A kinetic treatment of glass formation V: Surface and bulk heterogeneous nucleation

An analytical method is described for calculating the detailed distribution of crystallite sizes in a supercooled liquid, and the changes in this distribution as a function of temperature (time) while the liquid is cooled from above the melting point.This method, termed the analysis of crystallization statistics, is applied to the calculation of continuous cooling curves for anorthite and o-terphenyl as representative of inorganic and organic systems. In addition to homogeneous nucleation, bulk as well as surface heterogeneous nucleation are considered. The effects of distributions of heterogeneities with contact angles between 40 and 100° as well as overall concentrations of heterogeneities between 10³ and 10⁹ cm^?3 are considered. Heterogeneities with contact angles higher than about 100° are shown not to have an effect on the critical cooling rate for typical concentrations of heterogeneities.For liquids containing distributions of heterogeneities, the nucleation behavior is dominated by small concentrations of heterogeneities having small contact angles. Theoretical log (I_vη) versus (T_r³ΔT_r²)^?1 curves have been constructed for homogeneous nucleation + heterogeneous nucleation with a single type of heterogeneity and for homogeneous nucleation + heterogeneous nucleation with the heterogeneities distributed with regard to contact angle. In the former case, the curve is composed of two linear portions; and in the latter case, the curve shows pronounced curvature. The curvature reflects a continous change in the frequency of heterogeneous nucleation.Surface heterogeneous nucleation was assumed to originate at discrete surface heterogeneities and was shown to give rise to continuous cooling curves similar to those calculated for bulk heterogeneous nucleation.     

A kinetic treatment of glass formation VII: Transient nucleation in non-isothermal crystallization during cooling

The analysis of crystallization statistics has been modified to allow for time-dependent (transient) nucleation. To establish its accuracy, the numerical analysis has been applied to isothermal crystallization kinetics and shown to yield crystallization versus time curves which compare very closely with curves calculated analytically with or without the inclusion of transient nucleation.The numerical analysis including transient has been used to calculate the critical cooling rates for glass formation in anorthite and o-terphenyl considering (1) only homogeneous nucleation and (2) homogeneous nucleation + heterogeneous nucleation for 10⁷ heterogeneities cm^?3 with contact angles between 40° and 100°. It has been shown that inclusion of time-dependent nucleation in the calculations does not change the critical cooling rates for glass formation calculated assuming steady-state homogeneous nucleation in both materials. The critical cooling rate in anorthite calculated including steady-state heterogeneous nucleation was found to be decreased only slightly by the inclusion of time-dependent nucleation; while the critical cooling rates calculated for o-terphenyl were not change at all by the inclusion of time-dependent nncleation.The lack of an effect of time-dependent nucleation on the critical cooling rates calculated assuming only homogeneous nucleation is explained by the relatively small transient times on the high temperature side of the nucleation peak (a temperature range which has an overwhelming effect on the overall crystallization process because of the relatively high crystal growth rates in this range).Although the critical cooling rates associated with heterogeneous nucleation are large, the nucleation here takes place at relatively small undercooling where the transient times are relatively small. Thus, transient nucleation causes only a temporary delay in the over all crystallization, and its effect on the critical cooling rate is small.     

The structure of phosphate glass evidenced by small angle X-ray scattering

Numerous phosphate glass systems with compositions covering the entire glass forming range have been examined by small angle X-ray scattering. The experiments were carried out in a widely extended interval of s values between 0.055 and 31 nm⁻¹. A small angle scattering effect was detected for all samples investigated with the exception of the aluminium metaphosphate glass. The small angle scattering recorded indicates the presence of two differently-sized heterogeneity regions of electron density. The small-scale heterogeneities are present in magnesium and zinc phosphate glasses only. Their size is about 1 nm diameter in the magnesium and about 2 nm in the zinc phosphate glasses. The species do not result from liquid–liquid phase separation. Examinations to extract information on the nature of these heterogeneity regions are described in detail. There is no fundamental knowledge on the large-scale heterogeneities established. The small angle scattering suggests that their occurrence is related to water contamination. Anomalous small angle X-ray scattering experiments of a series of zinc polyphosphate glasses and a strontium metaphosphate glass sample are performed to examine the distribution of the Zn or Sr atoms, respectively.     

Anisotropy of the Work of Adhesion for a Nemiatic Crystal on a Shaped Support

Under dynamic conditions, experimental data on contact angles of wetting for p-azoxyanizole on glass have been obtained. The contact angle of wetting is found to depend on support relief and the values of the contact angle are observed to change at the temperature of the liquid crystal phase transition. The value of energy required for turning a molecule of a nematic crystal by 90° on a shaped surface has been calculated.     

The kinetics of formation of A AuGeSi metallic glass

The glass-forming ability of a Au_0.778Ge_0.138Si_0.084 alloy is analyzed theoretically by computing a time-temperature-transformation curve which describes the time required to produce a barely detectable fraction of crystallization, at various temperatures. The calculation is based on an interpolated viscosity-temperature curve, this alloy being exceptional among metallic glass formers in that experimental viscous-flow data are available at both high and low temperatures. Allowing for uncertainties, the critical cooling rate for glass formation lies within the range 10⁶?10⁸ K/sec which is in satisfactory agreement with experimental estimates of cooling rates in splat quenching. This and previous comparisons for Ni and PdSi alloys suggest that the approach may have useful and general applicability to metallic glasses.     

Multi-scale structuration of glasses: Observations of phase separation and nanoscale heterogeneities in glasses by Z-contrast scanning electron transmission microscopy

Chemical fluctuations are probed in glasses obtained with different thermal histories using scanning transmission electron microscopy in high angle annular dark field mode. Direct imaging of the glass structure is obtained at the sub-nanometer scale with Z-contrast. Macroscopic glass-in-glass separation is probed in a slowly quenched melt where chemical resolution allows the determination of the regions associated with Zr/Zn atoms. In a quickly cooled glass, exempt of macroscopic phase separation, a segregation of Zr/Zn atoms is still evidenced but on a different length scale, suggesting either the beginnings of glass separation or intrinsic features of the glass structure. Glass inhomogeneities must be taken into account to have a quantitative evaluation of nucleation processes. These “nano”-heterogeneities can be associated with the nucleation of zirconia phases, giving important clues to understand the nucleation pathways and the structural role of nucleating agents in aluminosilicate glasses.     

The Behaviour of Contact Angles of Wetting for Liquid Crystalline Drops on Glass Near the Phase Transition

The experimental values of contact angles of wetting for pazoxyanisole - glass in the nematic and isotropic phase have been obtained. At the point the phase transition, a change in the value of contact angle of wetting is observed. The values of adhesion energy, have been calculated for different orientation of molecules with respect to the glass support.

It is well-known /I/that contact angles of drops on solid supports enable an information on interfacial energy γ_SL to be obtained. A change in the structure of liquid results in alteretion of the contact angle as it a has been shown recently for polymer solutions /2/. It seem to be quite possible that orientational ordering of liquid crystals has to affect the value of contact angles of wetting. Nevertheless, this value was not found to very upon phase transition from the isotropic to liquid crystalline state /3/.

We studied the behaviour of contact angle of wetting for a drop of a classical liquid crystalline compound p-azoxyanisole (PAA) in its nematic and isotropic phases.     

Transient nucleation effects in glass formation

We extend to the non-isothermal case a numerical technique that was developed to treat transient homogeneous nucleation in a one-component system by modeling directly the reaction by which clusters are produced. Calculations are presented for the nucleation frequency during the quench and for the number of nuclei produced and the volume fraction transformed at the end of quench for different rates of cooling from the melt. Three model systems are considered: an alkali silicate which is a relatively good glass former, and two metallic glasses. These show a wide range of critical cooling rates for glass formation. In some systems transient effects are predicted to be critical for glass formation. A simple technique is presented for determining when transient effects are important based on a calculation using steady state nucleation frequencies and macroscopic growth velocities.     

The structure of SiO2-GeO2 glasses: A spectroscopic study

Four glasses of the SiO₂-GeO₂ binary system have been synthesized via a sol-gel route followed by a heat treatment and a quench. Glass structure has been determined by Ge K-edge X-ray absorption spectroscopy (XAS) at low temperature and Raman spectroscopy. These mixed glasses present a continuous random network of interconnected GeO₄ and SiO₄ tetrahedra, with GeO₄ tetrahedra similar to the GeO₄ units in GeO₂ glass and continuous compositional variations from GeO₂-rich regions to SiO₂-rich regions. Such a random mixture is consistent with physical properties of these binary glasses as well as with the chemical dependence of their polyamorphism at high pressure. This EXAFS-derived mean Ge-O-Si angles are close to the Ge-O-Ge mean angle in GeO₂ glass, 134° and 130°, respectively. This misfit with the Si-O-Si angles might explain the ease of formation of isolated and pair defects centers, which are suspected to be at the origin of photo-induced modifications of optical properties in Ge-bearing SiO₂ glasses.     

Evaluation of the guided random parameterization method for critical cooling rate calculations

We focus on a recently suggested approach to the calculation of critical cooling rates for glass formation. It is a “random parameterization” method that is guided by a limited number of isothermal scanning calorimetry experiments. However, several assumptions have been made in its derivation that may not mirror the actual crystallization behavior of most supercooled liquids, which may jeopardize the estimation of glass forming ability. We evaluate those assumptions and the applicability of the method is tested for lithium disilicate glass (which displays moderate internal nucleation rates) and dibarium titanium silicate glass (which displays very high internal nucleation rates, similar to those of metallic glasses). Both glasses nucleate homogeneously and exhibit polymorphic crystallization. Our calculations show that some overlooked variables, such as the sample geometry, nucleation induction-times, surface crystallization and the breakdown of the Stokes–Einstein/Eyring equation, have significant roles on the calculated time–temperature–transformation curves during heating experiments. We demonstrate that the proposed random parameterization method can only be used when a glass forming liquid that undergoes internal crystallization is cooled from above its liquidus to various test temperatures. If the sample undergoes predominant surface crystallization or if it is heated to the test temperature several corrections must be made.     

Surface crystallization of leucite in glasses

The aim of this paper was to study surface crystallization of leucite in glasses derived from an SiO₂-Al₂O₃-K₂O base glass in a comparative study with another glass based on SiO₂-Al₂O₃-MgO. Monolithic samples and glass powder of SiO₂-Al₂O₃-K₂O glass were studied and phase formations were determined by using scanning electron microscopy. Heterogeneous nucleation was promoted by seeding the surface of the monolithic glass samples with glass dust to produce a highly disordered crystal as the primary phase. In addition to leucite formation, growth of a highly symmetric, flat, almost two-dimensional crystal phase with controlled diffusion was also observed. In glass granules, leucite demonstrated rapid, almost dendritic growth, from the nucleating centers. Use of leucite ceramic as a restorative dental product is considered.     

Zero-point entropy of glasses as physical reality

This paper presents an analysis of the physical nature of the author’s results obtained since 1995 in the field of thermodynamics of the vitreous state (classic approximation). Excess entropy and free energy at 0 K are considered as the measures of non-equilibrium extent of glass with respect to crystal. Experimental data for melts and glasses of various chemical natures are generalized. A general form of the relations between reversible changes in free energy, enthalpy and entropy and their frozen values at the formation of any glass is shown. The problem of functional dissimilarity of the heat capacity of glass and that of crystal has been solved within the framework of the principle of free energy minimization as a result of self-organization of the vibration spectrum according to the frozen structure. The complete stabilization of glass structure at Kauzmann’s temperature or below it is forbidden by topologic reasons and (or) by thermodynamics. The effects of pressure on the thermodynamic properties of glasses are shown. Possible particular applications of the analysis of self-organization in chaotic systems are exemplified by the modeling of the abilities of neural systems.     

A kinetic treatment of glass formation. VIII: Critical cooling rates for Na2OSiO2 and K2OSiO2 glasses

The critical cooling rates required to form glass have been measured for Na₂OSiO₂ compositions containing 15.4, 20.6, 29.9 and 34.0 wt% Na₂O and for K₂OSiO₂ compositions containing 15.3, 21.7, 34.3, 41.8 and 43.9 wt% K₂O. Pronounced minima in critical cooling rate are observed in the ranges about 25 wt% Na₂O and 33 wt% K₂O. The locations of these minima correlate with regions of low liquidus temperatures (near eutectics) in the phase diagrams.Calculations of critical cooling rates have been carried out using the analysis of crystallization statistics and the simplified model of glass formation. In both cases, the models predict well the measured critical cooling rates and their variation with composition.     

Surface crystallization of rare-earth aluminosilicate glasses

Surface crystallization in a rare-earth aluminosilicate glass (Nd₂O₃–Al₂O₃–SiO₂–TiO₂) was studied using an isothermal method and the crystal growth rate of the glasses was evaluated as a function of the composition. For measuring the surface crystal growth rate, two different methods: measurement of the crystal layer in the longitudinal and lateral growth direction. It was found that crystallization proceeded by surface crystallization only and TiO₂ did not act as a nucleating agent. The growth rate was strongly dependent on the viscosity of glass and agreed with prediction from the Preston model using the known viscosity and melting temperature. As the Si/Nd and Si/Al ratios decreased, the crystal growth rate increased. TiO₂ and Nd₂O₃ played the role of network modifier, which decreased the viscosity of the glass, facilitating crystallization of the rare-earth aluminosilicate glass.     

Continuous cooling approximation for the formation of a glass

Non-isothermal equations describing the liquid-crystal transformation are derived using the isothermal Avrami equations. A theoretical expression for the critical cooling rate for the formation of a glass is found. Calculations based on this expression are in better agreement with experimental values than those derived from TTT (time-temperature-transformation) curves. A study performed on typical glass forming materials enables the glass forming ability (GFA) to be determined by experimentally measuring crystallization temperatures at different cooling rates which are easily accessible with commonly available technology. The behaviour of the rate constant for crystallization is also obtained from the same data in the experimental range considered. In both cases no previous knowledge of the parameters involved is needed.With some assumptions the values of the viscosity in the crystallization temperature range can be estimated.Although the study was performed for an Avrami index of 4 an extension to other values of n is made under some restricted conditions and a more general treatment is outlined.     

Dynamical scaling analysis using the Lillie Number for vitrification of deeply supercooled glycerol

Thermal response was measured for a deeply supercooled glycerol specimen by applying calorimetric temperature scanning rate spectroscopy, cooling the specimen from liquid at a slow constant cooling rate until glass transition was observed. The effective fraction of glass as a function of temperature was determined and a new definition of glass transition temperature, T_gC, as the temperature at which the effective glass fraction to be 0.5 was presented. The relation between this and the cooling rate showed the Arrhenius behavior. The effective glass fraction curves shifted linearly as a function of ln(cooling rate). When T was scaled to the Lillie Number, the glass fraction lay on a master curve, which was successfully fitted with a Kohlrausch–Williams–Watts function. The Kohlrausch exponent, the relaxation time as a function of temperature and the kinetic fragility index were determined. The results were compared with literature values.     

Vacancy-induced densification of silica glass

We investigate vacancy-induced densification of silica glass using molecular dynamics simulations. Equilibration of defective glasses initially with various concentrations of vacancies yields glasses denser than the intact glass. The structural and vibrational properties of the densified glasses are characterized. Densification is related to structural changes induced by atomic rearrangement near vacancies, and increases with the concentration of vacancies. Vacancies may cluster and form voids, and the maximum densification for void-structured glasses occurs at a critical radius of about 0.44 nm. The glasses densified by vacancies and by simulated UV-laser irradiation display nearly identical structural and vibrational properties. These results appear to support the Douillard–Duraud point defect model as a common mechanism for radiation densification of silica glass.     

Spectroscopic studies of gamma irradiated Nd doped phosphate glasses

Ultra violet-visible (UV-Vis) and Fourier transform infrared (FT-IR) spectra of Nd doped phosphate glasses have been studied before and after gamma irradiation in order to understand the changes in the optical properties of glasses as well as to find the characteristics frequencies of the vibrational modes of chemical bonds, which decide the structural and spectral changes. UV, Vis, IR absorption and photoluminescence spectra of these glasses show changes depending on the composition of glass matrix. These changes are correlated on the basis of oxygen (O) and neodymium (Nd) concentration ratio obtained from energy dispersive X-ray spectroscopic (EDX) measurement. Gamma irradiation shows decrease in transmission below 700 nm for all the Nd³⁺ absorption lines from all the samples. Differential absorption spectra (UV-vis) of the samples before and after gamma irradiation show generation of some new bands below 700 nm along with dips (decrease) in the spectrum at the location of main Nd³⁺ absorption lines. This is attributed to the generation of different types of defects in the glass matrix along with possibility of change in the valence state of Nd³⁺ to Nd²⁺. IR absorption spectra of these glasses are found dominated mainly by the characteristics phosphate groups and water (OH) present in the glass network. The effects of gamma irradiation on IR absorption are observed in the form of bond breaking and possible re-arrangement of bonding. EDX and X-ray photoelectron spectroscopic (XPS) measurements indicate decrease in the relative concentration of oxygen in the glass samples after γ-irradiation.