Statistical Approach to Crystal Nucleation in Glass-Forming Liquids.

Joachim Deubener,Jürn W P Schmelzer

doi:10.3390/e23020246

Joachim Deubener, Jürn W P Schmelzer

Open Access

https://doi.org/10.3390/e23020246

Copy DOI

Journal: Entropy	Publication Date: Feb 20, 2021
Citations: 11	License type: CC BY 4.0

Affiliation: Clausthal University of Technology, University of Rostock

Abstract

In this work, methods of description of crystal nucleation by using the statistical approach are analyzed. Findings from classical nucleation theory (CNT) for the average time of formation of the first supercritical nucleus are linked with experimental data on nucleation in glass-forming liquids stemming from repetitive cooling protocols both under isothermal and isochronal conditions. It is shown that statistical methods of lifetime analysis, frequently used in medicine, public health, and social and behavioral sciences, are applicable to crystal nucleation problems in glass-forming liquids and are very useful tools for their exploration. Identifying lifetime with the time to nucleate as a random variable in homogeneous and non-homogeneous Poisson processes, solutions for the nucleation rate under steady-state conditions are presented using the hazard rate and related parameters. This approach supplies us with a more detailed description of nucleation going beyond CNT. In particular, we show that cumulative hazard estimation enables one to derive the plotting positions for visually examining distributional model assumptions. As the crystallization of glass-forming melts can involve more than one type of nucleation processes, linear dependencies of the cumulative hazard function are used to facilitate assignment of lifetimes to each nucleation mechanism.

Highlights

Crystal nucleation in an undercooled glass-forming liquid is a stochastic process.Nucleation events in the bulk of the liquid occur randomly in time and space and are independent from each other
In view of the above, and considering the increasing significance of statistical methods in glass technology, this study aims to provide the theoretical basis for the evaluation of time-to-event data generated by the application of statistical methods to crystal nucleation
The hazard function, h, measures the propensity to nucleate depending on the undercooling, ∆T, reached or the time, τ, waited. It plays the key role in characterizing the process of crystal nucleation and in classifying lifetime distributions

Summary

Introduction

Crystal nucleation in an undercooled glass-forming liquid is a stochastic process.Nucleation events in the bulk of the liquid (in the absence of heterogeneous nucleation cores) occur randomly in time and space and are independent from each other. Crystal nucleation in an undercooled glass-forming liquid is a stochastic process. Nucleation may proceed randomly in time at the given set of heterogeneous nucleation cores present in the liquid. In both cases, nucleation requires the transition via a thermodynamic potential barrier denoted as work of critical cluster formation [1,2]. The choice of the thermodynamic potential appropriate for the description of nucleation (entropy, Helmholtz, or Gibbs free energy) depends on the thermodynamic constraints. The size of the critical cluster corresponds, in general, to a saddle point of the appropriate thermodynamic potential [3]

Objectives

Results

Discussion

Conclusion