Chapter 5 ' Thermal Vibrations and Diffuse Scattering

1
Chapter 5 . Thermal Vibrations and Diffuse
Scattering
5.1 Introduction
In real crystals, atoms vibrate around the
lattice points.
Reduce the intensity of Bragg reflections by a
factor exp-2M. M Devye-Waller factor
The width of the peak does not change unless
the vibration is so large that a crystal melts.
maintain long-range order
M-th atom
Position of M-th atom
2
Harmonic Approximation
k phonon wave vector e phonon polarization
3
5.2 Debye-Waller Factor
Factor for overall decrease of the scattering
intensity
Thermodynamics
q2 dependence
Equipartition Theorem Each mode contribute
1/2kBT to total kinetic energy
4
Debye Waller Factor
5.3 First Order Thermal Diffuse Scattering
Io Bragg Peak with reduced intensity
I1 First Order Thermal Diffuse
I2 Second Order Thermal Diffuse
5
Mathematical identity
k
q
G
6
Transverse Phonon
Phonon Polarization direction
Longitudinal Phonon
Dispersion relation
Sound velocity
Bragg Peak
1/q2 thermal diffuse scattering
7
(No Transcript)
8
Longitudinal wave and diffraction pattern
Transverse wave and diffraction pattern
9
5.3 Thermal Diffuse Scattering and Elastic
Constants
Cubic Crystal
1. lt100gt direction - 1 longitudinal and 2
transverse(degenerate)
2. lt110gt direction
1 longitudinal and 2 transverse
10
3. lt111gt direction
1 longitudinal and 2 transverse
Other than the three symmetry directions,
solutions are no longer pure longitudinal or
transverse