Lattice spacings, ionic crystals

When we have an ordered assembly of atoms called a lattice, there is more than one bond per atom, and we must take into account interactions with adjacent atoms that result in an increased interionic spacing compared to an isolated atom. We do this with the Madelmg constant, ckm. This parameter depends on the structure of the ionic crystal, the charge on the ions, and the relative size of the ions. The Madelung constant fits directly into the energy expression (Eq. 1.25) ... 

First of all, electronic structure of nanoparticles was discussed. The influence of the size of particle on its electronic structure is determined by the nature of bonds in the particle lattice. In the lattice of molecular crystal intermolecular bonds cause only minor alterations in an electronic structure of molecules and are localized between the nearest neighbors in such lattice. In the lattice of inorganic crystal with purely ionic bonds the interaction of ion with medium is also localized in small space of the several coordination spheres surrounding an ion in the lattice. The transition of ion in the excited state gives essential disturbance of ionic lattice only in this space. 

Ionic Radii.—The first question that we naturally ask about the crystals is, what determines the lattice spacings Examination of the... 

The crystal structure is also determined by the ratio of the ionic radii (Goldschmidt). In a crystal of the rock-salt type each positive ion is surrounded by six negative ions arranged in an octahedron (Fig. 3) and vice versa. The distance from centre to corner of the octahedron is 1/2 a V 2 when a is the side. In NaCl with a Na-Cl distance 2.81 A, a is thus equal to 3.98 A, thus appreciably greater than the sum of the radii of two chlorine ions, so that the latter do not touch one another. If the positive ion now becomes steadily smaller, then the Coulomb attraction increases on account of the smaller lattice spacing. This finishes, however, when the negative ions just touch each other, that is to say, when ... 

Ionic crystals are formed by combinations of highly electropositive and highly electronegative elements, such as ordinary salts. Ions rather than atoms occupy positions in the space lattice and are held together by coulomb electrostatic forces. Ionic crystals obey valence rules and are good ionic conductors of electricity when molten. 

An ideal crystal is constructed by the infinite regular repetition in space of identical structural units. In the simplest crystals formed by monatomic elements, the basic structural unit consists of a single atom. For the organic molecules of pharmaceutical interest, the structural unit will contain one or more molecules. One can describe the structure of all crystals in terms of a single periodic lattice, which represents the translational repetition of the fundamental structural unit. For elemental or ionic crystal structures, each point in the lattice may be a single atom. For organic molecules, a group of atoms is often attached to a lattice point or situated in an elementary parallelepiped. 

In an ideal ionic crystal all ions are rigidly held in the lattice sites where they perform only thermal vibratory motion. Transfer of an ion between sites under the effect of electrostatic fields (migration) or concentration gradients (diffusion) is not possible in such a crystal. Initially, therefore, the phenomenon of ionic conduction in solid ionic crystals was not understood. Yakov I. Frenkel showed in 1926 that ideal crystals could not exist at temperatures above the absolute zero. Part of the ions leave their sites under the effect of thermal vibrations and are accommodated in the interstitial space leaving vacancies at the sites. 

Magnesium oxide is a highly ionic crystal, with the Mg O bonds having about 80% ionic character, and with a cubic face-centered crystal lattice (space group Fm3m). MgO has no polymorph transitions from room temperature to melting point at 3073 K. The physical properties of the MgO single crystal are listed in Table 1.3. 

Lehovec, K. (1953) Space-charge layer and distribution of lattice defects at the surface of ionic crystals. J. Chem. Phys., 21, 1123-1128. 

There is considerable evidence for the existence of space charge layers near lattice defects in ionic crystals. The experimental work has principally been concerned with the alkali and silver halides. With the alkali halides the experiments have mainly been aimed at determining the charge distribution near dislocations and grain boundaries, while the work on the silver halides arises from their use as photographic materials, although... 

The concept of charge density nvolves the total charge of an ion divided by the space that the ion occupies. Using Table 21.5, determine a trend between charge density of an ion and the lattice energy of similar ionic crystals. Can you justify this trend on physical principles ... 

Tables 2.1-2.4 relative to sodiiun, lithium, potassium, rubidium, and cesium salts, also show that, in general, the values of a obtained by fitting experimental data of activity coefficients are larger than the sum of ionic radii in solutions (or crystal-lattice spacing) and the interatomic distances, d. Also they are close to the values obtained from Kielland sdata and toab initio values calculated by using two models model I and model II, considering the absence and the presence of five water molecules between anion and cation, optimized in the gas phase, respectively), and also to those obtained fi om MM studies, where no water molecules are consid-...

---