Lindemann criterion, melting

Finally, if the temperature increases, becomes larger until the crystal melts. The Lindemann criterion predicts that melting sets in when becomes about 0.25 a2, where a is the interatomic distance of the metal. Because the mean squared displacements of surface atoms is higher we expect that the surface melts at lower temperatures than the bulk does [2]. Indeed, evidence has been presented that the (110) surface of lead starts to melt at 560 K whereas the bulk melting temperature is about 600 K [13]. 

In this section the results obtained from AIMD-B-LYP simulations by energizing three isomers of Li9" clusters will be analyzed [39]. For this purpose three types of quantities will be used. One of them is the root-mean-square (RMS) bond-length fluctuation 8 [25], which is calculated at the end of trajectories. A sharp increase of the 8 value is known as the Lindemann criterion for bulk melting, while in the context of finite-size clusters it can be taken as an indication of transition from solid-like to liquid-like state. We find it particularly instructive to analyze the trajectories in terms of atomic equivalence indexes ,... 

Fig. 4. Averaged relative root mean square bond length fluctuations for the Ar-Ar and Ar-SF distances for certain SF -(Ax) clusters. The shaded band identifies the 8 values chosen to define the Lindemann criterion for melting.

Each of the walls confining the film contains two (111) layers of an fee crystal. The axes are chosen so that the layers lie in the x-y plane and the film thickness is measured along the z-axis. Periodic boundary conditions are imposed in the x-y plane. Each wall atom is tied to a lattice site with a spring. These are stiff enough that thermal displacements are less than the Lindemann criterion for melting (20,27). 

For a simple calculation based on the Lindemann criterion and comparison with experiment see for example Tabor, D. Gases, Liquids and Solids, 1969, Penguin Books, Baltimore, p. 207. The calculation assumes harmonic vibration of the particles, against Young s modulus. Melting temperatures are calculated with reasonable accuracy for metals and even for quartz, but not for organic molecules. 

Between temperatures of 28 and 29 K the rms bond length fluctuations of the 13-particle system increase dramatically. Similar results have been obtained for all the other clusters N = 5, 6, and 7) for which S(T) is cal-culated. - The curves of S T) for these systems are similar to those occurring with first-order phase transitions of macroscopic systems.Lindemann s criterion states that melting occurs for such systems when rms fluctuations reach 10%.For the small clusters studied, the rise in this function occurs at values of S slightly below 10%—an effect that can be attributed to the large ratio of surface to core atoms. 

Perhaps the best known empirical melting rule for 3D melting is the Lindemann melting criterion, which states that a solid will melt when the root-mean-square displacement of particles from their lattice sites reaches a certain critical value, 8 = — 0.1 (a more extensive discussion... 

Assuming that dominates possible quantum fluctuations, Schilling et al. (1993) used the phenomenological Lindemann melting criterion (Lindemann 1910) to describe the experimentally observed irreversibility line in terms of vortex-lattice melting i.e.. 

The accuracy of Lindemann s criterion depends also on the steepness of its variation with temperature at phase transition and on the specification of its percentage increase which should be adequate to discriminate surface (partial) from all-cluster melting. In the present case, we assign to the temperature at which Lindemann s index starts increasing. This allows us... 

The lattice-vibration instability model [40, 55-59] extends Lindemann s vibrational-lattice instability criterion [60]. The melting behavior of a nanosolid is related to the ratio (/ ) of the root-mean-square displacement (RMSD, of an atom at the surface to the RMSD of an atom inside a spherical dot. p is a size-independent parameter ... 

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