The race within supercooled liquids—Relaxation versus crystallization

Zanotto, Edgar Dutra; Cassar, Daniel R.

doi:10.1063/1.5034091

Cited by 35 publications

(14 citation statements)

References 50 publications

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“…We note that the nucleation kinetics is controlled not by the viscosity (or rotational diffusion) but by the translational diffusion (see, e.g., refs. [12][13][14]. We stress that the decoupling in the temperature dependence between the viscosity and the translational diffusion coefficient becomes more and more significant with an increase in ∆T , which is known as the violation of the Stokes-Einstein relation.…”

Section: [2]mentioning

confidence: 84%

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid–liquid transition

Kurita

Tanaka

2019

Proc. Natl. Acad. Sci. U.S.A.

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Crystallization is one of the most familiar and fundamental phase transition phenomena. There is a possibility that crystallization may be enhanced by critical-like fluctuations associated with another nearby phase transition if the order parameter of the former is coupled to that of the latter; however, the mechanism of such order parameter coupling and its generality remain elusive due to the lack of experimental studies. Here we report experimental evidence for a nontrivial coupling between crystallization and liquid–liquid transition (LLT) for a molecular liquid, triphenyl phosphite. We find that the crystal nucleation frequency is drastically enhanced by short-time preannealing near but above the spinodal temperature of LLT. By successfully separating the thermodynamic and kinetic factors governing crystal nucleation, we show that this enhancement is induced by the lowering of the crystal–liquid interfacial energy due to the presence of critical-like order parameter fluctuations. This finding may be regarded as a fingerprint of the presence of LLT below the melting point. Thus, it may allow us not only to control the crystal nucleation frequency by LLT but also to unveil LLT hidden behind crystallization. This enhancement of nucleation frequency by critical-like fluctuations of another ordering phenomenon may be general to a variety of combinations of phase transitions. It would provide a way to control a crystal grain structure, which is a crucial control factor of mechanical and thermal properties of crystalline materials.

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Section: [2]mentioning

confidence: 84%

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid–liquid transition

Kurita

Tanaka

2019

Proc. Natl. Acad. Sci. U.S.A.

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“…In this temperature range, additional features have to be incorporated into the model of crystal nucleation accounting correctly for the interplay of crystal nucleation and glass transition [ 2 , 5 , 6 , 7 , 23 , 24 , 25 , 27 , 72 , 110 ]. Such additional factors could be (i) the evolution of elastic stresses and stress relaxation [ 4 , 5 , 27 , 49 , 50 ], (ii) variations of the size of the structural units in the melt responsible for crystallization [ 91 ], (iii) the effect of the spatially heterogeneous structure of glass-forming liquids on crystal nucleation [ 92 ], (iv) deviations of the bulk state parameters of the critical clusters from the respective macroscopic properties of the newly evolving crystalline phases [ 5 , 9 , 22 , 23 , 24 , 25 , 104 ] (this feature is expected to be of significant importance also at temperatures above

), and (v) the interplay of relaxation and crystal nucleation [ 6 , 7 , 25 , 27 , 102 , 110 , 111 , 112 ]. Of course, also in such generalizations, self-consistency corrections have to be accounted for in order to yield an agreement of numerical computations based on Equations ( 14 ) and ( 15 ) and the analytical expressions, Equations ( 27 ) and ( 32 ), and both of them with experimental data.…”

Section: Summary Of Results and Discussionmentioning

confidence: 99%

Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate

Abyzov

Schmelzer

Fokin

et al. 2020

Entropy

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Crystal nucleation can be described by a set of kinetic equations that appropriately account for both the thermodynamic and kinetic factors governing this process. The mathematical analysis of this set of equations allows one to formulate analytical expressions for the basic characteristics of nucleation, i.e., the steady-state nucleation rate and the steady-state cluster-size distribution. These two quantities depend on the work of formation, Δ G ( n ) = − n Δ μ + γ n 2 / 3 , of crystal clusters of size n and, in particular, on the work of critical cluster formation, Δ G ( n c ) . The first term in the expression for Δ G ( n ) describes changes in the bulk contributions (expressed by the chemical potential difference, Δ μ ) to the Gibbs free energy caused by cluster formation, whereas the second one reflects surface contributions (expressed by the surface tension, σ : γ = Ω d 0 2 σ , Ω = 4 π ( 3 / 4 π ) 2 / 3 , where d 0 is a parameter describing the size of the particles in the liquid undergoing crystallization), n is the number of particles (atoms or molecules) in a crystallite, and n = n c defines the size of the critical crystallite, corresponding to the maximum (in general, a saddle point) of the Gibbs free energy, G. The work of cluster formation is commonly identified with the difference between the Gibbs free energy of a system containing a cluster with n particles and the homogeneous initial state. For the formation of a “cluster” of size n = 1 , no work is required. However, the commonly used relation for Δ G ( n ) given above leads to a finite value for n = 1 . By this reason, for a correct determination of the work of cluster formation, a self-consistency correction should be introduced employing instead of Δ G ( n ) an expression of the form Δ G ˜ ( n ) = Δ G ( n ) − Δ G ( 1 ) . Such self-consistency correction is usually omitted assuming that the inequality Δ G ( n ) ≫ Δ G ( 1 ) holds. In the present paper, we show that: (i) This inequality is frequently not fulfilled in crystal nucleation processes. (ii) The form and the results of the numerical solution of the set of kinetic equations are not affected by self-consistency corrections. However, (iii) the predictions of the analytical relations for the steady-state nucleation rate and the steady-state cluster-size distribution differ considerably in dependence of whether such correction is introduced or not. In particular, neglecting the self-consistency correction overestimates the work of critical cluster formation and leads, consequently, to far too low theoretical values for the steady-state nucleation rates. For the system studied here as a typical example (lithium disilicate, Li 2 O · 2 SiO 2 ), the resulting deviations from the correct values may reach 20 orders of magnitude. Consequently, neglecting self-consistency corrections may result in severe errors in the interpretation of experimental data if, as it is usually done, the analytical relations for the steady-state nucleation rate or the steady-state cluster-size distribution are employed for their determination.

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“…The surface tension is assumed to be equal to the respective value of a critical crystallite in the metastable liquid and determined by indirect measurements, computer simulations or taken as a fit parameter to arrive at an agreement between theory and experiment. Utilizing CNT and employing the capillarity approximation and the Stokes-Einstein-Eyring equation (that relates the diffusion coefficient to the viscosity of the liquid), such approach can be confirmed theoretically [18,19,40] and also by a variety of experimental data [41,42,43,44,45].…”

Section: The Model: Basic Assumptionsmentioning

confidence: 98%

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Schmelzer¹,

Тропин²,

Fokin³

et al. 2020

Preprint

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In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Completing the analysis of elastic stress effects, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one if its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called \breakdown" of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far.

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The race within supercooled liquids—Relaxation versus crystallization

Cited by 35 publications

References 50 publications

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid–liquid transition

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid–liquid transition

Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

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