Isak Avramov

Effect of disorder on diffusion and viscosity in condensed systems

A simple theoretical model describing the influence of disorder on transport properties (viscosity, diffusion coefficients, etc.) in undercooled melts and crystals is suggested. The basic assumption is that structural disarray results in a random probability distribution of energy barriers for diffusion characterized by dispersion σ around some mean value 〈E〉. It is shown that the effect of σ on the mean jump frequency 〈v(E)〉 may lead to corrections of many order of magnitude as compared to the hopping frequency calculated traditionally in terms of the average activation energy 〈E〉 only. The temperature course of 〈v(E)〉 is then examined making use of the relation between σ and the entropy of the system S. Thus an analytical formula is obtained which properly describes molecular transport in both the crystalline and the amorphous state. Even in a simplified form, η=η0 exp(β/Tα), it reproduces well the existing data on temperature variation of viscosity η (or self-diffusion) in glassforming melts. In another aspect - in terms of the percolation theory - the model describes the diffusion of a foreign particle in a rigid host structure and yields also a qualitative estimate of the variation of the percolation threshold Ep with the degree of amorphisation σ.

Pressure dependence of viscosity of glassforming melts

Abstract We suggest a model in which the viscosity η is related to the entropy of the system. The model successfully describes the dependence of viscosity on pressure. A master equation is developed that allows a comparison of data obtained at different temperatures. Earlier, in the framework of the same model we described the dependence of viscosity on temperature. The present treatment gives a simple interpretation of T g , the glass transition temperature, which takes places when the disorder in the amorphous system decreases to an extent that the dispersion σ is only 3.5% of maximum value of the activation energy E max .

Nucleation and crystallization in glass-forming melts: Olds problems and new questions

Abstract A review is given of basic problems and results in the field of nucleation and crystallization in glass-forming melts. The temperature dependence of the driving force for crystallization and of the free energy of the crystal/melt interface, as well as the connection between the melt viscosity and entropy are considered in some detail. The influence of various factors on the rates of nucleation, crystal growth and overall crystallization is discussed and existing evidence for nonstationary nucleation is surveyed. A generalized kinetic criterion for vitrification is formulated accounting for the effect of nucleation nonstationarity. Finally, an approximate expression is obtained for the minimum cooling rate for glass formation.

Glass-forming ability versus stability of silicate glasses. II. Theoretical demonstration

Abstract Possible relationships between measures of glass stability (GS) against devitrification on heating (evaluated by the Hruby parameter KH=(Tch−Tg)/(Tm−Tch), and the parameter Kw=(Tch−Tg)/Tm) and a criterion of glass-forming ability (GFA) – the critical cooling rate – were investigated by computing non-isothermal crystallization for typical values of the main quantities that control crystal nucleation and growth in silicate glasses. We limit these quantities to one thermodynamic parameter – the melting entropy (ΔSm) and two kinetic parameters that control the viscosity (B and T0 in the Vogel–Fulcher–Tamman equation or Tg and α in Avramov’s equation). The effect of heterogeneous nucleation and, in particular, the possible role of the surface as active substrate is tested. The results presented herein demonstrate that GS and GFA are indeed related concepts.

Viscosity of glassforming melts

Abstract We suggest a model able to predict the changes of the viscosity η with chemical composition. Viscosity is related to entropy of the system. Earlier, in the framework of the same model we have described successfully the dependence of viscosity on temperature and on pressure. Angell and co-workers compare the thermal properties of many glasses to their “fragility”. The dimensionless fragility is a measure of the dependence of the activation energy for spatial rearrangement on the changes of structure. We propose to use the power (α) of our equation as a fragility parameter. The present treatment gives a simple interpretation of the glass transition temperature Tg: The glass transition takes places when disarray in the amorphous system decreases to an extent that the dispersity σ is only 3.5% of maximal value of the activation energy Emax. At the glass transition temperature the dimensionless activation energy e=E/RTg is about 30.

Glass formation and crystallization

Abstract A survey of the different approaches to the determination of the glass-forming ability of substances is given. A generalized criterion for glass formation, based on the kinetics of the overall crystallization process, is used to calculate the minimum cooling rate for glass formation. This criterion accounts for non-steady-state effects in nucleation and for the presence of active substances and surfactants in the melt. The classical structural criteria for glass formation are derived as limiting cases of the generalized kinetic treatment. The glass-forming ability of a number of substances (metals, halides and liquified noble gases) is discussed.

ZrTiO4 crystallisation in nanosized liquid–liquid phase-separation droplets in glass—a quantitative XANES study

The crystallisation of the nucleation agent ZrTiO4 in a low thermal-expansion lithium aluminosilicate glass-ceramics is monitored as a function of time by combining transmission electron microscopy with Ti-L2,3 X-ray absorption near-edge structure spectroscopy. The formation of liquid–liquid phase-separation droplets is shown to precede ZrTiO4 crystallisation within the latter nanosized droplets. Quantitative data on crystalline fractions enable conclusions on the self-limited growth of ZrTiO4 nanocrystals in low thermal-expansion glass-ceramics and based on Avramis equation, the growth is shown to be restricted by a barrier (the outer border of the phase-separation droplet). It is shown that liquid–liquid phase separation and crystallisation are temporally decoupled. The size of ZrTiO4 crystallites is determined by the restricted volume of the phase-separation droplets they crystallise in. The volume of the droplets in turn is restricted by the formation of a diffusion barrier in the surrounding residual glass.

Thermal analysis of Li2O TeO2 glass

The thermal properties of 0.30Li2O 0.70TeO2 glass are studied. Specific heat, Cp, is measured in the 170∞C < T < 270∞C interval. The Einstein temperature, hAa 840 K, is determined from the temperature course of Cp. In the glass transition interval, the heat capacity undergoes an S-shaped transition from the value, Cgl, of the glass to that of undercooled melt, Cp. It is found that Cgl=Cp 0:62. The activation energy, EOTfU, for structural relaxation depends on a fictive temperature, Tf . For the glass under study, it is demonstrated that: EOTfUa655a 300O 520 Tf ˇ 1U kJ/ mol. ” 2000 Elsevier Science B.V. All rights reserved.

Structural relaxation in two metaphosphate glasses

The results of an experimental study on the kinetics of structural relaxation of NaPO3- and LiPO3- glass are reported. Two types of experiments were performed. The dependence of the fictive temperature, Tf, on the cooling rate gives the activation energy, Δh, equal to the activation energy for shear viscosity. On the other hand, the value of the activation energy obtained from the dependence of the temperature of vitrification Tg on the heating rate is considerably lower. In this way the value x = 0.6 for the dimensionless factor proposed by Narayanaswamy is obtained for both substances. The results obtained by the method described in the present investigation are compared with previous findings

Crystal growth model with stress development and relaxation

During crystallization of glass-forming melts an important amount of stress energy may develop. The reason for this development is the difference in volume of the new system and that in the ambient phase. Therefore, the growth rate decreases with time. Here we develop an algorithm for the process of crystallization using Monte Carlo simulation techniques that takes into account the stress energy. We find that there is a short period of initial fast growth stage followed by a second period of much slower growth, controlled by the relaxation rate. This picture has also been recently observed experimentally. Additionally, we find that during the growth process the shape of the crystal is changing. Although we start from a highly symmetric crystal with flat 10 interfaces, a shape with a large number of facets is soon created.