Crystal interionic attractions

Crystals with the Rutile and the.Fluorite Structures Interionic Distances for Substances of Unsymmetrical Valence Type.—In a crystal of a substance of unsymmetrical valence type, such as fluorite, CaFs (Fig. 13-10), the equilibrium cation-anion interionic distance cannot be expected necessarily to be given by the sum of the crystal radii of the bivalent calcium ion and the univalent fluoride ion. The sum of the univalent radii of calcium and fluoride, 2.54 A, would give the equilibrium interionic distance in a hypothetical crystal with attractive and repulsive forces corresponding to the sodium chloride arrangement. 

Crystals with strong ionic bonds always have low coefficients of thermal expansion. Though the solids are non-conducting because the electrons are all firmly bound in atomic orbitals, conductance by migration of ions is possible in the fused state. Ionic bonds are often broken by media of high dielectric constant such as water (e = 78). Binary simple salts, exempUfied by NaCl, are generally more easily dissociated in aqueous solution than such compounds as MgO where the interionic attraction is large. 

The mosaic structure of a crystal is intimately connected with its mechanical strength. If we consider the lattice theory of a simple ionic crystal, such as sodium chloride, it is easy to calculate the stress necessary to rupture the crystal by separating it into two halves against the forces of interionic attraction. Such calculations lead to estimates of the tensile strength which are hundreds or thousands of times greater than those actually observed. If, however, the crystal possesses a mosaic structure the mechanism of fracture will be different. The two halves of the crystal will not now be separated simultaneously at every point instead there will be local stress concentrations at which the crystal will fail, the stress concentrations will then be transferred to other points and ultimately the crystal will break in two. The process may be likened to the tearing of a sheet of paper it is not easy to sever a piece of paper by means of a uniformly applied stress, but if a tear is started the stress is concentrated at the end of the tear, failure at that point takes place and the tear is rapidly propagated across the sheet. 

Consider the formation of a saltwater solution. Earlier we pointed out (Section 4.2) that solid ionic compounds are collections of ions held together by attractions between the opposite ionic charges. When an ionic compound dissolves, the orderly ionic arrangement is destroyed as the interionic attractions are overcome. Thus, the attractive forces between water molecules and ions must be stronger than the interionic attractions within the crystal. 

The above calculation applies to independent sodium and fluoride ions, and does not take into account the electrostatic attraction between the oppositely charged ions, nor the repulsive force which operates at small interionic distances. In the crystal of NaF the distance of nearest approach of the sodium and fluoride ions is 231 pm, and Coulomb s law may be used to calculate the energy of stabilization due to electrostatic attraction between individual ion pairs ... 

It might be thought that this treatment would provide a poor approximation because of the neglect of polarization of each of the two ions in the electric field of the other.36 However, there is reason to think that the neglect of polarization does not introduce great error. First, the effect of multipole polarization as well as of the partial covalent character of the bonds is taken into account in the treatment of the crystals by the evaluation of the Bom exponent n from the observed compressibility and of the repulsion factor from the observed interionic distance. Second, in the gas molecule, in which there is dipole polarization mainly of the anion, its effect in causing increased attraction of the ions may be largely neutralized by the increased repulsion caused... 

Ionic radii are discussed thoroughly in Chapters 4 and 7. For the present discussion it is only necessary to point out that the principal difference between ionic and van der Waals radii lies in the difference in the attractive force, not the difference in repulsion. The interionic distance in UF, for example, represents the distance at which the repulsion of a He core (Li+) and a Ne core (F ) counterbalances the strong electrostatic or Madelung force. The attractive energy for Lt F"is considerably over 500 kJ mol"1 anti the London energy of He-Ne is of the order of 4 kJ mol-1. The forces in the LiF crystal are therefore considerably greater and the interioric distance (201 pm) is less than expected for the addition of He and Ne van der Waals radii (340 pm). 

The distance between the ions in a crystal is determined by the equilibrium between the forces of attraction and repulsion. Values of the interionic distances may be obtained from x-ray data. On the basis of the Born theory of lattice energies we have,... 

The Madelung constant represents the interactions between ions in the attractive component of the interionic potential for ionic crystals. 

Theoretical values for lattice energy may be calculated. The crystal is assumed to be made up of perfectly spherical ions. From the geometry of the crystal, the interionic distance is known. The energy of attraction between all the oppositely charged ions and the energy of repulsion between ions of same charge are calculated. The final equation obtained is Bom-Lande equation -... 

Therefore, ionic crystals with small ions (short interionic distances), large values of A, and highly charged ions tend to have large attractive energies. 

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