This equation is from Eq. (2.60) with e = —2 as [ly, Jy] = —i2Ky. Thus, a 45° pulse can convert a state with single quantum coherence Jy) into a Ky state that contains quadrupole order Qz and double quantum coherence Kz- Note that ly and Qy are invariants of motion since they commute with the above r.f. Hamiltonian. Thus, in this case the coefficients a2 and ay are now time independent [Q, Ky are used instead of Qz Kz in Eq. (2.68)]. Precession diagrams (Fig. 2.3) also may be drawn for a quadrupole interaction with spin Hamiltonian Hq = ujqQz [Eq. (2.34) with r = 0]. In this case, there are four invariants of motion, Iz Qz Kz, and J. An initial Ix state will evolve under Hq = ujqQz by precessing about the Qz axis at a frequency ujq in the /a — Jx plane, while an initial Jy state will precess in the — ly plane at a frequency ujq. However, an initial ly state will precess in the — Jy plane at a frequency —ojq according to... [Pg.43]

The reciprocal space intensity is displayed in Fig. 7. It has the shape of a rod along the Qz axis. Any modulation of the platelet density profile along the z axis yields a form factor ... [Pg.21]

For simplicity, we assume a 2D-periodic structure ( 2D-crystallinity ) in the monolayer film floating on the subphase The molecules are arranged in identical unit cells which form a regular lattice. Then, in GID, Bragg diffraction occurs when the lateral scattering vector Qhor, c.f. Fig. 1.1b, coincides with a reciprocal lattice vector Ghk The scattering is concentrated in so-called Bragg Rods (parallel to the Qz axis), defined by two Laue conditions or, in vector notation, by the equation Qhor=Ghk- By constrast, XR... [Pg.122]

As no DC voltage is applied, the 3D trap will be operated along the qu axis, because in the absence of DC voltage, au = 0. As already explained, qz is given by the following equation ... [Pg.108]

reference axis system of choice and are connected to Qz.m by a rotation as shown in Eq. (4). The spin tensor elements 72, are given in terms of the Cartesian angular momentum operators by t... [Pg.89]

The CO scan of the (200) lattice node, obtained for the section along the qx axis at Qz = 0, is shown in Figure 7.32. As we illustrated in the previous example dealing with the study of lithium niobate, the increase in peak width is a result, in particular, of the relative disorientations of the crystals. Therefore, the width of this distribution yields an estimate of this mosaicity. For this film, we obtained a relative disorientation of 0.2°. [Pg.314]

Problem 3-27. Oscillating Cylinder as a Viscometer. Consider a cylinder immersed in a large bath of fluid with kinematic viscosity v that rotates sinusoidally about its axis with angular velocity Qz = sin( >t). The cylinder has a radius R, length L, and L/R p> 1. It is... [Pg.196]

It is important to note that, while P is a scalar density, Qz is one component of a vector density, the components transverse to the quantization axis being defined in a similar way. Analogous transition densities, in which KK is replaced by KL, are required in discussing transitions between states K and L of the system, but are not needed in the present work. [Pg.371]

For a sheet with isotropy perpendicular to the z axis, X44 = X55, so that the torque Qz about an axis perpendicular to the symmetry axis is given by... [Pg.128]

Qx = and Qz = 7r/d are the corresponding wave vectors of the instability along the x- and 2 -axis and is the electric field potential defined in (5.12). In view of this, the following dispersion relation ... [Pg.250]

For transversely isotropic sheets, a much simpler formula applies for torsion around the symmetry axis 3, where the torque Qz is given by... [Pg.179]

Thus, XR and GID measure different parts of the monolayer structure factor, corresponding to different projections of the monolayer structure. XR corresponds to the projection of the monolayer density onto the z-axis and includes also scattering from the sub-phase. GID - with Qz —0, i.e., grazing exit as well as grazing incidence - measures the structure of the 2D-crystalline part of the monolayer, as projected onto the x-y plane. Finally, measurement of the GID signal Ihk(Qz) versus Qz (so-called Bragg Rod scans) gives three-dimensional information about the 2D-crystalline part of the monolayer. [Pg.123]

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