FL&O_section_4[2] - 4 Ceramics and Semiconductors...

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4. Ceramics and Semiconductors. In this chapter we analyze the consequences of a filled valence band. The chemical bond that is obtained in this case is covalent for elemental solids and ionic or mixed covalent-ionic for compounds. The nature of the chemical bond controls the crystal structure of the materials. These bonds are generally stronger than the metallic bond and give the solid a high melting temperature that prevents casting from a melt. Ceramics are hard and brittle: they cannot be machined the way metals are. Ceramic pieces are fabricated by forming a paste, consisting of the ceramic powder and water, into a near-final shape and solidifying it by firing. Firing causes sintering of the ceramic particles through diffusion of atoms or molecules. Glass is an amorphous silicon oxide with the addition of sodium, magnesium or boron. These additions form positive ions that neutralize the oxygen atoms and allow a disordered structure. Glass does not have a melting point but increases its viscosity, upon cooling, to values so high that the glass cannot be deformed at room temperature. The fabrication of glass objects makes use of its high viscosity. Cement is a ceramic that hardens by a chemical reaction with water. Hardening increases with time and reaches its final value in more than a year. 4.1. A filled valence band and the resulting properties of the solid. Diamond (i.e. carbon), silicon and germanium, have 4 valence electrons. Their valence band is completely filled. An energy gap separates the filled valence band from a higher, empty band of electron orbitals. (See figure 4.1.C). Figure 4.1. Energy bands in metals and ceramics. Gray fields: occupied energy levels. White fields: unoccupied energy levels. A) Metal with less than 2 valence electrons per atom. B) Metal with 2 valence electrons per atom and overlapping bands. C) Insulating ceramic with full valence band separated by large energy from upper, empty band. D) A B C D Metal Metal Insulator Semiconductor N 2N 2N 2N Electron Energy Energy Gap
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Semiconductor with full energy band separated by small energy from upper, empty, conduction band. In diamond, this energy gap is 8.5 eV, which is too large for thermal excitation of electrons at any practicable temperature. By virtue of Pauli’s exclusion principle, none of the electrons can move from one orbital to another in the band since two electrons already occupy any possible orbital. The consequences are illustrated in figure 4.2. An applied electric field cannot accelerate the electrons in this material: no current can flow. The orbitals (shapes) of the four valence electrons dictate the positions of the four atoms to which any atom is bonded. To change the position of any atom would require novel orbitals (red arrow in figure 4.2) which do not exist in the valence band; the formation of an intermediate bonding orbital i would require the excitation of electrons into the higher, empty, band. This, in diamond, with a gap of 8.5 eV, would require an impossibly large stress. No plastic deformation is possible and diamond is the hardest material known.
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FL&O_section_4[2] - 4 Ceramics and Semiconductors...

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