3.091_Notes_3 - LN3 3.091 Introduction to Solid State...

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LN–3 1 3.091 – Introduction to Solid State Chemistry Lecture Notes No. 3 BONDING IN METALS, SEMICONDUCTORS AND INSULATORS – BAND STRUCTURE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sources for Further Reading: 1. Pascoe, K.J., Properties of Materials for Electrical Engineers , J. Wiley, 1974. 2. Wert, C.A., and R.M. Thomson, Physics of Solids , McGraw-Hill, 1970. 3. Azaroff, L.V., Introduction to Solids , McGraw-Hill, 1960. 4. Mayer, J.W., and S.S. Lau, Electronic Materials Science , MacMillan, 1990. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1. INTRODUCTION Characteristic properties of metals include: (1) electrical conductivity, (2) opaqueness and (3) malleability. A very simple model in which the metallic crystal is viewed as a lattice of positive ions surrounded by a “gas” of free electrons provides a crude understanding of the first and third properties. If the crystal has a gas of free electrons, it is easy to see why the application of an electric field will result in the motion of these electrons and thus for the high electrical conductivity. This model also allows one to explain the malleability of metals, as shown in fig. 1b. When a metallic crystal is subject to forces that displace one plane of atoms with respect to another, the environment of the charged species is left unchanged. In contrast, the displacement of neighboring planes in an ionic crystal as a result of a distorting force will lead to cleavage, largely because of changes in the interaction of the charged species (fig. 1a). The free electron gas theory ( Drude–Lorentz ) also explains in principle the nature of the attractive bonding forces which hold the metallic ions (the metal) together: the crystal is held together by electrostatic forces of attraction between the positively charged metal
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LN–3 2 Fig. 1a In ionic crystals the displacement of neighboring planes by shear forces frequently results in cleavage largely because of the establishment of repulsive forces in the cleavage plane. Fig. 1b In metallic crystals the displacement of neighboring planes does not lead to charge effects; slip is a common phenomenon; metals are malleable. Figure 1 Mechanical properties of ionic and metallic crystals ions and the non-localized, negatively charged electrons - the electron gas. The theory in its original form assumes that the classical kinetic theory of gases is applicable to the electron gas ; mutual repulsion between electrons was ignored and the electrons were expected to have velocities which are temperature dependent according to a Maxwell-Boltzmann distribution law. While the Drude-Lorentz theory of metallic bonding was considered a useful model, several shortcomings soon became apparent. The most notable failure consisted of the unexplainable discrepancy between the observed and predicted specific heats of metals (energy in the form of heat, required to increase the temperature of 1 g of a given metal by 1 _ C). The D-L theory predicted much larger specific heats than are observed (because the Maxwell-Boltzmann energy distribution has no restrictions as to the number of species allowed to have exactly the same energy). [If there are
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3.091_Notes_3 - LN3 3.091 Introduction to Solid State...

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