Electron excess

Atoms of elements that are characterized by a valence greater than four, eg, phosphoms or arsenic (valence = 5), are one type of dopant. These high valence dopants contribute free electrons to the crystal and are cabed donor dopants. If one donor atom is incorporated in the lattice, four of the five valence electrons of donor dopants are covalentiy bonded, but the fifth electron is very weakly bound and can be detached by only ca 0.03 eV of energy. Once it is detached, it is available as a free electron, ie, a carrier of electric current. A sibcon crystal with added donor dopants has excess electron carriers and is cabed n-ty e (negative) sibcon (Fig. Ic). 

The external circuit provides a path for the excess electrons at the negative electrode to move toward the positive electrode. Although the flow of electrons would seem to cancel out the two charges, chemical processes in the battery build the charges up as fast as the depletion rate. When the electrodes can no longer pass electrons between them, the battery dies. ... 

At any interface between two different phases there will be a redistribution of charge in each phase at the interface with a consequent loss of its electroneutrality, although the interface as a whole remains electrically neutral. (Bockris considers an interface to be sharp and definite to within an atomic layer, whereas an interphase is less sharply defined and may extend from at least two molecular diameters to tens of thousands of nanometres the interphase may be regarded as the region between the two phases in which the properties have not yet reached those of the bulk of either phase .) In the simplest case the interface between a metal and a solution could be visualised as a line of excess electrons at the surface of the metal and an equal number of positive charges in the solution that are in contact with the metal (Fig. 20.2). Thus although each phase has an excess charge the interface as a whole is electrically neutral. 

A simple model of the e.d.l. was first suggested by Helmholz in which the charges at the interface were regarded as the two plates constituting a parallel plate capacitor, e.g. a plate of metal with excess electrons (the inner Helmholz plane I.H.P.) and a plate of excess positively charged ions (the outer Helmholz plane O.H.P.) in the solution adjacent to the metal the... 

The medium considered by Holstein is a one-dimensional crystal that contains a single excess electron. The Hamiltonian of the system is composed of three... 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

Fig. 8. Scheme of the electronic structure of (A) [3Fe-4S] centers and (B) [4Fe-centers according to the standard model. The thin and thick dashed fines indicate the Emtiferromagnetic and double exchEmge coupling, respectively. Configurations a and b correspond to the two possible locations of the excess electron in the mixed-valence pair. In part (B), the local spin values are Sc = Sd = 2 in the case of [4Fe-4S] centers and Sc = Sd = i in the case of [4Fe-4S] + centers. 

When a zinc strip is dipped into the solution, the initial rates of these two processes are different. The different rates of reaction lead to a charge imbalance across the metal-solution interface. If the concentration of zinc ions in solution is low enough, the initial rate of oxidation is more rapid than the initial rate of reduction. Under these conditions, excess electrons accumulate in the metal, and excess cationic charges accumulate in the solution. As excess charge builds, however, the rates of reaction change until the rate of reduction is balanced by the rate of oxidation. When this balance is reached, the system is at dynamic equilibrium. Oxidation and reduction continue, but the net rate of exchange is zero Zn (.S ) Zn (aq) + 2 e (me t a i)... 

Figure 19-11 illustrates the zinc equilibrium at the molecular level. At equilibrium, the charge imbalance in the zinc strip is about one excess electron for every 10 zinc atoms. This is negligible from the macroscopic perspective but significant at the molecular level. 

The charge imbalances for copper and zinc have different values, because zinc is easier to oxidize than copper. Consequentiy, zinc creates a greater charge imbalance than copper. The concentration of excess electrons in the zinc eiectrode is greater than the concentration of excess electrons in the copper electrode, giving the zinc eiectrode more excess charge than the copper electrode. 

When two electrodes contain different amounts of excess charge, there is a difference in electrical potential between them. Because it has more excess electrons, the zinc electrode is at a higher electrical potential than the copper electrode. In a galvanic cell, the difference in electrical potential causes electrons to flow from a region where the concentration of electrons is higher to a region where the concentration of electrons is lower. In this case, eiectrons flow from the zinc electrode toward the copper electrode, as shown at the molecular level in Figure 19-12. 

Mills, G., Gordon, M.S. and Metiu, H. (2003) Oxygen adsorption on Au clusters and a rough Au(lll) surface The role of surface flatness, electron confinement, excess electrons, and band gap. Journal of Chemical Physics, 118, 4198-4205. 

In semiconductors, which have a bandgap, recombination of the excited carriers— return of the electrons from the conduction band to vacancies in the valence band—is greatly delayed, and the lifetime of the excited state is much longer than in metals. Moreover, in n-type semiconductors with band edges bent upward, excess electrons in the conduction band will be driven away from the surface into the semiconductor by the electrostatic held, while positive holes in the valence band will be pushed against the solution boundary (Fig. 29.3). The electrons and holes in the pairs produced are thus separated in space. This leads to an additional stabihzation of the excited state, to the creation of some steady concentration of excess electrons in the conduction band inside the semiconductor, and to the creation of excess holes in the valence band at the semiconductor-solution interface. 

Figure 1. The tunneling of a single electron (SE) between two metal electrodes through an intermediate island (quantum dot) can be blocked of the electrostatic energy of a single excess electron trapped on the central island. In case of non-symmetric tunneling barriers (e.g. tunneling junction on the left, and ideal (infinite-resistance) capacitor on the right), this device model describes a SE box .

Colloids of more electronegative metals such as cadmium and thallium also act as catalysts for the reduction of water. In the colloidal solution of such a metal, an appreciable concentration of metal ions is present. The transferred electrons are first used to reduce the metal ions, thus bringing the Fermi potential of the colloidal particles to more negative values. After all the metal ions have been reduced, excess electrons are stored as in the case of silver. 

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