E4511ps2-txt - Engineering 45 The Structure and Properties...

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Page 1 Engineering 45 The Structure and Properties of Materials Spring, 2011 Problem Set No. 2 Problem 1: Fig. 2.9 of the notes contains a schematic drawing of the energy bands in sodium (valence 1) as a function of the internuclear separation. Assume that a roughly similar diagram pertains to Mg (valence 2) and Al (valence 3), which are the next two elements in the same row of the periodic table. [This is only true in a rough approximation. Mg and Al do not even have the same crystal structure as Na. However, the three elements do have the common property that the bands arising from the 3s and 3p states overlap at separations near the equilibrium separation, r 0 .] Fig. 2.1: Energy bands as a function of internuclear distance in Na. Now suppose that you are given a means for controlling the internuclear separation precisely; for example, you may employ a well-disciplined troop of 10 23 Maxwell demons who push the atoms apart or pull them together on command. Show that at a critical value of the equilibrium separation Mg changes from a metal to a
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This note was uploaded on 04/05/2011 for the course ENGIN 45 taught by Professor Devine during the Spring '07 term at University of California, Berkeley.

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E4511ps2-txt - Engineering 45 The Structure and Properties...

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