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By the end of this section, you will be able to:
  • Describe the packing structures of common solids
  • Explain the difference between bonding in a solid and in a molecule
  • Determine the equilibrium separation distance given crystal properties
  • Determine the dissociation energy of a salt given crystal properties

Beginning in this section, we study crystalline solids, which consist of atoms arranged in an extended regular pattern called a lattice    . Solids that do not or are unable to form crystals are classified as amorphous solids . Although amorphous solids (like glass) have a variety of interesting technological applications, the focus of this chapter will be on crystalline solids.

Atoms arrange themselves in a lattice to form a crystal because of a net attractive force between their constituent electrons and atomic nuclei. The crystals formed by the bonding of atoms belong to one of three categories, classified by their bonding: ionic, covalent, and metallic. Molecules can also bond together to form crystals; these bonds, not discussed here, are classified as molecular. Early in the twentieth century, the atomic model of a solid was speculative. We now have direct evidence of atoms in solids ( [link] ).

Figure shows a 3 dimensional wavy structure with peaks and troughs.
An image made with a scanning tunneling microscope of the surface of graphite. The peaks represent the atoms, which are arranged in hexagons. The scale is in angstroms.

Ionic bonding in solids

Many solids form by ionic bonding. A prototypical example is the sodium chloride crystal, as we discussed earlier. Electrons transfer from sodium atoms to adjacent chlorine atoms, since the valence electrons in sodium are loosely bound and chlorine has a large electron affinity. The positively charged sodium ions and negatively charged chlorine (chloride) ions organize into an extended regular array of atoms ( [link] ).

Figure shows a crystal lattice structure with alternately placed small red spheres labeled sodium ions and bigger green spheres labeled chloride ions.
Structure of the sodium chloride crystal. The sodium and chloride ions are arranged in a face-centered cubic (FCC) structure.

The charge distributions of the sodium and chloride ions are spherically symmetric, and the chloride ion is about two times the diameter of the sodium ion. The lowest energy arrangement of these ions is called the face-centered cubic (FCC)    structure. In this structure, each ion is closest to six ions of the other species. The unit cell is a cube—an atom occupies the center and corners of each “face” of the cube. The attractive potential energy of the Na + ion due to the fields of these six Cl ions is written

U 1 = −6 e 2 4 π ε 0 r

where the minus sign designates an attractive potential (and we identify k = 1 / 4 π ε 0 ). At a distance 2 r are its next-nearest neighbors: twelve Na + ions of the same charge. The total repulsive potential energy associated with these ions is

U 2 = 12 e 2 4 π ε 0 2 r .

Next closest are eight Cl ions a distance 3 r from the Na + ion. The potential energy of the Na + ion in the field of these eight ions is

U 3 = 8 e 2 4 π ε 0 3 r .

Continuing in the same manner with alternate sets of Cl and Na + ions, we find that the net attractive potential energy U A of the single Na + ion can be written as

U coul = α e 2 4 π ε 0 r
Practice Key Terms 5

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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