Theory and Interpretation

A hot tungsten filament emits electrons.

The acceleration potential, 5-40kV, set by the user causes the W photoelectrons to strike the target with 5-40 keV energy.

The high energy electrons cause the target, typically Cu, to emit characteristic x-rays; these serve as the x-ray diffraction beam.

Water cycles through the system to cool the metal anode target.

The source emits x-rays that can be approximated as plane waves as they encounter the sample.

X-rays diffract through the interatomic spacing of the crystal lattice and produce a diffraction pattern of new x-rays.

New x-rays interfere and can be assumed to be plane waves when they reach the x--ray detector.

Only x-rays that exhibit constructive interference as described by the Bragg Condition will be detected. All other x-rays waves destructively interfere.

This image depicts Laue diffraction, a configuration for transmission diffraction. The diffractometer has a different geometric layout.

The geometry of our system is called "theta/theta" to indicate that the incoming x-ray angle = diffraction angle=theta.

This scan mode is "Locked-Coupled" to indicate a locked and coupled positions of the x-ray tube and detector.

In theta/theta geometry, only planes parallel to the specimen surface will give rise to x-ray diffraction.

Incident x-rays penetrate the sample and induce scattered x-rays from each electron. The scattered waves that add constructively are also those that meet the Bragg condition. They are called "Reflections."

Bragg's condition: n is an integer, d is the interplanar spacing, lambda is the wavelength, theta is the angle between the incident vector and vector normal to the plane.

Constructive interference occurs only when the path length difference between parallel planes of atoms is equal to integer multiples of the wavelength of incident x-rays.

All other scattered x-rays destructively interfere.

Powder samples ideally have an equal distribution of randomly oriented crystals.

Only planes parallel to the surface will diffract in a locked-coupled scan. If your specimen is neither powder nor randomly-oriented, the relative intensities will not match the library patterns.

For each peak, only certain orientations of crystal planes will produce constructive interference.

Use this formula for cubic lattices to calculate the lattice parameter, peaks, or composition of the sample. h, k, and l refer to the Miller indices of the diffracting plane. a is the lattice parameter.