Allowed band structure-solids

Eqn(3) allows a direct determination of LRO-parameter from resistivity measurement by using the constant A as a fit parameter. Eqn(l) is of more complicated character, where besides the SRO-parameters in the different coordination spheres there enter details of the band structure (Y,) which influence sign and magnitude of resistivity variation with degree of SRO. However, restricting to nearest neighbours and using an adequate model for the dependence of a on temperature and concentration, reliable SRO-parameters have been deduced from resistivity measurement for several solid solutions. ... 

First reported by Fredenhagen in 1926 F3, F4), the graphite-alkali-metal compounds possess a relative simplicity with respect to other intercalation compounds. To the physicist, their uncomplicated structure and well defined stoichiometry permit reasonable band-structure calculations to be made S2,12) to the chemist, their identity as solid, "infinite radical-anions frequently allows their useful chemical substitution for such homogeneous, molecular-basis reductants as alkali metal-amines and aromatic radical anions N2, B5). 

The band theory of solids provides a clear set of criteria for distinguishing between conductors (metals), insulators and semiconductors. As we have seen, a conductor must posses an upper range of allowed levels that are only partially filled with valence electrons. These levels can be within a single band, or they can be the combination of two overlapping bands. A band structure of this type is known as a conduction band. 

Schematic parabolic band structure for CdSe, which has a band gap of 1.75 eV. The conduction band is labeled C, and several valence bands (V,) are shown. The filled and open circle symbols indicate the position of quantized k values mr/ai allowed for the / = 1 and n = 2 states of an NC with radius a. The solid arrow shows the / = 1 transition in which an electron is excited and a hole is created (open circle). The dashed arrow shows how the position of this n = i transition would change for a nanocrystal of smaller radius 32- (Adapted from Ref. 7.) This simple diagram is for the cubic zinc blend structure the hexagonal wurtzite structure has a small gap k= 0 between the and V2 bands.

The electronic structure of solids and surfaces is usually described in terms of band structure. To this end, a unit cell containing a given number of atoms is periodically repeated in three dimensions to account for the infinite nature of the crystalline solid, and the Schrodinger equation is solved for the atoms in the unit cell subject to periodic boundary conditions [40]. This approach can also be extended to the study of adsorbates on surfaces or of bulk defects by means of the supercell approach in which an artificial periodic structure is created where the adsorbate is translationally reproduced in correspondence to a given superlattice of the host. This procedure allows the use of efficient computer programs designed for the treatment of periodic systems and has indeed been followed by several authors to study defects using either density functional theory (DFT) and plane waves approaches [41 3] or Hartree-Fock-based (HF) methods with localized atomic orbitals [44,45]. 

In this work we have reviewed some recent developments in the energy loss of ions scattered off solid surfaces. In the weak-coupling regime (Zj/v 1) linear response theory allows one to calculate the distance-dependent stopping power. In this respect, we have shown that a linear approach with the SRM is capable to reproduce the measured energy losses of fast protons reflected at metal surfaces. Additionally, in this weak-coupling limit we have seen that in the case of metal targets details of the surface band structure do... 

Electronic structures of crystalline solids are mostly calculated on the basis of DFT. In this approach an open-shell system is described by spin polarized electronic band structures, in which the up-spin and down-spin bands are allowed to have different orbital... 

Using band structure nomenclature for the host solids allows a much more detailed discussion of the intercalation reaction. The electronic transfer is influenced not only by the number of empty levels but also by the structure of the band itself, i.e, the number of electrons in orbitals, or density of states. A pseudo-plateau in the potential variation of a discharge curve may be related to the filling of a zone of high density of states. This pseudo-plateau does not mean a two-phase region but occurs because the difference in energy of electrons in the alkali metal, i.e., before intercalation, and in the host, i.e, after intercalation, remains quite constant. 

---