The Ionic Lattice

Conditions are simplest if the same force is effective in all three spatial directions in the given crystal in this case true ionic lattices, true atomic, metallic and molecular lattices are obtained. It may happen, however,— and these cases will later be shown to be of special interest— that in one and the same lattice different types of forces prevail in the different directions in space, and result in mixed lattices and transition phenomena which will be discussed after the simple cases. 

The nature of each of the four above named forces is already known to us from the discussion of intra- and inter-molecular forces and it remains only to describe here the type of product that results if these forces are lattice-forming. Table 52 gives a summary of pure lattice types, arranged according to the lattice forces acting. 

The development of the experimental technique for investigating crystal structure by x-rays led first to the study of the simplest inorganic substances, i.e. the binary salts, and to the elucidation of their space lattices. The abundant data thus obtained were naturally an inducement to a search for conformity to rules. 

Researches of W. L. Bragg, K. Fajans, H. G. Grimm and L. Pauling have thrown light on the fundamentals of these laws and the comprehensive work of V. M. Goldschmidt and his co-workers has formulated them decisively and proved them with much new experimental material. The principal results of this crystallo-chemical research are the following  

To a first approximation, the individual ions in the structure of sol d bodies behave as rigid spheres. Each of them, e.g. the univalent Na ion, the divalent Fe ion, etc. possesses a definite ionic radius which is specific to it and persists practically unchanged in the passage from one lattice 

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In Chapters 2 and 3 we have described basic structural properties of the components of an interphase. In Chapter 2 we have shown that water molecules form clusters and that ions in a water solution are hydrated. Each ion in an ionic solution is surrounded predominantly by ions of opposite charge. In Chapter 3 we have shown that a metal is composed of positive ions distributed on crystal lattice points and surrounded by a free-electron gas which extends outside the ionic lattice to form a surface dipole layer. 

The oxidizers used in high-energy mixtures are generally ionic solids, and the "looseness" of the ionic lattice is quite important in determining their reactivity [3]. A crystalline lattice has some vibrational motion at normal room temperature, and the amplitude of this vibration increases as the temperature of the solid is raised. At the melting point, the forces holding the crystalline solid to-... 

The way forward has already been hinted at in our discussion of the electron gas. The simplest approximation due to Hartree in 1928 is to assume that the individual electrons move independently of each other, so that each electron feels the average electrostatic field of all the other electrons in addition to the potential from the ionic lattice. This average field has to be determined self-consistently in that the input charge density, which enters... 

The corresponding calculations of the energy of the ionic lattice NH4X are at... 

Although there are similarities between the chemistry of the chalcogenide elements, the properties of selenium and tellurium clearly lie between those of non-metallic sulfur and metallic polonium. The enhancement in metallic character as the group is descended is illustrated in the emergence of cationic properties by polonium, and marginally by tellurium, which are reflected in the ionic lattices of polonium(IV) oxide and tellurium(IV) oxide and the formation of salts with strong acids. 

In chemical shift calculations for acylium ions, it was not necessary to model the ionic lattice to obtain accurate values. These ions have tetravalent carbons with no formally empty orbitals, as verified by natural bond orbital calculations (89). Shift calculations for simple carbenium ions with formally empty orbitals may require treatment of the medium. We prepared the isopropyl cation by the adsorption of 2-bromopropane-2-13C onto frozen SbF5 at 223 K and obtained a 13C CP/MAS spectrum at 83 K (53). Analysis of the spinning sidebands yielded experimental values of = 497 ppm, 822 = 385 ppm, and (%3 = 77 ppm. The isotropic 13C shift, 320 ppm, is within 1 ppm of the value in magic acid solution (17). Other NMR evidence includes dipolar dephasing experiments and observation at higher temperature of a scalar doublet ( c-h = 165 Hz) for the cation center. 

The stability of noble gas configurations was discussed in Chapter 4. where it was pointed out that many ions are not stable, that is, they are endothermic with respect to the corresponding atoms, but they arc stabilized by the ionic lattice. However, some chemists argue that these ions are stable because they exist in solution as well as in lattices. Discuss. 

SALT. A compound formed by replacement of part or all of the hydrogen of an acid by one (or more) element(s) or radrcal(s) that are essentially inorganic. Alkaloids, amines, pyridines, and other basic organic substances may be regarded as substituted ammonias in this connection. The characteristic properties of salts are the ionic lattice in the solid state and the ability to dissociate completely in solution. The halogen derivatives of hydrocarbon radicals and esters are not regarded as salts in the strict definition of the term,... 

A pseudo salt is a compound that has some of the normal characteristics of a salt, but lacks certain others, notably the ionic lattice in the solid state and the property of ionizing completely in solution. The absence of these properties is due to the fact that the bonds between the metallic and nonmetallic radicals are covalent or semicovalent instead of polar. Because these salts do not ionize completely, they are also called weak salts. 

The crystals of solids are built up of ions of non-metals, ions of metals, atoms, molecules or a combination of all these particles. These possibilities result in four different crystal lattices, i.e. the ionic lattice (e.g. sodium chloride, NaCl), the atomic lattice (e.g. diamond, C), the molecular lattice (e.g. iodine, I2) and the metallic lattice (e.g. copper, Cu). The forces which hold the building blocks of a lattice together differ for each lattice and vary from the extremely strong coulombic forces in an ionic lattice to the very weak Van der Waals forces between the molecules in a molecular lattice. 

Referred to the averaged eight-coordination of a B2 lattice, the equivalent separation, d8 =fd6 — (v/3/2)a. The ionic lattice energies of Table 5.3 are... 

It has to be stressed that the relationship is at best a rough guide. There will almost certainly be contributions to dielectric loss occurring at frequencies between the microwave region and the ionic lattice resonance frequency that complicate the Q(f) relationship. For example, such contributions may arise through polarization processes associated with dislocations and microstructural features. There is no alternative to making the measurement if reliable loss data at a particular frequency are required. 

The neutral-ionic transition (NIT) at t = 0 occurs abruptly[94] when the Madelung energy M of the ionic lattice exceeds the energy I — A to transfer an electron form D to A. Long-range Coulomb interactions are treated self-consistently as part of A in the modified Hubbard model[95],... 

Surface cracks. Most solid substances have very numerous small cracks in their surfaces.6 The first evidence for this comes from a comparison of the actual strength of crystals with that deduced from theoretical considerations. In the case of the ionic lattice of sodium chloride the theoretical strength calculated from consideration of the electrostatic forces between the ions is of the order 200 kg. per sq. mm. actually dry crystals of rock salt can be broken at 0 4 kg. per sq. mm. If strained in air the deformation of rock salt is very small, before it breaks. It has long been known, to those who work in salt mines, that rock salt can be bent... 

The concentration c that appears in the Debye-Hiickel-Onsager equation pertains only to the free ions. This concentration becomes equal to the analytical concentration (which is designated here as only if every ion from the ionic lattice from which the electrolyte was produced is stabilized in solution as an independent mobile charge carrier i.e., c if there is ion-pair formation. Whether ion-pair formation occurs depends on the relative values of a, the distance of closest approach of oppositely charged ions, and the Bjerrum parameter g = (z z Co/2 T) 1/e. When the condition for ion-pair formation is satisfied and when a > the ions remain free. 

The experimental value of the internuclear distance in gaseous sodium chloride is 2 51 A the sum of the covalent radii is 2-53 A whereas the sum of the ionic radii is 2 48 A. In obtaining this figure, allowance has been made for the decrease, by about ii per cent, of the ionic radii in the gaseous molecule compared with that in the ionic lattice. A similar result is obtained in the case of sodium bromide and iodide. Since the radius of the positive ion is less, and that of the negative ion is greater, than the corresponding covalent radii, it would appear that differences have been compensated. 

For the constitution of the ionic lattices also, the Van der Waals attraction has been found to be a very decisive factor. We know the forces at present much better for these ions than for the neutral molecules. Using an interaction of the form (21), Born and Mayer have calculated the lattice energy of all alkali halides for the NaCl-type and simultaneously for the CsCl-type and comparing the stability of the two types they could show quantitatively that the relatively great Van der Waals attraction between the heavy ions Cs, I , Br, Cl cf. Table II.) accounts for the fact that CsCl, CsBr, Csl, and these only, prefer a lattice structure in which the ions of the same kind have smaller distances from each other than in the NaCl-type. The contribution of the Van der Waals forces to the total lattice energy of an ionic lattice is of course a relatively small one, it varies from I per cent, to 5 per cent., but just this little amount is quite sufficient to explain the transition from the NaCl-type to the CsCl-type. 

These are crystalline compounds made by heating the metal in hydrogen calcium, for instance, reacts at 150°. Those of the alkali metals, XH, have the sodium chloride type lattice (p. 141) those of the Gp. IIA metals are less regular. All have stoichiometric compositions and the crystals are ionic, being somewhat denser than the metal from which they are made owing to the strong polar bonds in the ionic lattice. 

The ionic compound [Ta(Se2)2]2[TaBr6] was prepared in high yield from the elements by stoichiometric reaction at 450 °C.377 The positively charged polymeric component (formally [TavTaIV]) is constructed from chains of Ta(//2-f72-Se2)2Ta units. The ionic lattice is completed... 

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