Some Practical Uses of X-rays

Abstract

            For determining crystal structures and for the general identification of materials, X-ray diffraction is a very useful tool. Using the X-ray equipment involves some very high intensity X-rays and very accurate recording equipment. At the end of the experiment the computer produces a diffraction pattern, along with values for the intensity, d spacing and 2θ. Using this information we can identify the material by comparing to past data on many thousands of materials. For powdered samples, there are many diffracted rays so the diffraction patterns can be easily read, and using Bragg’s law, the crystal structure can be identified. With solid samples, there are fewer rays that can be diffracted so the diffraction pattern is harder to read.

Introduction

            X-rays are fundamentally part of the electromagnetic spectrum and can be generated one of two ways. The first and more dangerous way is by being emitted by radioactive materials. This is a danger to the users as it cannot be turned off. The second and much safer way is by being produced by the use of electricity.

            Electrical X-ray production occurs by focusing a beam of high velocity electrons with a series of slits onto the surface of a copper target within an X-ray tube. Within an atom there are three different electron shells, k, l, and m. These shells have specific energy levels and are stable when they have the correct amount of energy and electrons in them.[1]  To create an X-ray, an electron is fired at the atom and knocks an electron straight out of the ‘k’ shell, taking the fired electron with it. This creates an excited atom that can only stay in this state for a very short amount of time. The solution to this excited state is to move an electron from the ‘l’ shell down into the ‘k’ shell to lose some energy. In moving down to the ‘k’ shell the atom gives off energy in the form of an X-ray photon. This radiation given off in the form of an electron moving from the ‘l’ shell to the ‘k’ shell is known as Kα radiation, which is excellent for taking readings as it has a short wavelength and lower energy. There is another type of radiation that can be created by the movement of electrons through the shells, and that is Kβ radiation. This is when the electron moves from the ‘m’ shell to the ‘k’ shell. This has a bigger energy gap and a larger wavelength with higher energy, and only occurs roughly once in every seven X-ray exposures. To combat this, a nickel filter was used. This is to not only to combat the Kβ rays to produce a monochromatic graph, but also the white noise. When the X-ray slows down it emits what is referred to as white noise radiation, along with other surrounding factors such as background radiation, this creates a lot of unwanted graphical data.  X-ray diffraction is a very inefficient process. Only 1% of the power it takes for the whole process goes towards creating the X-rays, the remaining percentage gets used for other processes such as heat production and various other applications.

            Diffraction itself is a phenomenon which occurs when a wave hits a series of barriers with a regular spacing that can interfere with the waves’ wavelength. This interference can either be constructive or destructive depending on how the waves line up when they are reflected out of the material. In order for the interferences to become constructive, the waves have to enter a material, and exit it in phase. This creates a larger amplitude wave as the two waves’ amplitudes are added together thus creating a wave that is easily detected. Destructive interference occurs when the wavelength of the X-ray wave is larger than that of the inter-planar spacing within the material. This creates a wave that is not in phase and in essence, cancels itself out. This is very hard to detect, and is usually ignored.  This is especially important when talking about X-rays, as the wavelength for Kα rays are very small, and not coincidentally, they are roughly the same size as the atomic spacing within materials. The rules of whether the interference is going to be constructive or destructive all comes down to whether the conditions satisfy the Bragg equation: nλ = 2d sinθ, where n is the order of diffraction, d is the interplanar spacing, θ is the Bragg angle and λ is the wavelength of the X-ray. When all the variables are put into this equation and it is now satisfied the interference becomes constructive. If the Bragg equation is not satisfied, there will be destructive interference and the outcome will be a low intensity diffracted beam. _[2]

Experimental

            Using an X-ray Diffractometer set up at 40mA and 40kV, and with the use of a Nickel filter to knock out some of the white noise and the Kβ radiation, three samples were exposed to X-rays for roughly half an hour. Out of the three samples involved, two were in a powder form and another was in a solid metallic sheet. It was know that one of the powdered samples is the same material as the solid sample, but it is not known which one this is. Once the process was completed, the computer displayed the details of the intensity, d spacing and 2θ for each of the samples.

Results

            A theorem from a previous student stated that if the sin²θ value for the set of results was divided by the first value of sin²θ, it would yield a number that is in correlation with the list of h,k,l planes and their relevant number patterns. This sequence was always there, but sometimes it was necessary to multiply by a factor to find this illusive pattern. This, when referenced against the Miller indices h, k, and l, and their relevant set of numbers ascertaining which structure they are can determine the crystal structure of the material.

Sample A – White Powder

Sample D – Black Powder

Sample F – Solid Metallic Sample

Discussion

            The samples tested all have a set of Miller Indices, which when referenced against a table of Miller indices that represent the different structures, we can find the specific materials’ crystal structure. Upon construction of this list, it was found that for the integers 7, 15, 23 and 28 there were no Miller indices to be found. This is due to the face that there are no reflections at these integers. Taking into account these numbers allows you to think about how the other structures such as simple cubic and face centred cubic’s structure is set out when corresponding to the Miller indices. A simple cubic structure will have all apart from the 4 impossible reflections, whereas a BCC structure will not reflect where h+k+l is odd, and BCC lattices must have h,k and l all odd or all even.

            Looking at the first sample, the white powder, it was necessary to multiply the findings for the proposed Miller indices by three in order to create the S Number which lined up in conjunction with the actual Miller indices. The pattern emerged that the S Number we found worked perfectly with the Face Centred Cubic structure.

            The second sample we tested, the black powder, gave us a set of S numbers that when doubled, linked up directly with the set of numbers from the Miller indices for a Body Centred Cubic structure. This, coupled with the fact that the numbers were never odd, confirmed our thoughts. It is not necessary to look at the structure of the solid sample as it is known to be the same material as one of the powdered samples. One can easily find the crystal structures of the powdered materials through the use of the Miller Indices, but to identify the material itself the JCPDS Powder Diffraction file must be used to reference the various statistics that were recorded against the examples in the book. The statistics used to find the correct material were d spacings, relative intensities and 2θ. Using this file and referencing the samples that were tested it was found that the first sample, the white powder, was Aluminium, and the second, darker powder, was Tungsten.

            Looking at the solid metallic sample, it is clear that we cannot use the file for our identification, with only three reflections to compare in the file there are hundreds upon hundreds of different materials that have those same three reflections. A point to notice when looking at the number of reflections the materials have is that the different cubic structures have different amount of slip systems, and therefore will have differing amounts of slip planes for the X-rays to be reflected from. The FCC structure has 12 slip planes for the X-rays to reflect off of, the FCC structure has only 8, which is why it has fewer reflection results. To identify the solid sample it is necessary to then look at the values for intensity, and comparing them to the other powdered samples to see which one was closest. Upon seeing the comparison the solid sheet correlated strongest to Aluminium.

            X-ray diffraction works so well with powders due to the fact that in a powder there are thousands of particles which are all mixed up together, and therefore have slip planes that are facing every angle. This means that there is a much higher probability that the X-ray is going to reflect off of them as there is more chance that they are facing the direction of the approaching X-ray.

 In the solid metallic sample, you can see from the graph that the third peak is really the only one that can be identified. This is because the 1^st and 2^nd peaks are slip planes  within the Aluminium that during the forming and rolling process, have been deformed and elongated so that they are ultimately no longer along the same plane as the third peak. The third peak we are seeing in the graph as the larger black peak is the 2,2,0 plane that lines up with the X-ray beam and allows the X-ray to be diffracted and reflected back.

Conclusion

§  Powdered samples give much better diffraction patterns due to the random orientation of the planes in the particles allowing a larger portion of the material to give off a diffraction pattern.

§  X-ray diffraction is a conclusive way of identifying materials effectively

§  The white powder and solid sample were Aluminium

§  The black powder was Tungsten.

References

[1] http://www.physics.upenn.edu/~heiney/talks/hires/hires.html

[2] ‘Introduction to Engineering Materials’ 4^th Edition. Palgrave Macmillan, Gosport p60-70, 79-81

[3] ‘X-ray Diffraction’ B E Warren