INTRODUCTION AND SECTION 12.1 The structures and properties of solids can be classified according to the forces that hold the atoms together. Metallic solids are held together by a delocalized sea of collectively shared valence electrons. Ionic solids are held together by the mutual attraction between cations and anions. Covalent-network solids are held together by an extended network of covalent bonds. Molecular solids are held together by weak intermolecular forces. Polymers contain very long chains of atoms held together by covalent bonds. These chains are usually held to one another by weaker intermolecular forces. Nanomaterials are solids where the dimensions of individual crystals have been reduced to the order of 1–100 nm.

SECTION 12.2 In crystalline solids, particles are arranged in a regularly repeating pattern. In amorphous solids, however, particles show no long-range order. In a crystalline solid the smallest repeating unit is called a unit cell. All unit cells in a crystal contain an identical arrangement of atoms. The geometrical pattern of points on which the unit cells are arranged is called a crystal lattice. To generate a crystal structure a motif, which is an atom or group of atoms, is associated with each and every lattice point.

In two dimensions the unit cell is a parallelogram whose size and shape are defined by two lattice vectors (a and b). There are four primitive lattices, lattices where the lattice points are located only at the corners of the unit cell: square, hexagonal, rectangular, and oblique. In three dimensions the unit cell is a parallelepiped whose size and shape are defined by three lattice vectors (a, b and c), and there are seven primitive lattices: cubic, tetragonal, hexagonal, rhombohedral, orthorhombic, monoclinic, and triclinic. Placing an additional lattice point at the center of a cubic unit cell leads to a body-centered cubic lattice, while placing an additional point at the center of each face of the unit cell leads to a face-centered cubic lattice.

SECTION 12.3 Metallic solids are typically good conductors of electricity and heat, malleable, which means that they can be hammered into thin sheets, and ductile, which means that they can be drawn into wires. Metals tend to form structures where the atoms are closely packed. Two related forms of close packing, cubic close packing and hexagonal close packing, are possible. In both, each atom has a coordination number of 12.

Alloys are materials that possess characteristic metallic properties and are composed of more than one element. The elements in an alloy can be distributed either homogeneously or heterogeneously. Alloys which contain homogeneous mixtures of elements can either be sub-stitutional or interstitial alloys. In a substitutional alloy the atoms of the minority element(s) occupy positions normally occupied by atoms of the majority element. In an interstitial alloy atoms of the minority element(s), often smaller nonmetallic atoms, occupy interstitial positions that lie in the “holes” between atoms of the majority element. In a heterogeneous alloy the elements are not distributed uniformly; instead, two or more distinct phases with characteristic compositions are present. Intermetallic compounds are alloys that have a fixed composition and definite properties.

SECTION 12.4 The properties of metals can be accounted for in a qualitative way by the electron-sea model, in which the electrons are visualized as being free to move throughout the metal. In the molecularorbital model the valence atomic orbitals of the metal atoms interact to form energy bands that are incompletely filled by valence electrons. Consequently, the electronic structure of a bulk solid is referred to as a band structure. The orbitals that constitute the energy band are delo-calized over the atoms of the metal, and their energies are closely spaced. In a metal the valence shell s, p, and d orbitals form bands and these bands overlap resulting in one or more partially filled bands. Because the energy differences between orbitals within a band are extremely small, promoting electrons to higher-energy orbitals requires very little energy. This gives rise to high electrical and thermal conductivity, as well as other characteristic metallic properties.

SECTION 12.5 Ionic solids consist of cations and anions held together by electrostatic attractions. Because these interactions are quite strong, ionic compounds tend to have high melting points. The attractions become stronger as the charges of the ions increase and/or the sizes of the ions decrease. The presence of both attractive (cation–anion) and repulsive (cation–cation and anion–anion) interactions helps to explain why ionic compounds are brittle. Like metals the structures of ionic compounds tend to be symmetric, but to avoid direct contact between ions of like charge the coordination numbers (typically 4 to 8) are necessarily smaller than those seen in close-packed metals. The exact structure depends on the relative sizes of the ions and the cation-to-anion ratio in the empirical formula.

SECTION 12.6 Molecular solids consist of atoms or molecules held together by intermolecular forces. Because these forces are relatively weak, molecular solids tend to be soft and possess low melting points. The melting point depends on the strength of the intermolecular forces, as well as the efficiency with which the molecules can pack together.

SECTION 12.7 Covalent-network solids consist of atoms held together in large networks by covalent bonds. These solids are much harder and have higher melting points than molecular solids. Important examples include diamond, where the carbons are tetrahedrally coordinated to each other, and graphite where the carbon atoms form hexagonal layers through sp2 bonds.

Elemental semiconductors, like Si and Ge, as well as compound semiconductors, like GaAs, InP, and CdTe, are important examples of covalent-network solids. In a semiconductor the filled bonding molecular orbitals make up the valence band, while the empty antibonding molecular orbitals make up the conduction band. The valence and conduction bands are separated by an energy that is referred to as the band gap. The size of the band gap increases as the bond distance decreases, and as the difference in electronegativity between the two elements increases.

Doping semiconductors changes their ability to conduct electricity by orders of magnitude. An n-type semiconductor is one that is doped so that there are excess electrons in the conduction band; a p-type semiconductor is one that is doped so that there are missing electrons, which are called holes, in the valence band.

SECTION 12.8 Polymers are molecules of high molecular weight formed by joining together large numbers of small molecules called monomers. Plastics are materials that can be formed into various shapes, usually by the application of heat and pressure. Thermoplastic polymers can be reshaped, typically through heating, in contrast to thermosetting plastics, which are formed into objects through an irreversible chemical process and cannot readily be reshaped. An elastomer is a material that exhibits elastic behavior; that is, it returns to its original shape following stretching or bending.

In an addition polymerization reaction, the molecules form new linkages by opening existing π bonds. Polyethylene forms, for example, when the carbon–carbon double bonds of ethylene open up. In a condensation polymerization reaction, the monomers are joined by splitting out a small molecule from between them. The various kinds of nylon are formed, for example, by removing a water molecule from between an amine and a carboxylic acid. A polymer formed from two different monomers is called a copolymer.

Polymers are largely amorphous, but some materials possess a degree of crystallinity. For a given chemical composition, the crys-tallinity depends on the molecular weight and the degree of branching along the main polymer chain. Polymer properties are also strongly affected bycross-linking, in which short chains of atoms connect the long polymer chains. Rubber is cross-linked by short chains of sulfur atoms in a process called vulcanization.

SECTION 12.9 When one or more dimensions of a material become sufficiently small, generally smaller than 100 nm, the properties of the material change. Materials with dimensions on this length scale are called nanomaterials. Quantum dots are semiconductor particles with diameters of 1–10 nm. In this size range the material's band gap energy becomes size-dependent. Metal nanoparticles have different chemical and physical properties in the 1–100-nm size range. Gold, for example, is more reactive and no longer has a golden color. Nanoscience has produced a number of previously unknown forms of sp2-hybridized carbon. Fullerenes, like C60, are large molecules containing only carbon atoms. Carbon nanotubes are sheets of graphite rolled up. They can behave as either semiconductors or metals depending on how the sheet was rolled. Graphene, which is an isolated layer from graphite, is a two-dimensional form of carbon. Applications of these nanomaterials are being developed now for imaging, electronics, and medicine.


• Classify solids based on their bonding/intermolecular forces and understand how difference in bonding relates to physical properties. [Section 12.1]

• Know the difference between crystalline and amorphous solids. Understand the relationships between lattice vectors and unit cell. [Section 12.2]

• Understand why there are a limited number of lattices. Be able to recognize the four two-dimensional and the seven three-dimensional primitive lattices. Know the locations of lattice points for body-centered and face-centered lattices. [Section 12.2]

• Calculate the empirical formula and density of ionic and metallic solids from a picture of the unit cell. Be able to estimate the length of a cubic unit cell from the radii of the atoms/ions present. [Sections 12.3 and 12.5]

• Explain how homogeneous and heterogeneous alloys differ. Describe the differences between substitutional alloys, interstitial alloys, and intermetallic compounds. [Section 12.3]

• Use the molecular-orbital model to qualitatively predict the trends in melting point, boiling point, and hardness of metals. [Section 12.4]

• Predict the structures of ionic solids from their ionic radii and empirical formula. [Section 12.5]

• Be able to use the periodic table to qualitatively compare the band gap energies of semiconductors. [Section 12.7]

• Understand how n-type and p-type doping can be used to control the conductivity of semiconductors. [Section 12.7]

• Understand how polymers are formed from monomers and recognize the features of a molecule that allow it to react to form a polymer. Understand the differences between addition polymerization and condensation polymerization. [Section 12.8]

• Understand how the interactions between polymer chains impact the physical properties of polymers. [Section 12.8]

• Understand how the properties of bulk semiconductors and metals change as the size of the crystals decreases into the nanometer-length scale. [Section 12.9]

• Be familiar with the structures and unique properties of fullerenes, carbon nanotubes, and graphene. [Section 12.9]


Relationship between cation and anion coordination numbers and the empirical formula of an ionic compound