Materials for Biomedical Engineering. Mohamed N. Rahaman

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.

Figure 3.9 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

Several types of synthetic calcium phosphate materials have been studied or developed for use in biomedical applications such as bone reconstruction, drug delivery devices and coatings for metal prostheses (Chapter 7). Implants composed of hydroxyapatite, with the formula Ca₁₀(PO₄)₆(OH)₂, β‐tricalcium phosphate, Ca₃(PO₄)₂, and a two‐phase mixture called biphasic calcium phosphate (BCP), composed of varying ratios of hydroxyapatite and β‐tricalcium phosphate, for example, have been used for decades in healing bone defects. The primary building block of β‐tricalcium phosphate and hydroxyapatite is the phosphate ion (PO₄)³⁻ in which the phosphorus and oxygen atoms form a slightly distorted tetrahedron (Figure 3.10a). As the main inorganic (mineral) constituent of hard tissues such as bone and teeth is composed of a material that resembles hydroxyapatite, considerable attention has been devoted to the structure and properties of this material. Hydroxyapatite exists in a monoclinic or a hexagonal crystal structure. The unit cell in the hexagonal structure has dimensions a = b = 0.9430 nm and c = 0.6891 nm, and bond angles α = β = 90° and γ = 120°, and it is composed of 6 (PO₄)³⁻ ions surrounded by 10 calcium ions and with 2 hydroxyl (OH)⁻ ions along the c‐axis (Figure 3.10b).

Figure 3.10 (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.

A problem with silica glass is that it starts to soften only at high temperature (above ~1200 °C), making it difficult to form the glass into objects with desirable shapes. Consequently, metal oxides are commonly added to silica during the production process to obtain a glass that can be formed and shaped more easily. These metal oxides, referred to as network modifiers, add cations to the glass structure and break up a fraction of the Si–O–Si bonds. In quantities of a few percent to a few tens of percent by weight, the network modifiers often include sodium oxide (Na₂O) and calcium oxide (CaO), but a variety of network modifiers are used in many glasses to achieve the desired properties. Figure 3.11 illustrates the structure of a glass with one of the simplest compositions, formed by adding Na₂O to silica and referred to as a sodium–silicate glass. Overall, the positive charge of the sodium cations balance the negative charge of the oxygen atoms that are no longer bonded to two neighboring silicon atoms, called non‐bridging oxygen atoms.

Figure 3.11 Schematic representation 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.

Glasses, nondegradable or bioactive, find limited use as biomaterials, mainly to treat diseased or damaged tissues and organs where their compositional flexibility and ease of forming provide attractive benefits (Chapter 7). Radioactive glass microspheres, for example, are used to treat liver cancer. Bioactive glasses, such as the silicate glass designated 45S5, are used to a limited extent to heal bone defects while bioactive borate glass in a microfibrous form is used to heal skin wounds.

      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