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tetrahedra, in which the oxygen atoms are located at the corners of the tetrahedron in both the crystalline and amorphous states. Crystalline silica, for example, is composed of an ordered repeating pattern of three‐dimensional structures in which the oxygen atom at each corner of an SiO4 tetrahedron is shared with that of a neighboring tetrahedron. Crystalline silica occurs in three different crystalline forms (polymorphs) called cristobalite, tridymite, and quartz. Figure 3.9a illustrates the arrangement of the SiO4 tetrahedra in cristobalite.

Schematic illustration of (a) ordered arrangement of SiO4 tetrahedra in crystalline silica (cristobalite) and (b) non-ordered arrangement in amorphous silica glass.

      Crystal Structure of Hydroxyapatite

Schematic illustration of (a) Arrangement of atoms in a phosphate (PO4)3- ion; (b) arrangement of atoms (ions) in unit cell of hydroxyapatite.

      The name hydroxyapatite refers to a crystalline material with the stoichiometric composition Ca10(PO4)6(OH)2. In comparison, the inorganic constituent of hard tissues such as bone and teeth is not pure hydroxyapatite. Instead, it has a composition that deviates from this stoichiometric composition to varying extent, depending on the living organism and the location of the hard tissue in the organism. The host ions in hydroxyapatite are substituted by small to trace amounts of other ions, such as (CO3)2−, (HPO4)2−, Mg2+, Na+, Sr2+, K+, and F (Section 3.4.1). This substituted composition, is one factor that contributes to the unique properties of the hydroxyapatite‐like material of bone. As the properties of a material are dependent on its composition, there has been significant interest in producing synthetic hydroxyapatite‐like materials with compositions that approximate the inorganic constituent of bone (Chapter 7).

      3.3.3 Structure of Inorganic Glasses

      The term glass commonly refers to inorganic materials that have an amorphous structure. Although the structure of a glass has short‐range order arising from bonding of an atom with its immediate neighbors, the structure has no long‐range order. Silica can be produced in both crystalline and amorphous states and a comparison of their structures provides a useful illustration of the difference between a crystalline material and a glass (Figure 3.9). Although silica glass is composed of SiO4 tetrahedra with corner‐sharing oxygen atoms as in crystalline silica, its three‐dimensional structure is composed of a network with no long‐range order.

Schematic illustration of the structure of a sodium silicate glass.

      Silicate glasses, composed of the SiO2 glass‐forming network, are the most commonly used glasses, accounting for over ~95% of the tonnage in industrial and commercial applications. A common silicate glass composition is one that is used for windows of buildings, composed of ~70% SiO2, ~15% Na2O, and ~10% CaO by weight, plus minor amounts of other oxides. Borate glasses, composed of the B2O3 glass‐forming network, and borosilicate glasses, composed of interspersed SiO2 and B2O3 networks, also see considerable use commercially. Phosphate glasses, composed of the P2O5 glass‐forming network, are used to a more limited extent.

      3.3.4 Structure of Carbon Materials

      In the solid state, carbon can exist in several different structures, called allotropes, due to the different ways in which carbon atoms can bond together. Three allotropes, diamond and graphite, both of which are crystalline, and amorphous carbon have been well known for many years. Although they are not compounds, these three carbon materials are often classified as ceramics because they show several properties that are

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