X-Ray Crystallography

crystallography goniometer

Core Concepts

In this article, we learn all about x-ray crystallography, including the physics of x-ray diffraction, the process of crystallization, the crystallography apparatus, and the analysis of diffraction data.

Topics Covered in Other Articles

What is X-Ray Crystallography?

X-Ray Crystallography is a method used by chemists to analyze molecular structure using the physics of x-rays. While x-ray crystallography can yield molecular structures for a wide variety of molecules, the method tends to have the most use in solving large structures. Chemists most often use x-ray crystallography to analyze the structures of biomolecules, especially proteins, and organometallics.

Diffraction and X-Rays

Chemists solve molecular structures with x-ray crystallography by analyzing the diffraction pattern of the structure. In physics, diffraction is a phenomenon that occurs when the light of one wavelength interacts with a material with a “slit”. This slit only allows a small portion of light that can pass through the material. As a result of constructive and destructive interaction between light, the light expresses a unique pattern of bright and dark spots after passing through the slit. This pattern of light is the diffraction pattern of the light-slit system.

single-slit experiment
A typical single-slit diffraction experiment with a single-wavelength light beam, which results in a unique fringe of light spots called the diffraction pattern (right).

In x-ray crystallography, chemists use a crystal of the material they hope to analyze. As light passes through the crystal, the gaps between layers of molecules in a way that indicates their structure. 

x-ray crystallography basic set up
A simplified x-ray crystallography set-up, which similarly makes a unique diffraction pattern based on the “slits” of the crystal structure.

The two most important parameters for determining diffraction patterns include light wavelength and slit width. Specifically, these parameters have a direct relationship. To observe the same diffraction pattern at two different wavelengths, the shorter wavelength must have a narrower slit than the larger wavelength.

Physicists usually perform diffraction slit experiments of visible light (4-7 * 10-7m) with slits in micrometers (10-6m) to yield observable diffraction patterns. However, the gaps in crystals tend to have spacing in Ångstroms (10-10m), requiring a far shorter light wavelength. Thus, to generate an observable diffraction pattern to understand molecular structures, chemists instead use x-rays (10-11 – 10-8m).


In general, to form a crystal with which to perform x-ray crystallography, you take a supersaturated solution of your target molecule and slowly cool it. This results in the molecule slowly depositing out of the solution. The process of crystallization for crystallography is similar to the recrystallization you perform to purify a yield.

If you hope to crystalize a protein, the process can be especially difficult. Many proteins only crystalize under certain conditions of salts, pH, and precipitating agents. In practice, biochemists often have to test dozens of crystalizing conditions to yield a proper protein crystal. 

Once you generate your crystal, you then need to keep it cold. Any increase in temperature could disrupt the crystal lattice and result in poor crystallography readings.

X-Ray Crystallography Apparatus

Once you have your crystal, you then load it into the goniometer of the crystallography apparatus. The goniometer rotates the crystal while keeping it in the x-ray beam. This ensures that every angle of the crystal lattice performs diffraction on the x-ray, yielding the molecule’s complete 3D structure.

x-ray crystallography goniometer
Activity of the goniometer, twisting the crystal, generating diffractions from a range of angles.

To generate x-rays, the crystallography apparatus often includes what crystallographers call the “x-ray tube”. This tube involves a metal cathode, often made of tungsten, through which a high voltage of electrons passes. These electrons then hit a target anode, often made of copper, cobalt, or (also) tungsten, which produces x-rays. To yield accurate diffraction results, the x-rays then pass through a filter or “window”, often made of zirconium or beryllium. This filter absorbs certain x-ray wavelengths to limit the light that hits the crystal to a narrow range of wavelengths.

x-ray tube
X-ray tube diagram. The most important parts include the cathode, the anode and tungsten target, the electron stream, the useful (x-ray) beam, and the window.

Devices called synchrotrons also can produce x-rays for crystallography. Synchrotrons offer the advantage of having precise tunability.

In the chamber with the crystal, an x-ray imaging plate, x-ray film, or electronic detectors record the diffraction pattern. The apparatus specifically records spots of constructive interference in the diffraction pattern.

Analyzing X-Ray Crystallography Results 

x-ray crystallography diffraction
An x-ray crystallography diffraction pattern .

Your first crystallography image gives you considerable insight into the general nature of your crystal. The density, shape, and intensity of the diffraction spots tell you the dimensions of the crystal. Specifically, the spacing of the spots indicates the dimensions of the unit cell or the crystal’s smallest repeating unit. Depending on the dimensions, and particularly the angles, of the unit cell, you can determine the crystal system. There are seven possible crystal systems, with the most common including monoclinic, triclinic, and cubic. On a larger scale, the symmetry of the diffraction pattern determines the crystal’s space group, which relates to the packing of the crystal lattice.

Once you know these basic qualities after the first diffraction, you can adjust the apparatus’ parameters to improve later scans. You can optimize the crystal-to-detector distance and x-ray intensity to produce the highest quality diffraction images.

Once you get your optimized scans, computer algorithms generally work out the specifics of the molecule structure based on the refined diffraction pattern. The mathematics of crystal diffraction gets fairly complex, which makes working out the structure by hand infeasible. 

Bragg’s Law

Despite the complexity of many steps of x-ray crystallography analysis, much of it depends on the relatively straightforward Bragg’s Law. In 3D structures, like crystals, the pattern of diffracted light obeys Bragg’s Law, which involves the following mathematical relationship:

 mλ = 2dsinθ

λ = Wavelength of light 

θ = Angle between crystal layer and the ray of light

d = Distance between crystal layers and gaps

m = Some integer

Bragg’s Law specifically dictates the angle of the bright spots (constructive interference). Bright spots only diffract from the crystals at angles that fulfill this relationship; angles whose sine multiplied by twice the layer distance equals an integer multiple of the wavelength.