement with earlier measurementsw x40,41 . Using a different experimental techniqueŽ . w xdilatometry , Franz 42 found a decrease of 238Cper mol% H O, which agrees qualitatively with our2

results. Moreover, it seems to confirm the higherwater content of W-2 sample compared to W-1,corresponding to a lower T . The small deviation ing

T observed for D-2 sample, in comparison with theg

rest of dry glasses, could also be explained. It is theŽ .only glass which has been annealed slightly above

T , its cooling-rate thermal history being substitutedg

for a new one, different from that followed by therest of glasses.

Instead of the glass-transition temperature T , it isg

often more convenient to use the ‘fictive’ tempera-w xture T 6,43 . We have followed the method de-f

w xscribed by Chen and Kurkjian 40 , defining T asf

the temperature at which the equilibrium-liquid con-figurational enthalpy curve intersects that extrapo-

Ž .lated from the glass region see Fig. 3 . Fig. 3 showsŽ .the configurational enthalpy D H T of the sam-conf

Žples corresponding to Fig. 2, taking D H 670conf.K s0 as a reference:

TD H T s C yC dT , 2Ž . Ž .Ž .Hconf p p ,glass

670 K

where C is the vibrational contribution shownp,glass

in Fig. 2.

Fig. 4. Fictive temperature T versus mass density for all thef

B O glasses studied in this work.2 3

Fig. 5. Brillouin spectra of as-quenched and annealed B O2 3

glasses. Right-angle scattering geometry was used to observe bothŽ . Ž . Ž .longitudinal L and transverse T Brillouin lines. a Wet B O2 3Ž . Ž . Ž .glasses: W-2 above and W-1 below , b dry B O glasses: D-52 3

Ž . Ž .above and D-1 below .

It may be seen from Table 1 and Fig. 4 thatfictive temperature T decreases with increasing den-f

sity. This seems to originate either from sub-T struc-g

tural relaxations produced by annealing or from thehigher rigidity caused by increasing water in theglass.

It is to be stressed that the T determined heref

does not correspond to usual determinations in equi-librium, i.e. without the structural relaxations in-


Ž Ž ..Fig. 6. Specific refraction see Eq. 6 versus mass density fordifferent B O glasses, from the data collected by Eversteijn et al.2 3w x35 . Dashed line is a least-square fit, useful to extract therefractive index when mass density is known.

duced by the annealing processes. We think howeverthat T has still a physical meaning and is the bestf

characterization parameter to describe the thermody-Ž .namic state of the frozen and later annealed liquid.

Brillouin scattering provides information on theacoustic properties of condensed matter. For anisotropic medium, the frequency shifts Dn of theB

Žscattered light of wavelength l called Brillouin.shifts are related to the sound velocity by

Õ usDn s2n sin , 3Ž .B

l 2

Ž .where Õ is either longitudinal Õ or transverses LŽ .Õ sound velocity, n is the refractive index, and uT

is the scattering angle. For right-angle scatteringŽ . Ž .us908 , Eq. 3 becomes

Õs'Dn s 2 n . 4Ž .Bl

From the sound velocities and the mass density r,elastic constants can be deduced through the well-known relations

C sr Õ2 , C sr Õ2 5Ž .11 L 44 T

Fig. 5 shows four representative spectra obtainedat room temperature corresponding to as-quenchedand annealed samples of wet and dry B O glasses.2 3

Ž .The laser line has been reduced by a filter ODs3to avoid damaging the photomultiplier. The doublepeaks appearing approximately at 25 GHz from thecentral laser line are the nearest interference ordersand the splitting is due to the tandem construction.The contrast was calculated to be better than 107. Itmay be seen in Fig. 5 that annealing produces aconsiderable shift in Brillouin lines, indicating aremarkable increase in the acoustic velocity.

In order to determine quantitatively longitudinaland transverse sound velocities, the refractive indexn needs to be known. The refractive index of vitre-ous B O depends on thermal history and water2 3

content, ranging 1.45–1.47 in the literature. Ever-w xsteijn et al. 35 discussed this influence, by collect-

ing data on the density r and refractive index n of

Ž . Ž .Fig. 7. Longitudinal Õ and transverse Õ sound velocities ofL T

wet and dry B O glasses. Measurements taken from other works2 3w xin the literature 44–47 are also included.


different B O glasses and found that specific refrac-2 3

tion r, defined by

n2 y1 1rs , 6Ž .2 rn q2

is much more constant than n, and hence moremeaningful. However, by plotting in Fig. 6 these

w xspecific refraction data from Eversteijn et al. 35versus mass density, we find a slight but systematicdependence on density, no matter whether they aredry or wet glasses. A least-square fit of these dataŽ .see Fig. 6 can be used to determine the refractiveindex of a B O glass very accurately, if mass2 3

density is known. We have used this procedure toobtain the necessary refractive index for our samples.

Ž . Ž .Longitudinal Õ and transverse Õ sound ve-L T

locities of wet and dry B O glasses, determined2 3Ž .from Eq. 4 are shown in Fig. 7. Other measure-

w xments taken from the literature 44–47 are alsoincluded in Fig. 7, if mass density of glasses isreported. Many reported sound–velocity measure-ments of B O glasses of unknown density typically2 3

lie in the middle range of Fig. 7.

4. Discussion

Analyses and comparisons of physical propertiesof B O glasses are hindered by the variety of glass2 3

conditions used. We are interested in investigatinghow physical properties vary, and how to character-ize them, using a representative set of B O glasses.2 3

Two distinct variables have been employed to doŽ .that: i the ability of boron-oxide glasses to make

significant structural re-arrangements via sub-T re-gŽ .laxations; ii the wide range of water content found

in glassy B O . Both variation factors are intrinsi-2 3Žcally present although seldom characterized through

.relevant material parameters in all B O glasses2 3

used to carry out physical measurements.Our first observation has been the very different

behavior of the calorimetric glass-transition tempera-ture T and the fictive temperature T obtained fromg f

the configurational enthalpy. The former appearsinsensitive to structural relaxations induced by an-nealing the glass, only depending on the water con-tent – and presumably the cooling rate – of the

Ž . Ž .Fig. 8. Longitudinal Õ and transverse Õ sound velocities ofL T

our wet and dry B O glasses, plotted versus fictive temperature2 3

T .f

liquid. On the contrary, the latter temperature isclearly affected by sub-T structural relaxations,g

somehow being a more meaningful physical parame-ter, providing information about the whole of thethermodynamic state of the glass. For practical pur-poses, the direct relationship between the mass den-sity and fictive temperature T , but not with T ,f g

independent of whether density is varied throughstructural annealing or by increasing the water con-tent, seems interesting.

Sound velocity Õ increases remarkably with masss

density, again independently of whether this isachieved by relaxation or water content. As a conse-quence, sound velocity decreases systematically withT . This interesting correlation between an acousticf

and a thermodynamic property is shown in Fig. 8. Itis noteworthy that we have obtained sound-velocity


changes of almost 15% for different samples ofvitreous B O . Such a wide window of sound veloci-2 3

Žties is unusual even for non-crystalline solids at.reasonably low temperatures .

Ž .Elastic constants C longitudinal modulus and11Ž .C shear modulus of wet and dry B O glasses,44 2 3

Ž .calculated through Eq. 5 , are shown in Fig. 9.Other measurements corresponding to those sound-velocity values shown in Fig. 7 are also included. InFig. 10, we show the correlation between the elasticconstants of wet and dry B O glasses with fictive2 3

temperatures T , determined from enthalpy measure-f

ments around T . We wish to emphasize that elasticgŽconstants of annealed wet B O glasses high den-2 3

.sity are more than 30% higher than those of as-Ž .quenched dry B O glasses low density .2 3

Fig. 9. Elastic constants C and C as a function of mass density11 44

r for wet and dry B O glasses. Measurements taken from other2 3Ž .works see Fig. 7 are also included here.

Fig. 10. Elastic constants C and C of our wet and dry B O11 44 2 3

glasses, plotted versus fictive temperature T .f

This remarkable variation of elastic and acousticproperties from glass to glass is therefore caused bythe combination of two factors. It is clear that watercontent influences the structure and the rigidity ofthe network somehow. It may be questioned whetherwet B O glasses can still be considered as pure2 3

single-component B O . However, it is a fact that2 3

the different amount of water in those glasses used toextract published physical parameters acts as a vari-able. The structure of B O glasses appears to be2 3

very sensitive to thermal history. This could beunderstand since, in contrast to most of oxide glassespresenting a three-dimensional network, B O struc-2 3

ture has a more two-dimensional character with weakw xinteractions between the sheets 48 . In fact, from

w xRaman-scattering experiments 14,20 it is knownŽthat the fraction of boroxol rings and also the mass


.density decreases gradually with increasing temper-ature above T , although they are still present in theg

liquid state after substantial structure rearrangement.Similar processes are likely to be occurring in sub-Tg

w x w xstructural relaxations 40,43 or thermal anneals 35of B O glasses.2 3

Mass density r is a very useful parameter tosummarize and characterize the thermal history andthe water content of B O glass. By measuring the2 3

mass density of the glass, all the necessary materialparameters could be determined with good accuracyfrom interpolations of curves presented here.

5. Conclusions

Differential scanning calorimetry and Brillouin-scattering measurements of B O glasses showed2 3

that elastic, acoustic and thermodynamic propertiesŽvary strongly with thermal history sub-T structuralg

.relaxations and water content. Mass density r is asimple but extremely useful parameter to character-ize the state of a given B O glass, which allows2 3

accurate estimations of relevant material-parametersthrough interpolations of the experimental curvesplotted versus r.

The wide variation of some B O physical prop-2 3

erties may be related to the two-dimensional charac-ter conferred by its planar structural units, compris-ing both BO triangles and B O boroxol rings.3 3 3

Acknowledgements

We are grateful to Professor F.J. Piqueras, whoconducted infrared measurements carried out at the

Ž .Servicio Interdepartmental de Investigacion SIdI of´the Universidad Autonoma de Madrid. This work has´been supported in part by INTAS project No. 93-3230.

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Correlation of elastic, acoustic and thermodynamic properties in B2O3 glasses

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Transcript of Correlation of elastic, acoustic and thermodynamic properties in B2O3 glasses