Ionic solid defined

Ionic solids, such as lithium fluoride and sodium chloride, form regularly shaped crystals with well defined crystal faces. Pure samples of these solids are usually transparent and colorless but color may be caused by quite small impurity contents or crystal defects. Most ionic crystals have high melting points. 

The size of an atom is defined in terms of the interatomic distances that are found in solids and in gaseous molecules containing that atom. For an atom on the left side of the periodic table, gaseous molecules are obtained only at very high temperatures. At normal temperatures, solids are found and there are two important types to consider, metallic solids and ionic solids. Table 21-11 shows the nearest neighbor distances in the... 

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

The equilibrium constant for the solubility equilibrium between an ionic solid and its dissolved ions is called the solubility product, Ksp, of the solute. For example, the solubility product for bismuth sulfide, Bi2S3, is defined as... 

The lattice energy is defined as the energy required to separate the ions in one mole of an ionic solid. 

To understand the dissolution of ionic solids in water, lattice energies must be considered. The lattice enthalpy, A Hh of a crystalline ionic solid is defined as the energy released when one mole of solid is formed from its constituent ions in the gas phase. The hydration enthalpy, A Hh, of an ion is the energy released when one mole of the gas phase ion is dissolved in water. Comparison of the two values allows one to determine the enthalpy of solution, AHs, and whether an ionic solid will dissolve endothermically or exothermically. Figure 1.4 shows a comparison of AH and A//h, demonstrating that AgF dissolves exothermically. 

The activation energy represents the ease of ion hopping, as already indicated above and shown in Fig. 2.5. It is related directly to the crystal structure and in particular, to the openness of the conduction pathways. Most ionic solids have densely packed crystal structures with narrow bottlenecks and without obvious well-defined conduction pathways. Consequently, the activation energies for ion hopping are large, usually 1 eV ( 96 kJ mole ) or greater and conductivity values are low. In solid electrolytes, by contrast, open conduction pathways exist and activation energies may be much lower, as low as 0.03 eV in Agl, 0.15 eV in /S-alumina and 0.90 eV in yttria-stabilised zirconia. 

Equation (5.7) is a general equation defining conductivity in all conducting materials. To understand why some ionic solids conduct better than others it is useful to look at the definition more closely in terms of the hopping model that we have... 

The electrostatic (Madelung) part of the lattice energy (MAPLE) has been employed to define Madelung potentials of ions in crystals (Hoppe, 1975). MAPLE of an ionic solid is regarded as a sum of contributions of cations and anions the Madelung constant. A, of a crystal would then be the sum of partial Madelung constants of cation and anion subarrays. Thus,... 

An entirely different selectivity principle known as phase equilibrium comes into play in high-temperature ionic conductors. Many important gases dissolve in ionic solids at elevated temperatures. However, the solubility is rather sharply defined for the gas and the solid by the lattice parameters and the size of the gas molecule. The best example is the solubility of oxygen in zirconium dioxide. When Z1O2 is doped with yttrium ions, it exhibits a high mobility for the O anion. The solubility and anion mobility then become the basis for several electrochemical gas sensors, using yttria-stabilized zirconia (YSZ). 

Na(g) + Cl(g) - -NaCl(s), which defines the Na-Cl bond energy. The ionic solid is more stable than the equivalent number of gaseous atoms simply because the three-dimensional NaCl structure allows more electrons to be closer to more nuclei. This is the criterion for the stability of any kind of molecule all that is special about the ionic bond is that we can employ a conceptually simple electrostatic model to predict the bond strength. 

The lattice energy is often defined as the energy released when an ionic solid forms from its ions. However, in this book the sign of an energy term is... 

In Chapter 1 an ionic solid was defined as a lattice composed of anions and cations, where the atoms have lost or gained electrons to become ions. The loss or addition of electrons effectively completes a stable octet of outer electrons to create the ion. 

Repulsive Forces. As atoms approach one another or surfaces very closely, the electron clouds of the interacting atoms begin to overlap, with the result that repulsion (known as Bom repulsion) becomes the dominant force and closer approach becomes impossible. For this reason, the hard sphere model can be used to describe ionic solids. The individual atoms have well-defined radii that determine the distances of closest approach in close-packed arrangements. In equation 1.3, this distance is found to be 3.14 A for KCl. 

We normally define the energy level of electrons in a solid in terms of the Fermi level, eF, which is essentially equivalent to the electrochemical potential of electrons in the solid. In the case of metals, the Fermi level is equal to the highest occupied level of electrons in the partially filled frontier band. In the case of semiconductors of covalent and ionic solids, by contrast, the Fermi level is situated within the band gap where no electron levels are available except for localized ones. A semiconductor is either n-type or p-type, depending on its impurities and lattice defects. For n-type semiconductors, the Fermi level is located close to the conduction band edge, while it is located close to the valence band edge for p-type semiconductors. For examples, a zinc oxide containing indium as donor impurities is an n-type semiconductor, and a nickel oxide containing nickel ion vacancies, which accept electrons, makes a p-type semiconductor. In semiconductors, impurities and lattice defects that donate electrons introduce freely mobile electrons in the conduction band, and those that accept electrons leave mobile holes (electron vacancies) in the valence band. Both the conduction band electrons and the valence band holes contribute to electronic conduction in semiconductors. 

We can also determine lattice energy indirectly, by assuming that the formation of an ionic compound takes place in a series of steps. This procedure, known as the Born-Haber cycle, relates lattice energies of ionic compounds to ionization energies, electron affinities, and other atomic and molecular properties. It is based on Hess s law (see Section 6.5). Developed by Max Bom and Fritz Haber, the Bom-Haber cycle defines the various steps that precede the formation of an ionic solid. We will illustrate its use to find the lattice energy of lithium fluoride. 

Before we embark upon a discussion of the structures of ionic solids, we must say something about the sizes of ions, and define the term ionic radius. The process of ionization (e.g. equation 5.4) results in a contraction of the species owing to an increase in the effective nuclear charge. Similarly, when an atom gains an electron (e.g. equation 5.5), the imbalance between the number of protons and electrons causes the anion to be larger than the original atom. 

The heat of hydration is a key factor in dissolving an ionic solid. Breaking H bonds in water is more than compensated for by forming strong ion-dipole forces, so hydration of an ion is always exothermic. The A/Z ydr of an ion is defined as the enthalpy change for the hydration of 1 mol of separated (gaseous) ions ... 

Ion size plays an important role in determining the structure and stability of ionic solids, the properties of ions in aqueous solution, and the biologic effects of ions. As with atoms, it is impossible to define precisely the sizes of ions. Most often, ionic radii are determined from the measured distances between ion centers in ionic compounds. This method, of course, involves an assumption about how the distance should be divided up between the two ions. Thus you will note considerable disagreement among ionic sizes given in various sources. Here we are mainly interested in trends and will be less concerned with absolute ion sizes. 

You should note that some textbooks define lattice energy for the reverse process, i.e. the energy needed to convert an ionic solid into its constituent gaseous ions. 

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