Transversal effect

Quer-ebene, /. lateral plane, -effekt, m, transverse effect. -faser,/. transverse fiber cross grain, -feld, n. transverse field, cross field. 

The transverse effective conductivity 2t>eff requires a more involved computation. In this direction the DPF is a periodic medium, so its effective conductivity can be found by solving the heat conduction equation in the primary geometric unit (Fig. 34). 

A unit temperature difference is imposed to the top wall of Fig. 34 and the conductance is computed. The boundary conditions are T= 1 at the upper side, T= 0 at the bottom side and insulation for all the other sides. The gas conductivity is considered through the gas phase heat balance equation so is not taken into account here. Taking into account the gas conductivity to compute the transverse effective conductivity for the DPF structure is not correct. 

Structure, then for every tetrahedron there is another tetrahedron which has the exact opposite orientation the electric fields of the dipoles compensate each other. If, however, all tetrahedra have the same orientation or some other mutual orientation that does not allow for a compensation, then the action of all dipoles adds up and the whole crystal becomes a dipole. Two opposite faces of the crystal develop opposite electric charges. Depending on the direction of the acting force, the faces being charged are either the two faces experiencing the pressure (longitudinal effect) or two other faces in a perpendicular or an inclined direction (transversal effect). 

The conference was opened with a speech by Lorentz on the theory of electrons he had developed about 20 years before, followed by papers by Joffe on the electrical conductivity of crystals, Kamerlingh Onnes on superconductivity, and Hall on the metallic conduction and the transversal effects of the magnetic field. This last speech was followed by a discussion in which Langevin and Bridgman injected a few interesting remarks. 

The abbreviations mn and m L denote the longitudinal and transverse effective electron masses, respectively. m is the effective mass for isotropic conduction band minimum. 

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

Here /jn(f) is the intensity of the incident radiation and 0 is the phase of the interferometer in the dark. The functions N(< >) and M(< >) relate the intensities of the transmitted and intracavity fields to that of the incident light. The function 7ref (0 corresponds to the intensity of radiation from an additional source, which is very likely to be present in a real device to control the operating point. This description is valid in a plane-wave approximation, provided that we neglect transverse effects and the intracavity buildup time in comparison with the characteristic relaxation time of nonlinear response in the system. It has been shown that the Debye approximation holds for many OB systems with different mechanisms of nonlinearity. 

Provide a detailed description of the mechanism that shows precisely how transverse effects arise. 

In metals, where there is only one type of charge carrier, the Hall coefficient, Rb = (Ey / jxB), is very useful for measuring both the carrier density and the magnetic field B. Since the secondary field Ey and B are orthogonal, the Hall effect is a transverse effect and the Hall tensor is of rank three. It relates the axial vector Bj. to the antisymme-trical second-rank tensor Ey, which is equivalent to p yjx, where p y = PxyzBz-... 

It remains to discuss the influence of Hq on the mechanical relaxation modes. An estimate of this may be made by recalling that Eq. (95) is basically the equation of motion of a rigid dipole in a strong constant external field. Moreover, if inertial effects are neglected, it has been shown in Refs. 21 and 61 that the longitudinal and transverse effective relaxation times decrease monotonically with field strength from Xg, having asymptotic behavior... 

GaP (es = 11.02) determined by Vink et al. [259] allows one to also obtain an estimation of the transverse effective mass mt. The more recent data of [30] given in Table 5.2 have also been used for the calculation of the energy levels of Sica and the results obtained are close to those of [39], The calculated energy levels are given in Table 6.40, where they are compared with the results of [40], valid for the P-site donors. The optical ionization energy E-lo (Sica) derived from these calculations and from the absorption data is 86.73 meV and it compares with the value of 85meV given by Kopylov and Pikhtin [140],... 

With m in units of me, 7b = 4.2544 x 10 fi ( s/m )2 B(T). For shallow donors in multi-valley semiconductors, to is the electron transverse effective mass mnt of Table 3.4 and for QHDs in direct-band-gap semiconductors, it is the effective mass mn at the T minimum of the CB of Table 3.6. For the shallow acceptors where the effective Rydberg R oa is defined as Roo/li, Bo is equal to Rloa/jips- Values of Bo for shallow donors and acceptors in different semiconductors are given in Table 8.12. 

Expression (8.18) has been used to derive values of the transverse effective mass of donor electrons in silicon from experiments on the P donor for different orientations of the magnetic field [116]. The low-field data give mt = (0.195 0.002) me, a value slightly larger than the one derived for the free electrons from the CR experiments (see Table3.4). 

This should be an improvement to having only transverse effects. To find these on-site terms j(° it can be noticed that if one uses the DLM-MFT, the spin product vanishes, leading to ... 

Like other zinc-blende type compounds GeSi is an infrared active material. The optical phonon at the F-point is associated with an electric dipole moment which is related to the transverse effective charge e. In terms of ap and its volume derivative (see eq. (49) of Ref. [8]), is given by... 

More direct determination of electron effective masses was first performed by Kaplan et al [16] using electron cyclotron resonance (ECR) in n-type 3C-SiC epitaxially grown onto a silicon substrate. They obtained transverse effective mass m t = (0.247 0.011) n, and longitudinal effective mass m, = (0.667 0.015) m0. The effective masses derived from cyclotron resonance agree, within experimental error, with the values obtained from Zeeman luminescence studies [7] of small bulk crystals. An average effective mass of an electron, given by the equation me = (m t2m, )l/3, is 0.344m0. Recently, similar ECR measurements were made by Kono et al [17]. 

In general, good agreement is found for the longitudinal and transverse effective masses, when measured by several techniques, within the various polytypes. There is a wider variability for the values of the overall electron effective mass. Theoretical studies yield values for electron effective masses which are in good agreement with measured values. Data on hole effective masses is scarce and much of what is available is from theoretical studies. 

We can equally define a longitudinal effect for each direction I = (11,12 3) well as transverse effects (Section 4.4.2) for tensors of rank superior to 2. 

In certain directions, the transverse effect is absent. For tensors of rank 2, it is sufficient to calculate the eigenvectors of the matrix <7. Effectively, B = 0 if A satisfies... 

In order to determine the tensor longitudinal effects are measured in different directions (6 for a tensor of rank 2). A possible antisymmetric component would be neglected because it would create only transverse effects. 

Thus the transverse effect is not measured. The symmetric tensor for a triclinic crystal may be obtained from the measurement of in six different directions. Any possible antisymmetric contribution will not be revealed by these measurements (Section 4.2.5). 

The product IJJplq is invariant with espect to all permutations of the indices. The result of this is that only represents the totally symmetric part of S with respect to the indices. In particular, any possible antisymmetric component of S will only add a pure transverse effect to the transverse effects inherent to the symmetric part. 

By analogy with the electric polarization (4.47), the antisymmetric part of the tensor S does not contribute to the energy because it represents a pure transverse effect. There is no energetic reason for this effect to appear and the antisymmetric part of S is considered to be zero. The deformation energy becomes... 

The effective interstitial conductivity perpendicular to the fibers is identical with the DC transverse effective conductivity for skeletal muscle given in Equation 21.9... 

Fig. 1 Principle of field-flow fractionation. 1—Solvent reservoir, 2-carrier liquid pump, 3—injection of the sample, 4— separation channel, 5—detector, 6—computer for data acquisition, 7—transversal effective field forces, 8—longitudinal flow of the carrier liquid. A—Section of the channel demonstrating the principle of polarization FFF with two distinct zones compressed differently at the accumulation wall and the parabolic flow velocity profile. B—Section of the channel demonstrating the principle of focusing FFF with two distinct zones focused at different positions and the parabolic flow velocity profile. C—Section of the channel demonstrating the principle of steric ITF with two zones eluting at different velocities according to the distance of their centers from the accumulation wall.

Ves S, Strossner K, Cardona M (1986) Pressure dependence ofthe optical phonon frequencies and the transverse effective charge in AlSb. Solid State Common 57 483 86 Katayama Y, Tsuji K, Oyanagi H, Shimomura O (1998) Extended X-ray absorption fine structure study on hquid selenium under pressure. J Non-Cryst Solids 232-234 93-98 Gauthier M, Polian A, Besson J, Chevy A (1989) Optical properties of gallium selenide under high pressure. Phys Rev B 40 3837-3854... 

Goi AR, Siegle H, Syassen K et al (2001) Effect of pressure on optical phonon modes and transverse effective charges in GaN and AIN. Phys Rev B 64 035205... 

Reparaz JS, Muniz LR, Wagner MR et al (2010) Reduction of the transverse effective charge of optical phonons in ZnO under pressure. Appl Phys Lett 96 231906... 

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