Phonon soft mode

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... 

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... 

There has been speculation that anomalous electrical behavior may accompany a Peierls transition. In particular, the presence of a soft phonon mode at... 

There has been considerable theoretical discussion concerning the role of the Peierls soft phonon mode with wavevector 2kp in the indirect coupling of electrons into pairs to form the superconducting state in a one-dimensional metal. It has been suggested that this phonon could lead to an anomalously large attractive indirect electron-electron interaction (6, 97, 392). In contrast, some theoretical work shows that phonons of energy less than ksTc (such as the soft phonon mode near the Peierls transition) tend to suppress the superconducting transition (6, 333,348). Further theoretical and experimental work is necessary to fully resolve this point. 

Other examples of adsorbate induced changes in surface phonon dispersion show even stronger effects, such as soft phonon modes, Kohn anomalies and surface reconstractions. 

In ionic lattices these shifted (off-central) impurities are known to be the electric dipoles. The indirect interaction of such dipoles via soft phonon mode of a dielectric host exists in the incipient ferroelectrics like KTaOs, SrTiOs, PbTe. It leads to following fixed sign interaction ... 

Let us consider the system of electric dipoles and other defects randomly distributed in the film paraelectric phase. Similarly to the random field model for bulk relaxor ferroelectrics [83], this phase is called Burns reference phase. For example, the relaxor ferroelectric Pbo,92Lao,osZro,65Tio,3503 (PLZT) (where La ions are the main sources of random field) is known to have the Burns phase simply as the paraelectric phase of PbZro,65Tio,3s03 (PZT). Latter phase exists at T > Tj, Td is so-called Burns temperature and Td = 1), where Tc is transition temperature form paraelectric to ferroelectric phase in PZT. The indirect interaction of electric dipoles via soft phonon mode of a host crystal tends to order the system and so to generate the ferroelectric phase in it [84]. However, the direct interaction of dipoles and other defects like point charges, try to disorder a system, transforming it into relaxor ferroelectric. 

It should be noted that in the last years EuTiOs attracts a lot of attention of scientists. For instance, the comparative analysis of EuTiOs and SrTiOs has been performed recently. This analysis is based upon specific heat and soft phonon mode measurements. Refs. [23] and [24, 25] respectively. The obtained results made it possible for authors to ascribe new 282 K instability of EuTiOs to antiferrodistortive phase transition. 

It was suggested that both phenomena are caused by soft phonon modes. Soft phonon modes may profoundly influence the resistivity. Simultaneously, they may lead to the enhancement in Tc(P) at 25 kbar just as at the 53 kbar anomaly (fig. 10.3). In summary, it is possible that three slightly different fee phases exist in La at low temperatures. We have termed them and p in the order of increasing pressure (fig. 10.5). The phase diagram should be considered as a... 

Worlock, J.M., Scott, J.F., and Fleury, P.A. (1959) Soft phonon modes and the 110 K phase transition of SrTi03, in Light Scattering Spectra of Solids (ed. G.B. 

The inflexion point in the dependence of the total energy on elongation yields the maximum of the tensile stress if any other instability (violation of some stability condition, soft phonon modes, magnetic spin arrangement etc.) does not occur prior to reaching the inflexion point, it also corresponds to the theoretical tensile strength, Cth. 

It has been reported that the permittivity of a material decreases with decreasing film thickness. As a result, the capacitance increase is not as large as expected based on the inverse relation between C and t. The reason is the existence of dielectric dead layers at the dielectric s surface and interfaces, or interfacial layers between the dielectric and its neighboring materials, which in both cases are characterized by a much lower permittivity. As the dead layer is in series with the dielectric, the effective permittivity is reduced as well. In the case of MOS devices, a notorious interfacial reaction is the formation of silicates between the dielectric and silicon, hence the importance of the thermodynamic stability of the dielectric on Si. In the case of MIM (metal-insulator-metal) devices, alloy formation or in-diffusion of the electrode is a possibility, for example, in the case of Pt. However, also in case no secondary phases are formed, permittivity can be thickness dependent. Possible reasons include breaking of the lattice periodicity or the presence of ion vacancies at the interface, which disturb or inhibit the soft phonon mode and other intrinsic effects [6]. It was shown that electrodes with a shorter electronic screening length, for example, Pt or Au, lead to a smaller dead layer effect compared with, for instance, SrRuOs electrodes [13]. 

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