X-ray Diffraction- Geometry and Bragg Law Flashcards
What happens when one wave takes a longer path than another wave it was initially in phase with?
The wave with a longer path becomes delayed further along and the peaks with not always align with the other wave. This results in changes of their summed amplitude
What does it mean to say that two waves are in phase?
Their electric field vectors have the same magnitude and direction at each point measured along their path direction
When is the summed amplitude of two waves maximised?
When they are in phase. The path difference is an integral number of wavelengths, nλ, hence the phase difference is 2nπ and there is constructive interference
When is the summed amplitude of two waves zero?
If the waves are out of phase and the path difference is an integral number and a half of wavelengths, (n+1/2)λ. The phase difference is (2n+1)π and there is destructive interference
What causes difference in path lengths of x-rays from a crystal?
The scattering of x-rays by parallel planes of atoms. The incident waves were in phase but we’re reflected by successive planes causing a phase difference
Describe diffraction of x-rays
In certain directions, the summed amplitude of the scattered waves is maximised if the individual waves are in phase. The directions of diffraction are given by the Bragg law
Rule for reflection angles
Angle of incidence θ and angle of reflection are equal
For two planes of aligned atoms and two waves at an angle, what is the path difference δ between them?
Twice the extra distance travelled by one before it meets the atom in the second plane.
δ=2dhkl sinθ
Where d subscript hkl is the separation of the two miller planes
Bragg law
nλ=2dhkl sinθ
Comes from δ=nλ
Diffraction comes as consequence of λ being roughly d
What is n in the Bragg law?
The order of diffraction. Represents the number of wavelengths equal to the path between x-rays scattered by adjacent hkl planes
What is the second order reflection from the 001 plane equivalent to?
The first order reflection from the 002 plane
Because d001=2d002
What is the convention for assuming orders of reflection?
Assume first order reflection and take n=1. Particularly when we have not worked out the index (hkl) of a diffraction peak yet
How to work out track spacing on a CD
Shine laser pointer of known wavelength on CD. Wavelength is similar to spacing between tracks so they diffract laser beam. Measuring the angle of diffraction (between perpendicular incident ray and diffracted ray) can use Bragg law and assume n=1 to find d.
What does the scattering angle depend on?
Depends on d which is determined by the size and shape of the unit cell
Relationship between incident angle and diffraction angle
Incident angle θ
Diffraction angle 2θ
