Self-Similarity and the Dynamics of Coarsening in Materials

Journal Article · 18 December 2018 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-018-36354-8 · OSTI ID:1619563

Sun, Yue; Andrews, W. Beck ; Thornton, Katsuyo ; Voorhees, Peter W.

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 t ^1/3 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.

• Research Organization: Northwestern Univ., Evanston, IL (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: FG02-99ER45782
• OSTI ID: 1619563
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 8; ISSN 2045-2322
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English