Distortion of lattice

The importance of lattice coupling in direct molecular dissociation is at present poorly understood. However, there are at least two ways in which inclusion of the lattice can affect direct dissociative adsorption. First, conversion of Et to Eq competes with translational activation in dissociation. Second, thermal distortion of lattice atoms from their equilibrium positions may affect the PES, e.g., the barriers to dissociation V ( ). These two effects can be most simply thought of as a phonon induced modulation of the barrier along the translational coordinate and in amplitude, respectively. 

The solution of these problems has been performed by calculation and analysis of crystal free energy (1). The alloy free energy has been found by the configurational method within the approximation of the pair interaction of nearest atoms without considering geometric distortion of lattice. This structure B8i has two types of tetrahedral T2,T4 interstitial sites, defined by different type site surroundings, and one type of octahedral 02 interstitial site... 

No dissolution has been observed within 20 ps. The distortion of lattice of the crystal is less pronounced than that of NaF despite the smaller lattice energy of KF than NaF, probably due to the smaller hydration energy of K+ than Na+. 

The muon carries charge and spin and hence is not a completely innocuous probe. The question of how much materials properties are altered by the presence of a muon appears regularly, especially in situations where pSR senses an unusual behavior that defies simple explanation. The positive charge of the muon will repel surrounding atomic nuclei. This results in a local distortion of lattice symmetry. It usually deepens the... 

As an example of uncorrelated disorder, it may be shown that diffuse scattering arising from a system containing two structural motifs which may substitute for each other at random in the lattice sites, without implying any distortion of lattice distances, corresponds to a very simple formula given by... 

Point defect or zero-dimensional defect. This kind of defects include both the possible existence of vacancies and substituted impurity atoms on their sites of crystal lattice structure and include misplaced parts of atoms with each other in solid compound of AB, namely, A atom occupies the B atomic site, while inversely B atom occupies A, or to say there are misplaced atoms or variable valence ions on the sublattice sites. The interstitial atoms sited in the interstitials of lattice structure are also parts of those point defects. It can further be divided into Schottky defects and Frenkel defect. The former means a metal atomic defect and the original metal atoms are transformed to the metal surface and the latter is composed of an atomic defect and an interstitial atom, as presented in Fig. 3.23. It could be imagined that the existence of inner defects would bring the distortions of lattice, as shown in Fig. 3.24. The issue of point defect is the major subject and key problem for the studies of solid chemistry. 

Fig. 3.24 Distortion of lattice caused by three kinds of point defects...

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

Additional x-ray studies iadicate some degree of lattice distortion ia coatiags prepared from chloride-containing coatiag solutioas. This correlates with an analysis of 3—5% chloride ia the coatiag, which is reduced to aear zero if the coatiag is heated to 800°C. 

Fig. 8.8. Martensites are always coherent with the parent lattice. They grow os thin lenses on preferred planes and in preferred directions in order to cause the least distortion of the lattice. The crystallographic relationships shown here ore for pure iron.

Figure 11.9 shows that the hardness of martensite increases rapidly with carbon content. This, again, is what we would expect. We saw in Chapter 8 that martensite is a supersaturated solid solution of C in Fe. Pure iron at room temperature would be b.c.c., but the supersaturated carbon distorts the lattice. 

Fig. 11.9. The hardness of martensite increases with carbon content because of the increasing distortion of the lattice.

In the presence of lattice distortions, the k p equation is given by the 4x4 matrix equation given by... 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

In order to study lattice relaxation effect by ASR we assume a simple model. As a first step we consider the terminal point approximation. Here the distortion of the lattice taken into account is the stretching or the contraction and angular distortion of the bond connecting two sites in a lattice and the effect of neighbouring site is neglected. As a result of such distortion the structure matrix takes the form ... 

The equilibrium clathrate of methanol has the much higher value yA = 0.47 at 25°C. This is to be expected since the methanol molecule is so large that it distorts the lattice contrary to assumption (a) of Section II.A, thereby increasing the value of Ay to be taken in Eq. 25. The methyl cyanide molecule distorts the lattice even more, and as already noted by Powell,24 its equilibrium clathrate must therefore have a value of yA still higher than that for the methanol clathrate. (The CH3CN clathrate investigated by Powell, however, was not an equilibrium clathrate, cf. point B in Fig. 5). 

Before proceeding further it should be noted that there is a great difference in severity of the restrictions imposed by the earlier assumptions (a)-(d) and the present ones, (e) and (f). The earlier ones mainly restrict the size of the enclosed molecules to such a range that they neither distort the lattice, nor give rise to multiple occupancies or quantum effects. 

Crystal Structure and Lattice Parameters (nm) Orthorhombic, a = 0.283, b = 0.554, c = 1.1470 Cr3C2 is an intermediate carbide having carbon chains with C-C distance approximately 0.165 nm running through distorted metal lattice where the Cr atoms are at the corners of trigonal prisms and the carbon atoms in the center of the prisms.i li" ... 

Note that, when considering a particular value of lattice distortion Vcj) in the previous discussion, we did not specify the wavelength(s) of the phonons that contributed to this distortion therefore the estimate of g in Eq. (19) is correct as long as the form of the interaction term (Eq. (17)) is adequate. This surely holds for long-wave phonons relevant at the TLS temperatures. 

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