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]

Typical stability diagram for a 3D ion trap. The value at = 1 along the qz axis is qz = 0.908. At the upper apex, = 0.149 998 and = 0.780 909. Drawn with data taken from March R.E and R.J. Hughes, Quadrupole Storage Mass Spectrometry, Chemical Analysis Vol. 102, Wiley Interscience, 1989. [Pg.105]

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]

The elements V2,-m describe the spatial interaction in a 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 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]

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]

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]

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]

For a transversely isotropic sheet (with 3 direction as axis of symmetry), a similar expression describes torsion about an axis perpendicular to the symmetry axis. In this case, 44 = S55 and the torque Qz is given by [Pg.179]

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]

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]

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