17 | Network Solids

Covalent bonding where electrons are more localized between atoms in a structure do not follow the simple rules of sphere packing or eutactic maximum volume structures used to derive many of the fundamental ionic compounds discussed up to this point. Instead orbital mixing overlap play significant roles in determining the most stable structures that are observed. Two examples of covalent solids are the allotropes of carbon and the mineral silicates and aluminosilicates including quartz, feldspars, micas, and zeolites.

Allotropes of carbon

Diamond

Formula: C
Space group: \(Fd\bar{3}m\)
Lattice: Cubic-F
Cell: \(a = 3.567\,\text{Å}\)
Z: 8   V: \(45.39\,\text{Å}^3\)

Fig. 46 Crystal structure diamond with the space group \(Fd\bar{3}m\). Compart to zinc blende with the space group \(F\bar{4}3m\). cubic-BN is isostructural with diamond.

Graphite

Formula: C
Space group: \(P\frac{6_3}{m}mc\)
Lattice: Hexagonal-P
Cell: \(a = 2.464\,\text{Å},\,c = 6.711\,\text{Å}\)
Z: 4   V: \(35.29\,\text{Å}^3\)

Fig. 47 Crystal structure of hexagonal carbon graphite. hex-BN is isostructural with graphite.

Fullerenes

Formula: C₆₀
Space group: \(P a \bar{3}\)
Lattice: Cubic-P
Cell: \(a = 14.14\,\text{Å}\)
Z: 4   V: \(2827\,\text{Å}^3\)

Fig. 48 Crystal structure of the molecular carbon allotrope fullerene.

Silicates

The silicates form covalent bond networks base on vertex sharing tetrahedral SiO₄ building units. SiO₂ alone displays a diverse range of polymorphs including the structures quartz, cristobalite, and tridymite. With the addition of Al³⁺ cations and the alkali metal cations, the silicates and aluminosilicates comprise the vast majority of the earth’s crust. Quartz is the most common polymorph of SiO₂ while cristobalite and tridymite are high-temperature polymorphs of SiO₂.

Quartz

Formula: SiO₂
Space group: \(P 3_2 21 \)
Lattice: Trigonal-P
Cell: \(a = 4.921\,\text{Å},\,c = 5.400\,\text{Å}\)
Z: 3   V: \(113.2\,\text{Å}^3\)

Fig. 49 Crystal structure of SiO₂ quartz.

Cristobalite

Formula: SiO₂
Space group: \(F d \bar{3} m \)
Lattice: Cubic-F
Cell: \(a = 7.12 \text{Å}\)
Z: 8   V: \(360.9\,\text{Å}^3\)

Fig. 50 Crystal structure of SiO₂ cristobalite. Note the similarity to sphalerite and diamond though here the anions are two-coordinate.

Tridymite

Formula: SiO₂
Space group: \( C 2 2 2_1\)
Lattice: Orthorhombic-C
Cell: \(a = 8.755 \text{Å},\,b = 5.034 \text{Å},\,c = 8.212 \text{Å}\)
Z: 8   V: \(361.9\,\text{Å}^3\)

Fig. 51 Crystal structure of SiO₂ cristobalite.

Aluminosilicates

The earth’s crust is composed mostly of aluminosilicate minerals making aluminosilicates humanities most abundant materials.

Mica

Micas and clays are layered aluminosilicates. Of the two classes of materials micas are more crystalline and form as large flaky crystals. The atomic structures between the two groups are very similar. Muscovite is shown in muscovite-type where a relatively strong 2D bond network is formed in the AlSiO₁₂ layers and the K⁺ cations are sandwiched between the layers. Micas are known for their easy cleavage along the layers, indicative of only weak bonding between the AlSiO₁₂ layers. With smaller grain sizes clays also have relative fast ion exchange properties and are commonly used as adsorbents, and ion exchange materials for this reason. The adsorption of ammonium and other life essential nutrients into clays is one of the most import applications of intercalation chemistry by enabling the fertilization of soils.

Formula: KAl₃Si₃O₁₀(OH)₂
Space group: \(P3_1 12 \)
Lattice: Trigonal-P
Cell: \(a = 5.196 \text{Å},\,c = 29.97 \text{Å}\)
Z: 3   V: \(700.8\,\text{Å}^3\)

Fig. 52 Crystal structure of muscovite a layered aluminosilicate also known as common micas. Layered mica The elements shown are K in purple, Al in blue, Si in teal, and O in red.

Feldspar

Feldspar is the most abundant mineral in the early crust. While Feldspars have a range of chemical compositions, minerals with this structure account for over half of the material that composes the earth’s crust.

Formula: KAlSi₃O₈
Space group: \(C\frac{2}{m} \)
Lattice: Monclinic-C
Cell: \(a = 8.600 \text{Å},\,b = 13.02 \text{Å},\,\)
   \(c = 7.22 \text{Å},\,\beta = 116.1º\)
Z: 4   V: \(726.3\,\text{Å}^3\)

Fig. 53 Crystal structure of orthoclase a feldspar. The elements shown are K in purple, Al in blue, Si in teal, and O in red.

Zeolites

Zeolites are a class of both natural and synthetic aluminosilicates that form porous structures with a broad range of applications in gas storage, chemical separations, and catalysis. Two of the most common zeolite structures encountered in the chemistry lab are Linde Type A (aka, LTA, 3 Å and 4 Å molecular sieves), and Faujasite (13X molecular sieves). Both are synthesize using hydrothermal conditions and upon crystallization contain a large amount of water in the pores. The water can be removed by heating post-synthesis to create the activated zeolite. In Fig. 54 are shown simplified representations of these crystal structures with only the Si and Al tetrahedra shown. Linde Type A and Faujasite are only two of over 230 unique tilings of tetrahedra that are identified as zeolites.

Fig. 54 Crystal structure of Linde Type A, \(Na_{12}Al_{12}Si_{12}O_{48}\cdot 27H_2O\), and Faujasite, \((Na_2,Ca,Mg)_{3.5}[Al_7Si_{17}O_{48}]\cdot32 H_2O\), zeolites. The mixed Si/Al sites are shown as teal tetrahedron. Oxygen atoms are shown in red. Water and alkali metal cations not shown.