Crystal - Bonds, Structure, Lattice (2024)

Ionic bonds

Sodium chloride exhibits ionic bonding. The sodium atom has a single electron in its outermost shell, while chlorine needs one electron to fill its outer shell. Sodium donates one electron to chlorine, forming a sodium ion (Na⁺) and a chlorine ion (Cl⁻). Each ion thus attains a closed outer shell of electrons and takes on a spherical shape. In addition to having filled shells and a spherical shape, the ions of an ionic solid have integer valence. An ion with positive valence is called a cation. In an ionic solid the cations are surrounded by ions with negative valence, called anions. Similarly, each anion is surrounded by cations. Since opposite charges attract, the preferred bonding occurs when each ion has as many neighbours as possible, consistent with the ion radii. Six or eight nearest neighbours are typical; the number depends on the size of the ions and not on the bond angles. The alkali halide crystals are binaries of the AH type, where A is an alkali ion (lithium [Li], sodium, potassium, rubidium, or cesium) and H is a halide ion (fluorine, chlorine, bromine, or iodine). The crystals have ionic bonding, and each ion has six or eight neighbours. Metal ions in the alkaline earth series (magnesium [Mg], calcium [Ca], barium [Ba], and strontium [Sr]) have two electrons in their outer shells and form divalent cations in ionic crystals. The chalcogenides (oxygen, sulfur, selenium, and tellurium) need two electrons to fill their outer p-shell. (Electron shells are divided into subshells, designated as s, p, d, f, g, and so forth. Each subshell is divided further into orbitals.) Two electrons are transferred from the cations to the anions, leaving each with a closed shell. The alkaline earth chalcogenides form ionic binary crystals such as barium oxide (BaO), calcium sulfide (CaS), barium selenide (BaSe), or strontium oxide (SrO). They have the same structure as sodium chloride, with each atom having six neighbours. Oxygen can be combined with various cations to form a large number of ionically bonded solids.

Covalent bonds

Silicon, carbon, germanium, and a few other elements form covalently bonded solids. In these elements there are four electrons in the outer sp-shell, which is half filled. (The sp-shell is a hybrid formed from one s and one p subshell.) In the covalent bond an atom shares one valence (outer-shell) electron with each of its four nearest neighbour atoms. The bonds are highly directional and prefer a tetrahedral arrangement. A covalent bond is formed by two electrons—one from each atom—located in orbitals between the ions. Insulators, in contrast, have all their electrons within shells inside the atoms.

The perpetual spin of an electron is an important aspect of the covalent bond. From a vantage point above the spinning particle, counterclockwise rotation is designated spin-up, while clockwise rotation is spin-down. A fundamental law of quantum physics is the Pauli exclusion principle, which states that no two electrons can occupy the same point in space at the same time with the same direction of spin. In a covalent bond two electrons occupy the same small volume of space (i.e., the same orbital) at all times, so they must have opposite spin: one up and one down. The exclusion principle is then satisfied, and the resulting bond is strong.

In graphite the carbon atoms are arranged in parallel sheets, and each atom has only three near neighbours. The covalent bonds between adjacent carbons within each layer are quite strong and are called σ bonds. The fourth valence electron in carbon has its orbital perpendicular to the plane. This orbital bonds weakly with the similar orbitals on all three neighbours, forming π bonds. The four bonds for each carbon atom in the graphite structure are not arranged in a tetrahedron; three are in a plane. The planar arrangement results in strong bonding, although not as strong as the bonding in the diamond configuration. The bonding between layers is quite weak and arises from the van der Waals interaction; there is much slippage parallel to the layers. Diamond and graphite form an interesting contrast: diamond is the hardest material in nature and is used as an abrasive, while graphite is used as a lubricant.

Besides the elemental semiconductors, such as silicon and germanium, some binary crystals are covalently bonded. Gallium has three electrons in the outer shell, while arsenic lacks three. Gallium arsenide (GaAs) could be formed as an insulator by transferring three electrons from gallium to arsenic; however, this does not occur. Instead, the bonding is more covalent, and gallium arsenide is a covalent semiconductor. The outer shells of the gallium atoms contribute three electrons, and those of the arsenic atoms contribute five, providing the eight electrons needed for four covalent bonds. The centres of the bonds are not at the midpoint between the ions but are shifted slightly toward the arsenic. Such bonding is typical of the III–V semiconductors—i.e., those consisting of one element from the third column of the periodic table and one from the fifth column. Elements from the third column (boron, aluminum, gallium, and indium) contribute three electrons, while the fifth-column elements (nitrogen, phosphorus, arsenic, and antimony) contribute five electrons. All III–V semiconductors are covalently bonded and typically have the zinc blende structure with four neighbours per atom. Most common semiconductors favour this arrangement.

The factor that determines whether a binary crystal will act as an insulator or a semiconductor is the valence of its constituent atoms. Ions that donate or accept one or two valence electrons form insulators. Those that have three to five valence electrons tend to have covalent bonds and form semiconductors. There are exceptions to these rules, however, as is the case with the IV–VI semiconductors such as lead sulfide. Heavier elements from the fourth column of the periodic table (germanium, tin, and lead) combine with the chalcogenides from the sixth row to form good binary semiconductors such as germanium telluride (GeTe) or tin sulfide (SnS). They have the sodium chloride structure, where each atom has six neighbours. Although not tetrahedrally bonded, they are good semiconductors.

Filled atomic shells with d-orbitals have an important role in covalent bonding. Electrons in atomic orbits have angular momentum (L), which is quantized in integer (n) multiples of Planck’s constant h: L = nh. Electron orbitals with n = 0 are called s-states, with n = 1 are p-states, and with n = 2 are d-states. Silver and copper ions have one valence electron outside their closed shells. The outermost filled shell is a d-state and affects the bonding. Eight binary crystals are formed from the copper and silver halides. Three (AgF, AgCl, AgBr) have the sodium chloride structure with six neighbours. The other five (AgI, CuF, CuCl, CuBr, CuI) have the zinc blende structure with four neighbours. The bonding in this group of solids is on the borderline between covalent and ionic, since the crystals prefer both types of bonds. The alkali metal halides exhibit somewhat different behaviour. The alkali metals are also monovalent cations, but their halides are strictly ionic. The difference in bonding between the alkali metals on the one hand and silver and copper on the other hand is that silver and copper have filled d-shells while the alkalis have filled p-shells. Since the d-shells are filled, they do not covalently bond. This group of electrons is, however, highly polarizable, which influences the bonding of the valence electrons. Similar behaviour is found for zinc and cadmium, which have two valence electrons outside a filled d-shell. They form binary crystals with the chalcogenides, which have tetrahedral bonding. In this case the covalent bonding seems to be preferred over the ionic bond. In contrast, the alkaline earth chalcogenides, which are also divalent, have outer p-shells and are ionic. The zinc and cadmium chalcogenides are covalent, as the outer d-shell electrons of the two cations favour covalent bonding.

Metallic bonds

Metallic bonds fall into two categories. The first is the case in which the valence electrons are from the sp-shells of the metal ions; this bonding is quite weak. In the second category the valence electrons are from partially filled d-shells, and this bonding is quite strong. The d-bonds dominate when both types of bonding are present.

The simple metals are bonded with sp-electrons. The electrons of these metal atoms are in filled atomic shells except for a few electrons that are in unfilled sp-shells. The electrons from the unfilled shells are detached from the metal ion and are free to wander throughout the crystal. They are called conduction electrons, since they are responsible for the electrical conductivity of metals. Although the conduction electrons may roam anywhere in the crystal, they are distributed uniformly throughout the entire solid. Any large imbalance of charge is prevented by the strong electrical attraction between the negative electrons and the positive ions, plus the strong repulsion between electrons. The phrase electron correlation describes the correlated movements of the electrons; the motion of each electron depends on the positions of neighbouring electrons. Electrons have strong short-range order with one another. Correlation ensures that each unit cell in the crystal has, on the average, the number of electrons needed to cancel the positive charge of the cation so that the unit cell is electrically neutral.

Cohesive energy is the energy gained by arranging the atoms in a crystalline state, as compared with the gas state. Insulators and semiconductors have large cohesive energies; these solids are bound together strongly and have good mechanical strength. Metals with electrons in sp-bonds have very small cohesive energies. This type of metallic bond is weak; the crystals are barely held together. Single crystals of simple metals such as sodium are mechanically weak. At room temperature the crystals have the mechanical consistency of warm butter. Special care must be used in handling these crystals, because they are easily distorted. Metals such as magnesium or aluminum must be alloyed or polycrystalline to have any mechanical strength. Although the simple metals are found in a variety of structures, most are in one of the three closest-packed structures: fcc, bcc, and hcp. Theoretical calculations show that the cohesive energy of a given metal is almost the same in each of the different crystal arrangements; therefore, crystal arrangements are unimportant in metals bound with electrons from sp-shells.

A different type of metallic bonding is found in transition metals, which are metals whose atoms are characterized by unfilled d-shells. The d-orbitals are more tightly bound to an ion than the sp-orbitals. Electrons in d-shells do not wander away from the ion. The d-orbitals form a covalent bond with the d-orbitals on the neighbouring atoms. The bonding of d-orbitals does not occur in a tetrahedral arrangement but has a different directional preference. In metals the bonds from d-orbitals are not completely filled with electrons. This situation is different from the tetrahedral bonds in semiconductors, which are filled with eight electrons. In transition metals the covalent bonds formed with the d-electrons are much stronger than the weak bonds made with the sp-electrons of simple metals. The cohesive energy is much larger in transition metals. Titanium, iron, and tungsten, for example, have exceptional mechanical strength. Crystal arrangements are important in the behaviour of the transition metals and occur in the close-packed fcc, bcc, or hcp arrangements.