Cluster melting model

In support of this model, it is noted that LnFj - which has F ions on both octahedral and tetrahedral sites of a face-centred-cubic Ln -ion array - becomes a fast F -ion conductor below its melting point without any change in the cation array (O Keeffe and Hyde, 1975). This observation shows that some low-energy excitation other than the displacement of F ions into octahedral sites is operative, as is postulated with the cluster-rotation model for PbF2. 

It is known from studies using model potentials that even for a cluster as small as (H20)e, Monte Carlo simulations at temperatures between 50 and 200 K (the range typically considered to examine the issue of cluster melting) need to be carried out for on the order of 10 moves to achieve convergence. Such simulations at the MP2 level would... 

It is safe to assume, that cluster growth passes through coalescence of small nucleating seeds, melting with a rise in substrate temperature. In the framework of the same BOLS model, it is possible to determine the cluster melting temperature, knowing its size and m parameter by the following equation ... 

The simplest approach to understanding the reduced melting point in nanocrystals relies on a simple thennodynamic model which considers the volume and surface as separate components. Wliether solid or melted, a nanocrystal surface contains atoms which are not bound to interior atoms. This raises the net free energy of the system because of the positive surface free energy, but the energetic cost of the surface is higher for a solid cluster than for a liquid cluster. Thus the free-energy difference between the two phases of a nanocrystal becomes smaller as the cluster size... 

Figure 3a shows the mean-field predictions for the polymer phase diagram for a range of values for Ep/Ec and B/Ec. The corresponding simulation results are shown in Fig. 3b. As can be seen from the figure, the mean-field theory captures the essential features of the polymer phase diagram and provides even fair quantitative agreement with the numerical results. A qualitative flaw of the mean-field model is that it fails to reproduce the crossing of the melting curves at 0 = 0.73. It is likely that this discrepancy is due to the neglect of the concentration dependence of XeS Improved estimates for Xeff at high densities can be obtained from series expansions based on the lattice-cluster theory [68,69].

We have discussed some examples which indicate the existence of thermal anomalies at discrete temperatures in the properties of water and aqueous solutions. From these and earlier studies at least four thermal anomalies seem to occur between the melting and boiling points of water —namely, approximately near 15°, 30°, 45°, and 60°C. Current theories of water structure can be divided into two major groups—namely, the uniformist, average type of structure and the mixture models. Most of the available experimental evidence points to the correctness of the mixture models. Among these the clathrate models and/or the cluster models seem to be the most probable. Most likely, the size of these cages or clusters range from, say 20 to 100 molecules at room tempera-... 

Water is considered to be supercooled when it exists as a liquid at lower temperatures than its melting point, for example, at less than 0°C at atmospheric pressure. In this state, the supercooled water is metastable. The properties of supercooled water have been examined in detail in excellent reviews by Angell (1982, 1983) and Debenedetti (1996, 2003). A brief review of the properties of supercooled pure liquid water and the different liquid water models are discussed in this section. These structures comprise hydrogen-bonded water networks and/or water clusters ( cages ) that are the starting points to hydrate formation. 

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