Field-induced transition

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

Class II AF, with a SF field induced transition from the AF ground state dReversed coercivity in the isothermal hysteresis loop Expected structural motif, crystal structure not determined fNo CW behavior, 6 value obtained at high temperatures ECoercive field... 

Various types of work in addition to pV work are frequently involved in experimental studies. Research on chemical equilibria for example may involve surfaces or phases at different electric or magnetic potentials [11], We will here look briefly at field-induced transitions, a topic of considerable interest in materials science. Examples are stress-induced formation of piezoelectric phases, electric polarization-induced formation of dielectrica and field-induced order-disorder transitions, such as for environmentally friendly magnetic refrigeration. 

Sushko YV, Ito H, Ishiguro T, Horiuchi S, Saito G (1993) Magnetic-field-induced transition to resistive phase in superconducting k-(BEDT-TTF)2Cu[N(CN)2]C1. J Phys Soc Jpn 62 3372-3375... 

In n-type GaAs Ming-Way Lee et al. (1988) used far-infrared optical absorption to show that, in the metallic state near the magnetic-field-induced transition, the ls-2p absorption by donors persists, giving evidence that the transition lies in an impurity band. 

Kadomtseva et al. (2000) measured thermal expansion and longitudinal and transverse magnetostriction in pulsed magnetic fields up to 25 T in Lai - Sr MnOj single crystals (x = 0.1,0.125 and 0.15). The results were ascribed to a suppression of the O phase and field-induced transitions to a new orbital-ordered ferromagnetic state. 

When a) l/n3, the field required for ionization is E = 1/9n4, and as a> approaches l/n3 it falls to E=0.04n. These observations can be explained qualitatively in the following way. At low n, so that a> 1/n3, the microwave field induces transitions between the Stark states of the same n and m by means of the second order Stark effect. With only a first order Stark shift a state always has the same dipole moment and wavefunction, as indicated by the constant slope dW/d of the energy level curve. Thus when the field reverses, — — , the Rydberg electron s orbit does not change. With a second order Stark shift as well, the slope dW/d is not the same at E and —E, and as a result the dipole moment and wavefunction are not the same. If the field is reversed suddenly a single Stark state in the field E is projected onto several Stark states of the same n and m when E — - E. Since all the Stark states of the same n make transitions among themselves they ionize once the field is adequate to ionize one of them, the red one, at E = 1/9n4 for m n. 

Nakata M, Link DR, Takanishi Y, Takahasi Y, Thisayukta J, Niwano H, Coleman DA, Watanabe J, Iida A, Clark NA, Takezoe H (2005) Electric-field-induced transition between the polarization-modulated and ferroelectric smectic-CgPf liquid crystalline states studied using microbeam X-ray diffraction. Phys Rev E 71 011705... 

The list of materials which displayed such type of behaviour contains amorphous Mo Gei j, [1] and Moa,Sii a [2] films, amorphous InOx films [3, 4], ultrathin films of Be [5], crystalline films of Nd2-a Cea Cu04+y [6, 7]. Two typical examples of such sets of curves relevant to different limits are presented in Figs. 1 and 2. In Nd2-a Cea Cu04+ / (Fig. 1) the growth of the resistance with decreasing temperature on the non-superconducting side of the field-induced transition was below ten percent so that it reminded more a metal with quantum corrections to its conductivity than an insulator. In amorphous InO (Fig. 2), typical for insulator exponential temperature dependence of the resistance resulted in almost tenfold increase of the resistance. 

An effective scheme for controlling elementary process (i) has been proposed, which is based on the idea of quadratic chirping [24-29]. It is now well-established that laser field-induced transitions among energy levels can... 

Fig. 3.7. Field-induced transition from metallic to insulating regime, (a) W vs. T for a metallic PPV-H2SO4 sample (E from Fig. 3.4) at 0, 5 and 8 T fields, (b) Conductivity vs. T01 fit for the same data...

Fig. 3.9. W vs. T for a PPy-PF6 sample in the critical regime. The pressure-induced transition to the metallic regime and the field-induced transition to the...

In cholesterics, the structure is similar to nematics, but the director rotates in a corkscrewlike fashion along n. Electric-field-induced transitions between the cholesteric and nematic phases are used in the dye phase change display discussed below. 

To conclude, we have shown that the specific shape of Hc2(T) observed in the cobalt oxide superconductor can be explained in terms of the field-induced transition from singlet to triplet pairing. This scenario assumes a competition between singlet and triplet types of superconductivity, which remains in... 

Figure 12 Energy diagram for 5 = 3/2 spin system with E/D = 0. Typically the separation (2D) between each pair of doublets is much larger than the irradiating microwave field inducing transitions. Therefore, transitions only occur within each doublet and not between them...

A. C. Morteani, P. K. H. Ho, R. H. Friend, and C. Silva. Electric field-induced transition from heterojunction to bulk charge recombination in bilayer polymer light-emitting diodes. Appl. Phys. Lett., 86 163501, 2005. 

The setup for the first fine structure measurement is shown in Fig. 6(12). A slow e beam strikes a wall of a microwave cavity. The microwave electric field induces transitions from 2 S, to 2 Pj. Lyman a photons are detected in coincidence with IS annihilation y rays as the microwave frequency is swept through the resonance line. 

Here nd are elastic constants. The first, is associated with a splay deformation, K2 is associated with a twist deformation and with bend (figure C2.2.11). These three elastic constants are termed the Frank elastic constants of a nematic phase. Since they control the variation of the director orientation, they influence the scattering of light by a nematic and so can be determined from light-scattering experiments. Other techniques exploit electric or magnetic field-induced transitions in well-defined geometries (Freedericksz transitions, see section (C2.2.4.1I [20, M]. 

It is also possible to calculate field-induced transition dipole moments. When Pk Pk i the field-induced transition dipole moment between two states is given approximately by... 

All of these electronic transitions are technically forbidden by Laporte s rule, which states that electronic transitions can only occur if the orbital angular momentum changes by 1 during the transition. Since this does not occur for transitions from one d state to another d state, or from one f state to another f state, no absorption should occur for these ions. Fortunately, Laporte s rule is relaxed in solids due to the lack of perfect spherical symmetry, which results from the presence of a limited number of point sources, so that electronic transitions can occur with a low probability between 3d or 4f levels which are split by the fields of the neighboring ligands. The low probability of these transitions, however, does reduce the intensity of the absorption. As a result, ligand field induced transitions are much weaker than the charge transfer effects which occur in the ultraviolet. 

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