A cubical single crystal of sodium chloride (rock-salt structure) has a primitive…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Lattice dynamics and thermal properties of solids

Solid State Physics, Ch Lattice dynamics in three dimensions

Problem

A cubical single crystal of sodium chloride (rock-salt structure) has a primitive cell containing

p=2

ions, of volume

a^3/4

, where

a=5.64\,\text{\AA}

is the conventional cubic lattice constant. The crystal is a cube of edge

L=2.00\,\mathrm{mm}

. ((a)) How many primitive cells

N

does the crystal contain? ((b)) Using Born-von Karman boundary conditions, how many independent normal modes does the crystal have in total? ((c)) What is the spacing

2\pi/L

of allowed wavevectors, in

\text{\AA}^{-1}

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