X-ray Diffraction Outline Crystals and Bragg Diffraction

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

Crystal Structure

Sodium Chloride example NaCl is a FCC crystal with a two atom basis Real NaCl crystal similar to what you will use http://www.dawgsdk.org/crystal/en/library/NaCl#0005

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. 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

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