Abstract
Two-phase mixtures, from metallic alloys to islands on surfaces, undergo coarsening wherein the total interfacial area of the system decreases with time. Theory predicts that during coarsening the average size-scale of a two-phase mixture increases with time as t1/3 when the two-phase mixture is self-similar, or time independent when scaled by a time-dependent length. Here, we explain why this temporal power law is so robustly observed even when the microstructure is not self-similar. We show that there exists an upper limit to the length scales in the system that are kinetically active during coarsening, which we term the self-similar length scale. Length scales smaller than the self-similar length scale evolve, leading to the classical temporal power law for the coarsening dynamics of the system. Longer length scales are largely inactive, leading to a non-self-similar structure. This result holds for any two-phase mixture with a large distribution of morphological length scales.
Highlights
Coarsening, referred to as Ostwald ripening, occurs naturally in a wide array of materials, including metallic alloys[1,2], polymers[3], and semiconductors[4]
In most cases a classical t1/3 power law for the average size scale of a two-phase mixture is observed without a self-similar two-phase morphology[17,18,19,20,21,22,23]
The most striking example is given by Marsh and Glicksman[21] who show that even though a structure evolves in a non-self-similar fashion from a dendritic morphology to a polydisperse array of approximately spherical particles, the characteristic length scale of the two-phase system still increases as t1/3
Summary
Coarsening, referred to as Ostwald ripening, occurs naturally in a wide array of materials, including metallic alloys[1,2], polymers[3], and semiconductors[4]. The most striking example is given by Marsh and Glicksman[21] who show that even though a structure evolves in a non-self-similar fashion from a dendritic morphology to a polydisperse array of approximately spherical particles, the characteristic length scale of the two-phase system still increases as t1/3. We use both time-resolved three-dimensional X-ray tomography and numerical simulations to demonstrate why coarsening microstructures can have a temporal power law for the average length scale while evolving in a non-self-similar manner
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