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Crystalline nucleation in undercooled liquids: a Bayesian data-analysis approach for a nonhomogeneous Poisson process
A Filipponi1, A Di Cicco, E Principi
1Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, I-67100 Coppito, L'Aquila, Italy. adriano.filipponi@aquila.infn.it
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
This study introduces a Bayesian data analysis method for studying crystallization in materials. The approach effectively analyzes limited experimental data on maximum undercooling temperatures, crucial for understanding material properties.
Area of Science:
- Materials Science
- Statistical Physics
- Computational Chemistry
Background:
- Crystallization is a fundamental process in materials science.
- Understanding nucleation rates is key to controlling material properties.
- Analyzing undercooling data presents challenges, especially with limited experimental sets.
Purpose of the Study:
- To propose a novel Bayesian data-analysis approach for undercooling temperature data.
- To model the crystallization phenomenon using a nonhomogeneous Poisson process.
- To provide a robust method for analyzing scarce experimental data.
Main Methods:
- Bayesian data analysis.
- Modeling crystallization via a temperature-dependent nucleation rate J(T) within a nonhomogeneous Poisson process.
- Extensive computer simulations and application to real data (liquid Ge).
Main Results:
- The proposed Bayesian method is effective for analyzing maximum undercooling temperatures.
- The approach accurately describes crystallization using a nonhomogeneous Poisson process.
- Demonstrated utility in cases with scarce data, outperforming binned data analysis.
Conclusions:
- The Bayesian approach offers a powerful tool for analyzing undercooling data in materials science.
- This method preserves information from limited experimental datasets.
- It provides a reliable framework for studying nucleation kinetics and crystallization phenomena.
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