An introduction to Ionic Crystal Structures
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As you have seen in the lecture component of the course, atoms can bond to each other in a number of ways. Compounds may arise as a result of ionic, covalent, or polar covalent bonds between their constituent atoms. Other, considerably weaker types of bonding also sometimes contribute to the structure and properties of compounds.

Figure 1: Typical Bond Dissociation Energies

In this course, the focus is on the strongest bonds found in Nature: covalent, polar covalent, and ionic. For example, most organic molecules are held together by covalent and polar covalent bonds, while all salts feature ionic bonding. The primary determinant of the type of bonds encountered in a compound is the difference in electronegativity between the constituent atoms.

Figure 2: Typical Compounds with Ionic, Polar Covalent, and Covalent Bonds

What is electronegativity? It’s a simple way to describe how tightly an atom (alone in space, without other influences) holds on to its valence, outermost, and thus most easily removed electrons. Essentially, this value depends on the number of positively charged protons in the atom’s nucleus (the atomic number), and on the radius of the outermost electron shell. The more positive the nucleus, and the smaller the valence electron shell around it, the greater the attraction between nucleus and electrons, and thus, the more electronegative the atom. Thus, a high electronegativity value implies that the valence electrons are tightly held and require a large amount of energy to remove.

Figure 3: Factors Determining Electronegativity. Shown above are various parameters for Mg and F atoms. E is the electronegativity value for each and increases as the outermost electrons require more energy to remove. This value depends on the atomic radius of the atom (how far away the negatively charged outermost electrons are from the positively charged nucleus) and on the effective nuclear charge (Z_eff) "felt" by the outermost electrons. Note that Z_eff is not the same as the atomic number, or the total nuclear charge, because the inner, or core, electrons also interact with the nucleus and diminish its pull on the valence electrons. Convince yourself, using the principle that opposite charges attract, that as Z_eff increases and atomic radius decreases, E increases.

Precise electronegativity values can be looked up in reference tables in a textbook, but a qualitative, easy-to-remember trend is that electronegativities increase from the bottom left of the periodic table (francium, Fr) to the top right (fluorine, F), not including the noble gases.

Figure 4: Electronegativity Values Increase Going Up and to the Right on the Periodic Table

Compounds containing atoms with a large electronegativity difference form ionic bonds. This type of bonding can be described by assuming that the atom from the left side of the periodic table (low electronegativity, outermost electrons loosely held) gives up all of its valence electrons to the right-side atom (high electronegativity, outermost electrons tightly held). Therefore, a pair of oppositely charged ions is created, with an attractive electrostatic force between them that is the basis of an ionic bond.

Figure 5: Basis of Ionic Bonds. The formula at the bottom of the picture is Coulomb's Law. The attractive force, F, between two unlike charges is determined by q₁ and q₂, the charges of the two ions relative to an electron's, and the square of e, the absolute value of an electron's charge. The denominator includes a proportionality constant and the square of r, the distance between the two charges.

This picture is very simple for a pair of ions, because the attractive force only acts in a single direction. But we know that macroscopic amounts of ionic solids exist (just look inside your table salt shaker!), requiring that these electrostatic forces be optimized for very large numbers of ions. In essence, the question becomes: how do we arrange, say, 6.02 x 10²³ Na⁺ ions and 6.02 x 10²³ ions of Cl^- to optimize attraction between unlike charges and minimize repulsion between similar charges? Thankfully, Nature has worked out many elegant solutions to this very complex problem. We’ll be exploring some of the simpler ones in this lab activity.

Figure 6: While the optimal arrangement for a few ions is easily determined, the optimization becomes much more complicated when a large number of ions is involved.

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