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PHYS 3300 - Introduction to Biomedical Physics Research Paper

X-ray crystallography

by

Leo Tyler

16 April 2016

The technique of X-ray crystallography has been refined over the course of many years and by many scientists and has allowed for the exploration of the world in unprecedented detail. Unbeknownst to some, the technique of X-ray diffraction has facilitated more than just the ability to image crystals, but it has allowed for enlightenment in many areas and has transformed all of the sciences, relying on a rather beautiful piece of physics and mathematics. It has led to a better understanding of biology, chemistry, and minerology. For example, it has better informed the sciences about chemical bonds and non-covalent interactions, it has helped in establishing the idea of resonance between chemical bonds, and the elucidation of hydrogen bonding, just to name a few.

This technique doesn’t really have the appeal in the public domain that it deserves, in part because it relies on a phenomenon that is not readily available to the average person in their everyday lives, i.e. most don’t come across X-ray diffraction, which is the principle physical mechanism on which the method relies. However, it does speak to a broader subject, which is human kinds obsession with seeing things that are normally too small to see. This fascination has grasped the human imagination for as long as people have been putting lenses together to make telescopes and microscopes. For example, one of the most famous publications from the 1600’s, a book called Micrographia, which was very popular in its day, in where the author, Robert Hooke a pioneer of microscopy, included images of things that were familiar, such as his depictions of the flea, or the fly’s eye, or a plant cell. Even though his images were largely unseen by most people, the way in which they related to the everyday life of the masses delighted and enthralled the people whom read his books. However, the trouble with microscopy, unlike X-ray crystallography, henceforth XRC, is that it has limits. For example, microscopy illuminates a material using visible light. This only permits imaging of the surface and not the inside of things much like the simple 2 dimensional image of the flea. It also is limited in the size of things that it can image. If it is desired to view the molecules that the flea is made up of, microscopy won’t work, whereas X-ray crystallography to a certain extent, does. It has brought an acquaintance to the world at the molecular and atomic level which was largely unappreciated prior to the turn of the 20th century.

Even though the writer is assuming that the reader of this research project is a highly intelligent Physics Professor, I will be writing as if to the lay and as such, the hypothetical layman might have to work a little hard a couple of times as I discuss the theory. In the words of the Good Book i.e. the Holy Bible (KJV), “Even a fool, when he holdeth his peace, is counted wise: and he that shutteth his lips is esteemed a man of understanding.” Proverbs 17:28. Thus I will remain silent on many topics concerning the mathematics behind the theories in hopes to remain intellectually unscathed by sparing the reader of the gory details and minutia on the topic of XRC.

Let us first talk about how X-rays are used. From the very beginning it was obvious that X-rays were a special kind of light because it could see through matter. Having the properties of light, when X-rays are “shone” on an image a shadow is produced where the light is blocked from passing through, much like the sun casting a shadow on a person standing on the beach, fig.1.  Here is a picture of the very first image using X-rays that William Röntgen, the discoverer of X-rays, produced in an experiment using his wife’s hand in 1895, fig.2. Because matter is mostly transparent to X-rays, the skin and soft tissue is largely non visible in the image, yet the bone and the ring having relatively more electron (e-) density scatter X-rays and thus casts darker shadows. This is mostly because of the presence of the calcium atoms and presumably gold atoms in the bone and ring, resp.  The scattering of X-rays by the more e- dense materials, attenuates the transmitted beam and thus the shadow is visibly seen. Rather than being a solid shadow it is semitransparent because the X-rays are very penetrating.

X-rays as we now know, are indeed a special kind of light with a very short wavelength, and effectively consists of an oscillating electric and magnetic field, fig. 3. When an electric field hits a charged particle, in this case an e-, it causes that e- to oscillate up and down. An oscillating e- will itself emit radiation of the same wavelength, thus emitting X-rays and doing so in almost every direction. Most of the X-ray is unaffected but a small part of the energy is reradiated, or scattered, in all directions, fig. 4., by the e- in the atom. So the X-ray is in essence penetrating and sampling all of the structure that is inside the atom. When a medical X-ray is taken, for the purpose of creating an image which can be used diagnostically, the scattered radiation is ignored. However, the basis of the technique of XRC actually relies on the scattered radiation, because it contains information about the object that is doing the scattering. Because of the penetrating power of the X-ray, having also the peculiar property of light, when it interacts with matter of a similar size to its own wavelength, it shows the interior structure of things, allowing for the study of molecules and the orientation of atoms. This phenomena of diffraction, i.e. light scattering from an object that is about the same size as its wavelength, allows for an intimate understanding of many things, again, on an atomic level.

The idea of this phenomena is easier understood by repeating a classic optic experiment done by polymath and physician Thomas Young on the diffraction of light through narrow slits. When light is filtered into a beam of photons, like in the case of a laser, Young of  

 

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