1.4 Crystals II Flashcards
How are the BZ and the reciprocal lattice related?
A BZ is any primitive unit cell of the reciprocal lattice
When are waves in a crystal unchanged?
When k is shifted by a reciprocal lattice vector
What is unique about the values of the BZ in 2D and 3D
They have the same area in 2D
Same volume in 3D
What is the approximate order of magnitude for the wavelengths of an x-ray?
Angstroms = 10^-10m
Describe the relationship between the separation of diffraction maxima and the grating spacing for optical diffraction and how this is applied to x-rays and crystals
Can deduce grating spacing from the separation of the diffraction maxima using Bragg’s law
Use this idea for lattice planes in a crystal
In X-ray diffraction, what can be calculated from the separation of the maxima?
The spacing of the lattice planes
Describe the similarity to lattice planes and the grating
Lattice points/planes are the analogue of the grating
Describe the similarity of the basis and the x-ray path
Basis is the structure of the x-ray path
State the three XRD techniques
- Polychromatic X-rays which peak at multiple wavelengths
- Monochromatic X-rays and rotate the angle theta to find the maxima
- Powder X-ray diffraction where we get cones of scattered x-rays which satisfy Bragg’s law
Describe neutron scattering
A neutral particle that scatters off of nuclei
- Potential is very short range
Describe x-ray scattering
Scattering is from electrons and related to electron density
- Scatter strongly off of heavier atoms
Describe the selection rules for the values of h k l for simple cubics, BCC and FCC
Simple Cubic: all h k l allowed. Get diffraction peaks from different planes
BCC: h+k+l = even for a diffraction peak
FCC: h k l all odd or even for a diffraction peak
