Shift distortions

Figure 8.7 Digital Sine function - the frequency response for a zero order hold interpolator sample rate converter with L = 4, which puts the original Nyquist frequency at 0.25 7t. We can see rolloff in the passband of about -3.9 dB and very poor rejection of images outside of the passband, which result in artifacts perceived as pitch shifting distortion.

Note here how twistlike movements of the Tchek henchmark account for more risk than the shift distortions themselves. A simpler, duration-hased model would severely underforecast risk. 

Katritzky and Topsom have reviewed the information available, largely from infrared and n.m.r. studies, concerning the distortion of the tt-electron system in the benzene ring brought about in the ground state by substituents. Of particular interest is the observation that both n.m.r. studies (of m- F and chemical shifts) and infrared investigations (of the intensities of bands due to certain skeletal vibrations) suggest that the value of Taft s [Pg.226]

FIGURE 13 18 The appear ance of the splitting pattern of two coupled protons de pends on their coupling con stant d and the chemical shift difference Av between them As the ratio Av/d de creases the doublets be come increasingly distorted When the two protons have the same chemical shift no splitting IS observed... 

Distortions or shifts of a region that is aligned correctly with the template structures. 

It is known that a metallic ID system is unstable against lattice distortion and turns into an insulator. In CNTs instabilities associated two kinds of distortions are possible, in-plane and out-of-plane distortions as shown in Fig. 8. The inplane or Kekuld distortion has the form that the hexagon network has alternating short and long bonds (-u and 2u, respectively) like in the classical benzene molecule [8,9,10]. Due to the distortion the first Brillouin zone reduees to one-third of the original one and both K and K points are folded onto the F point in a new Brillouin zone. For an out-of-plane distortion the sites A and B are displaced up and down ( 2) with respect to the cylindrical surface [11]. Because of a finite curvature of a CNT the mirror symmetry about its surface are broken and thus the energy of sites A and B shift in the opposite direction. 

Fig. 8. Lattice distortions in a graphite sheet. For an in-plane distortion (left), the bond denoted by a thin line becomes shorter and that denoted by a thick line becomes longer, leading to a unit cell three times as large as the original. For an out-of-plane distortion (right), an atom denoted by a black dot is shifted down and that denoted by a white circle moves up.

The structure of KNbF6 consists of potassium ions and isolated NbF6 complex ions that were shown by Bode and Dohren to occur in the lattice in a configuration similar to that of a-CsCl [165]. The complex anion Nb(Ta)F6 has a configuration of a distorted bi-pyramid (four fluorine atoms are shifted in pairs from their positions in the basic plane, towards the vertexes). The structure of KNb(Ta)F6 compounds and of the Nb(Ta)F6 polyhedron are shown in Fig. 26. Nb/Ta-F distances are equal to 2.13 and 2.15 A, respectively, and F-F distances are 2.61, 3.03, 3.22 and 3.55 A. Each potassium atom is surrounded by 12 fluorine atoms that are at unequal distances from each other 8 of them are 2.50 A apart and four others are 2.94 A apart. 

According to crystal analysis performed by Stomberg [173], Na2NbOF5 is made up of sodium ions and isolated NbOF52 complex ions and is similar in structure to FeWC>6. NbOFs2" polyhedrons comprise slightly distorted octahedrons that are located in one of two equivalent positions. The niobium atom is shifted 0.234 A from the equatorial plane towards the oxygen atom. 

The niobium atom has a slightly distorted octahedral coordination. Interatomic distances between the niobium atom and the two oxygen atoms in trans positions, O-Nb-O are 1.81 and 2.14 A. The niobium atom is shifted from the base plane of the octahedron by 0.23 A, and this shift, in adjacent chains, is in opposite directions. Pakhomov and Kaidalova [204] concluded that the shorter Nb-O bond (1.81 A) is an intermediate between a single and double bond. 

The polyhedron NbF72 is more similar to a pentagonal bi-pyramid but is distorted due to a strong shift of F6 towards F3 (F6F3 and FiF distances are 2.39 and 3.08 A, respectively). This distortion renders the polyhedron structure closer to an Archimedes antiprism with a truncated comer, as shown in Fig. 31. 

However, other data such as the small difference observed in the Si NMR chemical shift (0.9 ppm upheld from TgPhg) and the absence of any measurable Si-F coupling show that the interaction between the huoride ion and the silicon atoms is small. Studies to evaluate the collision cross section of TgPhg using Na show that the cation attaches itself to the outside of the POSS cage and does not significantly distort the structure. 

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