Atomic Structure and Bonding
On the atomic level, the arrangement of electrons surrounding a nucleus determines how a particular atom will interact with other atoms . The modern understanding of electronic structure is built on the concept of the Bohr atom extended to atoms with many electrons using the principles of quantum mechanics . Each electron that surrounds a particular atom has a set of four quantum numbers that designates its shell (principal quantum number n = 1, 2, 3, etc.), its orbital (l = integer with values ranging from 0 to n – l representing the s, p, d, and f orbitals), its orientation (ml = integer with values from – l to +l), and its spin (ms = +1/2 or -1/2). By the Pauli exclusion principal, each electron surrounding an atom has a unique set of four quantum numbers . Standard versions of the periodic table are arranged in rows according to the electronic shell that is filled as the atomic number increases . For example, atoms in the first row of the periodic table (H and He) have electrons in the first shell (n = 1). The increasing number of species in the lower rows of the periodic table results from the increased number of orbitals available for occupancy as n, the principal quantum number, increases. The columns represent groups of atoms with the same outer shell configuration. For example, the atoms in column IA (H, Li, Na, K, etc.) have one electron in the s orbital of the outermost shell.
The outermost electron shell surrounding an atom is referred to as its valence shell and it is the valence shell electrons that participate in chemical bonding . Most often, it is the s and p orbital electrons (orbital quantum numbers 0 and 1) that affect the strength and directionality of chemical bonds . When bonding, atoms minimize
their energy by gaining, losing, or sharing electrons in an attempt to attain the electronic structure of the inert gas with the closest atomic number. When atoms gain or lose electrons they become ions. Ions with opposite charges form what are termed ionic bonds. If electrons are shared, directional covalent bonds are formed. Conversely, ionic bonding is nondirectional and the resulting solids tend to have high (6, 8, or 12) cation coordination numbers. For example, CsCl is an ionic compound composed of Cs+ and Cl – ions. Each Cs+ cation is surrounded by eight Cl – anions. Covalent bonds are directional based on the shape of the electron orbitals or the type of hybrid orbital that is formed to facilitate electron sharing . Covalent compounds tend to have lower cation coordination numbers (3 or 4) compared with ionic compounds. An example of a covalent compound is SiC, in which each Si atom is bound to four C atoms and the angle between each bond is ~109°, and the angle of separation for sp3 hybrid orbitals that is also known as the tetrahedral angle. In real oxide compounds, the bonds have both ionic and covalent characteristics. These bonds are referred to as iono-covalent or polar covalent [13, 16]. The degree of ionic character can be estimated using a variety of means including Pauling’s electronegativity scale, Sanderson’s model, or Mooser-Pearson plots . Oxides are not generally close-packed like compounds that are predominantly ionic, but are not as open as highly covalent compounds.
Regardless of the type of chemical bond that forms, the net force between two chemically bound atoms results from electrostatic attraction . The attractive component, Eattr, of the total bond energy between two atoms is a function of the distance between them, r. The normal form of the attractive force, based on Coulomb’s law, for ionic crystals is
where z1 and z2 are the valences of the two atoms, e is the charge on an electron (1.602 x 10-19 C), and e0 is the permittivity of free space (8.854 x 10-12 C2 N-1 m-2).
The attractive energy acts over long ranges and can take slightly different forms for covalent bonding . Without a repulsive force to balance the attractive force, all of the atoms in the universe would eventually be drawn into a single mass of infinite density. Fortunately, as atoms approach each other, a short-range electrostatic repulsion builds due to the overlap of the charge distributions from the two atoms . Most often, the repulsive energy is expressed as the Born repulsion:
where B is an empirical constant and n is the Born exponent, also an empirical constant, usually between 6 and 12.
The net energy between two atoms is the sum of the attractive and repulsive energies . The equilibrium atomic separation, r0, occurs at the point where the net energy shows a maximum in attraction. The value of r0 can be calculated by taking the first derivative of the net energy, setting it equal to zero, and solving for r. A representative plot of the attractive, repulsive, and net energies is shown in Fig. 2. The magnitude of the maximum in the attractive energy determines the bond strength and, therefore, the lattice energy, of a crystal. Considering compounds with the same structure, differences in lattice energy affect macroscopic properties . An example comparing the lattice energies, melting temperatures, and thermal expansion coefficients of alkaline
Table 6 Lattice energy, melting temperature, thermal expansion, and modulus for alkaline earth oxides with the rock salt structure
earth oxides that have the rock salt structure (MgO, CaO, and SrO) is outlined in Table 6 [13, 17, 18]. As observed by the trend in the data, melting temperature tends to increase and thermal expansion coefficient tends to decrease as the cohesive force, expressed as the lattice energy in this example, increases.