Bulk calculation

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Section 4.6 The calculations of the surface energy were as in Section 4.5, with the addition of the energy calculation of Cu in the bulk phase. The bulk calculation was carried out on an fee primitive cell with the DFT-optimized lattice parameter using llxllxll k points. 

In Table 2 we summarize the results of the DDCI calculations on the lowest excitation energies for terrace, step and comer F and F+ centers. As expected, for a given transition the excitation energy decreases as the coordination of the defect decreases. For F centers, the allowed singlet to singlet lowest transition occurs at 3.4 eV for the surface, 2.9 eV for the step and 2.6 eV for the comer. The same trend is found for the F+ centers, where the first doublet to doublet transition, goes from 3.6 eV for the surface, to 2.6 eV for the step and 2.4 eV for the comer. As observed previously for the bulk calculations, excitations for the F+ centers appear around 0.2 eV below the excitations due to F centers. The excitations at the step and comer sites are shifted about 0.5-1.2 eV compared to... 

The NRL tight-binding method has been used to address the adsorption of 02 on Pt(l 1 1) [99]. The Pt-Pt interactions were taken from a large data base of TB parameter for the elements which are posted on the world wide web [100]. These parameters were obtained from a fit to DFT bulk calculations. Still, it has been demonstrated that the pure Pt surface is also well-described by this parametrization [42], For the Pt-O and the 0-0 TB parameters a new fit had to be performed. They were adjusted in order to reproduce the GGA-DFT results of the 02/Pt(l 1 1) potential energy surface [91, 92], The root mean square error of the fit is below 0.1 eV [41] which is in the range of the error of the GGA-DFT calculations. The spin state of the oxygen molecule was not explicitly considered in the... 

Cost increases exponentially with the dimensionality of the system, following approximately the progression 1 2 8 30 from 0-D to 3-D. In this simple case, even the bulk calculation takes only a few seconds on a small PC. 

The cost of a bulk calculation is primarily a function of the unit cell size. Figure A2.2 shows the total time required for the calculation of the total energy with the MgO supercells that we used in the study of trapped-hole centers. We are considering the supercells before creating the defect. Therefore, the system possesses the full symmetry of the perfect crystal (48 point-symmetry operations). Calculations refer to the S4, Sg, Sie, S32, Sg4, S128, and S256 supercells nine AOs are used for every ion, so that the largest cell contains 4608 basis functions. 

Figure 1. Total density of states (DOS), in eV" per atom, for the majority and minority spin channels of bcc Fe bulk calculated with the TB-LMTO method (upper panel) and with Siesta (lower panel) using two different basis sets double zeta (continuous line) cind single zeta (dashed line), both of them including an extra p polarizing orbital.

In slab calculations [852] the displacements in the first two top planes were taken into account, which are considerably larger than those in deeper planes. Similar to the bulk calculations, the FM stoichiometric (110) slab for the O termination turns out to be energetically more favorable than AFM, by 0.9 eV per Mn. The calculated O-terminated surface energy is 3.5 eV for the unrelaxed slab and 0.7 eV for the relaxed one, i.e. the relaxation energy (per surface unit cell) is 2.8 eV. 

Using the Langmuir isotherm one cannot obtain a surface area number, unless one knows how the surface sites are distributed. If one knows that the approximate area required for one bonding location is 0.2 nm then one can conclude from a calculation of % what the area is. An assumption implied in this is that the activity of the surface site is proportional to the number of sites available divided by the original number, i.e. the mole fraction of species on the surface. In bulk calculations, this is referred to as the saturation limit. The assumption that full saturation is the same as the number of original sites may not be valid either in the bulk or on surfaces. 

Fig. 6.44 Normalized vacancy profiles for low symmetry ( S13) and high symmetry tilt grain boimdaries (E 3, 70.5° tilt grain boimdary) as obtained from the in-situ measurements shown in Fig. 6.43. In the case of the low-symmetry grain boundary (left) the fit reveals a space charge potential of 450 mV. In the case of the E 3 grain boimdary (right) the influence of grain boundary does not show up (corresponding to an upper limit of 300 mV for the potential), the continuous line corresponds to the bulk calculation with an effective surface rate constant of 3.6 x 10 cm/s (see following section). Prom Ref. [447].

Figure 8 shows Si/C stoichiometries of the PAS films measured by XPS. It is apparent that the Si/C ratio increases with increasing PDMS content for all PAS films. The thin line in Fig. 8 shows the Si/C ratio in bulk calculated from the PDMS contents. The Si/C ratio was approximately 44% when the... 

Figure 8 Si/C stoichiometries of PAS surface by XPS with PDMS contents (o) prepared by casting, ( ) prepared by spin-coating, (A) prepared by water-casting, ( ) Si/C in bulk, calculated from PDMS content.

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