Callister Chapter 2: Atomic Structure and Interatomic Bonding

The way atoms are arranged and how they interact with each other within a material directly affect the material’s properties. The most classic example of this is the comparison between graphite and diamond, both of which are made of carbon but which have very different properties. In graphite, each carbon atom is bonded to three other carbons, forming sheets that easily slide past each other. In diamond, each atom is bonded to four other carbons, forming strong tetrahedra throughout the crystal, making diamond the hardest known material. In this chapter, we will discuss atomic structure, bonding forces and energies, and types of bonds.

Atomic structure

-an atom consists of a tightly bound nucleus of protons and neutrons that are surrounded by an electron cloud

-towards the end of the nineteenth century, it became clear than many phenomena involving electrons could not be explained with classical mechanics, leading to the birth of quantum mechanics

-the main stipulation of quantum mechanics is that electrons have quantized energies (they can only have specific values of energy)

-two of the main models used to describe atoms are the Bohr atomic model and the wave-mechanical model

-the Bohr model assumes that electrons revolve around the nucleus in discrete orbitals, as seen in the figure below

-in the wave-mechanical model, an electron is not simply a particle moving in discrete orbitals; its position is described by a probability distribution instead

-the size, shape, and spatial orientation of an electron’s probability density can be described by four parameters (quantum numbers)

-the principal quantum number (n = 1, 2, 3, etc… or K, L, M, etc…) specifies the shell, which gives the electron’s distance from the nucleus

-the second quantum number (l = s, p, d, f) represents the subshell and is related to the shape of the electron subshell (restricted to number of shells n)

-the third quantum number, m_l, describes the number of energy states for each subshell

-the fourth quantum number, m_s, can be either +1/2 or -1/2 and corresponds to an electron’s spin moment

-electrons follow the Pauli exclusion principle when filling up energy states (each state can only hold two electrons, which must have opposite spins)

-the way energy states are occupied can be described by an atom’s electron configuration (ex: hydrogen is 1s¹, helium is 1s², sodium is 1s²2s²2p⁶3s¹)

Bonding forces and energies

-when two atoms are far apart, their interactions are negligible

-as they move closer together, they begin to exert forces on each other

-these forces include an attractive force and a repulsive force, both of which are a function of the distance between the two atoms (see figure below)

-when the attractive and repulsive forces balance each other out (that is, when the net force is zero), the two atoms will exist in a state of equilibrium at an equilibrium distance r_o

Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print.

-another way of looking at this is by considering the potential energies between the two atoms instead

-the relationship between force and energy is:

-the resultant graph in terms of potential energies can be seen in the figure below:

Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2007. Print.

-treating the situation this way allows us to understand the bonding energy of two atoms, E_o, which corresponds to the energy at the equilibrium distance

-the shape of these force curves and the magnitude of E_o vary with properties such a melting temperatures, mechanical stiffness, and bonding type — leading us to the last section…

Interatomic bonds

-there are three types of primary bonds: ionic, covalent, and metallic

-primary bonds occur between valence electrons and are driven by the tendency of atoms to assume their stable electron configurations

-secondary bonds, which are weaker, include van der Waals bonds and hydrogen bonds

-most interatomic interactions consist of a mixture of different types of bonds

Ionic bonding

-ionic bonding occurs between metallic and nonmetallic elements, with the metallic element giving up its valence electrons to the nonmetallic element such that all atoms have stable electron configurations

-as a result, the atoms become ions of positive and negative charge and thus are attracted to each other by coulombic forces

-the attractive energy has a -1/r dependence while the repulsive energy has a 1/rⁿ dependence (n depends on the system but is often ~8)

-bonding energies are fairly large, resulting in high melting temperatures in ionic solids

-ionic materials are usually hard and brittle as well as electrically and thermally insulative

Covalent bonding

-covalent bonds form when the sharing of electrons between adjacent atoms results in stable electron configurations

-an atom can form 8 – N covalent bonds, where N is its number of valence electrons

-covalent bonds are directional (they exist in the direction between the two atoms that are sharing electrons) and are very strong

Metallic bonding

-as the name suggests, metallic bonds are found in metals and their alloys

-metals generally have one to three valence electrons; these electrons are not bound to particular atoms and are called the “sea of electrons”

-atomic nuclei and nonvalence electrons form ion cores

-the “sea of electrons” shield these ion cores from each other’s repulsive forces and holds them together

-metallic bonds are thus nondirectional

-the “sea of electrons” explains why metals are good conductors

Secondary bonding

-van der Waals bonds are much weaker than the previously discusses primary bonds, but are always present

-this type of bonding is the result of attractive forces between electric dipoles (which can be either induced or permanent)

-hydrogen bonding is a special type of secondary bonding that occurs in molecules that have hydrogen (when hydrogen covalently bonds to a nonmetallic element, a highly polar molecule is formed)