Charge neutralization crystal

Fig. 1.23 Electro-neutrality of NiO with two metal vacancies. A perfect crystal (a) is oxidized to crystal (b) or (c). In crystal (b), there are two metal vacancies with 2 charge. In crystal (c), there are two metal vacancies with neutral charge and four metal ions with excess charge (-I- 3). (b) and (c) are alternative representations of the oxidized crystal.

If the chemical reactions described by eqns (1.184), (1.185), and (1.187) are in chemical equilibrium, the following charge neutrality condition in a crystal must hold... 

As mentioned earlier, only certain crystal exhibits piezoelectric behaviour. Only pressure on certain electrically neutral crystals - those not having a centre of structural symmetry - polarizes them by slightly separating the centre of the positive charge from that of the negative charge. Some examples of such crystals are ... 

FeCb, CaCfe, and MgCfc) were investigated. Precipitates were formed in all systems except SDS-MgCfe. The forming of these precipitates was attributed to adsorption-charge neutralization (AlJ), bridge connection (SDS-Fe land low solubility product of Ca(D )crystal respectively. 

A color center or F-center is formed from diffusion of a small quantity of M+ ion into an ionic crystal MX. Since the crystal must keep its charge neutrality, additional electrons readily move to fill the vacancies normally occupied by anions. Thus the composition of the crystal becomes (M+)i+i(X e ). The origin of the color is due to electronic motion, and a simple picture of an electron in a vacancy is illustrated by the particle in a three-dimensional box problem, which is discussed in Section 1.5.2. 

The structure of crystalline FeO belongs to the NaCl type. When iron(II) oxide is prepared under normal conditions, the composition of the product (wustite) is always Fei 50. In order to retain overall electric neutrality, part of the Fe2+ is oxidized to Fe3+, and the chemical formula becomes Fc Fe. O. Since the radius of Fe3+ is small, the Fe3+ cations tend to occupy the tetrahedral holes to form a short-range ordered Fe40io cluster, which is called the Koch cluster of Fei 0, as shown in Fig. 10.1.3. The Koch clusters are distributed randomly in the crystal structure. To satisfy charge neutrality, the formation of a Koch cluster must be accompanied by the presence of six Fe2+ vacancies, one of which is located at the center of the cluster, and the remaining five are distributed randomly at the centers of the edges of the cubic unit cell. 

As-synthesized Na-ZSM-5, which possesses an isostructure with TPA-ZSM-5, exhibits a hexagonal-lath-shaped morphology. Liquid phase Sil /A Oo ratio is important in controlling the formation of Na-ZSM-5 and mordenite, and the silica source influences the liquid phase composition. High yield of Na-ZSM-5 is obtained only when a small-sized silica sol is employed. A linear relationship between Na/Al starting atomic ratio and the nucleation rate indicates that charge neutralization of SBU is required for zeolite crystallization. 

The Mulliken arguments may be extended to charge-transfer crystals. The first solid charge-transfer crystals studied were colored, but had low thermodynamic stability relative to the separate neutral donor and acceptor crystals. However, if the donor D had low ID and if the acceptor had high Aa ... 

The qualitative properties of a defect such as a sulfur vacancy in ZnS are fortunately independent of the type of bonding in the compound. If we consider first that ZnS is an ionic compound composed of Zn+2 and S-2 ions, the removal of a neutral S atom to the gas phase to form S2 molecules leaves behind a neutral sulfur vacancy, Vs°, since charge neutrality must be preserved in the crystal. The two electrons left behind can be considered as being trapped in the vicinity of the vacancy and can be removed one at a time into the conduction band of the solid by thermal ionization. These processes can be written as ordinary chemical equations ... 

It should be noted here that the condition of charge neutrality in the crystal, whose satisfaction plays an important role in actual calculations, requires that... 

Generally, a crystal is electrically neutral. This implies that the crystal should have an equal number of positive and negative charges. Thus, when oppositely charged ions come together to form a neutral crystal structure, each ion coordinates with as many ions of opposite charge as the size permits. This coordination principle dictates both electrical neutrality of the crystal structure and compact packing of the atoms within the structure. 

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