{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture23_MS2 - 1 Structure of Solids Quantum Statistics...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 Structure of Solids Quantum Statistics Free Electron Gas in Metals Summary
Background image of page 2
3 Face-centered cubic (fcc) Salts: LiF, KF, KCl, KI, NaCl Metals: Ag, Al, Au, Ca, Cu, Ni, Pb
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 Simple cubic (sc) Examples: CsCl, NH 4 Cl, Ba, Fe, K, Na
Background image of page 4
5 Hexagonal close-packed (hcp) Examples: Be, Cd, Mg, Zn
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 -
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 8
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 .
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 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 - .
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}