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Correlation between maximum crystal growth rate and glass transition temperature of silicate glasses

Vladimir M. Fokin, Marcio L.F. Nascimento *, Edgar D. Zanotto *

Vitreous Materials Laboratory, LaMaV-UFSCar, 13565-905, Sao Carlos-SP, Brazil Received 1 May 2004; received in revised form 9 February 2005

Abstract

Recent publications demonstrate that the maximum homogeneous nucleation rates, Imax, of silicate glasses strongly diminish with the reduced glass transition temperature, Tgr (=Tg/Tm/L, where Tg is the glass transition temperature and Tm/L is the melting point or liquidus temperature). In addition, the critical cooling rates for metallic glass formation, Rc, also drop with rising Tgr. From these empirical observations as well as from theoretical considerations, it is expected that the maximum crystal growth rates, Umax, also depend on Tgr. In this paper we test and confirm this assumption by plotting experimental Umax vs. Tgr for 20 silicate glasses, and then use the most common crystal growth model – screw dislocation growth – to calculate and compare maximum experimental growth rates with theoretical predictions. Despite several assumptions made for the calculations, there is good agreement between theory and experiment, both in the magnitude of Umax(Tgr) and in the temperature of the maximum crystal growth rate, TUmax. These findings indicate that the screw dislocation growth model is a good approximation to describe crystal growth in silicate glasses.

2005 Elsevier B.V. All rights reserved.

1. Introduction

Fundamental studies of the mechanisms and kinetics of crystal nucleation and growth in glass-forming liquids not only provide valuable scientific insight, but also have practical relevance. Indeed, a plethora of novel oxide, chalcogenide and metallic glasses, as well as micro and nanostructured glass-ceramics, are being continuously developed based on such knowledge [1–5]. In a recent publication [6] we demonstrated that the maximum nucleation rates, Imax, of silicate glasses strongly diminish with reduced glass transition tempera- ture, Tgr = Tg/Tm/L, where Tg is the glass transition temperature (measured by conventional methods) and Tm/L is the melting point or liquidus temperature. In Ref. [6] we showed, for 51 glass-forming liquids, that the exper- imental Imax drops by 12 orders of magnitude, from panded version of Fig. 1 of Ref. [6], now with 5 glasses. The highest nucleation rate (about 1018 m 3 s 1) was estimated for a lithium silicate glass with 4 mol% of lithium oxide via X-ray diffraction line broadening of a fully crystallized sample [7]. Thus, the range of varia- tion of the nucleation rate with Tgr now extends to about 16 orders of magnitude.

In addition, Lu et al. [8] demonstrated that the critical cooling rates for metallic glass formation, Rc, drop from 1010 to 10 4 K/s when Tgr varies from 0.25 to 0.70. Since Rc is directly linked to both homogeneous nucleation where TL is the liquidus temperature, and In and Un refer to the nucleation and growth rates at the nose of the corresponding transformation–temperature–time curve

02-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.02.005

* Corresponding authors.

E-mail addresses: pmlfn@iris.ufscar.br (M.L.F. Nascimento), dedz@power.ufscar.br (E.D. Zanotto). URL: http://www.lamav.ufscar.br (Vitreous Materials Lab.).

w.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 351 (2005) 789–794 of the glass], it is reasonable to expect that the maximum crystal growth rates Umax ¼ UðTUmaxÞ also depend on Tgr.

This dependence of Umax is also expected from theoretical considerations, since the kinetic barriers for nucle- ation and growth should be similar. In this paper we test and confirm this hypothesis by plotting experimen- tal Umax vs. Tgr for 20 silicate glasses. We then use the most common crystal growth model – screw dislocation growth – to calculate and compare maximum experi- mental growth rates and their temperatures, TUmax, with theoretical predictions.

2. Experimental data

Figs. 2 and 3 show literature data for Umax and TU max

(collected in Table 1) for 20 silicate glasses, respectively, as a function of Tgr. The values of Tg were measured by DSC or calculated as the temperature where the visco-

The maximum growth rates, Umax, drop by about 10 orders of magnitude for silicate glasses having Tgr from 0.52 to 0.73, showing a well-defined tendency. The cal- culated lines shown in Figs. 2 and 3 will be discussed below.

3. Theory 3.1. Brief review of the main crystal growth models

For stoichiometric glass compositions that do not undergo compositional changes during crystallization, i.e., polymorphic crystallization, long-range diffusion is not necessary for crystal growth; thus, interfacial rearrangements are likely to control the crystal growth process. In this case, the focus of theoretical treatments has been directed at the nature of the interface. Three standard models are used to describe the crystal growth process in glasses, which are based on different views of the nature of the crystal/liquid interface. These models are: (i) the screw dislocation model; (i) the normal or continuous growth model; and (i) the two-dimensional surface nucleation growth. All these models are based on the assumption that the release of latent heat does not substantially alter the crystal-melt interface temperature. The two most common models for oxide liquids, (i) and (i), are summarized in the following paragraphs.

(i) The screw dislocation growth model

The screw dislocation growth model views the interface as smooth but imperfect on an atomic scale, with growth taking place at step sites provided by screw dis-

K O.2SiO PbO.SiO

CaO.Al O .2SiO 2MgO.2Al O .5SiO

2BaO.TiO .2SiO CaO.MgO.2SiO

Li O.2SiO

Na O.2SiO SiO

1U max (m/s)

Tgr

Fig. 2. Experimental data points for 20 silicate glasses, and calculated

Curves (2a, 2b): fixed T0r = 0.4 and varied melting entropy DSr =2 (2a); 8 (2b).

CaO.Al O .2SiO 2BaO.TiO .2SiO

Li O.2SiO K O.2SiO

CaO.MgO.2SiO 2MgO.2Al O .5SiO

Na O.SiO

SiO

Fig. 3. Temperatures of maximum growth rate vs. reduced glass transition temperature for 16 silicate glasses. Dashed lines refer to the case of Tmax/Tm = Tgr. Dotted lines are calculated with DSr = 5 and T0r = 0.4.

20 1Li O.1.27SiO 2BaO.TiO .2SiO

3MgO.Al O .3SiO

2Na O.CaO.3SiO Na O.2CaO.3SiO

CaO.SiO

Li O.2SiO BaO.2SiO log

(m

Tg / Tm/L

Fig. 1. Maximum nucleation rates vs. Tgr for 5 silicate glasses of stoichiometric and non-stoichiometric compositions. Lines were cal- culated from CNT with different thermodynamic barriers (see Ref. [6]).

790 V.M. Fokin et al. / Journal of Non-Crystalline Solids 351 (2005) 789–794

locations intersecting the interface. The crystal growth rate U is given by [9]:

where m is the frequency of atomic jumps at the inter- face, m0 is the vibrational frequency of the growth con- trolling atoms, DGD – the activation free energy for diffusion across the interface, k – the distance advanced by the interface in an unit kinetic process (usually taken as a molecular diameter), DG – the thermodynamic driving force for crystallization, i.e., the difference between the free energies of the undercooled melt and crystalline phase per mole, T – the absolute temperature, and R – the gas constant. The fraction of sites on the interface where atoms can preferentially be added or removed, f, is given by

f ¼ kDG 4prV m

2pTm and r is the specific surface energy of the liquid/crystal interface, Vm is the molar volume of the crystal, Tm is the thermodynamic melting point, and DT = Tm T is the undercooling.

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