I. Introduction
What does “condensed” mean?
Reciprocal lattice, importance in diffraction, definition of the Brillouin zone.
II. Lattice dynamics:
The heat capacity
The model of Dulong-Petite
The model of Einstein
The Bose-Einstein statistical distribution
Acoustic waves in elastic bodies
The discrete atomic structure and the importance of the Brillouin zone
The model of Debye
The Debye-Waller factor in diffraction
III. The electronic structure of materials
The basics of Quantum Mechanics and the notation of Eigenstates
The model of free electrons
Density of electron states
Fermi-Dirac Statistics
Contact voltage
Specific heat of the electrons
Electronic conductivity, heat conductivity and the Wiedemann-Franz Law
Definition of the reciprocal lattice
b ×c
c×b
a×b
a* = 2π
; b* = 2π
; c* = 2π
a (b × c)
b ( c ×a )
c ( a ×b )
Real lattice and reciprocal lattice are directly
joined to each other. E.g. if real lattice is rotated,
than also the reciprocal one.
V = a ( b ×c ) = b ( c× a ) = c ( a ×b )
Miller Indexes
e2
Lattice plane set
Real Lattice
e1
(1,2,.)
Miller indexes:
Reciprocal of the sections at the respective axes
(In the two-dimensional example here:
(1, 2, 0)
)
Relation between real and reciprocal lattice
[1,2,.]
e*2
e2
Reciprocal
Lattice
Plane Set
Real Lattice
e1
e*1
(1,2,.)
note the different style of brackets in crystallography:
Round brackets belong the reciprocal lattice (directions of plane normals)
Squared brackets belong to the real space (directions of real vectors)
Geometry of a scattering experiment
Incoming plane wave
Representation of diffraction condition by the „Ewald Sphere“
Reciprocal
lattice
Elastic scattering: Incoming and outgoing wave have the same
wave length (same length of the wave vector) ( k 0 = k ' )
Definition of the Brillouin Zone
perpendicular
bisectors
Wigner-Seitz cell in
the reciprocal lattice
bcc
fcc
hcp