Crystal lattice distortions

Figure 17. Crystal lattice distortion produced by the presence of (a) and (b) 0.75 ML adsorbed (on fee) and 0.25 ML absorbed oxygen in tetra-II (a) and octahedral (b) subsurface sites of Pt(lll) (c) 0.75 ML adsorbed OH (on top sites) and 0.25ML adsorbed oxygen on hep sites of Pt(lll) (d) 0.75 ML adsorbed OH (on top sites) and 0.25ML absorbed oxygen on tetra-II sites of Pt(lll) (e) 0.75 ML adsorbed OH (f) 0.75 ML adsorbed OH (on bridge sites) and 0.25 ML absorbed oxygen in tetrahedral sites of Pt(lOO).

The second inaccuracy is a mix-up between cause and effect. Obviously, the two phenomena, crystal lattice distortion and low-symmetry orbital ordering, are interrelated. However, the JT distortion can take place even without any long-range orbital ordering. Above the temperature of structural (JT) phase transition, in each elementary cell, the JT effect is still active. Considered separately from one another, due to the JT effect, elementary cells can be locally distorted. These local distortions are not ordered, and respective X-ray data provide evidence of time averaged high symmetry lattice. However, above the temperature of structural phase transition, disordered JT distortions manifest themselves in XAFS [58]. 

Miyauchi, K. and Toda, G. (1975) Effect of crystal-lattice distortion on optical transmittance of (Pb,La)(Zr,Ti)03 system, J. Am. Ceram. Soc. 58, 361. Doping PLZT with La to reduce the optical anisotropy. 

Another such example is the connection between interface stresses and crystal lattice distortion, and lamellar twisting. The latter phenomenon requires two additional ingredients, in addition to the interface stresses Firstly, the interface stresses must occur asymmetrically at the two opposite lamella surfaces [56,57], which can not be achieved in our simulations by construction of the simulation cell. Reasons for such asymmetries have to be found on different grounds. Secondly, lamellar twisting can only be predicted if also the material properties of the crystalline lamellae are incorporated, either based on experimental [58,59] or simulated data [60]. 

The solid reactions proceed very slowly, but can be speeded up by reduction of the particle size of the materials involved (i. e., larger surface area), raising of the burning temperature, presence of crystal lattice distortions. 

The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

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.

Although experimental studies of DNA and RNA structure have revealed the significant structural diversity of oligonucleotides, there are limitations to these approaches. X-ray crystallographic structures are limited to relatively small DNA duplexes, and the crystal lattice can impact the three-dimensional conformation [4]. NMR-based structural studies allow for the determination of structures in solution however, the limited amount of nuclear overhauser effect (NOE) data between nonadjacent stacked basepairs makes the determination of the overall structure of DNA difficult [5]. In addition, nanotechnology-based experiments, such as the use of optical tweezers and atomic force microscopy [6], have revealed that the forces required to distort DNA are relatively small, consistent with the structural heterogeneity observed in both DNA and RNA. 

The EFG parameters Vzz and described by (4.42a) and (4.42b) do not represent the actual EFG felt by the Mossbauer nucleus. Instead, the electron shell of the Mossbauer atom will be distorted by electrostatic interaction with the noncubic distribution of the external charges, such that the EFG becomes amplified. This phenomenon has been treated by Stemheimer [54—58], who introduced an anti-shielding factor (1 —y 00) for computation of the so-called lattice contribution to the EFG, which arises from (point) charges located on the atoms surrounding the Mossbauer atom in a crystal lattice (or a molecule). In this approach,the actual lattice contribution is given by... 

The structures of ionic compounds comprising complex ions can in many cases be derived from the structures of simple ionic compounds. A spherical ion is substituted by the complex ion and the crystal lattice is distorted in a manner adequate to account for the shape of this ion. 

A pyridine derivative related to dien with respect to the number and distribution of N-donor atoms, namely bis(2-pyridylmethyl)amine (bpma), also gives comparable complexes with Cd, e.g., [Cd(bpma)2](C104)2 with potentially three isomers (including a pair of enantiomers). As shown by the structure analysis (C2/c, Z = 4), a distorted octahedral fac-isomer with symmetry 2 —C2 has been isolated, necessarily with both enantiomers in the crystal lattice. No significant difference in the two kinds of Cd—N bonds (rav(Cd—N) 235.0 pm) is observed.189 Solid-state 13C NMR spectra of this complex and related Mn and Zn complexes have been discussed. 

Why is it possible to separate crystal size from lattice distortion — Limited crystal size broadens every reflection by the same amount20. On the other hand, the higher the order of a reflection is, the higher is the smearing effect caused by lattice distortions. 

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