Local charge neutrality

Local charge neutrality homogeneous phase 2.1 Correct way to find the neutral ground state... 

We have discussed the homogeneous 2-flavor quark matter when charge neutrality conditions are satisfied locally, and found that the local charge neutrality conditions impose very strong constraints on determining the ground state of the system. 

The introduction of Fca-atom vacancies modifies the energy diagram of Fig. 3. The preservation of local charge neutrality requires that each Fea-atom vacancy have five of its six nearest neighbors as Fee ions, which means that the ai(, ) states of five Fea ions neighboring a vacancy, , are raised an energy Ea above the Fermi energy. They become acceptor states inaccessible to the mobile electrons at low temperatures. It is possible to express this situation with the structural formula... 

These principles are phrased in the language of the ionic model, but they provide a simpler and more explicit description of stable structures than that given by the ionic model s energy minimization principle. Among the important ideas captured by Pauling s rules are those of local charge neutrality, the definition of electrostatic bond strength, and the rule of parsimony which is closely... 

Because both types of carrier are created uniformly in equal concentrations, and because sweep-ouf effects associated with the arrival of carriers at the specimen electrodes may be neglected in materials of low mobility, local charge neutrality is maintained and dielectric relaxation effects are not relevant. However, a disadvantage of the technique is that it is impossible to determine the polarity of the dominant carrier unless information from other measnrements, such as thermoelectric power, is employed. 

Fig. 7.13 Schematic representation of the ionic rigid-band and metallic common-band models of bonding in binary AB systems. The quantities and give the free-atom energy levels, whereas the positions of fA and B in the metallic bond reflect the small shift which takes place on alloy formation in order to maintain local charge neutrality.

This expression is stationary with respect to small variations in AE for just that value of AE = A LCN, which results from filling up the skew rectangular partial densities of states and requiring local charge neutrality. Thus, this simple model is internally consistent. 

The bond energy per atom, when the local charge neutrality condition eqn (7.59) is satisfied, is given by... 

We see that the simple rectangular d band model reproduces the behaviour found by experiment and predicted by Miedema s semi-empirical scheme. However, we must stress that the model does not give credence to any theory that bases the heat of formation of transition-metal alloys on ionic Madelung contributions that arise from electronegativity differences between the constituent atoms because in the metallic state the atoms are perfectly screened and, hence, locally charge neutral. Instead, the model supports... 

We have already seen in Section 2.2 how the transport of both anions and cations is a vital part of biochemistry. We will examine supramolecular models of biological ion channels in detail in Chapter 12 but here we focus on some simple ion transport systems (ionophores) relevant to simultaneous anion and cation binding. Because of the need to maintain overall and local charge neutrality during any transport process the transport of individual ions across a biological or artificial membrane never occurs in isolation. There are two kinds of primary transport processes. Ion exchange or antiport, occurs when chemically different ions of like charge such as Na+ and K+ are simultaneously transported in... 

As noted in [4] and [5], and in the discussion above, the electronic structure of Ti " " has been addressed for both Ti20s [14], and the hydrated ion Ti(H20)6 complex [11]. However it is important understand these two applications are different. The d description applies exactly to each hydrated Ti ion. In contrast, the d designation for the Ti-atoms in Ti203 is based on a SALC molecular orbital representation of the Ti203 electronic structure, in particular on overall and local charge neutrality. 

The only yet unknown quantity in Eqs (4.132) is the chemical potential fi. It can be determined from the condition of local charge neutrality, which for intrinsic semiconductors is simply zic = J v-... 

Inserting (D.la) to (D.ld) into (5.12a) and comparing terms of equal order in k yields two results. The k term gives the local charge neutrality condition... 

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