The X-Ray and the Structure of Molecules

X-Ray diffraction is responsible for for some of the most important discoveries of the 20th century, from determining the structure of DNA, to the intricate carbon lattices of diamonds and graphite. The technique has developed over the years to cover more than just molecular solids, non-molecular solids and gaseous molecules. Modern techniques are capable of revealing information of polymers, proteins and other macromolecules.

There are several types of diffraction methods:

The two most common X-ray methods being powder x-ray diffraction and single crystal diffraction.
Electron diffraction is a method used for the elucidation of gaseous molecules and studying solid surfaces, Neutron diffraction is also another method used for diffracting lighter atoms such as A,D, and Li and distinguishing atoms with similar atomic numbers (not covering these).

What is X-ray diffraction?

X-rays exist in the wavelength of 10-10 m, or about 100 pm - which is approximately the same order of distances between molecules. This, in turn, means x-rays interact electrons present between molecules in a crystalline solid. These interactions are capable of producing high-resolution images of the structure of crystalline solids (or polycrystalline, i.e. DNA).

Here's an example of an x-ray diffractometer:

An X-ray diffractometer consists of: an x-ray source, a mount for the sample, a turntable, allowing you to adjust the angle of the sample in regards to the x-ray beam and the detector. Modern diffractometers, make use of imaging plate detectors, or charge coupled devices (CCD) area detectors. These components convert x-rays into light before recording the data, which allows for faster data collection. There are pixel detectors being researched, which will enable data collection to become more efficient by skipping the light-conversion step and instead measuring the radiation directly.

Diffractometers make use of the fact that the x-rays are scattered by the electrons orbiting nuclei and hence, the scattering power of nuclei is dependent on the number of electrons present in the system. The variable electron densities allow us to distinguish different types of atoms present in a sample. Using the X-ray diffraction method, being able to detect light atoms such as H bonded to heavier atoms is difficult, if not impossible because of the electron densities. Neutron diffraction is used for that purpose.

The Bragg Equation

If we take say, a crystal lattice and the atoms are in the form of the black dots (above), which are arranged into lattice planes (two). Now consider two waves (dotted lines), each of which are reflected by one of the lattice planes. These waves which are scattered (reflected) will only be in phase if the second wave is equal to the multiple (n) of the wavelength (𝜆). The spacing of the lattice also plays an important role (how far apart the lattice planes are from each other), which is represented by d. Using trigonometry, it can be deduced that the distance travelled by the second wave will be 2d x sin 𝜃. This relationship leads to Bragg's equation:

2d x sin 𝜃 = n𝜆

Before the waves are scattered they are in phase, so in order to remain in phase as they are scattered, the equation above must hold.

Check the links below for some more interesting info about this technique.

I'll update this post with some more images relating to simple diffraction patterns.

Thanks for reading!

Furtherther Reading:

Reference image in header (background):

https://commons.wikimedia.org/wiki/File:Zn-Mg-HoDiffraction.JPG