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- W3183258148 abstract "It was found by Jagle and Mittenmeijer [Acta Mater. 59 (2011) 5775-5786] as a result of computer simulations that Cahn’s equation underestimates pronouncedly the transformed fraction in reality. To test the hypothesis that a strong correlation in the arrangement of grains in the Cahn model (they are “tied” to planes) can be responsible for this phenomenon, the paradox of packing is described: the structures composed of the same elements (random parallelepipeds) transforming in the same way, but packed differently, give different transformation rates. One of these structures is a special Cahn model – the grain structure of parallelepipeds formed by three sets of random parallel planes orthogonal to each other. An alternative structure consists of the same parallelepipeds, but randomly packed; it looks like a real grain structure. It is shown analytically that the kinetics of transformation in the first structure is considerably slowed down in comparison with that in the second. For the various intermediate structures under consideration, the kinetic curves are between these two, so that the following rule is established: the transformation kinetics is accelerated, when the correlation in the arrangement of the parallelepipeds weakens. Preliminarily, volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang process) of arrangement of planes is considered for the first time. The exact volume-fraction expression obtained for this case shows that it cannot be derived by Cahn’s method, i.e. the extended-volume approach is applicable only to Poisson processes. The volume fraction equations for regular planes are used to study cubic grain structures, both regular and random. It is shown that Cahn’s equation underestimates the transformation kinetics in both regular and random structures with four different size distributions of cubes; the degree of underestimation depends on the size distribution, being the largest in the regular structure." @default.
- W3183258148 created "2021-08-02" @default.
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- W3183258148 date "2021-01-01" @default.
- W3183258148 modified "2023-09-23" @default.
- W3183258148 title "Kinetics of Grain-Boundary Nucleated Transformations in Rectangular Geometries and One Paradox Relating to Cahn's Model" @default.
- W3183258148 doi "https://doi.org/10.2139/ssrn.3890349" @default.
- W3183258148 hasPublicationYear "2021" @default.
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