Electromagnetic waves form a continuous spectrum covering at least 15 orders of magnitude in wavelength. All travel at 300,000 km/sec in a vacuum, reflect, refract according to Snell's Law, are diffracted by edges, slits and gratings and can be related to their energies by the equation:
Where E is energy, v is frequency, c is velocity of light, lambda is wavelength, and h is Planck's constant. The equation shows the inverse relationship of energy to wavelength; the shorter the wavelength, the more energetic the wave. X-rays are that portion of the spectrum where lambda is between about 100 and 0.02 Angstroms - we are most interested in those X-rays with wavelengths around 1 Angstrom because this is the order of the interplanar spacings in crystals.
Generation of X-rays:
In a vacuum, a tungsten filament (the cathode) is heated and boils off electrons which are then accelerated across a potential and impact onto the anode which can be made of different metals. Above some minimum energy of the incoming electrons, a continuous spectrum of x-rays is generated from the target material. Greater potential gaps lead to both more x-ray emission at all energies and the production of higher energy x-rays (the lower wavelength limit becomes lower). The lower wavelength (higher energy) cutoff corresponds to complete stoppage of the electron in a single interaction; the rest of the "white radiation" or "continuous radiation" is caused by smaller amounts of energy loss per collision or interaction. The x-ray tube is generally water cooled to remove the heat produced by these collisions.
At some critical voltage (dependent on the target element) a line spectrum characteristic of the target material is produced and superimposed on the background radiation. These discrete lines are caused by the incoming electrons having enough energy to dislodge an electron from the K, L, or M shells of the target atoms and then this hole is filled by an outer electron falling back into the hole.
L to K transitions produce 'K alpha' emission while M to K transitions produce 'K beta' emission. Similarly, M to L transitions produce 'L alpha' emissions. Because there are several energy sublevels in the L, M, N levels from which electrons can drop down to fill in the K-shell, there are in fact 'K alpha 1' and 'K alpha 2' peaks which are very close to one another in energy. The value below (e.g. 1.5418 for Cu) is the weighted average of these energies - for careful x-ray work it is important to actually work with the 2 energies separately.
The most common targets and their characteristic 'K alpha average' wavelengths are:
Molybdenum 0.7107 Copper 1.5418 Cobalt 1.7902 Iron 1.9373
In class we will use 2 different lasers and several sieves to demonstrate diffraction. Because atoms are too small to see and x-rays are invisible, we will start with a sieve and a red laser - both of which are visible. As detailed in Brady and Boardman (1995, J. Geol. Education 43, 471-6) it is a simple matter to develop the Fraunhofer Equation which relates the periodic repeat distance to the wavelength of light and the angle of diffraction, i.e.:
By comparing the results from different size sieves and different wavelength lasers, we can gain an intuition into the process of diffraction which can be applied to x-rays and the invisible periodic arrays of atoms that we call crystals.