Displacements from ideal positions

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

The behaviour of Re03 in a variety of aqueous, acidic solutions has been studied and the nature of the species formed discussed.668 A low-temperature neutron-diffraction study of cubic Ba2CoReOe has shown that the oxygen atoms are slightly displaced from the positions of an ideal perovskite towards the rhenium atoms, and... 

Table 9. Experimentally determined and calculated values of displacements of Si atoms from ideal positions, the distance between Al adatom and the second-layer Si atom and bond lengths in the...

Table 41. Displacement of Si atoms from ideal positions in the Si(lll) Vs xVs-Pb a-phase T4 adatom model) as determined using LEED I-V analysis [91D3]. Ar corresponds to lateral displacement towards adatom, Az corresponds to vertical displacement into the bulk. Atoms are numbered as in Fig. 73.

Fig. 73. Side view of the Si(l 11)X /3 -Pb (a phase, 1/3 ML Pb) T 4 Pb-adatom model. The values of displacements of Si atoms from ideal positions, the distance between Pb adatom and second-layer Si atom and the bond lengths are listed in Tables 41 and 42. Pb adatom is shown in black and Si atoms in white.

By relaxation of a substrate surface we mean small atomic displacements from ideal or clean-substrate positions. The displacements shall be small compared to near-neighbor distances, such that no rebonding (bond breaking or new bond formation) takes place within the substrate. Such relaxation may induce the formation of a two-dimensional superlattice if the displacements modify the initial substrate surface symmetry. This is especially common in adsorption, since the adsorbate itself often creates a superlattice. 

All real crystals have deviation from the ideal crystallographic structure due to atomic displacements from their ideal positions in the unit cell. These displacements may... 

Pei et al. looked at the structure of the orthorhombic phase of Ba1 xKxBiOs powders by time of flight powder neutron diffraction (59). Neutron diffraction intensities should be considerably more sensitive to oxygen atom positions than are X-ray diffraction intensities for compounds such as this. The structural parameters at 300K for x=0.1 and x=0.2 are presented in Table 5. The crystal structure is the same as that of BaPbOs (Table 2) with small differences in cell parameters and atomic coordinates. The refinements show that the atoms are displaced from the ideal positions by many standard deviations, and the thermal parameters for the oxygen atoms make physical sense. The crystal structure is one in which relatively regular Bi-O octahedra (Bi-O distances... 

Vibrational energy and transitions As seen in Fig. 3.2a, the bond between the two atoms in a diatomic molecule can be viewed as a vibrating spring in which, as the internuclear distance changes from the equilibrium value rc, the atoms experience a force that tends to restore them to the equilibrium position. The ideal, or harmonic, oscillator is defined as one that obeys Hooke s law that is, the restoring force F on the atoms in a diatomic molecule is proportional to their displacement from the equilibrium position. 

Figure 5.16 Willis clusters in UOj+y Open circles, oxygens small filled circles, uranium atoms in the UO2 structure. A 2 2 2 defect cluster consists of two interstitial oxygen atoms (large filled circles) and two normal oxygen atoms displaced from their ideal positions (open squares) to new interstitial positions (hatched circles). A 2 1 2 defect cluster would consist of one interstitial oxygen and two normal oxygens displaced from their ideal positions. (After Anderson, 19726.)...

Figure 7. Idealized model of the thermal anisotropy of the atoms located in the Cr-H-Cr plane based on the representation of the nuclear thermal ellipsoids of axial carbonyl atoms as composites of two half-carbon and half-oxygen atoms, each displaced from their neutron-determined positions by ca. 0.08 and 0.15 A, respectively. The estimated overlap region in the bond lies near the centrosym-metric midpoint of the Cr-Cr line in accord with a closed-type,...

Thermally-induced network vibrations broaden the absorption edge and shift the band gap of semiconductors. The thermal disorder couples to the optical transition through the deformation potential, which describes how the electronic energy varies with the displacement of the atoms. The bond strain in an amorphous material is also a displacement of atoms from their ideal position, and can be described by a similar approach. The description of static disorder in terms of frozen phonons is a helpful concept which goes back 20 years. Amorphous materials, of course, also have the additional disordering of the real phonon vibrations. 

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