nascimento 2006

nascimento 2006

(Parte 1 de 3)

Mechanisms and dynamics of crystal growth, viscous flow, and self-diffusion in silica glass

Marcio Luis Ferreira Nascimento* and Edgar Dutra Zanotto† Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos,

13.565-905 São Carlos-SP, Brazil Received 9 August 2005; revised manuscript received 28 November 2005; published 30 January 2006

We analyzed extensive literature data on crystal growth rate and viscosity in the temperature range between

1.1 Tg glass transition temperature and the melting point of silica, Tm. We selected data for one silica glass type, having similar impurity contents, and confirmed that the normal growth model describes quite well the experimental growth rate data in this wide undercooling range. We then calculated effective diffusion coeffi- cients from crystal growth rates, Du, and from viscosity, D through the Eyring equation , and compared these two independent diffusivities with directly measured self-diffusion coefficients of silicon and oxygen in the same silica glass for which viscosity was measured. Our results show that silicon not oxygen controls the diffusion dynamics involved in both crystal growth and viscous flow in undercooled silica. This study not only unveils the transport mechanism in this important glass-forming material, but also validates the use of easily measured viscosity to account for the unknown transport term of the crystal growth expression in a wide range of undercoolings.

On cooling most liquids from the equilibrium temperature, spontaneous crystallization frequently impairs glass formation. On the other hand, controlled crystallization of certain glasses may lead to unusual glass ceramics pore-free, polycrystalline materials of nanometric and uniform grain size having many and diverse interesting properties and applications. However, key questions regarding nucleation and crystal growth kinetics in undercooled liquids and glasses are still open. For instance, which ions or “molecular units” move collectively above and below the glass transition range, Tg, and control these important phenomena? Is the often used viscosity coefficient capable of describing mo- lecular transport at the crystal/liquid interface?

Recent research on crystal growth and diffusion kinetics in diopside glass1 demonstrated that i screw dislocationmediated growth is the operative mechanism in a wide range of undercoolings from the melting point, Tm,t o1 .1 Tg; i at low undercoolings T 0.9 Tm , where the diffusion data of Si and O are available, the diffusion coefficients calculated from crystal growth kinetics and from viscosity agree with the direct measurements of Si and O mobility. Therefore, these two ions move together and control the transport mechanism involved in crystal growth and viscous flow. But diffusion data were not available to test what occurs at deep undercoolings T 0.7 Tm . Reference 1 constituted a significant step in the knowledge of transport processes control- ling crystal growth in undercooled silicate liquids, which had been poorly documented. It not only unveiled the diffusion mechanism in undercooled liquid diopside, but also validated the use of viscosity to account for the kinetic term of the crystal growth expression from Tm to 1.1 Tg. Since, in Ref. 1 diffusion data of Si and O were only available at a narrow temperature interval near the melting point of diopside, these important results should be generalized or not by additional studies with other glass-forming systems for which silicon and oxygen diffusivities are available in a wider range of undercoolings. In the present article we perform a detailed analysis of crystal growth kinetics, viscous flow, and self-diffusion of Si and O in another sys- tem, that is silica, in a wide range of undercoolings, from Tm to 1.1 Tg for crystal growth and viscosity , from 0.84 Tm to

0.95 Tg for Si self-diffusion, and from 1.02 Tg to 0.74 Tg for O self-diffusion to discover which of these ions move col- lectively and control these two important kinetic phenomena.

Silica SiO2 is an important mineral from the geological standpoint and is also the most important glass former. In addition, high-silica glasses, having 9.9% SiO2, best known as quartz glass or vitreous silica, have many and di- verse important commercial applications, such as laboratory glassware, telescopic mirrors, optical filters, and fibers. Silica glass producers generally divide the whole spectrum of commercial, transparent silica glasses into five types, depending on the production method, content and type of impurities, denominated types I, I, II, IV, and V. In a forthcoming review paper we describe in detail and revisit the crystal growth behavior of each one of these five families of silica glasses.2 A relevant outcome of Ref. 2 is that the crystal growth rates and viscosities of silica glasses are extremely dependent on the impurity level, much more than in multicomponent silicate glasses, corroborating earlier findings of other authors, e.g., Hetherington et al.3 Thus, for the present study, it was important to compare crystal growth, viscosity, and self-diffusion data for similar silicas. We thus made a careful analysis by choosing all diffusivity, viscosity, and crystal growth rates for type I silica glasses having a similar impurity content Table I .

In brief, type I glasses are obtained by melting natural or synthetic quartz crystals in electrical furnaces. Such glasses contain impurities, such as alkali metals inherited from the initial raw material, and a very small amount of structural water OH− . Type I glasses are obtained by melting grains of natural or synthetic quartz in hydrogen-oxygen gas flames.

These glasses contain impurities inherited from mineral quartz a similar content as in type I glasses and several hundred ppm OH−. Type I glasses are obtained by the hightemperature hydrolysis of volatile compounds of silicon and are characterized by very low content of metal impurities, but contain a considerable concentration of structural water and chlorine. Type IV glasses are obtained by the high- temperature oxidation of SiCl4 and contain a very small amount of metal impurities, virtually no structural water, but several hundred ppm of chlorine. Type V silica is a synthetic material that involves sintering of a sol-gel-derived powder into a glass. This silica glass typically has contamination levels of about 0.1 ppm OH− and 400 ppm Cl−. Thin film silicas, on the other hand, have not yet been classified, but their properties depend on the level of impurities and on the specific technique used for their synthesis.

Several authors have determined crystal growth rates and viscosity at several undercoolings of several silica glasses having different impurity contents,2 but none of these previous studies analyzed crystal growth kinetics in a wide range of temperatures, from Tm to 1.1 Tg. To the best of our knowledge, crystallization rates and melting of cristobalite— including the region of maximum growth rate—were only obtained by Wagstaff.4,5 Also, there are no new crystal growth data for type-I silica in such a wide range of temperatures. Another reason that led us to choose Wagstaff’s data was because, coincidently, among all the available data for silica glass type I, his glass presents the smallest crystal growth rates. Therefore it must have the least impurity content. Fortunately, Wagstaff’s data cover the widest temperature range among all the available growth rate data for silica glasses. Hence, in a consistent way, in our analysis we combine the lowest crystal growth rates with the highest viscosity.

Despite its kinetic sensitivity to impurities, silica glass is an adequate model system for the type of study proposed here because it displays polymorphic crystallization, there is plenty of viscosity, crystal growth rate, and thermodynamic data, such as the melting point and Gibbs free energy of crystallization G , which substantially helps with the analysis. A final and most important motivating factor is that hard to measure self-diffusion coefficients of oxygen DO and particularly silicon DSi , the slowest diffusing species in silicate glasses, are also available in wide temperature inter- vals.

In this paper we use the same strategy proposed and tested in Ref. 1 for diopside to infer which ion s control the crystal growth kinetics and viscous flow in undercooled liquid silica. We compare the effective diffusion coefficients determined in three distinct ways, i.e., calculated from crystal growth rates, Du, estimated through viscosity data, D via the Eyring relation , and directly measured self-diffusion coeffi- cients of silicon and oxygen.

To the best of our knowledge, this is the first time the transport mechanism that controls crystal growth kinetics and viscous flow in undercooled liquid silica are analyzed in detail in a wide temperature 380 °C and diffusivity range, covering eight orders of magnitude using independent, reliable experimental data on the thermodynamic driving force, viscosity, crystal growth rates, and diffusion coefficients. As the diffusion mechanisms involved in crystal nucleation and growth are unknown for most glasses, we go deeper into this question, by relating crystal growth kinetics with both viscous flow and directly measured diffusion data.

Three phenomenological models are normally employed to describe interface controlled crystal growth processes in

TABLE I. Impurity contents of type-I silica glasses used in this paper.

8 Puropsil A® is no longer produced, but it is similar to Puropsil B® Ref. 20

3 Glass used by Kalen et al. Ref. 16


10 The glass used by Haul and

I. The commercial brand name is unknown, but its composition is probably similar to that of modern Infrasil® Ref. 21


Type I silica glass should contain only a few ppm of OH−, similar to GE 124® glass inorganic glasses: normal growth, screw dislocation growth, and two-dimensional (2-D) surface nucleated growth. According to Jackson’s treatment of the interface, materials with low melting entropy Sm 2R, where R is the gas constant , such as silica Sm 0.46R , are expected to exhibit crystal growth kinetics of the form predicted by the normal growth model.6,7 Thus, in principle, the low melting entropy of silica Sm 4R excludes the screw dislocation and the 2-D surface nucleated growth models. However, to be on the safe side, we first tested all these growth models.

According to the normal growth model, the surface is atomically rough and the degree of roughness is independent on the temperature. The corresponding temperaturedependent growth rate u may be expressed by6,7

where Du is an effective diffusion coefficient m2/s of the unknown molecular species that control atomic or molecu- lar attachment at the liquid/crystal interface; is the unknown diameter of the diffusing building molecules m , which is equivalent to the jump distance, the crystal lattice parameter, or the unit distance advanced by the interface; G is the free energy change upon crystallization J/mol ; R is the gas constant J/mol K ; T is the absolute temperature K ; and f 1 is the fraction of preferred growth sites at the interface. In general, one uses G calculated by the Turnbull’s

ing enthalpy Hm of silica is approximately 7.679 kJ/mol.4,5 In the screw dislocation model, the surface is considered smooth, albeit imperfect on an atomic scale, and growth takes place at step sites provided by screw dislocations, con-

growth model considers the surface atomically smooth and defect-free. In this model, growth occurs by the formation of two-dimensional nuclei on the top of primary crystals, which grow laterally.6,7 The surface nucleation model is given by Eqs. 2a – 2c :

where Vm is the molar volume m3/mol , kB is the Boltz- mann constant, is the surface energy J/m 2 , Ns is the number of growth sites per unit area m−2 , and is the gamma function.

Crystallization is an exothermic process and knowledge of the crystal/liquid interface temperature is essential for analyzing crystal growth kinetics. Based on direct measurements for several glasses, Herron and Bergeron8 suggested and suc- cessfully tested empirical equations to estimate the liquidcrystal interface temperature for temperatures near the maxi- mum crystal growth rate umax and relatively far from it u 0.67umax . Such expressions for interface temperature corrections are presented in Table I. For silica, these tem- perature corrections are only about 0.1 °C for the maximum growth rate, because of the low growth rates and melting enthalpy. This correction was thus irrelevant for this particular glass.

The effective diffusivity can be estimated via the Eyring expression, Eq. 3 , assuming that the molecular motion required for interfacial rearrangements controlling crystal growth is similar to that controlling viscous flow in the bulk where is the shear viscosity, is the jump distance or the unknown diameter of the unknown diffusing molecules, which has the order of a few angstroms. The Eyring E and Stokes-Einstein SE equations differ only by a factor of 3 . The SE expression describes a moving solid sphere with radius R in a viscous liquid. Thus, for silicate glasses most authors prefer the Eyring equation because the meaning of the parameter , the jump distance, is most appropriate. However, the overall conclusions of this paper would not be altered if we employed the SE equation. A recent study9,10 demonstrates that below the glass tran- sition temperature, Tg, atomic motion through a metallic glass involves single-atom hopping, whereas motion above

Tg is more collective. Other authors11 previously observed such a substantial change in the diffusion mechanism for organic and Lennard-Jones liquids, but occurring at higher temperatures, i.e., at about 1.2–1.3 Tg, and this temperature has been denominated decoupling temperature, Td. A similar change in the diffusion mechanism at some Td Tg is also suggested to occur for undercooled oxide liquids, but has not been firmly proved yet. It has thus been a matter of discussion if the Stokes-Einstein and Eyring equations can be used for calculations of crystal growth kinetics at deep undercool- ings, below Td 1.2 Tg, where it has been suggested that these equations fail.1,12 However, these equations are con- sidered to be valid at temperatures greater than Td, which includes the range of interest in this paper.

From the previous discussion, to test the governing mechanism of crystal growth, one must know the glass viscosity, T the free energy change due to crystallization, growth mechanism is confirmed, one can calculate and compare two distinct diffusion coefficients, obtained from crystal growth rates, and viscosity with directly measured selfdiffusion coefficients.

A. Growth mechanism and the jump distance

A large collection of viscosity and crystal growth rates from different authors, using several silica type-I glasses,

with distinct impurity contents, were analyzed elsewhere.2,3 Arrhenius plots describe all these viscosity data in wide temperature ranges. Most viscosity curves for the purest type-I silica glasses are similar to that of Puropsil A glass,13 and the resulting equation is listed in Table I. This equation was thus used throughout this paper.

(Parte 1 de 3)