Phonon instability

They found a whole bunch of soft phonons, which are primarily horizontally polarized, near the zone boundaries between M and X. The most unstable mode they observed is the Mj phonon, the displacement pattern of which is shown in Fig. 40 note the similarity between this pattern and the reconstruction model in Fig. 39. According to Wang and Weber, these soft phonons are caused by electron-phonon coupling between the surface phonon modes and the electronic 3 surface states at the Fermi surface. They attributed the predominant Ms phonon instability to an additional coupling between d(x — y ) and d(xy) orbitals of the Zj states. 

Cowley RA (1976) Acoustic phonon instabilities and stractrrral phase transitiorrs. Phys Rev B 13 4877-... 

Shirane G, Axe JD (1971) Acoustic-phonon instability and critical scattering in NbsSn. Phys Rev Lett 27 1803-1806... 

Unfortunately, the analytical theory of surface melting has been so far not developed in a more explicit way, simply because one is lacking reliable quantitative theories of the melting transition in the bulk. Thus theories that locate the onset of surface melting from lattice-dynamical phonon instabilities (Pietronero and Tosatti, 1979 Jayanthi et al., 1985a, b Tosatti, 1988 Trayanov and Tosatti, 1988) need to be viewed with the caution that analogous treatments of melting in the bulk do not work. While computer simu-... 

Analysis of in situ synchrotron diffraction and spectroscopy data first revealed the presence of the unusual isostructural phase transition occurring within semiconductor clathrate materials, that was associated with a large change in the compressibility but with no apparent change in the crystal stmcture (Fig. 4.8) [69,74]. The pressure range associated with this unexpected transformation occurs between 13-16 GPa, but it also appears to depend upon the hydrostatic nature of the pressurization conditions. Various possible explanations for the transition have been advanced, including the presence of electronic [73,79] or phonon instabilities [71], or potential vacancy formation occurring on the framework silicon sublattice [80]. 

M. Wautelet, Estimation of the variation of the melting temperature with the size of small particles, on the basis of a surface-phonon instability model. J. Phys. D-Appl. Phys. 24(3), 343-346 (1991)... 

The surface-phonon instability model [40, 52, 53] suggests that the 7) (5) varies with 7 ,(oo) and with the energy for defect formation at the surface. Within the thermodynamic limit (particle radius larger than 2 nm), the effects of size reduction and electronic excitation combine [54]. 

The currently defined T ni(x)/7)n(0)-BOLS curve overlaps the curve derived from Born s criterion, T ni(x)/ri (0)-Bom, which indicates the consistency in the respective physical mechanisms of melting. BOLS notation suggests that the melting is governed by the skin-resolved depression of the atomic cohesive energy (I m oe zE but the Born s criterion Eq. (28.5) requires that the shear modulus or mechanical strength disappears at T [90]. The trend of the 7 m(x)/rm(0) curves also agree with the models derived from Lindermann s criterion of atomic vibration [91-93], surface lattice/phonon instability [94, 95], liquid drop [96], and surface area difference [97]. Therefore, all the models are correct despite different perspectives. 

Fig. 57. W(llO) H. Phonon dispersion curves for the different H phases, measured along (F-S) (F-H) and ( F- N). The data were recorded at T=l 10 K. The data for the (1x1) H phase along ( F- H ) show evidence for the phonon instability. No temperature dependent frequency shifts were observed. HREELS data are reported as open symbols, HATOF data as filled circles. Main references [92Hull, 92Hul2, 96Bal, 94Ball, 94Bal2].

---