# X-Ray Crystallography

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X-ray diffraction has perhaps been one of the most critical and exigent discoveries of the 20th century. Early X-ray diffraction images for tobacco mosaic virus had been collected before World War II. By 1954, Watson had discovered from his X-ray diffraction images that the tobacco mosaic virus had a helical structure, and was able to apply this to his famous DNA structure research. It is so valued because it allows the structure of a crystalline material can be determined, based on the diffraction of x-rays due to electron density within the crystal. The mystery of the arrangement of atoms can be solved when the electrons in the crystal, which has a particular, repeating arrangement of atoms, scatter a beam of x-rays. It can be applied to study many crystalline materials, from ionic molecules to biomolecules. The technique can also be used to determine the degree of crystallinity of a sample. Due to increased data and knowledge, identification of compounds can now be performed using x-ray diffraction data.

X-ray crystallography uses the physical phenomenon of diffraction of electromagnetic radiation. Diffraction occurs when light passes through a slit with size comparable to its wavelength. When the light passes through the slit it is spread out. When several slits are present light from different slits may hit the target no longer in phase. When the beams of light are in phase it causes high intensity to be observed. When the light is out of phase by 180 degrees than the waves destructively interfere with each other and causes no intensity to be detected. This constructive and destructive interference is observed when light passes through a series of slits. When this situation occurs the pattern of differing intensities is called a diffraction pattern. This phenomenon can be used to determine the placement of objects by determining the space in between. Since crystals contain an ordered arrangement of atoms, a diffraction pattern can be created. Using this diffraction pattern the arrangement of structures within the crystal can be determined. The phenomenon is only experienced when the wavelength of the electromagnetic radiation is comparable to the slit size. Because of this to determine the structure of molecules, in a crystal, electromagnetic radiation with a wavelength of about 2- 20 Ð"... is used. Electromagnetic radiation with this wavelength is in the x-ray region of the electromagnetic spectrum.

Calculations allow the determination of the distance between the planes of a crystalline lattice. The major equation that is used in crystallographic studies is the Bragg equation. The Bragg equation is defined as n&#955;=2*d*sin &#952;; where n is the order of diffraction, d is the distance between planes, &#955; is wavelength of the x-rays, and &#952; is the angle. Gathering information at several angles and putting the information together allows the overall structure of the crystal to be determined.

X-ray crystallography is not a product of this generation. The use of x-rays to determine a crystalline structure was first explored by William and Lawrence Bragg in 1913. However, the most famous use of early x-ray diffraction was the discovery of the alpha helix shape of DNA. When x-ray crystallography was first performed the intensities of the x-rays was recorded using photographic film. Now the use of semiconductor array detectors has made the data collection process much faster and easier. Currently, the collection of x-ray diffraction data is much faster because of the use of computers. To determine the structure, many data points must be collected at many angles. Computers are also able to change the angle and store more information than in the past.

One thing to consider when using this technique is the availability of an energy source. There are several sources available to produce x-rays. The types of sources that are commonly used are x-ray tubes, radioisotopes, and synchrotron radiation light sources. Several detectors are available for use in x-ray crystallography. However, when x-ray crystallography was first used, the diffraction pattern was collected on film. The transition to electronic detectors allows a greater degree of automation and speed compared to when film was used. Three types of detectors are commonly used to detect the diffracted x-rays. These include gas filled, scintillation, and semiconductor detectors. Most modern instruments use charge coupled device semiconductor detectors.

X-ray crystallography experiments also have other uses than just to determine the crystalline structure of a compound. This technique can be used on powdered crystalline samples. The powdered crystals are packed into a capillary column or onto a flat surface. Because of the random orientation of crystals in the powder, diffraction rings are generated instead of spots. The position and intensity of these rings can be used to identify a crystalline compound. An example of a powder diffraction spectrum is shown in figure one. The International centre for Diffraction Data maintains a database with greater than 50,000 crystalline powder x-ray diffraction patterns. Using this same concept, mixtures of crystalline powders can be identified. This does not work if the crystals were formed in the presence of an impurity, because this impurity can change the position and intensity of the diffraction lines.

Figure One: Simulation of BenedrylTM powder diffraction data.

The determination of the degree of crystallinity of a polymer is another essential use of x-ray crystallography. The crystalline part of the polymer will create sharp peaks in intensity while the amorphous part causes increased background because of scattering. The ratio of the peak height to the background height is proportional to the ratio of crystalline to amorphous structures in the polymer. To conduct this technique known standards must be used to calibrate the instrument. Similarly, this technique can be used to determine the orientation of crystals in a polymer or metal. If diffraction data is collected at different temperatures, phase transition studies between amorphous and crystalline phases or different crystalline structures can be studied. Also, the material's thermal expansion coefficient can be determined. This technique can be used to determine the level of annealing a metal has undergone. If a metal is well annealed it will be mostly crystalline, and therefore will have sharp diffraction lines.

X-ray crystallography is a useful technique but has its limitations. One of the largest limitations is that the material being studied must be in a crystalline

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