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Phenomenological description of grain growth stagnation for nanocrystalline films and powders

Abstract

At fixed hold temperatures, grain growth usually stagnates indefinitely after sufficiently long hold times. The change in the growth behavior can be very abrupt, resulting in a sudden plateau in plots of grain size versus time at fixed temperature. Standard grain growth laws do not formally predict the rapid onset of growth stagnation, merely a slow down of grain growth to imperceptible rates. Therefore, the grain size in the plateau regions for long hold times is typically not in agreement with that predicted with kinetic variables derived from the size versus time curves for short hold times where there is pronounced curvature. Standard laws lead to endpoint grain sizes with strong dependences on the hold times. The experimental observation in many cases is a nearly linear temperature dependence that is independent of the hold times after a sufficient duration. Additionally, the growth process may restart from a stagnated state with sufficient temperature increases, where again, the stagnated grain size temperature dependence is linear. For growth laws including size dependent opposing forces, endpoint grain sizes are predicted to be either independent of temperature, or exponentially temperature dependent with thermodynamic reversibility, the latter an impossibility. We derive, heuristically, a stagnation force, phenomenologically incorporating these observations: a near linear temperature dependence of endpoint grain sizes, and irreversible growth. This description reduces to standard laws commonly used for data fitting, and leads to a normal grain size distribution. Other laws are discussed and compared. Fits to size versus time data are successfully made.

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