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The various theories describing molecular kinetic mechanisms for solidification are discussed with particular emphasis on the distinction between the stepwise and continuous growth mechanisms. The theory of Cahn based on the diffuse interface concept is reviewed. It predicts the former growth mode at sufficiently small undercoolings and the latter at large undercoolings. Criteria for testing the validity of the various theories are given. These consist of qualitative and quantitative observations of solidification kinetics as related to undercooling at the interface as well as the occurrence of certain topological and/or morphological features. The existing pertinent experimental data on metals, organic, and inorganic compounds are reviewed. Of the presently known theories only the diffuse interface model is consistent with all of the observations. In those cases where sufficient data were available, several independent checks have been made. The diffuseness parameter g and the molecular accommodation coefficient β are tabulated.

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