2.2 Atomic Bonding

We have been considering various single-crystal structures. The question arises as to why one particular crystal structure is favored over another for a particular assembly of atoms. A fundamental law of nature is that the total energy of a system in thermal equilibrium tends to reach a minimum value. The interaction that occurs between atoms to form a solid and to reach the minimum total energy depends on the type of atom or atoms involved. The type of bond，or interaction，between atoms，then，depends on the particular atom or atoms in the crystal. If there is not a strong bond between atoms，they will not “stick together” to create a solid.

The interaction between atoms can he described by quantum mechanics. The quantum-mechanical description of the atomic bonding interaction is beyond the scope of this text. We can nevertheless obtain a qualitative understanding of how various atoms interact by considering the valence，or outermost，electrons of an atom.

The atoms at the two extremes of the periodic table（excepting the inert elements）tend to lose or gain valence electrons，thus forming ions. These ions then essentially have complete outer energy shells. The elements in group I of the periodic table tend to lose their one electron and become positively charged. While the elements in group Ⅶ tend to gain an electron and become negatively charged. These oppositely charged ions then experience a coulomb attraction and form a bond referred to as an ionic bond . If the ions were to get too close，a repulsive force would become dominant，so an equilibrium distance results between these two ions. In a crystal，negatively charged ions tend to be surrounded by positively charged ions and positively charged ions tend to he surrounded by negatively charged ions，so a periodic array of the atoms is formed to create the lattice. A classic example of ionic bonding is sodium chloride.

Fig.2.4 Representation of（a）hydrogen valence electrons and（b）covalent bonding in a hydrogen molecule.

The interaction of atoms tends to form closed valence shells such as we see in ionic bonding. Another atomic bond that tends to achieve closed-valence energy shells is covalent bonding，an example of which is found in the hydrogen molecule. A hydrogen atom has one electron and needs one more electron to complete the lowest energy shell. A schematic of two noninteracting hydrogen atoms，and the hydrogen molecule with the covalent bonding，are shown in Fig.2.4. Covalent bonding results in electrons being shared between atoms，so that in effect the valence energy shell of each atom is full.

Fig.2.5 Representation of（a）silicon valence electrons and（b）covalent bonding in the silicon crystal.

Atoms in group Ⅳ of the periodic table，such as silicon and germanium，also tend to form covalent bonds. Each of these elements has four valence electrons and needs four more electrons to complete the valence energy shell. If a silicon atom，for example，has four nearest neighbors，with each neighbor atom contributing one valence electron to be shared，then the center atom will in effect have eight electrons in its outer shell. Fig.2.5（a）schematically shows live noninteracting silicon atoms with the four valence electrons around each atom. A two-dimensional representation of the covalent bonding in silicon is shown in Fig.2.5（b）. The center atom has eight shared valence electrons.

A significant difference between the covalent bonding of hydrogen and of silicon is that，when the hydrogen molecule is formed，it has no additional electrons to form additional covalent bonds，while the outer silicon atoms always have valence electrons available for additional covalent bonding. The silicon array may then be formed into an infinite crystal，with each silicon atom having four nearest neighbors and eight shared electrons. The four nearest neighbors in silicon forming the covalent bond correspond to the tetrahedral structure and the diamond lattice. Atomic bonding and crystal structure are obviously directly related.

The third major atomic bonding scheme is referred to as metallic bonding. Group I elements have one valence electron. If two sodium atoms（Z=11），for example，are brought into close proximity，the valence electrons interact in a way similar to that in covalent bonding. When a third sodium atom is brought into close proximity with the first two，the valence electrons can also interact and continue to form a bond. Solid sodium has a body-centered cubic structure，so each atom has eight nearest neighbors with each atom sharing many valence electrons. We may think of the positive metallic ions as being surrounded by a sea of negative electrons，the solid being held together by the electrostatic forces. This description gives a qualitative picture of the metallic bond.

A fourth type of atomic bond，called the Van der Waals bond，is the weakest of the chemical bonds. A hydrogen fluoride（HF）molecule，for example，is formed by an ionic bond. The effective center of the positive charge of the molecule is not the same as the effective center of the negative charge. This non symmetry in the charge distribution results in a small electric dipole that can interact with the dipoles of other HF molecules. With these weak interactions，solids formed by the Van der Waals bonds have a relatively low melting temperature—in fact，most of these materials are in gaseous form at room temperature.