Brillouin Zone-Solid State Physics-Lecture Slides, Slides of Solid State Physics

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 A Wigner-Seitz Cell in the reciprocal lattice is called Brillion Zone

 Brillouin Zone gives a vivid geometrical interpretation of diffraction condition 2k.G = G^2

 Where k is wave vector and G is reciprocal lattice vector

 It is also known as first Brillouin Zone

 General, the n -th Brillouin zone consists of the set of points that can be reached from the origin by crossing exactly n − 1 distinct Bragg planes

 The 1st^ Brillouin zone is the smallest volume entirely

enclosed by the planes that are perpendicular bisectors

of the reciprocal lattice vectors drawn from the origin.

 Extended Zone Scheme

 That region of wave number space giving rise to second Brillouin zone, similarly the 3rd, 4th^ and 5th, so on…, could be constructed. This procedure is called extended Brillouin zone scheme

 Reduced Zone Scheme

 From different zone schemes, in which all bands are drawn in the first brillouin zone is called reduced zone scheme

 Periodic Zone Scheme

 A scheme in which every band is drawn in every zone

 The crystal structures are all cubic close-packed (fcc) except He^3 and He^4

 He, Ne, Ar, Kr, Xe are called the inert gases

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Inert Gases Nearest Neighbor distance (Å)

Experimental cohesive energy

Melting point (k)

Ionization energy KJ/mol eV/atom^ (eV) He Liquid at zero pressure 24. Ne 313 1.88 0.02 24 21. Ar 3.76 7.74 0.080 84 15. Kr 4.01 11.2 0.116 117 14. Xe 4.35 16.0 0.17 161 12.

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 Symmetry is when one shape becomes exactly like

another if you flip, slide or turn it.

The simplest type of Symmetry is "Reflection" (or

"Mirror") Symmetry

 There are three basic types of defects in crystals

 Point Defect

 Atoms missing or in irregular places in the lattice (lattice vacancies, substitutional and interstitial impurities, self- interstitials)

 Linear Defect

 Groups of atoms in irregular positions (e.g. screw and edge dislocations)

 Planar Defect

 The interfaces between homogeneous regions of the material (grain boundaries, stacking faults, external surfaces)

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