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Published on: December 4, 2017
Finite volume Kolmogorov-Johnson-Mehl-Avrami theory
1Department of Physics, Florida State University, Tallahassee, Florida 32306-4350, USA.
This study explores phase conversion in finite volumes using the Kolmogorov-Johnson-Mehl-Avrami theory. We found conversion time depends on volume size and expansion dynamics, revealing size-dependent limits for nucleation and spinodal decomposition.
Area of Science:
- Materials Science
- Physical Chemistry
- Thermodynamics
Background:
- The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory describes phase transformations.
- Understanding phase conversion in finite volumes is crucial for materials design.
- Previous models often assumed infinite systems, neglecting size effects.
Purpose of the Study:
- To extend the KJMA theory to finite volumes.
- To investigate the relationship between conversion time and system parameters.
- To analyze the influence of volume size on phase conversion mechanisms.
Main Methods:
- Theoretical analysis based on the KJMA framework.
- Derivation of a new relationship for conversion time: tau(con)=tau(nu)[1+f(d)(q)].
- Calculation of the scaling function f(d)(q) in 1D, 2D, and 3D.
Main Results:
- The conversion time (tau(con)) is linked to nucleation time (tau(nu)) and a scaling function f(d)(q).
- The scaling function's argument q relates expansion time (tau(ex)) to nucleation time.
- Phase conversion limits (nucleation vs. spinodal decomposition) are shown to be volume-size dependent.
Conclusions:
- Finite volume effects significantly influence phase conversion kinetics.
- The derived relationship provides a quantitative description of size-dependent phase transformations.
- This work offers insights into controlling phase conversion in nanoscale materials and systems.
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