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Fluctuations provide strong selection in Ostwald ripening.
1The Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel. meerson@vms.huji.ac.il
Summary
This study reexamines Ostwald ripening selection, finding that fluctuations in minority domain sizes create an infinite tail in the distribution function. This drives the system towards a specific limiting solution, refining Lifshitz-Slyozov theory.
Area of Science:
- Materials Science
- Physical Chemistry
- Statistical Mechanics
Background:
- Ostwald ripening describes the evolution of microstructures in materials over time.
- The Lifshitz-Slyozov (LS) theory provides a theoretical framework for understanding this process.
- A key challenge is selecting the correct self-similar size distribution function for minority domains.
Purpose of the Study:
- To reexamine the selection problem within the Lifshitz-Slyozov theory of Ostwald ripening.
- To identify the mechanism responsible for selecting a unique self-similar distribution function (DF) for minority domain sizes.
- To investigate the role of fluctuations in this selection process.
Main Methods:
- Theoretical analysis of the Lifshitz-Slyozov (LS) theory.
- Incorporation of fluctuation effects into the domain size distribution function (DF).
- Mathematical modeling to derive the selection rule.
Main Results:
- A strong selection rule for the distribution function (DF) of minority domain sizes was identified.
- Fluctuations were found to introduce an infinite tail into the DF.
- The DF is driven towards the "limiting solution" of the LS theory or analogous solutions for other growth mechanisms.
Conclusions:
- Fluctuations play a crucial role in selecting the correct self-similar distribution function in Ostwald ripening.
- The findings refine the understanding of Ostwald ripening and related growth phenomena.
- This work provides a more robust theoretical basis for predicting material microstructure evolution.