Bond-length fluctuation

Egami (2001) has developed pair-density-function analysis of pulsed neutron-diffraction data to determine the structure in a time interval that is short relative to a bond-length fluctuation. This method provides a direct observation of the pattern of bond-length fluctuations. Several other measurements have been shown to provide indirect signatures of the presence of bond-length fluctuations (Goodenough and Zhou, 2001). For example,... 

The phonon contribution to the thermal conductivity is strongly suppressed by bond-length fluctuations. 

Figure 61 shows the ZFC and FC M(T) curves for the FMM phase II, which show a first-order transition at 7c where the bond-length fluctuations become frozen out to restore the phonon contribution to the thermal conductivity, fig. 62. In the I + II two-phase samples t = 0.973 and t = 0.974, phase II is suppressed and phase fluctuations inhibit phonon formation below Tco or 7c. Tokura et al. (1996) applied hydrostatic pressure to the FM phase II of (Ndo.i25Smo.875)o.5Sro.5Mn03 having / /c they reported the appearance of a CE AFI second phase having a volume fraction that increased with pressure below Too = 7n- Since pressure... 

Figure 10. (a) Relative rms bond length fluctuations 6(T) for Ar,3 as obtained from MC studies. (b)S Rs a function of long-time averaged kinetic energy for isoergic Ar,3. ... 

Figure II. N-dependent melting temperatures and coexistence temperature ranges A7. a—longtime averaged kinetic energy values at which rms bond length fluctuations S rise sharply (see Fig. 10). Dashed lines correspond to coexistence temperature ranges AT = T — 7) ) for clusters that display a bimodal form for short-time averaged temperatures. (Beck et al. )...

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. 

The rms bond length fluctuation data of Davis et al. are pictured in Fig. 4. 8(T) is similar to those previously obtained form Etters and Kaelberer and Jellinek et al. in that the apjjearance of a second, more diffusive form of the cluster is dramatically reflected by a sudden rise in this function occurring over a narrow range of temjjeratures. The increase in this function is observed at lower temjjeratures here than in the curve of Etters and Kaelberer. The... 

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 ,... 

The analysis of trajectories in terms of ai t) quantities, the power spectra, short-time-averaged kinetic energy per atom (Ei /n) and bond-length fluctuations 8 are presented in Figures 2.5-9. 

Figure 2.9 Root-mean-square bond-length fluctuations 5 as a function of the total energy. The full and open symbols correspond to trajectories initialized from the and C2v, structures of the isomers I and II, III, respectively, of Li9 drawn with symmetry labels and energy sequence in eV [39]...

In previous work on Van der Waals clusters, it was established that the behaviour of a parameter characterizing the relative root mean square bond length fluctuations,... 

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.

---