Lecture23_MS2

Lecture23_MS2 - 1 Structure of Solids Quantum Statistics Free Electron Gas in Metals Summary 2 Face-centered cubic(fcc Salts LiF KF KCl KI NaCl

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2 Structure of Solids Quantum Statistics Free Electron Gas in Metals Summary
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3 Face-centered cubic (fcc) Salts: LiF, KF, KCl, KI, NaCl Metals: Ag, Al, Au, Ca, Cu, Ni, Pb
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4 Simple cubic (sc) Examples: CsCl, NH 4 Cl, Ba, Fe, K, Na
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5 Hexagonal close-packed (hcp) Examples: Be, Cd, Mg, Zn
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6 + - + + + - - The electric potential at a given ion is the sum of the electric potentials due to every other ion in the solid. Na + Cl -
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7 Therefore, the net electrostatic potential energy of an ion such as Cl - is given by U = e k e i r i i For the 6 nearest neighbors of the chlorine ion the electrostatic potential energy is Na + Cl - r
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8 When the sum is extended over the whole solid, the factor of 6 is replaced by the factor α called the Madelung constant and the net electrostatic potential energy is given by For NaCl α = 1.7476 and the equilibrium separation between the ions is r 0 = 0.282 nm Na + Cl - r
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9 The potential energy associated with the repulsive force can be modeled by So the total potential energy of an ion is Na + Cl - r The constant A can be found by noting that U is a minimum at r = r 0 .
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The equilibrium separation, r 0 , can be deduced from the density of the solid and its crystal structure. Example : The density of NaCl is ρ = 2.16 g/cm 3 and each ion is associated with a cube of volume r 0 3 , i.e., 2 r 0 3 for Na + Cl - . The molar mass of NaCl is
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This note was uploaded on 02/17/2010 for the course PHY PHY3101 taught by Professor Prosper during the Spring '10 term at FSU.

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Lecture23_MS2 - 1 Structure of Solids Quantum Statistics Free Electron Gas in Metals Summary 2 Face-centered cubic(fcc Salts LiF KF KCl KI NaCl

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