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Crystal growth kinetics in cordierite and diopside glasses in wide temperature ranges

Stefan Reinsch a,*, Marcio Luis Ferreira Nascimento b, Ralf Müller a, Edgar Dutra Zanotto bFederal Institute for Materials Research and Testing, 12205 Berlin, GermanyVitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos, 13595-905 São Carlos-SP, Brazil article info

Article history: Received 1 April 2008 Received in revised form 1 September 2008 Available online x

PACS: 81.05.Kf 81.10. h 81.10.Aj

Keywords: Crystal growth Oxide glasses Silicates abstra ct

We measured and collected literature data for the crystal growth rate, u(T), of l-cordierite

(2MgO 2Al2O3 5SiO2) and diopside (CaO MgO 2SiO2) in their isochemical glass forming melts. The data cover exceptionally wide temperature ranges, i.e. 800–1350 C for cordierite and 750–1378 C for diopside. The maximum of u(T) occurs at about 1250 C for both systems. A smooth shoulder is observed around 970 C for l-cordierite. Based on measured and collected viscosity data, we fitted u(T) using standard crystal growth models. For diopside, the experimental u(T) fits well to the 2D surface nucleation model and also to the screw dislocation growth mechanism. However, the screw dislocation model yields parameters of more significant physical meaning. For cordierite, these two models also describe the experimental growth rates. However, the best fittings of u(T) including the observed shoulder, were attained for a combined mechanism, assuming that the melt/crystal interface growing from screw dislocations is additionally roughened by superimposed 2D surface nucleation at large undercoolings, starting at a temperature around the shoulder. The good fittings indicate that viscosity can be used to assess the transport mechanism that determines crystal growth in these two systems, from the melting point Tm down to about Tg, with no sign of a breakdown of the Stokes–Einstein/Eyring equation. 2008 Elsevier B.V. All rights reserved.

1. Introduction

Crystal growth kinetics in glass forming liquids has been extensively studied and reviewed elsewhere [1–5]. For isochemical or polymorphic crystallization, the crystal growth rates have been described in terms of standard models of interface-controlled growth (see, e.g., [6–8]) such as normal growth, screw dislocation growth or 2D surface nucleated growth. Detailed studies of crystal growth mechanisms are known for various glass forming compositions, such as SiO2 and GeO2 (normal growth) [9,10],N a2O 2SiO2 (screw dislocation) [1] and K2O 4B2O3 (2D nucleated growth) [12]. However, in most studies the inferred crystal growth mechanisms are typically restricted to temperature ranges near the melting point, Tm, or somewhat above the glass transformation tempera- ture, Tg, where crystal growth rates can be most easily measured. In one of the first studies of crystal growth in glasses in wide temperature ranges, Burgner and Weinberg [13] analyzed the growth rates of internally nucleated lithium disilicate crystals in isochemical Li2O 2SiO2 glass forming melts between the glass transition temperature, Tg, and the melting point, Tm. Their analysis suggested that different governing growth mechanisms may be ac- tive for distinct temperature ranges, and that the usual phenome- nological models could be applicable only for limited temperature ranges.

Meanwhile, crystal growth rate data for other two silicate glasses, cordierite and diopside, have also been measured in similarly broad temperature ranges. Thus, the extensive studies of surface nucleated, isochemical crystallization of high-quartz solid

5SiO2), in cordierite glasses reported in Refs. [14–21] allow a similar analysis. Some of these studies were part of a cooperative effort of the TC 7 Committee of the International Commission on Glass [2], which’s aim was to advance the understanding of surface crystallization phenomena. Herein, numerous glasses close to the stoichiometric cordierite composition were melted in different laboratories and crystal growth experiments were conducted over a long period of time covering various experimental conditions. As another case of surface nucleated crystallization, the crystal growth rates of diopside (CaO MgO 2SiO2) in isochemical melts have also been comprehensively studied. Thus, crystal growth rate data are known for diopside glasses between 750–15 C and 1277–1378 C [14,23–27]. In addition, thermodynamic and kinetic data, such as melting enthalpy and viscosity as a function of temperature are available for both systems, which facilitate quantitative comparisons between theory and experiment.

The objective of the present work is thus to summarize all measured growth rate data for l-cordierite and diopside crystals in

02-3093/$ - see front matter 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.09.007

* Corresponding author. Tel.: +49 30 6392 5950; fax: +49 30 6392 5976. E-mail address: stefan.reinsch@bam.de (S. Reinsch).

Journal of Non-Crystalline Solids x (2008) x–x Contents lists available at ScienceDirect

Journal of Non-Crystalline Solids journal homepage: w.elsevi er.c om/locate/jnoncrysol

Please cite this article in press as: S. Reinsch et al., J. Non-Cryst. Solids (2008), doi:10.1016/j.jnoncrysol.2008.09.007 their isochemical liquids in wide temperature ranges, then to analyze and discuss their observed temperature dependencies in terms of the classical crystal growth models. We also present a proposal using combined growth mechanisms to explain the shoulder in the crystal growth curve of l-cordierite.

2. Experimental 2.1. Samples

2.1.1. Cordierite glasses

Most of the data for the crystal growth rates of l-cordierite refer to glasses having the nominal composition of cordierite (in wt%): 51.3 SiO2, 34.9 Al2O3 and 13.8 MgO. In this work and in Refs. [14,15,19] cordierite glasses were melted from reagent grade MgO and Al2O3 (both from Merck) and SiO2 (quartz sand, Walbeck GmbH, Weferlingen) at 1590 C in air for at least 8 h in Pt-cruci- bles. Meltings of 500 ml batches were carried out in conventional electric furnaces and in medium frequency inductive furnaces (4l batches). In the latter case, glass homogeneity was improved by stirring. Diaz-Mora et al. [20,21] used two cordierite glasses from Schott Glaswerke: one glass (B9455) had the nominal cordierite composition; another (GM30870) had 14.6 MgO, 3.2 Al2O3, 52.3 SiO2 wt%. Yuritsyn et al. [16,17] used stoichiometric cordierite glasses melted from chemically pure Al(OH)3, MgCO3 and SiO2 n-

H2O in Pt/Rh crucibles at 1600 C for 4 h. All compositions are summarized in Table 1.

In this work and Refs. [14,15,19], glass plates of 10 15 1c m3 were prepared by casting the melts onto steel plates and slowly cooling to room temperature from 750 C. Wet chemical analysis of the quenched glasses showed that no oxide component deviates more than 0.8 wt% from the nominal composition. The water content determined by hot vacuum extraction and IR spectroscopy [28] for one of the glasses was 0.033 mol/l (226 wt ppm).

2.1.2. Diopside glasses

The diopside glasses reported by several authors [14,23–27,29– 34] and that used in the present study were melted in air in Pt crucibles. In this work and Ref. [14], glass plates of 10 15 1c m3 were splat cooled onto steel plates and slowly cooled to room temperature from 740 C. Briggs and Carruthers [23] made an X-ray fluorescence analysis confirming that the composition of their glass was very close to the nominal composition, and was free of iron, titanium and alkali metal oxides, but had 0.25 mol% Al2O3. Nascimento et al. [25] used the ICP technique for chemical analysis, which showed that his glass composition deviates less than 1 wt% from the diopside stoichiometry. Reinsch [14] used a diopside glass with addition of 1 wt% Al2O3. Chemical analysis of this glass (19.7

MgO, 25.8 CaO, 54.5 SiO2,1 Al2O3 wt%) showed that no oxide component deviate more than 1 wt% from the nominal composition.

The water content measured by hot vacuum extraction was 0.12 mol/l (758 wt ppm) [28]. Zanotto [27] used also a diopside glass with 1 wt% Al2O3. Kirkpatrick et al. [24] analyzed their glass with an electron microprobe, indicating a composition of 19.1

MgO, 26.4 CaO, 56.2 SiO2 wt%, thus having only a minor discrepancy from the nominal diopside composition. Unfortunately, how- ever, impurity and water contents were not always reported, but all these glasses have small departures from the stoichiometric diopside (18.61 MgO, 25.9 CaO, 5.49 SiO2 wt%). All compositions are summarized in Table 1.

2.2. Measurements

2.2.1. Viscosity In the present work, the viscosities of cordierite and diopside melts were determined by complementary methods. Tg was determined by a horizontal dilatometer (heating rate 5 K/min, Netzsch

402 E). Beam bending viscometry (heating rate 5 K/min, BAM) was used for the range log10(g/(Pa s)) = 12.3 9 and for log10(g/ (Pa s)) < 5 (T > 1000 C) rotational viscometry (BAM, measuring head Haake VT550) was applied.

The viscosity of the cordierite melt was also measured by Giess and Knickerbocker [35] at 900 and 920 C with a parallel plate vis- cometer. Yuritsyn et al. obtained Tg data by means of dilatometry [16]. The viscosity of the diopside melt was measured by Licko and Danek [29] in an oscillating viscometer using a platinum–rhodium crucible and a cylinder with conical end. Nascimento et al. [25], Kozu and Kani [30] and McCaffery et al. [31] used a rotation viscometer. Sipp et al. [3] measured g by a compression method. Taniguchi [34] applied the counterbalanced method with Pt body and crucible, and the fiber elongation method. And finally, Neuville and Richet [32] did not disclose the technique used in their work.

2.2.2. Crystal growth rate l-Cordierite. Crystal growth rate measurements were performed using bulk pieces of glass ( 5 5 5m m3) with fractured, polished, or SiC ground surfaces in the present study as well as in Refs. [14–21]. Most of the thermal treatments were performed in air with 20% relative humidity (dew point 8.5 C). The influence of the ambient water vapor pressure was checked by crystal growth experiments in argon/air atmospheres of different humidity [14,36] (dew point = 60 to 25 C). Different techniques were used to measure the crystal growth rates of l-cordierite at low and high temperatures. Below 830 C we measured the growth of pre-existing crystals by electron or optical microscopy (increase of the maximum radius of selected surface crystals). Between 830 and 920 C the maximum radius of crystals grown during one-step crystallization treatments were measured. Above 1000 C we measured the thickness of the crystalline surface layer. Between 900 and 1050 C both methods were used.

Isothermal treatments at 830–10 C were carried out in a conventional laboratory furnace. The samples were driven into the hot furnace using a platinum thermocouple as the sample holder. In other cases, annealing steps were made in a quartz glass tube furnace under controlled ambient conditions within a steel glove box. The accuracy of temperature measurement was ±10 K. Short time thermal treatments at high temperatures (10– 1350 C) were performed in a specially designed vertical corundum tube furnace. The thermocouple and the platinum specimen holder were quickly moved along the tube axis where a linear gradient of 20 K/cm between 300 and 1500 C was maintained. Due to the small heat capacities of small samples and the platinum holder, very high heating rates, up to about 1200 K/min, at least in the vicinity of the glass surface were attained. An empty sample holder

Table 1 Composition of all glasses used for crystal growth measurements in wt%

Cordierite glasses SiO MgO Al O Impurities

Diopside glasses SiO MgO CaO Al O Diopside 5.49 18.61 25.9

2 S. Reinsch et al./Journal of Non-Crystalline Solids x (2008) x–x ARTICLE IN PRESS

Please cite this article in press as: S. Reinsch et al., J. Non-Cryst. Solids (2008), doi:10.1016/j.jnoncrysol.2008.09.007 reached thermal equilibrium within 10 s. We measured the thickness of the crystalline surface layer between 200 and 10 lm using annealing times between 1 and 3 min to ensure thermal equilibrium at least within the near surface layer of the sample. Nevertheless, for these short time measurements we have to assume a higher inaccuracy than for the other measurements. It is not possible to quantify this inaccuracy because of the unknown thermal conductivity of our samples and the resulting influence on the measured crystal layer thickness. But, the error is likely not larger than 50%, which is twice the size of the used symbols in Fig. 2(a) still fully embedded within the present data scatter. Diopside. Numerous crystal growth rate data for diopside glasses between 750–15 C and 1277–1378 C are known from literature. For instance, Briggs and Carruthers [23] measured crystal growth rates from 900 to 1150 C by hot stage microscopy. Zanotto [27] measured the growth rate at 820 C. Reinsch ([14] and new measurements shown in this article) measured u from 750 to 1050 C by optical microscopy and SEM on polished and fractured surfaces. Fokin and Yuritsyn [37] measured growth rates between 800 and 875 C by optical microscopy using polished and fractured surfaces. Nascimento et al. [25] measured diopside crystals on fire polished surfaces at 913, 923 and 950 C. Crystal growth rates at low undercoolings (DT = Tm T 6 115 K) were determined by Kirkpatrick et al. [24] using a hot stage microscope.

2.3. Melting temperature

The melting temperature of diopside in its isochemical melt is

Tm = 1397 C [38]. Tm of the metastable l-cordierite cannot be directly measured. Therefore, we assume that its upper bound is the melting point of the stable high temperature polymorph of cordierite,denotedasindialite,h-ora-cordierite,at1467 C[38].Thelower boundofTm is assumedtobe 1350 Csince metastablel-cordierite is detectable as the primary crystal phase up to 1300 C [19].

3. Results 3.1. Viscosity

Viscosity data for cordierite melts are shown in Fig. 1 (upper curve). Our data are combined with data of Giess and Knickerbocker [35] and Yuritsyn et al. [16]. The fitted VFTH curve for cordierite glass is given by Eq. (1a), where g is given in Pa s and T in K. The measured viscosity of our diopside melt and related literature data [25,27,29–34] are also shown in Fig. 1 (lower curve). The resulting average curve for diopside, by fitting all data, is given by Eq. (1b), with g in Pa s, and T in K. For any given temperature, the cordierite melt is more viscous than liquid diopside

3.2. Crystal growth rates

Crystal growth rates of l-cordierite in its isochemical melt, measured in this work (open circles in Fig. 2(a)) and in previous studies [14–21], and similar data for diopside, measured here (open circles in Fig. 2(b)) and in Refs. [14,23–25,27,37], are shown in Fig. 2(a) and (b), respectively. These collected data cover an exceptionally wide temperature range, i.e. 800–1350 C( l-cordierite) and 750–1378 C (diopside). The maximum of u(T) occurs at about 1250 C for both glasses. A smooth shoulder is observed around 970 C for l-cordierite (arrow in Fig. 2(a)). For diopside, such a shoulder is much less pronounced and possibly hidden by the large data scatter in this temperature range. As expected from the viscosity curves, the crystal growth rates of diopside are somewhat higher than of l-cordierite at any temperature. However, at their respective Tg (1012.3 Pa s) the growth rate of diopside is about one order of magnitude lower than that of l-cordierite.

3.2.1. Data scatter

Whereas for diopside, u(T) data from different authors show remarkable similarity, significant scatter is evident for l-cordierite. This scatter can be partially attributed to the decisive influence of humidity in different melts. This effect was measured in Refs. [14,36], where, e.g., u at 945 C increased from 0.2 to 0.6 lm min 1 for increasing air humidity (dew points between 60 and +25 C). The other important factor is that liquid diopside is much more depolymerised (has much more Q2 units in NMR notation) than cordierite melt, thus its highly broken structure is not so sensitive to a few percent more or less impurities.

Another source of data scatter could be impurities and small departures of stoichiometry and the different techniques used to obtain crystal growth rate data, i.e. by measuring the dimension of separate crystals or the thickness of the crystalline surface layer. However, these two types of data are not significantly different, especially in logarithmic scale. This finding is illustrated for l-cordierite in Fig. 3(a), where a large l-cordierite surface crystal is growing from a pristine, vacuum-fractured glass surface (parallel to the paper plane). Its radius is comparable to the thickness of the l-cordierite surface layer that grew perpendicularly from the sample surfaces (the latter surface was ground with SiC causing a high number density of surface crystals). Small deviations (a factor of two) due to the crystal orientation would not appear in the logarithmic scale of Fig. 2(a). Fig. 3(b) shows diopside crystals on a polished glass surface annealed in air at 830 C for 210 min. Diopside crystals mainly appear as separately grown squares.

4. Data analysis 4.1. Basic equations

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