Defective lattice method

The simulations reported here of perfect (bulk) and defective lattices are described in some detail in Chapters 3 and 7 of this volume. The methods have been applied to an ever increasing range of ceramic materials over the past 15 years (e.g. Catlow and Mackrodt, 1982 Cormack 1993). The same ionic model is used throughout wherein charges are assigned to ions according to the conventional valence rules, i.e. 2+ for copper, calcium and strontium,... 

Since the partide collisions are localized, different regions of configuration space can be advanced concurrently, so that the LGA-based method lends itself readily to parallelization. Although this approach makes simulations much more effi-dent than continuum methods, it was found that LGA suffers horn several native defects lattice artifacts, lack of Galilean invariance, and so on. 

Lutsko J F ef a/1989 Molecular-dynamic study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential Phys. Rev. B 40 2841... 

Catlow C R A and W C Mackrodt 1982. Theory of Simulation Methods for Lattice and Defect Energy Calculations in Crystals. In Lecture Notes in Physics 166 (Comput. Simul. Solids), pp. 3-20. 

Sometimes, the system of interest is not the inhnite crystal, but an anomaly in the crystal, such as an extra atom adsorbed in the crystal. In this case, the inhnite symmetry of the crystal is not rigorously correct. The most widely used means for modeling defects is the Mott-Littleton defect method. It is a means for performing an energy minimization in a localized region of the lattice. The method incorporates a continuum description of the polarization for the remainder of the crystal. 

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro-... 

Further improvements on the previously discussed models were proposed in the latest model for y - and e - Mn02 by Chabre and Pannetier [12, 43, 44], Starting from De Wolff s model they developed a structural description of manganese dioxides that accounts for the scattering function of all y - and e - Mn02 materials and provides a method of characterizing them quantitatively in terms of structural defects. All y — and e - Mn02 samples can be described on the basis of an ideal ramsdellite lattice affected by two kinds of defects ... 

Point defects are changes at atomistic levels, while line and volume defects are changes in stacking of planes or groups of atoms (molecules) m the structure. Note that the curangement (structure) of the individual atoms (ions) are not affected, only the method in which the structure units are assembled. Let us now examine each of these three types of defects in more detail, starting with the one-dimensional lattice defect amd then with the multi-dimensional defects. We will find that specific types have been found to be associated with each t3rpe of dimensional defect which have specific effects upon the stability of the solid structure. 

The explanation lies in the defect reactions controlling the formation of the phosphor itself. The defect reactions occurring were found to be the substitution of a trlvalent cation on a divalent site and the defects reactions thereby associated. This is shown in the following table which compares these two methods of preparing such materials. In this case, the increase in brightness was found to be related to the amount of activator actually being incorporated into the lattice. It is well known that phosphor brightness is proportional to the numbers of Sb3+ ions (activators) actually incorporated into cation sites of the pyrophosphate structure. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

Alkaline earth oxides (AEO = MgO, CaO, and SrO) doped with 5 mol% Nd203 have been synthesised either by evaporation of nitrate solutions and decomposition, or by sol-gel method. The samples have been characterised by chemical analysis, specific surface area measurement, XRD, CO2-TPD, and FTIR spectroscopy. Their catalytic properties in propane oxidative dehydrogenation have been studied. According to detailed XRD analyses, solid solution formation took place, leading to structural defects which were agglomerated or dispersed, their relative amounts depending on the preparation procedure and on the alkaline-earth ion size match with Nd3+. Relationships between catalyst synthesis conditions, lattice defects, basicity of the solids and catalytic performance are discussed. 

At variance with the evaporated samples, Am and did not change much for the sol-gel ones, in spite of the difference between AE cation radii size (Fig. lb, c). It can be suggested that the sol-gel method succeeded in better introduction of Nd into a solid solution (supported by the TPD results) which also depended to a lower extent on the cation radii size match. The increase of the lattice anisotropy AO (Fig. Id) and the trend of the local strain values to decrease or remain about constant (Fig. lc) indicated that there was competition between disorder sources of different nature dispersed lattice defects and Nd3+ agglomerates. 

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