Stress development and relaxation during crystal growth in glass-forming liquids
ABSTRACT We analyze the effect of elastic stresses on the thermodynamic driving force and the rate of crystal growth in glass-forming liquids. In line with one of the basic assumptions of the classical theory of nucleation and growth processes it is assumed that the composition of the clusters does not depend significantly on their sizes. Moreover, stresses we assume to be caused by misfit effects due to differences in the specific volume of the liquid and crystalline phases, respectively. Both stress evolution (due to crystallization) and stress relaxation (due to the viscous properties of the glass-forming liquids) are incorporated into the theoretical description. The developed method is generally applicable independently of the particular expressions employed to describe the crystal growth rate and the rate of stress relaxation. We show that for temperatures lower than a certain decoupling temperature, Td, elastic stresses may considerably diminish the thermodynamic driving force and the rate of crystal growth. The decoupling temperature, Td, corresponds to the lower limit of temperatures above which diffusion and relaxation are governed by the same mechanisms and the Stokes–Einstein (or Eyring) equation is fulfilled. Below Td, the magnitude of the effect of elastic stresses on crystal growth increases with decreasing temperature and reaches values that are typical for Hookean elastic bodies (determined by the elastic constants and the density differences of both states of the system) at temperatures near or below the glass-transition temperature, Tg. By these reasons, the effect of elastic stress must be properly accounted for in a correct theoretical description of crystal nucleation (as some of us have shown in previous papers) and subsequent crystal growth in undercooled liquids. The respective general method is developed in the present paper and applied, as a first example, to crystal growth in lithium disilicate glass-forming melt.
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ABSTRACT: We review a plethora of relevant experimental results on internal homogeneous crystal nucleation in silicate glasses obtained in the last four decades, and their analyses in the framework of the classical nucleation theory (CNT). The basic assumptions and equations of CNT are outlined. Particular attention is devoted to the analysis of the properties of the critical nuclei, which, to a large extent, govern nucleation kinetics. The main methods employed to measure nucleation rates are described and the possible errors in the determination of the crystal number density (and, correspondingly, in nucleation rates) are discussed. The basic regularities of both time and temperature dependencies of nucleation rates are illustrated by numerous experimental data. Experimental evidence for a correlation between maximum nucleation rates and reduced glass transition temperatures is presented and theoretically justified. Special attention is given to serious problems that arise in the quantitative description of nucleation rates when using the CNT, for instance: the dramatic discrepancy between calculated and measured nucleation rates; the high value of the crystal nuclei/melt surface energy, σcm, if compared to the expected value estimated via Stefan’s rule; the increase of σcm with increasing temperature; and the discrepancies between the values of the surface energy and the time-lag for nucleation when independently estimated from nucleation and growth kinetics. The analysis of the above mentioned problems leads to the following conclusion: in contrast to Gibbs’ description of heterogeneous systems underlying CNT, the bulk thermodynamic properties of the critical nuclei generally differ from those of the corresponding macro-phase resulting simultaneously in significant differences of the surface properties as compared with the respective parameters of the planar interfaces. In particular, direct experimental evidence is presented for compositional changes of the crystal nuclei during formation of the critical nuclei and their growth from critical to macro-sizes. In addition, detailed examinations of crystal nucleation and growth kinetics show a decrease of both the thermodynamic driving force for nucleation and of the critical nuclei/liquid interfacial energy, as compared with the respective properties of the macro-phase. However, despite significant progress in understanding crystal nucleation in glasses in the past four decades, many problems still exist and this is likely to remain a highly interesting subject for both fundamental and applied research for a long time.Journal of Non-Crystalline Solids 08/2006; 352:2681-2714. DOI:10.1016/j.jnoncrysol.2006.02.074 · 1.72 Impact Factor
Article: The Prigogine-Defay ratio revisited.[Show abstract] [Hide abstract]
ABSTRACT: One of the basic characteristics of the glass transition, the Prigogine-Defay ratio, connecting jumps of the thermal expansion coefficient, isothermal compressibility, and isobaric specific heat capacity in vitrification is rederived in the framework of the thermodynamics of irreversible processes employing the order-parameter concept introduced by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)]. In our analysis, glass-forming liquids and glasses are described by only one structural order parameter. However, in contrast to previous approaches to the derivation of this ratio, the process of vitrification is treated not in terms of Simon's simplified model [Z. Anorg. Allg. Chem. 203, 219 (1931)] as a freezing-in process proceeding at some sharp temperature, the glass transition temperature T(g), but in some finite temperature interval accounting appropriately for the nonequilibrium character of vitrifying systems in this temperature range. As the result of the theoretical analysis, we find, in particular, that the Prigogine-Defay ratio generally has to have values larger than 1 for vitrification in cooling processes. Quantitative estimates of the Prigogine-Defay ratio are given utilizing a mean-field lattice-hole model of glass-forming melts. Some further consequences are derived concerning the behavior of thermodynamic coefficients, in particular, of Young's modulus in vitrification. The theoretical results are found to be in good agreement with experimental data.The Journal of Chemical Physics 12/2006; 125(18):184511. DOI:10.1063/1.2374894 · 3.12 Impact Factor
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ABSTRACT: Contrary to the common belief that a glassy state is stable against crystallization, Oguni and co-workers discovered unusual enhancement of the crystal growth rate of a few molecular liquids below the glass transition temperature Tg. We studied this phenomenon using o-terphenyl (OTP) and phenyl salicylate (salol), focusing on the roles of volume contraction ΔV upon crystallization. We confirmed enhancement of crystal growth below Tg for OTP. For salol, which has two kinds of crystal, the crystal growth rate below Tg is faster for a crystal of larger ΔV than for another crystal of smaller ΔV. Our results suggest the following physical scenario for the phenomenon: for a material having large ΔV, the volume contraction upon crystallization provides a crystal-glass interface with large excess free volume, which results in the mobility increase at the growth front and leads to enhancement of the crystal growth. This mechanism may be effective only below Tg, where density fluctuations cannot be quickly relaxed by hydrodynamic transport.Physical review. B, Condensed matter 01/2007; 76(22). DOI:10.1103/PhysRevB.76.220201 · 3.66 Impact Factor