Disorders virtual crystal

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

Thus, we study the binary alloy (cf. Section IV.B) with the intermolecular interactions W of Section I. We are in the case of weak disorder A W, e.g. of a virtual crystal with one polariton band, and for A W we have separation into two bands, around vA and vB, each one embodying a polariton broadened by the disorder. 

Virtual Crystal Approach for the Study of Disordered Perovskites. 

There are two possible shortcomings of our calculations. One is the neglect of off-diagonal disorder and the other is setting the on-site parameter for a vacancy equal to infinity. The off-diagonal matrix elements in our Hamiltonian are treated in a virtual crystal sense which is adequate only when the parameters involved are similar. On the other hand we have found that the "infinity" assumption is reliable for alloys with high hydrogen content. 

We shall see that the coherent potential defined in this way is different from the simple potential of a disordered system obtained by averaging the potentials of the components according to the composition of the system. This latter, so-called virtual crystal approximation only gives acceptable results if the different chemical components of the system are rather similar. ... 

Focusing on the high-temperature cubic phase, the high degree of disorder in the Ag and Bi atoms makes the exact electronic band stmcture calculations impossible. For treating such materials systems by first principles methods, two general methods have been usually carried out, i.e., the supercell method and the virtual crystal approximation (VGA) method [8], but the VGA method is not well suited to simulate the details of this phase transition although it is simpler and more efiftcient. So, in our case, a cubic superceU with 64 atoms is used for the disordered phase in the supercell approximation. 

There are practical problems in achieving a true virtual crystal. For example, to avoid some amount of disorder in the lattice, the average number of A atoms which were second-nearest-neighbors to B atoms in an Ai.xBxC alloy would have to be constant. At a composition of x = 0.5, this would mean that every B atom would have two A atoms and two B atoms for second-nearest-neighbors. This arrangement exists in some materials and leads to structures such as chalcopyrite. Such a well-organized structure is no longer a random alloy. Rather, it is a new compound with unique symmetry and, consequently, a different band structure. Thus, even in the perfectly distributed alloy case, one can expect to have deviations from a virtual crystal behavior because a perfect distribution is not random. The reason a virtual crystal... 

As mentioned above, the /3 phase of (ET)2l3 undergoes a structural order-disorder transition at 175 K. Based on the different crystal structures at 9K under ambient pressure [157] and at 4.5K under 1.5kbar [158], the band structures have been determined [155]. However, virtually no difference is found from the calculations. 

The crystal structure of [Bu N] jRe2Clg has been described. The molecules exhibit a subtle form of disorder such that 74 % of the Re—Re units are aligned in one direction with the remaining 26 % perpendicular to this direction. On the basis of this structural information it has been found possible to determine the polarization relative to the molecular axis of the absorption band at ca. 700 nm. The bond is found to be entirely Z polarized, which virtually assures its assignment to the 6 6 transition. The... 

Mixed crystal is a homogeneous crystal of two or more substances. Solid solution is a homogeneous solid mixture of substances. Both are virtually equal, although the latter can be amorphous. In general, mixed crystals are obtained from molecules of similar shapes and sizes. The forces between molecules are usually weak. Compositions can vary throughout a certain range and crystal structures are disordered,... 

Disordering of the crystal structure is not an error on the part of the crystallographer unless it goes undetected. That said, a disorder presents its own set of practical problems for setup in a virtual screen. Disorder reflects a situation where a part of the underlying molecule can be positioned in alternative locations. If detected, the modeler is effectively presented with two or more different models for the protein in question. The modeler then has to decide whether to dock into one or the other, or dock into both. Ensemble and flexible side chain docking methods are well suited to this problem, as they allow the user to model multiple conformations in a single docking run. 

The structure of the free Diels-Alderase ribozyme was found to be virtually identical to the structure of the product complex, providing strong support for the concept of a preformed catalytic pocket, established by chemical probing. The anthracene-RNA conjugate could also be crystallized, however, the anthracene module and its linker were found to be disordered in the crystal. The RNA mapped well with the other crystal structures. 

There exist crystals which have much more equivalent lattice sites available for one type of ion than ions are present in the lattice. At sufficiently high temperatures all ions are mobile and may be statistically distributed among these lattice sites. In this case we say a partial lattice of the crystal is in a quasi-molten state, the crystal has now a structural disorder. If such a disorder is present, the natural limit of the concentration of the mobile species is reached because all ions of one kind are now mobile. The best electrolytes known have such a disorder. Examples for such types are among others RbAg4l5 at room temperature and Agl above 149°C. At this temperature Agl makes a transition from the p to the oc phase the partial lattice of Ag becomes quasi-molten, and there exist regions throughout which the silver ions virtually perform random motions as shown in Fig. 3. 

In order to illustrate the problem, let us take a KCl crystal which has been doped with CaCl2. The concentration of dopant is much greater than the thermal Schottky disorder of the pure crystal. Thus, in the absence of interaction between the defects, the number of dissolved Ca ions is virtually equal to the number of cation vacancies V. However, as described in section 3.2.2, neutral associates will form by virtue of elastic and electrical interactions. Their energy of formation is of the order of 1 kcal/mole. Therefore, at constant P and T, there exists a dynamic equilibrium of the form... 

---