Ewald procedure

For ionic crystals, within the classical treatment of ion motion (see (2)), and for molecular crystals in the Frenkel exciton spectral region (see (3) and Section 2.2), the Ewald procedure was successfully used to exclude the macroscopic part of longitudinal field. This permitted one to compute the tensor e j(w, k) using the... 

Most simulations of amorphous materials have described the structure in terms of a large simulation box to which periodic boundary conditions are applied. The periodicity is, of course, artificial, but if the simulation box is sufficiently large the effect of imposing periodicity should be unimportant. Given this approximation we may use the standard Ewald procedure (Chapter 4) for undertaking the Coulomb summation. 

The hypersphere method, as discussed below, is a very efficient way to sample the configurations of charged or dipolar particles, in particular, because the pair potentials have a closed analytical expression. It was demonstrated to give results identical to those obtained by using the Ewald procedure. The method is certainly an eloquent illustration of the equivalence... 

While FMM has opened the door to greatly improved efficiency in lattice sum evaluation, it may be useful to observe that (unlike the Ewald procedure) it is not a... 

Establishing kinematical BE and weak beam DF conditions. The procedures to be followed for establishing these diffracting conditions are best described in terms of the Ewald sphere construction (Sections 3.4 and 3.7). 

Figure 5.19. Ewald sphere diagrams and corresponding diffraction patterns illustrating the procedures for setting up the conditions for weak beam dark field imaging using the first-order diffracted beam g. Continued, p. 160)...

Before discussing this new method it is useful to recall briefly the methods which we have already discussed. Note, first of all that calculations of the dielectric tensor must be based, as is known, upon a microscopic theory Such a theory for ionic crystals was first developed by Born and Ewald (2) for the infrared spectral region. The application of this approach for the region of exciton resonances has also been demonstrated in (3). In an approach identical to that of Born and Ewald (2) the mechanical excitons (see Section 2.2) are taken as states of zeroth-approximation. In the calculation of these states the Coulomb interaction between charges has to be taken into consideration without the contribution of the long-range macroscopic part of the longitudinal electric field. If this procedure can be carried out, then the Maxwell total macroscopic fields E and H can be taken as perturbations. In the first order of perturbation theory, we find... 

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