Soft phonons

A basic concept in the reconstruction theory of solid surfaces is the soft phonon approach of displacive structural transitions. An essential property of these structural phase transitions is the existence of an order parameter which... 

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. 

According to the concept of the displacive-type ferroelectric phase transition [10], an increase in the dielectric constant corresponds directly to the softening of the IR-active transverse phonon. When the crystal can be regarded as an assembly of the vibrators of normal coordinates, the soft phonon... 

Deducing the electronic entropy change from the specific heat, it appears that about one-third is due to the electrons. The rest must be the result of soft phonon modes. 

The origin of the pyroelectric effect, particularly in crystalline materials, is due to the relative motions of oppositely charged ions in the unit cell of the crystal as the temperature is varied. The phase transformation of the crystal from a ferroelectric state to a paraelectrlc state involves what is called a "soft phonon" mode (9 1). In effect, the excursions of the ions in the unit cell increase as the temperature of the material approaches the phase transition temperature or Curie temperature, T. The Curie temperature for the material used here, LiTaO, is 618 C (95). The properties of a large number of different pyroelectric materials is available through reference 87. For the types of studies envisaged here, it is preferable to use a pyroelectric material whose pyroelectric coefficient, p(T), is as weakly temperature dependent as possible. The reason for this is that if p(T) is independent of temperature, then the induced current in the associated electronic circuit will be independent of ambient temperature and will be a function only of the time rate of change of the pyroelectric element temperature. To see this, suppose p(T) is replaced by pQ. Then Equation U becomes... 

An additional feature of the temperature dependent X-ray scattering is the persistence above Tc of intensity at the superlattice positions51). This is consistent with a soft phonon mode at a wave vector commensurate with the changes that occur on dimerization. It has been suggested that this low frequency lattice mode may be a requirement for the observation of a spin-Peierls transition. 

An isolated CS plane is referred to as a Wadsley defect and a random array of CS planes is considered to constitute planar (extended) defects which are entirely different from point defects. It is obvious that when CS planes occur at regular intervals, the composition of the crystal is stoichiometric, whereas a random array of CS planes results in nonstoichiometric compositions. While we have invoked anion vacancies which are later annihilated in our description of CS plane formation, we must point out that vacancies are not essential precursors for the formation of CS planes. Accommodating anion-deficient nonstoichiometry through CS mechanism is a special feature restricted to d° metal oxides such as W03, Nb205 and TiOz which exhibit soft phonon modes. Soft phonon modes in metal oxides arise from soft metal-orxygen potentials which permit large cation relaxation. The latter... 

Uwe H, Sakudo T (1976) Stress-induced ferroelectricity and soft phonon modes in SrTiOa. Phys Rev B 13 271... 

Sirenko AA, Akimov lA, Pox JR, Clark AM, Li H-C, Si W, Xi XX (1999) Observation of the first-order Raman scattering in SrTi03 thin films. Phys Rev Lett 82 4500 Akimov lA, Sirenko AA, Clark AM, Hao J-H, Xi XX (2000) Electric-field induced soft-mode hardening in SrTiOa films. Phys Rev Lett 84 4625 99. Tenne DA, Clark AM, James AR, Chen K, Xi XX (2001) Soft phonon modes in Bao.5Sro.5Ti03 thin films studied by Raman spectroscopy. Appl Phys Lett 79 3836-3838... 

Fujimori H, Yashima M, Kakihana M, Yoshimura M (2000) Phase transition and soft phonon modes in SrZrOs around 1200°C by ultraviolet laser Raman spectroscopy. Phys Rev B 61 3971... 

In the metallic state below about 150 K a set of diffuse streaks was found in X-ray studies as shown in Fig. 18 which suggests the onset of the periodic lattice distortion with = 0.295 b having no correlation among them perpendicular to the one-dimensional b-axis [55,56]. Corresponding to these x-ray streaks inelastic neutron scattering studies revealed the decrease in the phonon frequency for the wave vector = 0.295 b with decreasing temperature as shown in Fig. 19 [60]. This soft phonon is considered to be frozen out at the metal-insulator transition temperature 53 K causing the superstructure described above. This type... 

Swainson IP, Dove MT (1995b) On the thermal expansion of p-cristobalite. Phys Chem Minerals 22 61-65 Tantz FS, Heine V, Dove MT, Chen X (1991) Rigid unit modes in the molecular dynamics simulation of qnartz and the incommensurate phase transition. Phys Chem Minerals 18 326-336 Teznka Y, Shin S, Ishigame M (1991) Observation of the silent soft phonon in p-quartz by means of hyper-raman scattering. Phys Rev Lett 66 2356-2359... 

Tezuka Y, Shin S, Ishigame M (1991) Observation of the silent soft phonon in p-quartzby means of hyper-Raman scattering. Phys Rev Lett 18 2356-2359... 

The spectral function leading to a quasi-first-order Raman spectrum close to the critical point of a displacive system contains basically three contributions from 1) the soft mode, 2) the central peak and 3) higher order Raman scattering arising from processes involving hard and soft phonons... 

For ice X and the (fee) antifluorite structure the quantification of various aspects of their structural and chemical character and their dependence with pressure was found using AIM in a novel approach. Metallic character was found to be present in the antifluorite structure, but did not persist with increased pressure since the BCPs then fell within the pseudopotential core radii. In future studies on the antifluorite structure it will be necessary to replace the core with the true all electron distribution. In addition we present a hypothesis for the physical meaning of the O—O bonding interactions, namely that they indicate the onset of, soft phonon modes that are known to accompany structural changes. The fact that there are no O—O interactions in the antifluorite structure is consistent with this hypothesis, since to date there aren t any higher pressure phases of ice than antifluorite ice and so no pressure induced phase change can occur in this structure. Thus our hypothesis would explain why there are no O—O interactions in the antifluorite structure. 

Second-order phase transitions also show up via the critical slowing down of the critical fluctuations (Hohenberg and Halperin, 1977). In structural phase transitions, one speaks about soft phonon modes (Blinc and Zeks, 1974 Bruce and Cowley, 1981) in isotropic magnets, magnon modes soften as T approaches Tc from below near the critical point of mixtures the interdiffusion is slowed down etc. This critical behavior of the dynamics of fluctuations is characterized by a dynamic critical exponent z one expects that some characteristic time r exists which diverges as T - TCl... 

The distinctions between these two pure types may also be viewed from entropic considerations and the nature of the driving mode. The entropic change in an order-disorder phase transition is mainly configurational, and the driving mode is of diffusive (nonpropagating) nature. On the contrary, for a displacive phase transition, the entropy change is mainly vibrational, with an associated underdamped soft phonon. 

To summarise, it seems clear that at low T the conductivity of HMTSF TCNQ arises from small pockets of electrons with a degeneracy temperature of about 2CK and there is mounting evidence that these are an intrinsic property of the material. The proposed band structure accounts for many of the experimental observations but a number of problems remain. One interesting experiment is X-ray diffuse scattering at low T. It is known that there is a longitudinally polarised "2kp" soft phonon down to 100, if this condenses to... 

Bulk rutile shows a high dielectric constant and low-fiequency ( soft ) phonons, but how is this manifest at the surface An FP study finds a soft, anisotropic and anharmonic surface mode (0.15 A ionic displacements at room temperature), which could accoimt for some of the discrepancy between SXRD and zero-temperature FP structures [60]. More generally, this illustrates that many oxide surfaces can be expected to show vibrational anisotropy [40], complicating the use of FP to provide quantitative predictions of structure at a given temperature. 

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