Radial distribution function, cluster dynamics

Considerable evidence exits of the survival of Zintl ions in the liquid alloy. Neutron diffraction measurements [5], as well as molecular dynamics simulations [6, 7], give structure factors and radial distribution functions in agreement with the existence of a superstructure which has many features in common with a disordered network of tetrahedra. Resistivity plots against Pb concentration [8] show sharp maxima at 50% Pb in K-Pb, Rb-Pb and Cs-Pb. However, for Li-Pb and Na-Pb the maximum occurs at 20% Pb, and an additional shoulder appears at 50% Pb for Na-Pb. This means that Zintl ion formation is a well-established process in the K, Rb and Cs cases, whereas in the Li-Pb liquid alloy only Li4Pb units (octet complex) seem to be formed. The Na-Pb alloy is then a transition case, showing coexistence of Na4Pb clusters and (Pb4)4- ions and the predominance of each one of them near the appropiate stoichiometric composition. Measurements of other physical properties like density, specific heat, and thermodynamic stability show similar features (peaks) as a function of composition, and support also the change of stoichiometry from the octet complex to the Zintl clusters between Li-Pb and K-Pb [8]. 

Another perspective on the time-dependent microstructural evolution in supercooled liquids was presented by a new resolution of the radial distribution function. The concept of neighbourship was invented by Keyes. " The g(r) was resolved into a series of separate radial distributions for the first neighbour, second neighbour and so on." As the temperature decreased it was found that these shells became more radially separated and that the dynamics of the first shell departed from a simple diflusive model, which is indicative of the onset of slow collective cluster dynamics." ... 

Using the hybrid ADMP/ONIOM technique, Rega et al. [104] have published the result of a molecular dynamics simulation at the B3LYP/6-31+G(d,p) level and with AMBER/TIP3P water model of a chloride anion embedded in a cluster of 256 water molecules. The time step was 0.25 fs and they have performed a 3 ps simulation after thermalization, allowing them to report the atom-atom radial distribution functions. 

Nauchitel and Pertsin have studied the melting properties of 13-, 19-, and 55-particle Lennard-Jones clusters.Questioning the validity of results obtained from free-volume simulations of such systems, they have used hard-sphere boundaries to constrain their clusters to finite volumes. The results of Nauchitel and Pertsin are most interesting for the 55-particle cluster. For certain ranges of temperature and mean density, structural evidence for surface melting was obtained projections of the cluster s coordinates, and radial density distribution functions, like those given in Fig. 17, characterize the cluster as a 13-particle icosahedral core surrounded by a fluidlike shell. However, dynamic calculations like those described for other clusters in the previous section have yet to be obtained to determine how fluidlike these outer atoms really are. 

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