Interstitial region

The LMTO method [58, 79] can be considered to be the linear version of the KKR teclmique. According to official LMTO historians, the method has now reached its third generation [79] the first starting with Andersen in 1975 [58], the second connnonly known as TB-LMTO. In the LMTO approach, the wavefimction is expanded in a basis of so-called muffin-tin orbitals. These orbitals are adapted to the potential by constmcting them from solutions of the radial Scln-ddinger equation so as to fomi a minimal basis set. Interstitial properties are represented by Hankel fiinctions, which means that, in contrast to the LAPW teclmique, the orbitals are localized in real space. The small basis set makes the method fast computationally, yet at the same time it restricts the accuracy. The localization of the basis fiinctions diminishes the quality of the description of the wavefimction in die interstitial region. 

Calculations were done with a full-potential version of the LMTO method with nonoverlapping spheres. The contributions from the interstitial region were accounted for by expanding the products of Hankel functions in a series of atom-ce- -ered Hankels of three different kinetic energies. The corrected tetrahedron method was used for Brillouin zone integration. Electronic exchange and correlation contributions to the total energy were obtained from the local-density functional calculated by Ceperley and Alder " and parametrized by Vosko, Wilk, and Nusair. ... 

We will refer to this as the one center expansion. The components pRx are easily calculated in LMTO and are known on a radial mesh. In the interstitial region we choose to expand the charge density in the SSW s xp) and their first two energy derivatives. 

Typically we fit up to the / = 3 components of the one center expansion. This gives a maximum of 16 components (some may be zero from the crystal symmetry). For the lowest symmetry structures we thus have 48 basis functions per atom. For silicon this number reduces to 6 per atom. The number of random points required depends upon the volume of the interstitial region. On average we require a few tens of points for each missing empty sphere. In order to get well localised SSW s we use a negative energy. 

In the alveolar-interstitial region, human lung clearance has been measured. The ICRP model uses two half-times to represent clearance about 30% of the particles have a 30-day half-time, and the remaining 70% are assigned a half-time of several hundred days. Over time, AI particle transport falls, and some compounds have been found in lungs 10-50 years after exposure. 

Re-organization of amorphous chains in the interstitial regions between pre-existing crystallites leads to the formation of secondary crystallites. The new crystallites have smaller a , b , and "c dimensions than the primary crystallites. 

It has been known since the mid 1950s that graphite can form intercalation compounds with lithium ions, which are accommodated in the interstitial region between the planar graphene sheets. ° The most lithium-enriched intercalation compound of this family has a stoichiometry of LiCe, and its chemical reactivity is very similar to that of lithium metal. There have been a number of different chemical approaches to the preparation of these compounds, for example, by direct reactions of graphite with molten lithium at 350 with... 

It was noted earlier that the charge density of a narrow resonance band lies within the atoms rather than in the interstitial regions of the crystal in contrast to the main conduction electron density. In this sense it is sometimes said to be localized. However, the charge density from each state in the band is divided among many atoms and it is only when all states up to the Fermi level have contributed that the correct average number of electrons per atom is produced. In a rare earth such as terbium the 8 4f electrons are essentially in atomic 4f states and the number of 4f electrons per atom is fixed without reference to the Fermi level. In this case the f-states are also said to be locaUzed but in a very different sense. Unfortunately the two senses are often confused in literature on the actinides and, in order not to do so here, we shall refer to resonant states and Mott-localized states specifically. 

The pseudopotential method relies on the separation (in both energy and space) of electrons into core and valence electrons and implies that most physical and chemical properties of materials are determined by valence electrons in the interstitial region. One can therefore combine the full ionic potential with that of the core electrons to give an effective potential (called the pseudopotential), which acts on the valence electrons only. On top of this, one can also remove the rapid oscillations of the valence wavefunctions inside the core region such that the resulting wavefunction and potential are smooth. 

---