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While the definition of the di-, tri-, tetra-, penta-,..., i-mers is evident in the case of vapor condensation for which the kinetic approach was originally developed, the meaning of these terms for the crystallization of a liquid is not all that clear. They can be perhaps best visualized as especially favorable (low potential energy) molecule pairs, triplets, tetrahedra,..., that have, therefore, larger lifetimes than their (more distorted) average liquidlike counterparts. These molecular units probably assume the typical crystalline bond angles only after reaching a size large enough to ensure nearly complete crystal-like first-neighbor coordination. These difficulties in defining the smallest clusters suggest that crystallization is rather a short range cooperative rearrangement of molecules than a single molecule attachment/detachment process. The success of the kinetic approach in describing the nucleation transient in various substances (see Ref. 4) implies, however, that it is at least a fairly reasonable first approximation.
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f, although with a lower probability.) The molecules incorporated into such clusters cannot act as monomers (albeit only temporarily, since they reappear as monomers when the clusters dissociate), resulting in the depletion of monomers in the liquid.
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sr is shorter than the induction time of nucleation by about one to two orders of magnitude suggesting that interference between nucleation kinetics and structural relaxation is probably negligible.
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sr is shorter than the induction time of nucleation by about one to two orders of magnitude suggesting that interference between nucleation kinetics and structural relaxation is probably negligible.
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Smith, G.L.1
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85034143224
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note
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When quenching the liquid, a structure freezes in that relaxes to a lower free energy state provided that the mobility of the molecules is high enough. Accordingly, the free energy of the glass/crystal interface depends on the heat treatment. At high temperatures where γ(T) is approximately linear, the relaxation is fast and the true γ(T) can be observed. However, the relaxation time increases steeply as the temperature decreases. Thus at low temperatures the steady-state nucleation occurs in the unrelaxed glass (structure frozen in at a higher temperature), i.e., the respective y is higher than for the relaxed state. Consequently, in a temperature range below the glass transition (occurring during quenching), nucleation takes place in differently relaxed states that span from the fully relaxed state at high temperatures to the unrelaxed state at low temperatures, a phenomenon that explains the minimum in the interfacial free energy shown in Fig. 8. However, considering the short structural relaxation times of glass (Ref. 44), this mechanism is likely to occur only if the structural relaxation in the glass/crystal boundary layer is considerably slower than in the bulk glass.
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