M. P. Shepilov

Computer simulation of crystallization kinetics for the model with simultaneous nucleation of randomly-oriented ellipsoidal crystals

Abstract Methods of calculation of crystallization kinetics are discussed. The Kolmogorov model and some other models are reviewed. It is concluded that the problems of theoretical description of crystallization kinetics need further discussion. Computer simulation of crystallization kinetics for the non-Kolmogorov model with simultaneous nucleation of randomly-oriented ellipsoidal crystals has been carried out. From the results of this computer simulation, it follows that the Kolmogorov equation is practically exact for this model if the crystal anisotropy is not high (if the ratio, a , of the large principal diameter of ellipsoid to the small one is ⩽ 2). At higher anisotropy ( a ⩾ 5), the results of computer simulation cannot be described by the Kolmogorov equation with sufficient accuracy; in particular, the kinetics do not correspond to the constant value n = 3 of the Avrami exponent, and the dimensionality of crystal growth cannot be established on the basis of Avramis analysis. The results should be kept in mind in the discussion of experimental data on crystallization kinetics in the cases of growth of anisotropic crystals.

Structural states of Ni(II) in glasses and glass-ceramic materials of the lithium-aluminium-silicate system

Abstract Optical absorption spectra of Ni(II) have been investigated in glass-ceramic materials of the lithium-aluminium-silicate system at various phase transition stages. Four types of absorption spectra have been revealed. The Ni(II) absorption bands have been attributed based on the calculation of the energy level diagram. It has been shown that in the case of heat treatment at the initial stage of phase decomposition, there arise aluminium titanium nickel regions that decompose in subsequent heating into titanium phases and aluminium-nickel spinel microcrystals. In crystallizing the main phase, i.e. solid solutions of β-eucryptite, Ni(II) is built into the structure of this phase replacing lithium isomorphously.

A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment

Abstract A model is described for calculating the kinetics of a diffusion-limited nucleation-and-growth type phase separation. A homogeneous melt of glass is cooled to a temperature, at which the nucleation, growth and Ostwald ripening of particles of a new phase are possible. In the model, a spatial inhomogeneity of nucleation rate, caused by the formation of diffusion zones around particles, and an effect of interaction of these zones on growth of particles are taken into account. Criteria for application of the model are formulated and parameters of the model are calculated for a model binary glass. A conclusion is drawn that the proposed model is applicable to systems where supersaturation is not too high. In particular, nucleation must not be so plentiful as to suppress a growth from supersaturated solution and to initiate Ostwald ripening at the nucleation stage. It is noted that such situations are observed in experiments on phase separation in glasses. The model seems to be applicable to some other types of phase transformations as well.

Calculation of kinetics of metastable liquid-liquid phase separation for the model with simultaneous nucleation of particles

The questions of calculation of phase separation kinetics in the case of nucleation and growth type processes are discussed. The model with diffusion-limited growth of ‘simultaneously nucleated’ spherical particles is considered in detail. This model corresponds to the case where the nuclei have been formed previously (intentionally or unintentionally) in the process of material preparation. The conditions are determined under which the stage of growth from supersaturated solution may be observed without appreciable Ostwald ripening and the description of this stage is given. Using the conditions arising in the system towards the end of growth stage as the initial conditions, computer simulation of Ostwald ripening kinetics has been carried out. In particular, the computations show that the transition period from the growth stage to Ostwald ripening stage exists when the mean radius of particles does not vary and the size distribution is significantly transformed. The calculated results may be used for description of phase separation kinetics in glasses and other systems. Some results of experimental study of metastable liquid-liquid phase separation in glasses are reviewed which are in agreement with results of presented theoretical analysis.

Crystallization of Glasses in the K2O–Nb2O5–SiO2System

The changes in the structure and phase composition of glasses in the K2O–Nb2O5–SiO2system upon their heat treatment in the temperature range 700–800°C are studied by the small-angle X-ray scattering (SAXS) technique and X-ray powder diffraction. It is demonstrated that the crystallization is the primary process giving rise to microinhomogeneities in glasses due to heat treatment. Nanocrystals of an unidentified niobium-containing phase precipitate in glasses with the formation of regions with a decreased content of potassium and niobium oxides. An increase in the duration of heat treatment at the studied temperatures results in an increase in the size of nanocrystals without change in their phase composition. This is accompanied by the disappearance of diffusion zones, which leads to a decrease in the SAXS intensity in the range of small scattering angles and, correspondingly, to a decrease in the light scattering intensity.

Variation of the transmittance and the Kerr constant during the crystallization of sodium-niobium-silicate glasses

This paper discusses the interconnection of the structure of sodium-niobium-silicate glasses, heat-treated isothermally in the temperature interval 660-700 °C for various times, with their extinction coefficient and Kerr constant. A spinodal phase separation occurs during heat treatment, followed by precipitation of a nano-size crystalline phase of sodium niobate. The volume increase of the crystalline phase is associated with nucleation of the crystals during the entire period of crystallization, whereas the size of the crystals remains virtually constant. The extinction coefficient substantially decreases toward the end of the crystallization stage as a consequence of interference effects in the scattering, caused by ordering elements in the relative position of the crystals. A model is proposed to describe how the extinction coefficient depends on the degree of crystallinity and the wavelength of the light. The dependence of the Kerr constant on the volume fraction of the crystalline phase is well described in terms of the effective-medium approximation.

Crystallization Kinetics of Sodium-Niobium Silicate Glasses

The crystallization of glasses in the Na2O-Nb2O5-SiO2 system in the temperature range 690–750°C is investigated by measuring the material density and X-ray powder diffraction analysis. It is found that the kinetics of precipitation of the NaNbO3 crystalline phase can be described by the Avrami equation with the Avrami exponentn ≈ 1. The model describing the crystallization kinetics is proposed. The crystallization of amorphous inhomogeneity regions, which are formed as a result of phase separation, is considered in the model. The consideration refers to the crystallization process governed by the nucleation of crystals in these regions. The calculated Avrami exponents are close to unity. The proposed model does not contradict the available data on the X-ray small-angle scattering that have been obtained upon crystallization of the samples and qualitatively explains a nonmonotonic variation in the material transparency during crystallization.

Phase Separation and Crystallization in Glasses of the Na2O–K2O–Nb2O5–SiO2 System

The structure of initial glasses in the Na2O–K2O–Nb2O5–SiO2 system with an Nb2O5 content ranging from 5 to 39 mol % and their structural transformations in the course of isothermal treatments at different temperatures are investigated using small-angle X-ray scattering (SAXS) and X-ray powder diffraction. It is demonstrated that, in glasses containing 15 mol % Nb2O5 and more, the metastable phase separation is the primary process responsible for the formation of a microinhomogeneous structure. With further heat treatment of these glasses, NaNbO3 crystals precipitate in regions with a high Nb2O5 content. In this case, each region has a heterogeneous structure and consists of NaNbO3 microcrystals surrounded by layers of the high-silica matrix. These layers hinder transfer processes and, consequently, recrystallization, which ensures the stability of the heterogeneous structure and, correspondingly, constant sizes of microcrystals at temperatures up to 750–800°C. The intensity of light scattering is determined primarily by the sizes of regions formed upon phase separation. A decrease in their size with an increase in the niobium oxide content leads to a decrease in the light scattering loss and an increase in the transparency of heat-treated samples. The interference effects associated with the heterogeneous structure of high-niobate phase regions also favor an increase in the transparency of the prepared materials.

Computer simulation of the crystal volume distribution in a fully crystallized glass. Application to the estimation of the precipitate size distribution after the completion of the stage of diffusion-limited growth from supersaturated solid solution

Abstract The crystal volume distribution functions in fully crystallized glasses were calculated by computer simulation methods for the β-, α- and D-model of crystallization. In the β-model the crystals start to grow simultaneously from nuclei distributed at random. In the α- and D-models the nuclei appear at different moments, the rate of nucleation being constant. The crystals grow isotropically with constant rate in the β- and α-models, and in accordance with the diffusional law in the D-model. Obtained in the form of histograms, the volume distribution functions for the three models differ qualitatively. An analytical approximation of the histograms for the β- and D-models was performed. It was ascertained that approximation of the crystal volume distribution by the crystal age distribution existing in the literature for the α-model is unacceptable for small and large volumes. Using the volume distributions for the β- and D-models, estimations have been obtained of the precipitate size distributions by the moment when the stage of diffusion-limited growth from supersaturated solid solutions is completed.

Features of the anomalous scattering of light in two-phase sodium borosilicate glass

This paper is devoted to the study of light scattering in inhomogeneous glasses. The spectral behavior of the extinction coefficient of the initial sodium borosilicate glass and two glasses obtained by heat treatment is experimentally studied. It is established that the extinction coefficient of heat-treated glasses in the visible region is determined by the scattering of light. Experimental data on the anomalous spectral dependence of the extinction coefficient of the glass subjected to more prolonged heat treatment are compared with the results of calculations carried out in terms of various scattering models based on literature data on the structure of this glass, which consists of liquation spherical particles in a matrix. It is shown that the ordering effects observed earlier in the relative position of the particles play an important role in the light scattering. It is pointed out that, to theoretically describe the scattering properties of a system of polydisperse particles, it is necessary to know the pairwise correlation function of the particles, which depends on the size of the particles in the pair.