Journal of Non-Crystalline Solids

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1 Journl of Non-Crystlline Solids 8 (15) 1 11 Contents lists ville t ScienceDirect Journl of Non-Crystlline Solids journl homepge: locte/ jnoncrysol Effects of lithium oxide on the crystlliztion kinetics of N O CO 3SiO glss Leonrdo Snt'An Gllo, Tigo De Mrchi Mosc, Bruno Henrique Teider, rin Polykov, An Cndid Mrtins Rodrigues, Edgr Dutr Znotto, Vldimir M. Fokin c, Vitreous Mterils Lortory, LMV-DEM, Mterils Engineering Deprtment, Federl University of São Crlos, P.O. Box 676, São Crlos SP , Brzil Greenshchikov nstitute of Silicte Chemistry, Russin Acdemy of Sciences, ul. Odoevskogo -, St. Petersurg, Russi c Vvilov Stte Opticl nstitute, ul. Bushkin 36-1, St. Petersurg, Russi rticle info strct Article history: Received 1 August 1 Received in revised form 18 Octoer 1 Accepted Octoer 1 Aville online 3 Octoer 1 Keywords: Glss; Crystlliztion; Nucletion; Growth The crystl nucletion () nd growth (U) rtes of N O CO 3SiO glsses with incresing dditions of Li O were mesured for the primry crystlline phse over wide nd overlpping temperture intervls. A prtil section of the phse digrm N O CO 3SiO Li O ws constructed vi DSC nlysis nd shows nrrow rnge of solid solution formtion tht is close to tht of N O CO 3SiO. n the four-component system (N O Li O CO SiO ), pseudo-inry eutectic system of N O CO 3SiO Li O SiO exists. The role of Li O in the formtion of the crystlline phses ws investigted using DSC nd X-ry nlyses. The ddition of Li O results in decreses in the glss trnsition (T g ) nd liquidus (T L ) tempertures. With incresing Li O content, oth the reduced glss trnsition temperture T gr (T gr = T g /T L ) nd the frgility index, m, pss through minimum. These findings extend nd confirm the known inverse correltion etween T gr nd mx (lower vlues of T gr correspond to higher vlues of mx ) nd provide evidence for similr correltion etween m nd mx. When using the low temperture dt for the crystl growth rte (U) the viscosity (η) nd diffusivity (D) were decoupled t T 1.1 T g. Next, prmeter (U η t T g ) tht chrcterized the decoupling phenomenon ws proposed. 1 Elsevier B.V. All rights reserved. 1. ntroduction While most fundmentl studies of glss crystlliztion rely on the use of stoichiometric compositions, most commercil glss-cermics re sed on the controlled crystlliztion of non-stoichiometric glsses, i.e. for which the prent glss composition differs from the crystlline phse [1]. Minor components tht re solule t high tempertures cn sometimes precipitte t lower tempertures during the initil stges of phse trnsformtion nd form their own crystlline phses. Under some conditions, the ltter my serve s n ctive center for heterogeneous nucletion nd the susequent growth of the min crystlline phse [ ]. Moreover, solule dditives cn ffect the crystlliztion kinetics of the min phse y chnging the melt viscosity nd its temperture dependence or the free energy of the melt/crystl interfces [5,6]. For exmple, smll dditions of sodium oxide to lithium disilicte glss re known to cuse drmtic decrese (7 8 orders of mgnitude) in the internl nucletion rtes [7]. A detiled study of nucletion inhiitors for lithium disilicte glss ws recently performed in [8]. n contrst, dding reltively smll percentges of nucleting gents strongly increses the crystl nucletion rtes in glsses. n ddition, Corresponding uthor. E-mil ddress: vmfokin@gmil.com (V.M. Fokin). minor mounts of some foreign components my e incorported into the structure of the min crystlline phse nd form solid solutions. Thus, the possile effects of compositionl chnges on the pthwys nd kinetics of crystlliztion should e systemticlly investigted from oth prcticl nd theoreticl stndpoints. n this study, we used glss with stoichiometric composition of N O CO 3SiO (N 1 C S 3 ), which undergoes spontneous internl crystlliztion when properly heted, to study the influence of the ddition of Li O on its crystlliztion kinetics. The crystlliztion kinetics of N 1 C S 3 glss nd glsses with similr compositions were investigted in detil (see e.g., [9 1]). The N 1 C S 3 glss elongs to the technologiclly importnt sodium clcium silicte system, nd lthough this glss is stoichiometric (i.e., n isochemicl crystl phse exists), its crystlliztion follows n unusul pthwy. n fct, t deep undercooling (~T g ), crystlliztion egins with the homogeneous nucletion of solid solution tht is enriched with sodium reltive to the prent (stoichiometric) glss composition [1]. The crystl phse composition only pproches the expected stoichiometry in its more dvnced stges of phse trnsformtion. The evolution of the residul glss composition during crystlliztion is such tht it reches stte in which the refrctive indexes of the glss nd the crystl phses re similr, which underlies the development of highly crystlline nd trnsprent glss cermics with lrge (micron size) grins [13]. TheN 1 C S 3 glss is lso employed s se-glss for ioctive mterils [1]. n cursory study, it ws 1 Elsevier B.V. All rights reserved.

2 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) shown tht mong severl oxide dditives only Li O ccelertes the crystlliztion kinetics of N 1 C S 3 glss [15]. Therefore, in this pper we return to the preliminry results of [15] to perform deeper systemtic investigtion of the crystlliztion kinetics of N 1 C S 3 glss with different dditions of Li O.. Mterils nd methods Glsses of the following compositions were prepred from nlyticl grde sodium, clcium (Mllinckrodt), lithium crontes (Synth) nd ground Brzilin qurtz (Vitrovit N 99.99% SiO ): (1-x)(N O CO 3SiO )xli Owithx=1,,3ndwt.%, which correspond to 1.9,.3, 5.6, nd 7.5 mol% Li O nd re referred to herefter s Li-1.9,, nd. The chemicls were thoroughly mixed nd melted in pltinum crucile in n electricl furnce t C for h efore pouring on steel sl nd pressing with steel plte. The glss compositions re shown in Tle 1.Thechemicl nlysis performed for the nd glsses shows resonle greement with the nominl compositions (see e.g., Fig. 1). The Tmmnn method ws used to estimte the numer of crystls per unit volume N V (t) (the crystl numer density) tht were nucleted during ny given period of time (t) t low tempertures T n close to the glss trnsition temperture, T g. The nucleted crystls were developed t higher temperture T dev N T n up to microscopic sizes (plese see detils in [16]). After development, the N 1 C S 3 crystls hd spherulitic shpe. Cross sections of the glss smples with developed crystls were prepred for susequent nlyses. A Leic DMRX opticl microscope (Leic Microsystems, Wetzlr, Germny) coupled with Leic DFC9 CCD cmer ws used to estimte the size nd the numer densities (N V ) of the crystls emedded within the glss interior y using stndrd stereologicl methods. Next, the stedy-stte nucletion rtes nd the nucletion time lgs were evluted from the N V (t) plots. The crystl growth rtes, U, were estimted s U(T) = dr/dt t the given tempertures, where R is the spherulites rdius. n the cse of simultneous nucletion nd growth processes with detectle rtes, the vlue of R is relted to the lrgest crystls formed. A Netzsch differentil scnning clorimeter (Netzsch, Sel/ Bvri, Germny) with pltinum crucile ws used to nlyze the generl pthwys of the phse trnsformtion, including the crystlliztion nd melting processes, nd to estimte the chrcteristic trnsformtion tempertures. Bulk glss pieces with weights of pproximtely 3 mg were used for the DSC nlysis. Heting nd cooling were performed t rte of 1 C per min. The viscosities of the studied glsses were estimted using the penetrtion method. X-ry diffrction (XRD) mesurements were conducted on powdered smples y using Siemens D55 (Siemens, Munich, Germny) XRD Tle 1 Glss compositions. Glss N O CO SiO Li O Mol% Li-, Li (16.66) (33.33) (5.) (15.5) (31.6) (5.9) (16.66) (33.33) (5.) 1.8 (16.) 9. (31.3) 8.7 (5.7) 7.5 The vlues in rckets re reclculted while neglecting lithium oxide. By nlysis. Tken from [17]. Li O y nlysis, in mole % 8 6 operting t ma nd kv CuKα (λ =.156 nm) used s the incident rdition. 3. Results 3.1. Crystl nucletion Some exmples of the dependency of the crystl numer density (N V ) on time in the,, nd glsses re shown in Fig. for severl tempertures. The solid lines were plotted y using Eq. (1) for the time-dependency of the numer of super-criticl nuclei (see e.g. []). N V ðþ¼ t st τ t τ π 6 X m¼1 ð 1Þ m m! exp m t : ð1þ τ This eqution includes two fundmentl prmeters tht cn e estimted s fit prmeters, the stedy-stte nucletion rte ( st ) nd the time lg for nucletion (τ). The temperture dependencies of st nd τ re shown in Figs. 3 nd, respectively. The dt for the Li- glss were otined from [17]. The rrows in Fig. 3 denote the vlues of the glss trnsition tempertures tht were otined from the DSC heting curves. 3.. Crystl growth Fig. 5 shows n exmple of the time dependency of the crystl size t two tempertures tht were used for determining the crystl growth rtes in the glss. The temperture dependencies of the crystl growth rtes (log (U)) re presented in usul nd Arrhenius coordintes (inset) s shown in Fig. 6 for the Li-,,, nd glsses. The growth dt for the Li- glss were otined from [17]. The temperture intervl of the crystl growth mesurements overlps with the intervl tht ws used for estimting the nucletion rtes (plese compre Figs. 6 nd 3). n fct, for the glss, the temperture intervl includes the glss trnsition temperture Viscosity 6 8 Li O y tch, in mole % Fig. 1. Lithium oxide content y nlysis versus synthesis. The line corresponds to the cse when the Li O content y th is equl to tht y nlysis. The temperture dependences of the viscosities re shown in Fig. 7 for the Li-, Li-1.9,,, nd glsses. The mesurements for the Li-1.9,,, nd glsses were kindly performed y V.P. Klyev, who used the penetrtion method. The lines were plotted

3 1 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) o C 5 o C 1E1 Li- Li- N V x 1-6, mm -3 N V x 1-6, mm -3 N V x 1-6, mm o C o C t, min 51 o C o C 5 o C c st, m -3 s -1 1E11 1E1 y using the Vogel Fulcher Tmmnn (VFT) Eq. () with prmeters of A, B, ndt o estimted s fitting prmeters, which re listed in Tle. logη ¼ A þ B T T o T g The solid lines correspond to the intervls of the viscosity mesurements. These intervls re reltively nrrow nd only relte to the high vlues of viscosity. t my e the cuse of the unusul vlues of the A prmeters for glsses Li-1.9 nd Li-1. on Tle 1. Therefore, we only used these fit prmeters for the nlysis of the viscosity ner the glss trnsition temperture, which ws similr to the temperture intervl of the crystlliztion mesurements. 3.. Thermo nlysis T g T g T Li- g T, o C Fig. 3. The stedy stte nucletion rtes versus temperture for the different glsses. The rrows show the glss trnsition tempertures. Dt for Li- glss were otined from [17]. Fig. 8 shows the DSC heting nd cooling curves for the ulk glss. n ddition, severl chrcteristic tempertures, the glss trnsition ln( min) 8 6 Li- ðþ Fig.. Crystl numer densities versus the time of nucletion t severl tempertures in the Li-.5 (), Li-5,6 (), nd (c) glsses. The solid lines re plotted y Eq. (1), nd the dshed lines re the proper symptotes.,11,1,13,1 1/T, K -1 Fig.. Nucletion time-lg versus the inverse tempertures for the different glsses. Dt for Li- glss were otined from [17].

4 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) R, m t, h 7 o C 51 o C Fig. 5. Rdius of the 1NC3S crystls in glss versus time of growth t 7 C nd 51 C. log(, P s) T, o C Li- - Li Fig. 7. Viscosity versus temperture for the different glsses. The lines re plotted ccording to the VFT eqution with the prmeters collected in Tle. The solid portions of the lines correspond to the mesured temperture intervl. The strs show the glss trnsition tempertures tht were estimted from the DSC heting curves. 1 temperture (T g ), the solidus (T S ), liquidus (T L ), nd the temperture of the polymorphic trnsition (T pm ) re shown X-ry phse nlysis Fig. 9 shows the X-ry diffrction spectr of the Li-, Li-1.9,, Li- 5.6, nd glsses, which were previously crystllized over 3 min t the tempertures just fter the respective crystlliztion peks in the DSC heting curves (see Fig. 8).. Discussion The min topics of this reserch include i) the non-monotonic nd monotonic evolutions of the nucletion nd growth rtes, respectively, with incresing Li O content; ii) the influences of Li O on the melt viscosity nd its frgility; nd iii) the role of Li O in the formtion of the crystl phse. log(u, m/s) /T, K Li -7.5 Tg Li -5.6 Tg Li -.3 Tg Li - Tg Li T, o C Fig. 6. Crystl growth rtes versus temperture for the different glsses. The rrows show the glss trnsition tempertures. The inset shows the sme dt in Arrhenius coordintes. Dt for Li- glss were otined from [17]..1. Min equtions The nlysis of the crystlliztion kinetics (nucletion rtes nd crystl growth rtes) ws performed in the frmework of the clssicl nucletion theory (CNT) nd the screw disloction growth model. The min equtions re shown elow Nucletion rte According to CNT, the stedy stte nucletion rte cn e written s follows []: st ¼ o exp W þ ΔG D k B T ; ð3þ with σ3 W ¼ K ΔG ; nd V o ¼ N 1 k B T h! 1= σ ; k B T where W is the thermodynmic rrier for nucletion (i.e., the increse in the free energy of system due to the formtion of nucleus with criticl size), σ is the specific surfce free energy of the criticl nucleus/melt interfce, K is the shpe fctor, which is equl to 16π/3 in the cse of sphericl nucleus, nd ΔG V is the difference etween the free energies of the liquid nd crystl per unit volume of the crystl (i.e., the Tle Prmeters of the VFT eqution for viscosity in P s. Glss A B, K T o,k Li Li , ,

5 16 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) Tg V/mg TL TS 1 - Li- - Li ΔGV ¼ ðt L T ÞðΔSm R lnxþ=v m ; LS T Tpm V/mg kb T ΔGD exp h kb T D¼ ðþ Here, kb nd h re the Boltzmnn nd Plnck constnts, respectively. The pre-exponentil term in Eq. (3) (o) depends wekly on the temperture when compred with the exponentil function. n this study, we used the following eqution for the thermodynmic driving force (ΔGV), which ws derived in [18] for inry (metllic) melts: (i.e., the ctivtion free energy for the trnsfer of structurl unit from the melt to crystl nucleus), which determines the effective diffusion coefficient D. 8 1 where TL is the liquidus temperture, ΔSm is the entropy of fusion per mole of the pure crystl, x is the molr frction of the precipitting sustnce in the melt nd Vm is its molr volume. n our cse, x is relted to the min crystlline phse (NO CO 3SiO) for which the nucletion rtes were estimted. t should e noted tht when x = 1 (stoichiometric crystlliztion), Eq. (5) is trnsformed into the well-known Turnull eqution []. Strictly speking, x should e introduced into the preexponentil term of Eq. (3) to ccount for the decrese in the numer of structurl units tht prticipte in the nucletion of the new phse reltive to the stoichiometric crystlliztion. However, in our cse, this fctor is wek nd cn e neglected. n ddition, when using Eq. (5), we neglected the soluility of Li in the NO CO 3SiO crystls (see Section.) nd ssumed tht most of the LiO remined in the undercooled liquid phse, t lest during the nucletion stge. The time scle prmeter, τ (see Eq. (1)), for the estlishment of the stedy stte nucletion rte (st) is commonly denoted s the timelg for nucletion nd cn e written s follows [19]: 1 τ¼ o T, C ð5þ 16 hσ ΔGD exp kb T π ΔGV ð6þ Fig. 8. The DSC heting () nd cooling () curves for the different glsses otined for the heting/cooling rtes C = 1 C/min. By comining Eqs. (3) nd (6), one cn write the following eqution for the stedy-stte nucletion rte: thermodynmic driving force for crystlliztion). n ddition, N1 1/3 is the numer density of the structurl units with size of tht is involved in the formtion of the crystl phse nd ΔGD is the kinetic rrier st ¼ 1= LS - [9-88] 16 1 cps+shift T 1= W exp : kb T ΔGV τ ð7þ For first pproximtion, the sher viscosity (η) is often used to estimte the kinetic rrier y ssuming tht the free ctivtion energy of the viscous flow (ΔGη) in Eq. (8) [] is equl to ΔGD η¼ ΔGη kb T ; τo ¼ h=kb T; τ exp o kt 3 ð8þ where τo is chrcteristic time of the order of the period of tomic virtion nd is estimted t pproximtely 1 13 s. Under the ove ssumption (ΔGD = ΔGη), the comintion of Eqs. (8) nd (3) gives 1= 1 kb σ 5 1= T 1= W exp : η kb T st ¼ Li- Eq. (9) supposes the vlidity of the Stokes Einstein Eyring Eq. (1). Dη ¼ 3= Li kb σ π 6 kb T η ð9þ ð1þ 7 degrees Fig. 9. X-ry diffrction pttern of the fully crystllized glsses t tempertures just fter the DSC exothermic crystlliztion pek. Unmrked peks correspond to N1CS Growth rte According to Jckson's tretment of the interfce [1], the mterils with high melting entropy (N R) re expected to exhiit crystl growth kinetics tht re predicted y either the screw disloction or

6 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) the D surfce nucletion growth models. The melting entropy (ΔS m )of the min crystlline phse, N O CO 3SiO,is7R []. Becuse the choice from the ove two models does not ffect the result of the nlysis performed in Section.3, we will use the screw disloction model ecuse it is the simplest. According to this model, the crystl growth rte (U) cn e written s follows []: "!# U ¼ f D U 1 exp 1 ΔG V 3 with k B T f 1 ð11þ T L T ; π T L where f is the frction of the preferred growth sites t the interfce (i.e., the disloction edges). By ssuming tht D U = D η,eq.(11) cn e rewritten s follows: U ¼ f "!# k B T η 1 exp 1 ΔG V 3 k B T.. Nucletion rte versus Li Ocontent ð1þ From Fig. 3,thefirst ddition of lithium oxide to the N O CO 3SiO glss resulted in n increse in the mximum stedy-stte nucletion rte, mx st (T mx ) (plese compre the Li- nd glsses), which corresponded with the results of [1]. The susequent increse in the Li O content resulted in decrese in the mx. Thus, the influence of Li O on the nucletion rte is non-monotonic nd revels mximum t some Li Oconcentrtion.Fig. 1 shows the reduced sum of the nucletion rriers (W + ΔG D ), which ws estimted from the experimentl vlues of st (see Fig. 3) vieq.(3), versus the temperture. To evlute o,weusedσ =.1J/m [3] nd (V m /N A ) 1/3 = m (V m is the molr volume nd N A is Avogdro's numer). The preexponentil term, o, only depends wekly on temperture, if compred to the exponentil function, nd vries etween 1 1 nd m 3 s for the different condensed systems []. Hence, the ritrry ntures of the employed prmeters nd σ do not strongly ffect the finl result. nterply etween the thermodynmic nd kinetic rriers (the decrese of the former nd the increse of the ltter with decresing temperture) results in the temperture mximum of the nucletion rte (minimum of (W + ΔG D )/k B T). The temperture of the mximum nucletion rte (T mx ) is determined from the condition of equlity etween the solute vlues of the temperture derivtives of W nd ΔG D. T mx is normlly ner the glss trnsition temperture. This experimentl fct underlies the following trend: the lower the reduced glss trnsition temperture (T gr = T g /T L ), the higher the undercooling chieved t T g, nd the higher the mximum nucletion rte mx = st (T mx T g ) [5] due to the incresed thermodynmic driving force ΔG V (T g ), which increses with undercooling. The ove definition of T gr is relted to the primry crystllizing phse, in our cse N O CO 3SiO. At constnt pressure, the vrition of T gr cn only e relized y chnging the glss composition. Generlly, such vrition is ccompnied y smller or lrger chnges in the other prmeters tht ffect the nucletion rte. Therefore, to oserve the trend discussed ove, one must collect plethor of nucletion dt or select dt for nucletion of the sme crystls in glsses with similr compositions. A detiled nlysis of the correltions etween mx nd T gr my e found in [5]. Fig. 11 shows the mx () nd T gr () vlues s function of the Li O content. The vlue of T gr psses through minimum t Li O concentrtion of mol%, which is ner the composition of the glss tht revels the highest mx vlue. Thus, we my ssume tht the highest vlue of mx minly results from the lowest vlue of T gr for this series of glsses. Fig. 1 shows the mx () nd T mx (c) dt for the N 1 C S 3 glsses with different Li O contents s function of the reduced glss trnsition temperture. The sme dt re plotted in Fig. 1 ndd mx, m -3 s -1 3x1 1 x1 1 1x (W * + G D )/k B T Li- T gr T, o C 6 8 Li O, mole % Fig. 1. Sum of the thermodynmic nd kinetic rriers versus temperture for glsses with different Li Ocontents. Fig. 11. mx () nd T gr = T g /T L () versus Li O content. The vlues of T g nd T L were tken from the DSC curves (see Fig. 8). The line is guide to the eyes.

7 18 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) 1 11 mx, m -3 s -1 3x1 1 x1 1 1x1 1 Li- log( mx, m -3 s -1 ) Li- 1.6 c d T mx / T g Li- T mx / T g Li T gr T gr Fig. 1. mx (, ) nd reduced temperture T mx /T g (c, d) versus the reduced glss trnsition temperture T gr for the Li-,,, nd glsses. For the purpose of comprison, pnels nd d present dt for severl glsses tht re tken from [5]. The line is included s guide to the eye. with vriety of other dt for severl glsses tken from [5].Todemonstrte the correltion etween mx nd T gr, we used dt from the,, nd glsses, for which the T gr vlues incresed s the Li O content incresed (see Fig. 11). The mx for these glsses decresed s the T gr (Fig. 1) incresed, which corresponded with the generl trend shown in Fig. 1. Despite the sence of nucletion dt for the glsses contining Li O etween to.3 mol%, it is cler tht the mximum nucletion rtes must increse in this compositionl intervl, s schemticlly shown y the dshed line in Fig. 1. Fig. 1c shows one more correltion: the higher is the reduced glss trnsition temperture T gr, the closer is the temperture of mximum nucletion rte T mx to the glss trnsition temperture T g (the T mx /T g rtio ecomes closer to one). This trend grees with the results for severl glsses tht were collected in [5] (see Fig. 1d). Thus, Li O minly ffects the nucletion rte y ltering the reduced glss trnsition temperture ecuse oth the T L nd T g vry. A correltion etween the mximum crystl growth rte U mx = U(T U mx ) nd the T gr (the lower the reduced glss trnsition temperture, the higher the mximum crystl growth rte) ws lso demonstrted for different glss-forming systems including not only oxides [5] ut lso orgnics, chlcogenides, nd metls [6]. However, this correltion is much weker thn tht for the nucletion rte. n ddition, it must U e rememered tht T mx T mx ecuse the former is closer to T g nd the ltter is closer to T L (T S ). The growth rtes presented in this U study re relted to low tempertures tht re fr from the T mx (high undercooling) nd re minly determined y the effective diffusion coefficient (see Eq. (1)), which increses monotoniclly s the Li Ocontent increses. Another unexpected correltion is shown in Fig. 13. Fig. 13 shows the reltionship etween the frgility index (m) tht ws estimted y Eq. (13) [7] nd the reduced glss trnsition temperture (T gr ). m ¼ dðlog 1ηÞ d T g =T T¼T g ð13þ Generlly, T 1 (the temperture corresponding to the viscosity of η =1 1 P s) is used insted of T g. This pproximtion is rther consistent, s shown in Fig. 1. According to Fig. 13, the dependencies of oth m nd T gr on the Li O content revel minimum for the glss. The glss hs the highest mximum nucletion rte ( mx ). At first glnce, the frgility is not connected with the crystlliztion kinetics ecuse it does not include the temperture of the liquidus nd the undercooling tht determines the thermodynmic driving force for crystlliztion. However, s previously mentioned, the temperture of the mximum nucletion rte (T mx ) is determined y the conditions of equlity etween the solute vlues of the temperture derivtives of W nd ΔG D. The frgility index reflects the vrition of viscosity with temperture ner the T g, (i.e., close to T mx ), eing equl to the reduced ctivtion enthlpy of viscous flow. Replcing ΔG D y the ctivtion energy of viscous flow, ΔG η,sdoneineq.(9), we cn suppose tht the lower is m the lower temperture t which the conditions for mx is chieved. AdecreseintheT mx is ccompnied y decrese in the thermodynmic rrier for nucletion [16]. However, in every specil cse

8 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) x1 1 m mx, m -3 s -1 x1 1 1x1 1 Li m.5 Fig. 15. Mximum nucletion rtes versus the frgility index. The lines re included s guide to the eye. T gr.53.5 Li O, mole % 6 8 Fig. 13. Frgility index () nd the reduced glss trnsition temperture () versus the Li O content in the prent glsses. The line is included s guide to the eye. one hs to tke into ccount not only the vrition of the temperture dependence of viscosity ut lso its solute vlue. For our cse, ccording to Fig. 15, lower frgility indexes (m) correspond with higher mx vlues. Similr to Fig. 1, the dependence of mx on m in the full composition rnge (Li- ) exhiits kink-like shpe ecuse two glss compositions correspond to just one vlue of m. This kink lso demonstrtes the dependence of m on T gr (Fig. 16). n light of the prolem discussed ove, it is desirle to study the crystlliztion kinetics in the glsses with compositions etween those of Li- nd. n his recent review entitled Erly stges of crystl formtion in glss-forming metllic lloys, G. Wilde [8] concluded tht the frgility index does not provide suitle criterion for metllic glss-forming systems ecuse the lrge rnge of criticl cooling rtes for metllic lloys (pproximtely 8 orders of mgnitude) is not ccompnied y significnt chnge in the frgility prmeter (35 m 55). Here the following comment could e mde: the criticl cooling rte minly reflects the kinetics of the overll crystlliztion process rther thn only the nucletion rte. However, our dt refer to the mximum 6 6 T g, o C (from DSC ) Li T 1, o C Li Fig. 1. Correltion etween T 1 nd T g, which ws estimted from the DSC heting curves with heting rte of 1 C/min for the N O CO 3SiO glsses with nd without Li O. The solid line is liner fit, nd dshed line corresponds to the condition of T g = T 1. Fig. 16. Frgility index versus the reduced glss trnsition temperture. The lines re included s guide to the eye.

9 11 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) 1 11 nucletion rtes ( mx ). To first pproximtion, the viscosity is responsile for the kinetic rrier for nucletion nd the frgility index, which chrcterizes the rte of viscosity chnge in the glss trnsition rnge, could ffect the vlues of T mx nd mx.butthisinfluence is not strong, (e.g., n increse of m from pproximtely 3 to 6 is ccompnied y decrese in mx of only 8 times, see Fig. 15). Thus, our findings regrding the correltion etween m nd mx did not contrdict those of G. Wilde [8]..3. Crystl growth nd viscosity n ddition to the thermodynmic driving force, nucletion nd crystl growth re oth determined y the effective diffusion coefficients (D τ or D U, respectively) of the elements tht prticipte in the formtion nd further development of the crystlline phse. The U nd τ suindexes re designed to show tht D U could generlly differ from D τ governing nucletion kinetics. As first pproximtion, the Stokes Einstein-Eyring Eq. (1) is frequently employed with viscosity to estimte the effective diffusion coefficient D U (D τ ). This pproximtion is vlid t reltively high tempertures ut does not work under deep undercooling conditions T 1.T g (see e.g., [9,3]). Consequently, t sufficiently low tempertures, decoupling occurs etween the mechnisms tht control viscous flow nd the diffusion tht determines 5 Li- the crystl growth. This decoupling is chrcterized y decoupling temperture T d. A simple wy to demonstrte the decoupling phenomenon is to nlyze plot of U η versus T. According to Eq. (1), which ws derived under the ssumption tht D U = D η, the vlue of U η is wek function of temperture. Fig. 17 contins these plots of U η versus T for the Li-O nd glsses. ndeed, t reltively high tempertures, the vlue of U η vries wekly. However, when the temperture pproches the glss trnsition temperture (T g ) it egins to increse (slowly t first nd then drsticlly). This mens tht, strting from the decoupling temperture T U d, the viscosity increses more rpidly thn the diffusion coefficient controlling growth decreses. The correltion etween T g nd T U d (T U d 1.1 T g ) corresponds with dt found in the literture ecuse T U d (1.1 1.) T g (e.g., [9,3]). The following comments cn e mde regrding the growth rte dt in connection with the decoupling phenomenon. The U η vlues t the glss trnsition temperture differed for the Li- nd glsses y more thn one order of mgnitude (see Fig. 17). At first glnce, ccording to Eq. (1), similrity etween the U(T g ) η(t g ) vlues is expected ecuse the expression in squre rckets of Eq. (1) is close to 1 under conditions of high undercooling nd the vlue of f kbt only chnges wekly in the understudied temperture rnge. However, this expecttion is only correct under the condition of equlity D U = D η i.e. t tempertures higher thn T U d. Hence, D U must e employed rther thn D η. Consequently, the lrge differences etween the U η vlues t T g for the Li- nd glsses provide more evidence for the decoupling phenomenon, nd reflect the different degrees of the devition of D U from D η for the different glsses. As shown ove, for the Li- nd glsses, the growth rtes were mesured for tempertures ner T g (see Fig. 6). Bsed on the ove oservtions, it would e interesting to collect nd nlyze the U(T g ) dt for severl glsses with their proper frgility indexes. U J/m 3 1 T g T U d.. The role of Li O in the formtion of the crystlline phse As previously shown in Sections 3.3 nd., the ddition of Li Oto the N O CO 3SiO glss results in decrese in the melt viscosity nd chnges its temperture dependence. Together with the vrition of the liquidus, the chnge of viscosity ffects the mximum nucletion rte nd the temperture t which it occurs heting heting cooling U J/m.3..1 T g T U g T pm, o C 36 3 N 1 C S T, o C Fig. 17. Dependence of U η versus temperture for the Li- nd glsses. The lines re included s guide to the eye N O, mole % Fig. 18. Temperture T pm of the polymorphic trnsition from the DSC heting nd cooling curves s function of the N O content in the solid solution [1]. The lines re included s guide to the eye.

10 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) n this section, we consider how the Li prticiptes in the formtion of the crystlline phses. For this purpose, we first nlyzed the DSC curves. The heting curve of the Li- glss (i.e., glss without lithium oxide) revels the glss trnsition temperture, the exothermic pek tht corresponds to the crystlliztion of the N O CO 3SiO phse nd, finlly, n endothermic pek tht corresponds to the melting of this phse (Fig. 8, curve 1). According to the CO SiO N O SiO phse digrm, the solid solution (N +x C x [Si 6 O 18 ]; x 1) is formed etween the N O CO 3SiO nd N O CO SiO compounds [31]. For the present discussion, it is importnt tht the N O CO 3SiO crystls nd its solid solution N +x C x [Si 6 O 18 ] present reversile polymorphic trnsition t temperture T pm tht is ccompnied y remrkle het effect (see e.g., Fig. 8,curve1).TheincreseoftheN O content in the solid solution results in strong decrese in the T pm (see Fig. 18), which is ccompnied y decrese in the het of the phse trnsition [1,3,33]. Let us consider the DSC curves of the N O CO 3SiO glsses with extr Li O. The ddition of Li O results in decrese in the glss trnsition temperture nd the temperture of the crystlliztion pek (see Fig. 8). The first ddition of lithium oxide (Li-1.9) chnges the shpe of the melting pek, which mkes it more symmetric with the onset of lower temperture. Regrdless, it is difficult to estimte the temperture t which the first liquid ppers, the expnded profile of the melting pek gives indirect evidence of the melting of solid solution [3]. This interprettion of the melting pek will e confirmed lter y using X-ry nlysis. The endothermic event of the heting curve of the revels two types of processes. The first process is represented y reltively wek endothermic pek (see the enhnced portion of the proper prt of curve 3 in Fig. 8) tht corresponds to the melting of the eutectic mixture just ove the temperture of the solidus, T S. The re of this pek increses with incresing Li O content (Fig. 19), indicting the direction of the eutectic point. A susequent strongly extended endothermic event reflects the melting of solid solution in the temperture intervl etween the solidus nd liquidus. The finl stge of this melting corresponds to the liquidus temperture, T L. The tempertures of T S nd T L with the glss trnsition temperture re presented in Fig. s function of the Li O content of the prent glss. Thus, we cn suppose tht the fully crystllized glss contins smll mount (not detectle y X-ry nlysis) of the lithium-contining phse eyond the min phse (solid solution Li OintheN O CO 3SiO structure). ndeed, the X-ry diffrction spectr of the fully crystllized nd glsses reveled two peks tht elong to the Li O SiO (LS) crystls T, C Li O, mole % Fig.. T g, T S,ndT L versus the Li O contents for the studied glsses. The lines re included s guide to the eye. (Fig. 9) tht do not mtch the peks of the min N O CO 3SiO phse. The reflected light opticl microgrph nd the SEM BSE imge of the cross-sections of the glss fully crystllized t 66 C nd 58 C re shown in Fig. 1. The photos mke it cler tht the smples contin two phses. Moreover, ecuse the BSE imges re sed on chemicl contrst, we cn ttriute the drk crystls to the Li rich phse (i.e., to T L T S T g 3 S eut in.u Li O, mole % Fig. 19. Are of the melting pek of the eutectic mixture versus the Li O content in the studied glsses. Fig. 1. Reflected light opticl microgrph (top) nd the SEM BSE imge (ottom) for the cross-sections of the glsses tht were fully crystllized t 66 C for 16 min nd 58 C for 8 h, respectively.

11 11 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) 1 11 T, o C S,.u T pm -onset T pm -pek T LS -onset T LS -pek 6 8 S pm S LS T LS 6 8 Li O,mole % T pm Fig.. Temperture of the solid solution polymorphic trnsition (T pm ) nd the LS crystlliztion (T LS ) peks () nd their res () versus the Li O contents tken from the cooling DSC curves of the glsses under study. lithium metsilicte, LS). n ddition, increse of the re of the melting pek of the eutectic mix with incresing Li O content in the prent glss (see Fig. 19) provides evidence of the incresing volume frction of the LS crystls in the fully crystllized glsses. The crystlliztion of the two phses (Li O SiO nd s/s N O CO 3SiO )islsoconfirmed y two crystlliztion peks (see zooms of curves nd 5 in Fig. 8). Besides the first (high temperture) strong exothermic pek (cused y the full crystlliztion of the undercooled melt), the cooling curve of the Li-1.9 revels second wek exothermic pek t lower tempertures (see the enhnced portion of curve in Fig. 8). This pek is cused y reversile polymorphic trnsition of the solid solution. n ddition, similr pek ws discussed ove for curve 1 tht corresponded to the Li- glss. ts temperture T pm nd the corresponding re S pm systemticlly decresed s the Li O content incresed (Fig. 8). Thus, we ssumed tht theliionswereemeddedinthestructureofthen O CO 3SiO crystl nd formed n interstitil solid solution with limited soluility. t should e reclled tht the crystl structure of Li O CO 3SiO is unknown [31]. Fig. shows the tempertures (the onset nd the mximum of the exothermic pek on the DSC cooling curves) of the polymorphic trnsition T pm nd their res S pm versus the Li O contents eginning with the N O CO 3SiO glss (Li-). The vlues of T pm for the Li-1.9 nd glsses re pproximtely 7 nd 35 C, respectively. n the cse of the sodium-enriched solid solution (reltive to the stoichiometric composition of N O CO 3SiO ), the tempertures of T pm = 7 nd 35 CcorrespondedtoexcessN O concentrtions of. nd.1 mol% respectively (see Fig. 18). These vlues re similr to the Li Oconcentrtions in the Li-1.9 nd glsses. This result supports the ssumption tht Li enters into the N O CO 3SiO crystls nd results in decresed T pm nd S pm vlues. However, it should lso e considered tht the fully crystllized glss lredy contins lithium metsilicte crystls tht consume SiO from N O CO 3SiO. Thus, the structurl disordering of the min phse (N 1 C S 3 )isfirst cused y the entrnce of lithium nd then y the loss of Si. The chnges in the composition of the solid solution sed on the N 1 C S 3 structure (due to the loss of silic during the formtion of the LS crystls) re shown in the concentrtion tringle (see Fig. 3). The evolution of the crystl cell prmeters with incresing Li O content provides more informtion regrding the formtion of the solid solution sed on the N O CO 3SiO structure. Fig. shows the chnges of the nd c prmeters nd the volume (V) of the hexgonl crystl cell s function of lithium oxide content in the prent glss. According to these dt, the first ddition of Li (glss Li-1.9) results in shrp decrese in V. This chnge is ccompnied y chnges in the melting pek shpe (plese see curve in Fig. 8), which re discussed ove, nd is interpreted s result of the formtion of Fig. 3. Chnges in the phse composition of completely crystllized N O CO 3SiO glss with Li O ddition. The shded region is hypotheticl re of the solid solutions; the lck dots re the figurtive points of the glsses; the numers t the points indicte the Li O content in the glsses; the red lines re the tie-lines which determine the decy directions under the glsses crystlliztion in the concentrtion tringle.

12 L.S. Gllo et l. / Journl of Non-Crystlline Solids 8 (15) , A Besides the exothermic pek of T pm, which reflects the reversile polymorphic trnsition of the solid solution sed on the N O CO 3SiO structure, the cooling curve for the glss (Fig. 8) revels n exothermic pek t higher temperture T LS. Becuse the heting curve of this glss () clerly shows the melting of eutectic mixture, which reflects the ppernce of lithium metsilicte (see zoom of curve 3 in Fig. 8), we ttriuted this exothermic pek on the cooling curve to the lithium metsilicte crystlliztion. Further increses of Li O in the prent glss result in incresing res for this pek (S LS ) nd do not chnge its position (see Fig. ), which is ner the solidus. According to the X-ry nlysis, fully crystllized nd glsses contin LS crystls. Moreover, the increse of this exothermic pek is ccompnied y n increse in the re of the first melting pek following heting in the DSC scns (Figs. 8, 19). This correltion provides dditionl indirect evidence for our ssumptions regrding the origin of the second exothermic pek in the cooling curve (T LS ). 5. Conclusions c, A V, A Li O, mol% Fig.. Prmeters () nd c () of the hexgonl crystl cell of the NCS crystls with cell volume V (c) versus the Li O content in the prent glsses. The lines re included s guide to the eye. solid solution. When entering the N O CO 3SiO structure, Li results in smller V. Furthermore, increses in the Li O content of the prent glsses (; ; ) result in greter V, which could e explined y the depletion of SiO due to the formtion of lithium metsilicte. However to confirm the ove resonle ssumption, Rietveld refinement is needed to define the tomic positions in the crystl elementry cell. c To investigte the crystlliztion pthwys nd kinetics of nonstoichiometric glsses thoroughly, detiled nd systemtic study of the crystl nucletion nd growth rtes ws conducted with viscosity mesurements nd DSC nlysis of N O CO 3SiO glsses with dditions of Li O. The min conclusions re presented elow. Additions of Li OintheN O CO 3SiO glsses resulted in lower viscosities nd liquidus tempertures. A prtil section of the phse digrm of N O CO 3SiO Li O ws constructed here vi DSC nlysis. t indictes nrrow rnge of solid solution formtion, close to tht of N O CO 3SiO.nthe four-component system (N O Li O CO SiO ), pseudo-inry eutectic system N 1 C S 3 LS exists. The influence of Li O on the crystlliztion kinetics is minly due to the liquidus temperture vritions with the evolution of the melt viscosity. With incresing Li O content in the prent glsses, the frgility index nd the reduced glss trnsition temperture exhiit minimum. The compositions of these minim re similr to the composition of the glss tht revels the highest nucletion rte, mx.thesefindings extend nd confirm the previously determined correltion etween T gr nd mx (the lower the T gr the higher is mx ) nd provide evidence for similr correltion etween m nd mx. At tempertures fr elow the liquidus, the crystl growth rtes increse s the Li O content increses. An nlysis of the temperture dependence of the crystl growth rtes shows decoupling etween the effective diffusion coefficients tht govern the crystl growth, U, nd viscosity, η, tt 1.1T g. This phenomenon hs een reported efore for vrious stoichiometric glsses. Finlly, the vlue of the U η product t T g is suggested s prmeter for chrcterizing the decoupling phenomenon. Overll, these results provide new insights regrding the crystlliztion of non-stoichiometric glsses. Acknowledgements The uthors thnk the Brzilin funding gencies CNPq nd FAPESP the São Pulo Reserch Foundtion CEPD process # 13/ References [1] W. Höllnd, G. Bell, Glss-cermic Technology, Wiley Americn Cermic Society, Hooken, NY,. []. Gutzow, J. Schmelzer, The Vitreous Stte: Thermodynmics, Structure, Rheology nd Crystlliztion, Springer, Berlin, [3] G.P. Souz, V.M. Fokin, E.D. Znotto, J. Lumeu, L. Gleov, L.B. Gleov, Phys. Chem. Glsses Eur. J. Glss Sci. Technol. B 5 (9) 311. []. Dymnt, A.S. Ayzov, V.M. Fokin, E.D. Znotto, J. Lumeu, L.N. Gleov, L.B. Gleov, J. Non-Cryst. Solids 378 (13) 115. [5] V.M. Fokin, E.D. Znotto, J.W.P. Schmelzer, J. Non-Cryst. Solids 31 (3) 5. [6] V. Guenchev, C. Rüssel, V.M. Fokin,. Gutzov, Eur. J. Glss Sci. Technol. 8 (7) 8. [7] J. Deuener, J. Non-Cryst. Solids 7 () 195. [8] K. Thieme, C. Rüssel, J. Eur. Cerm. Soc. 3 (1) 3969.

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