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There are two other elements, Ce and Pu, whose phase diagrams (the shape of the melting curve) look similar to that of water. However, their locally favored structures are not well known. Thus, we have no firm basis for extending our argument to these elements at this moment.
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We believe that to the understanding of the thermodynamic anomalies of tetrahedral liquids, the concept of short-range tetrahedral bond order, which focuses on the local bond symmetry and the resulting coupling to local density, is more relevant than the popular concept of tetrahedral network formation. Whether tetrahedral units form network or not may not be important for the phenomena.
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Here we neglect a subtle difference in the symmetry of crystals that belong to the same category and just classify crystals into the two types, S crystal and p crystal, although real crystals should have various mixed symmetries due to the competition between p ordering and S ordering, depending upon the pressure.
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In the model of Kivelson and Tarjus et al. (Refs. 37 and 38), for example, the competition between short-range tendency to order and the strain generated by frustration leads to the breakup of a system into frustration-limited domains so that a phase transition into a quasicrystalline state is avoided.
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49
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33744559314
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m makes vitrification extremely difficult. What we want to emphasize here is that the symmetry of short-range bond ordering and its compatibility with that of the crystal into which a liquid tends to crystallize are also the important factors determining the ease of vitrification.
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50
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33744715275
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Note that the absence of locally favored structures, S̃∼0, also leads to the ease of crystallization, which is the case of Lennard-Jones liquids such as liquid argon. Note that small S̃ means the small number density of locally favored structures. For these liquids, ΔE is too weak to form rather stable locally favored structures that have considerable frustration effects on crystallization. This also means low viscosity, which makes vitrification difficult.
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On the role of the kinetic factor, or viscosity, see the discussion in Sec. IV C.
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cP upon nucleation. In some cases, thus, a ρ crystal can be nucleated as a metastable state even if it is not the equilibrium crystal having the lowest energy at that pressure (Refs. 45 and 46)
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