X-ray Diffraction
Outline
1.Crystals and Bragg Diffraction
2.Generating X-rays
3.Experimental Details
4.Analysis of Data
Crystal Structure
Sodium Chloride example
NaCl is a FCC crystal with a two atom basis
http://www.dawgsdk.org/crystal/en/library/NaCl#0005
Real NaCl crystal
similar to what
you will use
14 Bravais Lattices in 3D
Bragg Diffraction
In a cubic crystal there is one lattice constant = ao
but many sets of Bragg planes with spacings = d
X-rays scattered from different planes have path differences given by:
PD = 2dsin(q) and so will interfere constructively when PD = nl, or
2dsin(q) = nl - the Bragg condition
In the case of NaCl, d = ao/2 for planes parallel to the crystal face and we get
nl = ao sin(q)
Generating X-rays
Electrons are accelerated through high voltage
to collide with a metal plate. In our case V =
35kV and the plate is molybdenum.
Inner shell
electrons are
ejected by high
velocity incident
electrons – then
transitions from an
outer shell cause
emission of
characteristic
x-rays
Note that K
lines
predominate
and that Ka
energy < Kb
energy
Experiment
The collimated x-ray beam diffracts from
the crystal sample with the detector set at
an angle of 2q where q is the incident angle
the beam makes with the crystal planes.
At each angle the detector accumulates counts
for a fixed time, Dt, and then the
sample/detector apparatus shifts the angle q
by a fixed step (~0.1o) and repeats the
measurement through a range of angles that
can be pre-set.
Apparatus
Analysis of Data
• The x-ray software package will give you a real-time
plot of the detected intensity (cts/s) vs the diffraction
angle (2q).
• Save your measurements in a desktop folder
• Locate the peaks by right clicking the mouse to select
‘calculate peak center’ – then mark the full width of
each peak and record the center values and their SD,
shown in lower left of display
• Tabulate your results and plot the Bragg equation to
find a best value for the lattice constant with its
uncertainty for each crystal studied
• Export your spectra and plot them up as your raw data
in Excel graphs