1. X-ray Diffraction Outline Crystals and Bragg Diffraction
Generating X-rays
Experimental Details
Analysis of Data

2. Crystal Structure

3. Sodium Chloride example
NaCl is a FCC crystal with a two atom basis
Real NaCl crystal
similar to what
you will use

4. 14 Bravais Lattices in 3D

5. 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)

6. 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.
Note that K lines predominate and that Ka energy < Kb energy
Inner shell electrons are ejected by high velocity incident electrons – then transitions from an outer shell cause emission of characteristic x-rays

7. 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.

8. Apparatus

9. 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