New SubmissionA Kinetic Model for Fractal Ferroelectric Domains

ORAL

Abstract

The Avrami equation, also known as the Johnson-Mehl-Avrami-Kolmogorov (JMAK) or Kolmogorov-Avrami-Ishibashi (KAI)1,2,3,4 equation, is a widely used model for describing first-order phase transformations that proceed through nucleation and growth mechanisms. Due to its simplicity and versatility, it has been extensively applied to modeling the evolution of state variables across various fields. It is expressed as

f(t) = 1- exp(-ktn)

where f(t) denotes the fraction of the sample that has undergone transformation from a state to another state as a function of time, k is the rate constant, and n is a fitting parameter that gives information on the dimensionality of growth. In real solid-state systems, the exponent (n) corresponds to the number of physical dimensions (d) plus an additional factor 1 that accounts for the influence of the nucleation rate on growth kinetics. However, in our recent multiscale modeling of AlN switching5, we observed the formation of fractal domains violates the assumptions of the original KAI equation. In this work, we present a modified KAI equation that incorporates a budding term to capture the kinetics of fractal domain growth in wurtzite ferroelectrics, which have been observed to have n values that exceed physically meaningful values. Our approach successfully reproduces the experimentally6 and computationally observed evolution of polar domains in AlN and related materials, without invoking non-linear nucleation or growth rates.

*This work was supported by the U. S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences Energy Frontier Research Centers program under Award Number DE-SC0021118. Computational support was provided by the High-Performance Computing Modernization Office of the Department of Defense and the National Energy Research Scientific Computing Center (NERSC), a DOE, Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231.

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Publication: 1. Kolmogorov, A. N. On the statistical theory of the crystallization of metals. Bull Acad Sci URSS (Cl Sci Math Nat) (1937), 3, 335.
2. Arami, M. Kinetics of phase change. I General theory. J. Chem. Phys. (1939), 7, 1103–1112.
3. Avrami, M. Granulation, phase change, and microstructure kinetics of phase change. III. J. Chem. Phys. (1941), 9, 177–184.
4. Ihibashi, Y.; Takagi, Y. Note on Ferroelectric Domain Switching. J. Phys. Soc. Jpn (1971), 31, 506–510.
5. Bhrendt, D.; Samanta, A.; Rappe, A. M. Ferroelectric Fractals: Switching Mechanism
of Wurtzite AlN. arXiv preprint arXiv: (2024), 2410,18816.
6. Kazawa, K.; Hayden, J.; Maria, J.-P.; Zhu, W.; Trolier-McKinstry, S.; Zakutayev, A.;
Brennecka, G. L. Ano. Mater. Horiz. (2023), 10, 2936–2944.

Presenters

  • Atanu Samanta

    • University of Pennsylvania

Authors

  • Atanu Samanta

    • University of Pennsylvania