Xray Diffraction Outline 1 Crystals and Bragg Diffraction

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

14 Bravais Lattices in 3 D

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 = 2 dsin(q) and so will interfere constructively when PD = nl, or 2 dsin(q) = nl - the Bragg condition In the case of Na. Cl, 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 = 35 k. V 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 2 q 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. 1 o) 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 (2 q). • 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