Journal of Non-Crystalline Solids

Transcription

1 Journl of Non-rystlline Solids 62 (21) ontents lists ville t SciVerse ScienceDirect Journl of Non-rystlline Solids journl homepge: locte/ jnoncrysol Nonstoichiometric crystlliztion of lithium metsilicte clcium metsilicte glsses. Prt 1 rystl nucletion nd growth rtes Vldimir M. Fokin,, Rphel M..V. Reis, Alexnder S. Ayzov c, lever R. hingli, Edgr D. Znotto Vvilov Stte Opticl Institute, ul. Bushkin 6-1, St. Petersurg, Russi Vitreous Mterils Lortory, Deprtment of Mterils Engineering, Federl University of São rlos, UFSr, , São rlos-sp, Brzil c Ntionl Science entre, Khrkov Institute of Physics nd Technology, Ukrine rticle info strct Article history: Received 11 August 212 Received in revised form 18 Novemer 212 Aville online xxxx Keywords: Glss; rystlliztion; Nucletion; Growth; Eutectic The initil stges of the crystlliztion kinetics of lithium metsilicte (LS) in glsses of the Li 2 O SiO 2 O SiO 2 join which hs simple eutectic ws investigted t high undercoolings, somewht ove the glss trnsition tempertures. lcium metsilicte crystls precipitte nd grow only in the dvnced stges of crystlliztion. The vrition of glss composition from the eutectic (26.5 mol% Li 2 O) towrds lithium metsilicte (5 mol% Li 2 O) results in shrp increse of the internl nucletion rte of LS crystls, wheres the growth rtes increse only wekly. This strong increse of the nucletion rte is primrily cused y decrese of the thermodynmic rrier for nucletion due to n increse of the thermodynmic driving force for crystlliztion nd decrese of the nucleus/liquid interfcil energy s the glss composition pproches the crystl composition. 212 Pulished y Elsevier B.V. 1. Introduction The vst mjority of rticles imed t testing crystl nucletion, growth nd overll crystlliztion models using experimentl studies of the crystlliztion kinetics of glss-forming liquids ddress their stoichiometric or polymorphic crystlliztion, i.e., the growing crystls nd supercooled liquid hve the sme composition. However, very few glsses stisfy the ove condition [1,2], nd moreover, the true nture of the criticl nuclei in such stoichiometric glsses remins (mostly) unknown []. In other words, some reserch indictes tht, even in the cse of polymorphic crystlliztion, the composition of the criticl nuclei might differ from the prent glss [2]. Most oxide glsses disply more thn one crystlline phse fter crystlliztion with different composition from the prent glss, t lest in the dvnced stges of crystlliztion. Hence, detiled study of the kinetics of non-stoichiometric crystlliztion is quite importnt from oth theoreticl nd prcticl points of view. For the present study, we hve chosen glsses elonging to the Li 2 SiO (LS) SiO (S) pseudo-inry join tht hs single eutectic etween LS nd S. To the est of our knowledge, only dt on the crystlliztion kinetics of the stoichiometric end-memer compositions (Li 2 SiO nd SiO glsses) exist for this system. However, the nucletion rte in LS glss is so high tht it is extremely difficult to prepre such glss, wheres, ccording to Ref. [4], the internl nucletion rte of S glss is very low, which is corroorted y our inility to detect internl nucletion in smll (mm) pieces of this glss orresponding uthor. Tel.: E-mil ddress: vmfokin@gmil.com (V.M. Fokin). treted for severl hours ove the T g. Therefore, strong difference oviously exists etween the nucletion kinetics in these two glsses (LS nd S). This difference correltes to the reduced glss trnsition tempertures (T gr =T g /T m ; where T g is the glss trnsition temperture nd T m is the melting point of the crystl). It should e stressed tht, ccording to empiricl findings [5], the higher the T gr, the lower the mximum nucletion rte, I st mx. The mximum crystl nucletion rte in the stoichiometric LS glss is expected to e pproximtely m s 1, i.e., close to the vlues reported for some metls (e.g., I st mx ~1 29 m s 1 for tin [6]). The im of this systemtic study is to shed some light on the nucletion nd growth processes of two stoichiometric crystlline phses (S nd LS) in non-stoichiometric glsses from the LS S join. The relevnce of this type of reserch is relted to the crystlliztion of commercil glss-cermics, which is never stoichiometric! This pper ddresses the first prt of the present study, the nucletion kinetics nd dt on the very initil stges of crystl growth when, to first pproximtion, the growth rtes depend entirely upon the temperture nd not on the tretment time. The forthcoming pper, prt 2 [7], is devoted to the evolution of the residul melt composition during the more dvnced stges of crystlliztion. 2. Mterils nd methods The glsses were prepred from lithium nd clcium crontes nd fumed silic. The solid-phse rections of the desired mixtures of these regents were performed t 8 9. The produced mteril ws then melted for 4 h in n electricl furnce t 14 in pltinum crucile. These melts were poured on steel (or rss) sl nd pressed 22-9/$ see front mtter 212 Pulished y Elsevier B.V.

2 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) y steel (or rss) plte. The nominl composition of the tches is shown in Tle 1. The het tretment of the glss smples ws performed in stilized verticl electric ox furnce kept within pproximtely 1 of the chosen temperture. The chrcteristic tempertures for the prent glsses nd residul glss mtrices were estimted using Netzsch 44 differentil scnning clorimeter (Netzsch, Sel/Bvri, Germny) with pltinum crucile t 1 /min. A Leic DMRX opticl microscope (Leic Microsystems, Wetzlr, Germny) coupled with Leic DF49 D cmer ws used to investigte the morphology, size nd numer density of crystls emedded within the glss interior. Both trnsmitted light nd reflected light modes were used. Thin sl-sided pltes were prepred for trnsmitted light opticl microscopy from het-treted pieces of glss y cutting, grinding nd eo 2 polishing. A Philips XL field emission gun SEM (Philips, Amsterdm, The Netherlnds) ws used for oth secondry electron (SE) nd ck scttering (BS) imging s well s EDS. X-ry diffrction mesurements were crried out on oth powdered nd monolithic smples using n Ultim IV X-ry diffrctometer (Rigku orp., Jpn) operting t 2 ma nd 4 kv. ukα (1.546 Å) incident rdition ws used. The glss densities were mesured with Mettler Toledo Blnce (Model AX24).. Results.1. Phse digrm, concentrtion dependency of the glss trnsition temperture, nd glss densities The phse digrm of the LS S join ws constructed y A.R. West in 1978 [8]. We used DS nlysis of 25 mg glss smples to confirm nd enhnce the dt in Ref. [8]. Fig. 1 shows typicl DS heting curve performed t rte of 1 /min. The first exothermic pek corresponds to the formtion of LS nd the second, to the crystlliztion of the residul glss in oth LS nd S. The solidus, T S, nd liquidus, T L, tempertures were determined y the eginning nd the end of the melting pek, respectively (see lso Ref. [9]). We lso mesured the glss trnsition temperture, T g, nd the re, A eut/m, of the prt of the endothermic pek corresponding to the eutectic melting. The vlues of T L nd T S (points in Fig. 2) corroorte the dt in Ref. [8], which is denoted y the solid lines. It should e noted tht only some of the compositions close to the eutectic were studied in Ref. [8]. By plotting the re, A eut/m, versus the melt composition, we were le to determine the so-clled Tmmnn tringles (Fig. 2). Becuse the A eut/m reches mximum t the eutectic composition, this procedure helped us detect nd refine the position of the eutectic point. Figs. nd show the dependence of the glss trnsition temperture nd glss density on the glss composition, respectively. The liner dependence of the ltter provides indirect evidence for the similrities etween the tch nd ctul glss composition. This Tle 1 The nominl composition of the tches. Glss O SiO 2 Li 2 O SiO 2 mol% B B B B µv/mg dependence lso llows us to suppose tht in the frmework of the model of ssocited solutions [12] the glsses elonging to the LS S join only contin structurl units similr to the lithium nd clcium metsilicte crystls. This ssumption is corroorted y the fct tht the LS S join is inry t ll tempertures [8], i.e., onlytwo crystlline phses (Li 2 SiO nd SiO ) re oserved..2. rystlliztion B 67 B 6 B 5 T g T, o Volume nucletion Only glsses contining less thn 5 mol% O SiO 2 reveled homogeneous internl nucletion t resonle lortory time scle (hours). We mesured the nucletion rtes of the lithium metsilicte crystls (LS) in glsses B 5,, nd using the development method [2] in which the nucletion het tretments were followed y crystl growth, i.e., higher-temperture development to crystl sizes tht were visile with n opticl microscope. lcium metsilicte crystls (S) only ppered during the dvnced stges of the phse trnsition. The X-ry diffrction spectr of crystllized glss B 5 re shown in Fig. 4 with microgrphs for different doule tretments. According to the X-ry nlysis, glss smple sujected to nucletion het tretment t 484 for 15 h nd 5 min plus development tretment t 675 for 1.5 min contins only LS crystls (Fig. 4). To confirm this finding, we decresed the XRD scnning rte in the ngulr rnge corresponding to the min diffrction peks of S y fctor of 2. The new XRD spectrum lso did not show ny trce of S crystls. But prolonging the het tretment t 675 to 6 min resulted in full crystlliztion; t this point, the X-ry spectrum revels oth LS nd S crystl phses (Fig. 4). T S T L T L 11 1 T L T L 1 11 Fig. 1. DS curves for the different glsses of this study. The insets show zoom of the eutectic melting. A heting rte of 1 /min nd mg glss pieces were used. T, Aeut/m,.u Li 2 SiO + liquid liquid Li 2 SiO + SiO SiO + liquid Li 2 SiO mole% SiO Fig. 2. S LS phse digrm () nd the Tmmnn tringle (). The lines in the top figure were tken from Ref. [7].

3 58 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) m Tg, crystl SiO m,g/cm Two different methods were used to estimte the crystl numer density, N V, in the glss volume. Becuse the nucletion rtes for glsses B 5 nd re extremely low, we polished the sides of two plne-prllel pltes with thickness etween 8 nd 2 μm (depending on the vlues of N V ) fter the het tretment. These smples were then nlyzed y trnsmitted light microscopy to estimte the numer of crystls in given volume. ross sections of the het treted smples with high cps cps Li 2 SiO mole % SiO Li 2 SiO (29-828) SiO (4-146) 4s/step Li 2 SiO SiO 2s/step crystl Li 2 SiO Fig.. Glss trnsition temperture () nd glss density, mesured t room temperture, () versus glss composition. The doted nd dshed lines show the density of the pproprite crystlline phses [11]. The density of the Li 2 SiO glss ws tken from Ref. [1]. 5 m Fig. 5. Trnsmitted light opticl microgrph of plte of glss B 5 treted t T n =494 for 12 h nd then t T d =675 for min. The inset shows the detils of the crystl morphology. nucletionrtes(glss ) were prepred, nd their numer densities, N V, were estimted using stndrd stereologicl methods. During the initil stges of growth, the LS crystls in glsses B 5 nd re needle-like dendrites with complex structure (Fig. 5), while glss hd spherulitic shped crystls (Fig. 6). It should e noted tht prolonging the isotherml nucletion tretment nd development time of glsses B 5 nd led to the trnsformtion of these needle-like LS crystls into str-like LS crystls y creting new growth directions (see Fig. 7 nd inset in Fig. 4). The numer density, N V, of LS crystls (nucleted on cooling during the glss preprtion nd/or on heting to the development temperture) in glss ws very high, pproximtely 1 6 crystls mm, ecuse of this mteril's extremely high nucletion rte. In contrst, glsses B 5 nd without ny preliminry nucletion het tretment primrily displyed surfce crystlliztion. The smll numer (~1 mm ) of crystls in these ltter two glsses could only e detected fter long development time. These crystls hve spherulitic shpes nd ccording to X-ry nlysis (Fig. 8)contin LS crystls nd trces of S (wollstonite) which most likely forms within the residul glss remining inside the spherulites. In contrst to glss, the spherulitic crystls in the glss consisted of only lithium metsilicte (Fig. 9). This could e cused not only y the difference in the prent glss compositions ut lso y the lrge difference in the sizes of the spherulites, which hve grown out 1 times Fig. 4. X-ry diffrction spectr of prtly nd fully crystllized B 5 glss fter nucletion t T n =484 for 15 h nd 5 min plus growth t T d =675 for () 1.5 nd () 6 min. The photos show the corresponding trnsmitted () nd reflected () light opticl microgrphs. 1 μm Fig. 6. Trnsmitted light opticl microgrph of plte of glss treted t T d =56 for min. ross-polrized contrst.

4 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) Li 2 SiO (29-828) cps m Fig. 9. X-ry diffrction spectrum of powdered glss prtly crystllized t T=56 for 2 min, nd reflected light opticl microgrph of its cross section. longer in the glss. The residul glss within the spherulites hs lredy strted to form S. Thus, the first crystlline phse formed vi internl homogeneous nucletion t reltive low tempertures in glsses contining over 5 mol% LS ws lithium metsilicte. Therefore, ll mesurements of the nucletion kinetics of this pper refer to LS crystls. Fig. 1 shows the typicl kinetic dependence of N V on nucletion time, t, for glsses B 5,,nd. The solid lines were plotted using Eq. (1) for the time-dependence of the numer of super-criticl nuclei, tken from Ref. [1]: N V ðþ¼i t st τ t τ π2 6 2X m¼1 ð 1Þ m m 2! exp m 2 t : ð1þ τ This eqution includes two fundmentl prmeters, the stedy-stte nucletion rte, I st, nd the time-lg for nucletion, τ, which were estimted s fit prmeters. The temperture dependences of I st nd τ re shown in Figs. 11 nd 12,respectively rystlliztion t tempertures close to the liquidus, T L, nd solidus, T S In contrst to the previous chpter, we consider the result of fst crystlliztion t tempertures close to the T S nd T L in this chpter. The reflected light opticl microgrph in Fig. 1 (top) shows cross section of the smple from glss treted for 1 min t T=9 immeditely fter melting t T =125 (for this composition T L =T S =126 ) for 1 min. A fine mixture of lternting crystls (LS nd S) is typicl for eutectic crystlliztion s it is the cse of cps Li 2 SiO (29-828) SiO (4-146) 4 μm Fig. 7. Trnsmitted light opticl microgrph of plte of glss treted t T n =515 for 1 h. ross-polrized contrst. 2 m Fig. 8. X-ry diffrction spectrum of powder tken from n internl prt of smple of glss crystllized for 6 min t T=62. The inset shows trnsmitted light opticl microgrph of spherulite in the glss interior. the glss (see Fig. 2). The nd Si concentrtion profiles (see Fig. 14) long the white line showed in the top SEM BS imge provide direct evidence for such lterntions. The chemicl contrst in the BS imge lso corroortes the profile; the right nd drk crystls re S nd LS, respectively. It should e noted tht the Si concentrtion is the sme in oth crystls s the two crystlline phses re metsilictes. A smple of glss B 66 (see Fig. 1 ottom) heted for 2 min t T=11 (i.e., t temperture etween the T L nd T S ) nd cooled to temperture elow the T g t pproximtely 2 /min shows N N V,mm - V,mm- N V,mm c B 5 T n = 46 o T n = 46 o t, h T n = 44 o t, h Fig. 1. N V (t)plotsforglssesb 5 (), (), nd (c) for severl nucletion tempertures, T n. The lines were plotted using Eq. (1) with proper fitting prmeters I st nd τ.

5 6 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) I st,m - s B T, o m Fig. 11. Stedy-stte nucletion rtes versus temperture of lithium metsilicte crystls in glsses B 5,, nd. very different morphology. According to the phse digrm (Fig. 2), only S crystls formed (lrge fceted crystls in Fig. 1, ottom) t T=11 (region of primry crystlliztion). Then, cooling to tempertures elow the T S cuses the rpid crystlliztion of the residul glss mtrix with composition close to the eutectic with formtion of fine structure tht is typicl for eutectics. Similr results re shown in Fig. 15, which presents DS cooling curve for glss B 66 with photo (inset) of the smple surfce tken directly fter the DS run. By ccounting for the temperture of the crystlliztion peks, we my ttriute the first pek to the formtion of S crystls nd the second one to the crystlliztion of the residul eutectic liquid. It should e noted tht dely ws oserved for the two crystlliztion peks reltive to T L nd T S. Fig. 1. Reflected light opticl microgrphs of cross-sections of glsses () nd B 66 () sujected to the following het tretments: T=125, 1 min+t=9, 1 min; T=11, 2 min. Full crystlliztion occurred during cooling of the smples t temperture TT S (126 ). m.2.. rystl growth rtes The dt presented in this section relte to the growth of the LS crystls t reltively low tempertures (s for the nucletion dt shown in Section.2.1). Once the chnge in the residul glss composition cn no longer e neglected, the dependence of the crystl size on time egins to devite from liner. The evolution of the residul glss composition nd ssocited phenomen will e presented nd discussed in detil in compnion pper [7]. In the present pper, we restrict our considertions to the initil stge of crystl growth, i.e., when the growth rtes cn e considered time-independent to 14 B 5 12 ln(,s) /T, K Fig. 12. Temperture dependencies of the nucletion time-lgs for glsses B 5,, nd in Arrhenius coordintes. The top solid line is liner fit of dt of the B 5 glss. In the cse of glsses nd the solid lines re plotted prllel to the former. Si,.u.,.u h, m Fig. 14. SEM BSE imge nd concentrtion long the cross section of smple of glss treted t 125 for 1 min nd then t 9 for 1 min.

6 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) μv/mg 9 6 TL 1 μm T, o Fig. 15. DS cooling curve (1 /min) of B 66 melt. The inset shows reflected light opticl microgrph of the surfce of smple fter the DS run. The rrows point to S crystls nd the crystllized residul (eutectic) melt. first pproximtion. Such restriction llows us to study nd compre the temperture dependence of the crystl growth rtes in glsses B 5,, nd. For glsses B 5 nd, we mesured the growth rtes of the crystlline surfce lyer, which consisted of needle-like LS crystls seprted y the residul liquid, t different tempertures. Without preliminry nucletion tretment, these glsses contin primrily surfce crystlliztion s previously mentioned. Fig. 16 shows n exmple of the reflected light opticl microgrphs nd SEM imges from the cross sections of the B 5 glss smple fter treting t T= 675 for 1 min. These cross-sections were mde in two different directions, prllel (tken from the vicinity of the smple surfce) nd perpendiculr to the externl surfce of the smple, s shown y scheme in Fig. 16. The morphology of the surfce nucleted crystls is similr to tht of crystls nucleted in the glss volume (plese compre with Fig. 5). It should e emphsized tht there is no contct etween the numerous LS crystls (Fig. 16 ottom) due to the Li-depleted diffusion zones round ech crystl! The study of the residul melt composition etween the needle-like LS crystls tht formed oth on the surfce lyer nd fr from it will e presented in Ref. [7]. Fig. 17 presents the X-ry diffrction spectr of the cross sections shown in Fig. 16, oth prllel(fig. 17c) nd perpendiculr (Fig. 17) 5 m TS cps (1) 65% c (2) 45% 1:45 22:1 :1 (11) 19% (2) (111) to the externl surfce. The ottom curve (Fig. 17) reltes to finely ground smple (2 μm). A strong crystllogrphic orienttion of the surfce nucleted LS crystls ws oserved. The reflection (2) ws gretly enhnced for the smple cut prllel to the surfce (Figs. 16 ottom, nd 17c) while ll the other reflections hve een strongly suppressed. The opposite is seen for the smple cut perpendiculr to the surfce, with enhnced peks corresponding to (2) nd (2). This result indictes tht the crystls re highly oriented with their c xis perpendiculr to the smple surfce. It should e noted tht the smples hve different res nd crystl frctions due to sectioning, so direct comprison etween the solute intensities of peks from different curves is not possile. Fig. 18 shows the dependence of the crystl lyer thickness, h, on time, t, for different tempertures for glsses B 5 () nd (). All of the plots were nerly liner. This feture llows us to conclude tht, t lest up to the vlues of h in these experiments, the crystlliztion front dvnces towrds the inner prts of the smple without chnging the liquid composition inside the glss smple. In other words, only the composition of the inter-dendritic residul glss, which is trpped etween the LS rms, chnged. Thus, the estimted (2) 2% θ Li 2 SiO (29-828) Fig. 17. ) X-ry diffrction spectrum of powder of the B 5 glss smple crystllized t T=675 for 1 min. ) nd c) X-ry diffrction spectr of different cuts of the sme smple: cross section prllel (c) nd perpendiculr () to the externl surfce of the smple (see scheme in Fig. 16). The rtio etween the res of the diffrction peks re shown close to the spectr. The dshed verticl lines correspond to the positions of the diffrction peks tken from crd c B 5 5 m h, m m Fig. 16. Reflected light opticl microgrphs of cross sections perpendiculr nd prllel to the externl surfce (see scheme) of B 5 glss smple treted t T=675 for 1 min. The inset is n SEM imge t, min Fig. 18. Thickness of the crystlline surfce lyer of B 5 () nd () glss smples versus het tretment time t different tempertures. The solid lines re liner pproximtions to the dt.

7 62 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) L/2 nd l/2, μm 2 1 L/2 l/2 L l log( U, m/min) -2 B5 B47 B t, s Fig. 19. Sizes L/2 nd l/2 (see inset) of LS crystls nucleted in the volume of glss t 47 for 45 h versus time of growth t 675. The solid lines re liner pproximtions to experimentl dt. The dshed line is the h~t plot shown in Fig. 18 for 675 nd shifted y 26 s to higher times /T, K -1 Fig. 21. Temperture dependencies of the LS crystl growth rtes for,, nd B 5 glsses in Arrhenius coordintes. crystl growth rte, U=dh/dt, is function of just the temperture. It should e noted tht, t ny given temperture, the growth rte of the surfce nucleted crystls equls tht of the internlly nucleted crystls. Fig. 19 shows the hlf length nd width of the needle-like crystls nucleted within the volume of glss (see inset of Fig. 19) versus their growth time t 675. According to this figure,.5dl/dt (slope of the solid line) is very close to dh/dt (slope of the dshed line). The pprent induction period, pproximtely 26 s, of the L/2 nd l/2 time dependencies likely refers to the time necessry for smple heting. Fig. 2 shows the time dependence of the rdius, R(t), of the LS spherulites in t severl tempertures. The plot of R(t) t T=52 shows stronger devition from linerity thn t higher tempertures. This devition is discussed in Ref. [7]. In the present pper we restrict our nlysis to the initil liner portion of the R(t) dependence. The temperture dependencies of the growth rtes estimted from the dt presented in Figs. 18 nd 2 re shown using Arrhenius coordintes in Fig Discussion The following equtions for the stedy-stte nucletion rte, I st, (see e.g., [14]), the time-lg for nucletion, τ ([1], see lso Eq. (1)), R m t, min Fig. 2. Rdii of the LS crystls in the glss versus time of het tretment t different tempertures. nd the crystl growth rte, U (screw disloction model, [14,15]) were used to nlyze the crystl nucletion nd growth kinetics: rffiffiffiffiffiffiffiffi σ DI W I st ¼ exp ; ð2þ k B T 4 k B T W ¼ 16 π σ ; ðþ ΔG 2 V τ ¼ 16 k B Tσ ΔG 2 V 2 D I ; "!# U ¼ f D U 4 1 exp 1 ΔG V 2 k B T ; ð5þ f ¼ 1 ðt L TÞ ; ð6þ 2π T L where k B is the Boltzmnn constnt; T is the solute temperture; is chrcteristic size prmeter (size of the uilding units in the melt); σ is the specific energy of the liquid/criticl nucleus interfce; ΔG V is the thermodynmic driving force for crystlliztion per unit volume of crystl; W is the work of formtion for nucleus of criticl size, i.e., the so clled thermodynmic rrier; D I nd D U re the effective diffusion coefficients for the uilding units in the cse of nucletion nd growth processes respectively; nd f is the frction of screw disloctions on the crystl surfce. Strictly speking, Eq. (2) ws derived for single-component systems. When the crystl composition is the sme s tht of the liquid (stoichiometric crystlliztion) nd the possile dissocition of structurl units is neglected, the liquid could e considered to only consist of uilding units similr to the crystlline cell. The system is often considered single component in such situtions. Two corrections should e mde when employing Eq. (2) for non-stoichiometric crystlliztion, i.e., for precipittion of crystlline phses with different composition from the prent liquid. First, the vlue of the molr frction of the precipitting sustnce in the melt, x, hs to e introduced into the pre-exponentil term. Thus, the decrese in the numer of uilding units prticipting in the nucletion of the new phse reltive to stoichiometric crystlliztion will e tken into ccount. However, the effect of this fctor is much less thn tht for the chnge in the thermodynmic driving force for crystlliztion, ΔG V. This driving force ws derived for inry (metllic) melts in Ref. [16] ð4þ

8 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) B J/m sed on the regulr solution model for the liquid nd solid. In the limiting cse involving the sence of solid solutions, i.e., when the soluility of second component in the crystlline phse is zero, the following formul ws proposed for the driving force [16]: ΔG V ¼ ðt L TÞðΔS m R lnxþ=v m ; ð7þ where T L is the liquidus, ΔS m is the entropy of fusion per mole of pure crystl, nd V m is the molr volume. Using ΔS m =5 J K 1 mol 1 [17] for lithium metsilicte, we clculted the thermodynmic driving force versus the crystlliztion temperture for LS in severl glsses elonging to the LS S join s shown in Fig. 22. For glss B 5 the vlue of T L ws tken from the extension of the liquidus to the RHS of the phse digrm. This prolongtion corresponding to the metstle equilirium etween LS crystls nd liquid tkes plce up to the formtion of the S phse nd is discussed in detil in Ref. [7]. We plotted I st (T) nd U(T) for glsses B 5,, nd in Fig. 2,to compre the influence of the glss composition on the nucletion nd growth rtes. It is cler tht the crystl growth rte incresed no more thn 1 2 orders of mgnitude due to the increse in LS content from.5 to.65 molr frction, wheres the nucletion rte incresed y seven orders of mgnitude. At high undercoolings the crystl growth I st,m - s T, K Fig. 22. Thermodynmic driving force for crystlliztion of lithium metsilicte crystls in glsses B 5,, nd, nd in the liquid with Li 2 O SiO 2 composition B B T, Fig. 2. rystl nucletion nd growth rtes in glsses B 5,, nd s function of temperture U, m/ mi n rte is primrily determined y the effective diffusion coefficient (see Eq. (5)). Hence, ssuming D U D I, we cn conclude tht the strong increse in the nucletion rte is cused primrily y the decresed thermodynmic rrier for nucletion W. omining Eq. (4) with Eq. (2) nd correcting y using the molr frction, x, of LS in the glss (see discussion ove), one cn rewrite the eqution for the stedy-stte nucletion rte s: I st ¼ x 16 pffiffiffiffiffiffiffiffi k B T 1 ΔG 2 V 6 τ σ = x LS, mole frction Fig. 24. Energy of the liquid/criticl LS crystl interfce versus glss composition. The empty circles refer to the present glsses. The solid line is liner fit. The str is the expected vlue corresponding to the LS melt. W exp : ð8þ k B T Eq. (8) ws employed to estimte σ s fit prmeter. One should recll tht σ enters into the thermodynmic rrier W (see Eq. ()). In our clcultions, we used =(V m /N A ) 1/ m, nd the results re shown in Figs. 24 nd 25 for 477, close to the temperture of the mximum nucletion rte in glsses B 5,, nd.asws expected, the thermodynmic rrier strongly decreses with incresing Li 2 O content in the glss (Fig. 25). Fig. 26 shows the mximum nucletion rtes versus the reduced glss trnsition temperture. The lrge squres relte to the glsses B 5,, nd, wheres the other points, tken from Ref. [2], relte to different silicte glsses. The I st (T mx ) vlues for glsses B 5,, nd confirm the strong correltion etween the I st (T mx ) nd T gr =T g /T L. Becuse the new dt reltes to the sme crystl (LS) nd the sme glss system, the correltion etween I st (T mx ) nd T gr W/k B T mx B LS,mol frction Fig. 25. W/k B T mx versus the molr frction of LS in the glss.

9 64 V.M. Fokin et l. / Journl of Non-rystlline Solids 62 (21) LS second tht is proportionl to the difference etween the crystl nd melt compositions. log(i mx,m - s -1 ) Fig. 26. Mximum stedy-stte nucletion rtes in different silicte glsses versus reduced glss trnsition temperture [2,5]. Squres show the dt of Fig. 11. Str see text. T gr B 5 5. onclusions The nucletion nd growth rtes of lithium metsilicte crystls were mesured for severl glss compositions of the Li 2 O SiO 2 O SiO 2 pseudo-inry join with simple eutectic t.5 Li 2 O SiO 2 mole frction. Incresing the LS content in the glss from.5 to.65 mole frctions increses the mximum stedy-stte nucletion rte y pproximtely seven orders of mgnitude, wheres the growth rte only increses y one or two orders of mgnitude. This extreme increse in the nucletion rte ws primrily cused y decrese in the thermodynmic rrier for nucletion due to the incresed thermodynmic driving force for crystlliztion nd decresed nucleus/liquid interfcil energy, σ. In the studied composition rnge, σ linerly decreses when the melt composition pproches the crystl composition nd cn e represented y two portions: the first is the surfce energy of the crystl in its own melt, nd the second is proportionl to the difference etween the crystl nd melt compositions. is quite cler, despite the reltive nrrow T gr intervl. According to this correltion, the lower the reduced glss trnsition temperture, the higher the mximum nucletion rte [5]. The physicl reson for this trend is the similrity etween the T mx nd T g. Becuse T gr reflects the undercooling chieved t T g ~T mx, decresing the T gr nd thus incresing the undercooling increses the thermodynmic driving force for crystlliztion. The thermodynmic rrier for nucletion, nd hence the nucletion rte, depends strongly on the specific surfce energy of the criticl nucleus/melt interfce. Therefore we revert to Fig. 24 presenting the dependence of σ on the melt composition. The empty circles refer to the glsses studied here. The solid line is the liner fit oftheσ(x): σðþ¼:75 :154x; x where σ is given in J/m 2 nd x is the LS content in mole frction. According to the extrpoltion of this liner dependence, the specific surfce energy of lithium metsilicte in its own melt (x=1) is.18 J/m 2. omining this vlue with τ=. s nd ΔG V (see the top line in Fig. 22) wegeti st = m s 1 t T=477, which is very close to the T mx for glsses,,ndb 5.ThisI st vlue follows the trend of the dt in Fig. 26 (compre the empty str to the solid line), especilly if one ccounts for the pproximte chrcter of these estimtes. To refine the rel form of σ(x) for wide x rnge, mesuring the nucletion rtes for glsses contining more thn.5 mole frction of LS would e necessry. Nevertheless we cn conclude tht shifts in the glss composition wy from tht of the precipitted crystlline phse increses the interfcil energy. Thus, one could represent the nuclei surfce energy s two prts: the surfce energy of the crystl in its own melt, nd ð9þ Acknowledgments Finncil support from Brzilin funding gencies FAPESP nd NPq re fully pprecited. References [1] E.D. Znotto, V.M. Fokin, Phil. Trns. R. Soc. Lond. A 61 (2) [2] V.M. Fokin, E.D. Znotto, N.S. Yuritsyn, J.W.P. Schmelzer, J. Non-ryst. Solids 52 (26) [] V.M. Fokin, N.S. Yuritsyn, E.D. Znotto, J.W.P. Schmelzer, A. rl Jr., J. Non-ryst. Solids 54 (28) [4] L. Grnsy, T. Wng, P.F. Jmes, J. hem. Phys. 18 (1998) [5] V.M. Fokin, E.D. Znotto, J.W.P. Schmelzer, J. Non-ryst. Solids 21 (2) [6] V.P. Skripov, M.Z. Fizullin, rystl Liquid Gs Phse Trnsitions nd Thermodynmic Similrity, Wiley & Sons, 26. [7] V.M. Fokin, R.M..V. Reis, A.S. Ayzov,.R. hingli, J.W.P. Schmelzer, E.D. Znotto, Nonstoichiometric crystlliztion of lithium metsilicte clcium metsilicte glsses. Prt 2 evolution of the residul melt composition in the dvnced stges of crystlliztion nd ssocited phenomen J. Non-ryst. Solids (in preprtion). [8] A.R. West, J. Am. erm. Soc. 61 (1978) [9] E.B. Ferreir, E.D. Znotto, S. Feller, G. Lodden, J. Bnerjee, T. Edwrds, M. Afftigto, J. Am. erm. Soc. 1 9 (211) [1] Sciglss_dtse, [11] IEM Dtses nd Dtsets, [12] B.A. Shkhmtkin, N.M. Vedishchev, M.M. Shultz, A.. Wright, J. Non-ryst. Solids 177 (1994) [1] D. Kshchiev, Surf. Sci. 14 (1969) [14] I. Gutzow, J. Schmelzer, The Vitreous Stte: Thermodynmics, Structure, Rheology, nd rystlliztion, Springer, Berlin, [15] J.W. hristin, The Theory of Trnsformtions in Metls nd Alloys. Prt I, Pergmon, Oxford, [16].V. Thompson, F. Spepen, Act Metll. 1 (198) [17] P. Richet, Geochim. osmochim. Act 49 (1985)