Susceptibility soft mode

The soft mode concept can be extended to all distortive phase transitions (transitions with relatively small atomic displacements), even if they are only close to second order. In the case of a ferro-distortive transition, as for example in BaTiOs or KDP, the order parameter is proportional to the spontaneous electric polarization Fj. d F/ dp is not only proportional to co, but also to the dielectric susceptibility. This does not, however, mean that all components of the order parameter eigenvector must contribute to Ps. 

Some insight into the mechanism by which Pc is changed is provided by the frequency of the soft mode responsible for the phase transition. In the stability field of the high symmetry (tetragonal) phase, the inverse order parameter susceptibility, x of the order parameter varies as... 

Thin pills and nanowires. To be specific, hereafter we put ai(T) = ar (T — Tc) and use typical (for screened ferroelectric thin pills) form of depolarization field Ef = ((P3) - P3)/(soSi), P3 is polarization directed along the pill symmetry axes (see inset to Fig. 4.25), where is so-called dielectric permittivity of the background [89] or reference state [90] unrelated to ferroelecfiic soft mode (typically Sb < 10). Linearized solution of Eq. (4.17a) gives the averaged value of susceptibility in paraelectric phase ... 

We see, that the phase transitimi temperature increases, because the dipole-dipole interactions (f -term) stabilise the smectic C phase. Note that the held induced tilt angle (or electroclinic coefficient Cc) diverges at a temperature T. This means, that at even inhnitesimally low held would create a finite tilt. This is the soft mode of the director motion any small force (not necessary electric) would cause the tilt of the director, because, at the transition, the medium becomes soft with respect to the tilt. The corresponding dielectric susceptibility shows the Curie-Weiss law ... 

With the chiral term in the expansion, the Curie type temperature dependence of the low field soft-mode susceptibility in the smectic A phase becomes somewhat smoothed ... 

In the low field limit, expanding (9s + 89) we shall find the soft mode susceptibility of the SmC phase using exactly the same procedure as for crystalline ferroelectrics, see Eq. (13.8) ... 

Fig. 13.8 Qualitative temperature dependence of dielectric susceptibility in the SmC phase with the Goldstone mode plateau and the soft mode cusp...

Figure 14. Contributions of soft mode (a) and Gold-stone mode (b) deformations to the electric susceptibility.

Strictly speaking, even for an infinitely small electric field the second-order A-C transition disappears. However, the soft-mode dielectric susceptibility maximum characteristic of that transition is still observed at the apparent transition temper-... 

Figure 1. The voltage dependence of the shift in the soft-mode susceptibility maximum temperature [14] (a) mixture 1 (b) mixture 2, Dotted lines correspond to Eq. (6). Cell thickness 10 pm.

Quasilocal soft modes modulate the local dielectric susceptibility of the glass Scik oc aikx and therefore, causes the inelastic light scattering. As a consequence of the fluctuation-dissipation theorem the frequency and temperature dependence of the stokes Raman scattering intensity are determined by... 

The mode of action of metronidazole (Flagyl) is not well understood, but it is thought to disrupt DNA and protein syndiesis in susceptible organisms. This drug may be used in the treatment of serious infections, such as intraabdominal, bone, soft tissue, lower respiratory, gynecologic, and CNS infections caused by susceptible anaerobic (able to live without oxygen) microorganisms. 

The imaginary part of the generalied susceptibility (self part only) for the 2-d binary soft-sphere model at Feif = 1.4 is shown in Fig. 5. The peak around w 3 10 (in units of r ) corresponds to the thermal vibrations (highest-frequency mode). The peak around w = 2 is the / peak. This frequency is consistent with the time scale of the collective motions mentioned above. Therefore, these collective motions can be an origin of the / peak of x (9,w). Analyzing the temperature dependence of CMi, we have found that the size of correlated domains becomes significantly larger as the temperature is lowered. 

Alkynes are more susceptible than alkenes to external soft nucleophiles, as demonstrated in the reaction of (37) with formaldehyde, where an excess of Nal dramatic ly changes the cyclization mode (Scheme 20). ... 

If we take into account the chiral terms, the low field susceptibility would consists of two parts (the soft and Goldstone modes) ... 

Modes of resuspension interactively depend on the concentration profile. The vertical structure of concentration is conveniently subdivided into four zones (Fig. 27.11). In the upper zone the suspension layer (DSL) is dilute, and is characterized by Newtonian flow behavior. The lower zone is occupied by the benthic nepheloid layer (BNL), which contains fluid mud. In the benthic suspension layer (BSL), the concentration is intermediate between DSL and BNL. The suspension in BSL is non-Newtonian but the concentration is not high enough for setthng to be hindered. Finally, at the bottom a consolidating bed (CB) occurs. It possesses an effective stress but is soft enough (i.e., not fully consolidated) for the sediment to be susceptible to resuspension when wave forcing is sufficiently strong. 

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