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Continuous compositional changes of crystal and liquid during crystallization of a sodium calcium silicate glass

V.M. Fokin a,*, E.D. Zanotto b a S.I. Vavilov’s State Optical Institute, ul. Babushkina 36/1, St. Petersburg 192131, Russia b Vitreous Materials Laboratory, Federal University of Sao Carlos, 13565-905 Sao Carlos, SP, Brazil

Received 17 September 2006; received in revised form 20 December 2006


This paper deals with a systematic study of crystal nucleation and growth kinetics in a 14.6Na2O–34.0CaO–51.4SiO2 mol% glass, which is close to the CaO Æ SiO2–Na2O Æ SiO2 pseudo-binary section, just left of the stoichiometric Na2O Æ 2CaO Æ 3SiO2 (N1C2S3) compound. We show that crystallization begins with nucleation of a Na4+2xCa4 x[Si6O18]( 0 < x < 1) solid solution that is enriched in sodium as compared with both parent glass and the N1C2S3 compound; while a fully crystallized sample is composed only by a solid solution that is stable at very high temperatures, but is metastable in the temperatures under investigation. We thus confirm a continuous composi- tional change of the crystals during the course of crystallization. 2007 Elsevier B.V. All rights reserved.

PACS: 64.70.Kb; 64.60.Qb Keywords: Crystallization; Crystal growth; Glass ceramics; Nucleation

1. Introduction

The thermodynamic barrier for nucleation or the work for critical nucleus formation, W*, to a great extent determines the nucleation rate in supercooled liquids. For this reason, to use any nucleation theory one must first define the composition, structure and thermodynamic properties of the critical nucleus to evaluate W*. This task, and especially its experimental solution, is not trivial due to the

extremely small critical nucleus sizes (only a few nanometers) at the deep undercoolings needed to attain detectable homogeneous nucleation in typical glass forming liquids. This is one of the reasons why the newly evolving macrophase (predicted by the respective equilibrium phase diagram) is commonly used as a reference to describe the properties of the critical nucleus. This approach is consistent with assumptions of the classical nucleation theory

(CNT) employing Gibbs’ description of heterogeneous systems. However, a maximum thermodynamic driving force, i.e. that of the stable phase, is not a necessary condition to attain the minimum value of the thermodynamic barrier and maximum nucleation rate, because W* is a combination of the thermodynamic driving force, DGV, for crystal- lization and the specific surface energy, rc/l, of the nucleus/ liquid interface:


Particularly, preferred nucleation of the phase having the lowest thermodynamic barrier rather than other thermodynamically possible phases is the basis of the kinetic argumentation of Ostwald’s rule of stages, according to which any system prefers to reach intermediate stages having the closest free energy difference to the initial state [1]. Thus, some serious problems that often arise during quantitative analyses of nucleation data in the framework of CNT (e.g. see [2]) could be caused, at least in part, by the

02-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.04.014

E-mail address: vfokin@pisem.net (V.M. Fokin). URL: w.lamav.ufscar.br (E.D. Zanotto).

w.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 353 (2007) 2459–2468 erroneous employment of DGV for crystallization of the stable macro-phase for the critical nuclei using the specific sur- face energy as a fitting parameter. Indeed, in the last decade, indirect and direct experimental evidences appeared pointing out to the difference between the critical (and near critical) nuclei, and the corresponding stable macro-phase. Some of these evidences are listed below:

(a) A strong discrepancy between the time-lags for nucleation estimated from crystal nucleation and growth kinetics [3,4] in lithium silicate glasses with compositions between di- and metasilicate.

(b) Discrepancy between the rc/l estimated from the nucleation rate, and from the effect of dissolution of sub-critical nuclei as the temperature increases [5]. This problem could be avoided by assuming that the thermodynamic driving force is smaller than that for macro-phase crystallization. (c) Crystallization of sodium–calcium silicate glasses (in particular of the stoichiometric composition Na2O Æ

2CaO Æ 3SiO2) by nucleation of solid solutions whose composition continuously varies during the phase transformation [6,7] approaching the composition of the stable phase only in the end. (d) A remarkable size-dependence of the cluster composition has also been observed during primary crystallization of NiP particles in a hypoeutectic Ni–P amorphous alloy [8]. In this case, the compositional evolution was completed when the clusters attained about 10 nm. (e) Variation of (micron size) crystal compositions with the degree of undercooling was found recently in

CaO–Al2O3–SiO2 glasses [9] where it was demonstrated, that equilibrium crystals form near the liqui- dus, while disordered and non-stoichiometric phases precipitate near the glass transition temperature. This finding corroborates the statement that ‘metastable crystalline phases commonly precipitate in the initial stage of low-temperature crystallization of multicomponent glasses’ made in Ref. [10]. (f) A size-dependence of the crystal composition has also been detected for crystals formed on the surface of a cordierite glass [1].

The above mentioned results are still not numerous. This situation is due to the fact that most authors do not pay attention to the exact composition of the crystalline phases that precipitate in undercooled liquids, especially in the initialstagesofphasetransformation.However,onecanexpect that the compositional and structural evolution of the crystalline phase during phase transformation is a general feature. Therefore, the search and study of such phenomenon are of great interest from both theoretical and practical points of view since they may help one to find out a realistic approach for the nucleation process in glasses. In particular, from these evidences it became clear that the choice of stoichiometric glass compositions as model systems does not guarantee that the crystal nuclei will have the same composition as the parent glass, i.e. the condition needed to treat the studied system as ‘one-component’ (or stoichiometric) is not necessarily fulfilled in this way.

This paper presents additional experimental evidence for a continuous evolution of the crystal composition during nucleation and growth in a sodium–calcium silicate glass, extending the composition interval studied earlier and described in Refs. [12,13]. In addition, existing crystal nucleation rates are analyzed and compared with our own as a function of glass composition and reduced glass transition temperature.

2. Materials and methods

We employed sodium and calcium carbonates, and amorphous silicon dioxide of analytical grade for the glass synthesis. The melt was cast on a massive steel plate after about 2 h at 1450 C in a platinum crucible. The glass com- position by analysis (14.6Na2O–34.0CaO–51.4SiO2 mol%) is close to the pseudo-binary meta silicate section CaO Æ

SiO2–Na2O Æ SiO2 and lies just left of the stoichiometric compound Na2O Æ 2CaO Æ 3SiO2, while the compositions of the glasses studied in Refs. [12,13] are between the com-

2SiO2 (N1C1S2), Fig. 1. To evaluate the number of crystals per unit volume,

N(t), nucleated at a given temperature versus heat treatment time we employed the well-known Tammann or socalled ‘development’ method (see e.g. [5]). Then, N(t) data were fitted into Collins’s/Kashchiev’s equation (2) [15,16]


Ists ¼ ts to estimate the time-lag for nucleation, s, and the steady- state value of the nucleation rate, Ist, as fitting parameters. For sufficiently long times, this expression can be approximated by

NVðtÞ¼ Istðt tindÞ; ð3Þ where

Moreover, to obtain quantitative information about nucleation kinetics in the advanced stages of phase transformation the overall crystallization kinetics were analyzed with the JMAK equation:

where a is the volume fraction transformed, n is the socalled Avrami coefficient, which can be estimated from the slope of a ln( ln(1 a(t)) versus ln(t)) plot. In the case of three-dimensional growth, the Avrami coefficient can be written as where j and m characterize the evolution of the crystal number (N tj) and size (D tm) with time.

2460 V.M. Fokin, E.D. Zanotto / Journal of Non-Crystalline Solids 353 (2007) 2459–2468

Well below the glass transition temperature, the crystals

ible polymorphic transition at a temperature Tpm, which is accompanied by easily distinguished thermal effect on a

DSC curve [17]. Since Tpm depends on the value of x, its variation was used to detect changes of the crystal compo- sition during phase transformation.

An EDS (Stereosxcan 440) – dot map technique – was employed for the qualitative estimate of the compositional difference between the glassy matrix and crystals using U = 20 kV and I = 1.5 na. The measurement time for each point in the dot map was about 0.2 ms.

To visualize the diffusion zones around the growing crystals special multi-stage crystallization heat treatments were performed.

3. Results 3.1. Nucleation kinetics

Fig. 2 shows the typical N(t) dependence used to esti- mate the time-lag (or the induction period tind) for nucle- ation and the steady-state nucleation rate Ist. Solid and dashed lines are plotted with Eqs. (2) and (3), respectively, using the parameters s and Ist obtained by mathematical fitting (see Section 2). It should be noted that the ‘develop- ment’ method allows one to estimate the nucleation rate in the very early stages of the phase transformation when the volume of crystalline phase is negligibly small. Fig. 3 pre- sents the steady-state nucleation rate (a) and the induction period (b) as functions of temperature.

3.2. Overall crystallization kinetics and crystal growth

Fig. 4(a) shows the crystallized volume fractions estimated by optical microscopy as a function of heat treatment timeatT = 610 C,whichisclose tothetemperatureTmaxof the maximum nucleation rate Imax Ist(Tmax) (see Fig. 3). The first experimental points correspond to times that

Fig. 1. Phase diagram of the pseudo-binary section CaO Æ SiO2–Na2O Æ SiO2 of the sodium–calcium silicate system [14]. The arrow indicates the composition of the glass under investigation.


, m t, s exp Eq.(1) Eq.(2)

Fig. 2. Crystal number density versus time of nucleation at T = 610 C estimated via the ‘development’ method. The inset shows the N t data on a larger scale. The solid and dashed lines were plotted with Eqs. (2) and (3), respectively.

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strongly exceed the period investigated by the ‘development’ method (see Fig. 2). An Avrami plot is shown in Fig. 4(b).

The crystal growth kinetics at the same temperature (610 C) is shown in Fig. 5 in normal (a) and logarithmic (b) coordinates. Fig. 6 shows the increase of crystal size at T = 710 C for different crystal number densities. Since the nucleation rates are very small at T =7 10 C, preliminary nucleation heat treatments were performed to change the crystal number density. In all cases the crystal size distributions were close to monodisperse. Lines represent approximations via the equation D = Atm.

3.3. Thermal analysis and reversible polymorphous transition

DSC heating and cooling curves are shown in Fig. 7. After crystallization from the liquid state the crystalline phase undergoes a reversible (exothermic) polymorphic transition at a temperature Tpm (well below the glass tran- sition temperature). Fig. 8 presents Tpm taken from DSC heating-curves of partly crystallized samples versus volume fraction of crystalline phase.

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