The wavelength of X-rays is on an atomic level and is much smaller than that of visible light (3000 to 8000 A). Since X-rays have a smaller wavelength than visible light, they have higher energy and are more penetrative. Its ability to penetrate matter, however, is dependent on density of the matter. Therefore, X-rays are useful in exploring structures of atoms.
X-rays are produced in a device called an X-ray tube. The X-ray tube consists of an evacuated chamber with a tungsten filament at one end, called the cathode, and a metal target at the other end, called an anode. When electrical current is put through the filament, excited electrons from the tungsten are emitted. If a high potential difference is placed between the cathode (positive end) and the anode (the negative end), the emitted electrons move at high velocity from the filament to the anode target. The electron will strike atoms at the target, dislodging inner shell electrons of the target atom. As a result, electrons on the outer shell emit jump down to fill the void in the inner shell. Because the inner shells have lower energy than the outer shells, when an outer shell electrons jump to inner shells, they emit radiation in the form of high energy X-rays. INTERFERENCE
Because X-rays are bundles of separate waves, each wave can interact with on another either constructively or destructively. The interaction between waves is called interference. If waves are in phase meaning that each of their crests and troughs occur exactly at the same time, then the waves will stack together to produce a resultant wave that has a higher amplitude. This is called constructive interference. If they waves are out of phase, then destructive interference occurs and the amplitude of the resultant wave will be reduced. If waves are exactly out of phase by a multiple of n/(2*lambda) then
there will be complete destructive interference and the resultant wave has no amplitude, meaning that it is completed destroyed.
X-RAY DIFFRACTION
One of the best methods of determining a crystal's structure is by X-ray diffraction. In macromolecular x-ray diffraction experiments, an intense beam of X-ray strikes the crystal of study. In general, crystal diffracts the X-ray beam differently, depending on its structure and orientation. The diffracted X-ray is collected by an area detector. The diffraction pattern consists of reflections of different intensity which can be used to determine the structure of the crystal. However, many different orientations of the crystal need to be collected before the true structure of the crystal can be determined.
The resolution of an X-ray diffraction detector is determined by the Bragg equation:
X-RAY SPECTRA
Just been learning how to produce x-rays by firing electrons at heavy atoms, but i am a tad confused about the x-ray spectra
graph with 'intensity' on the y and 'wavelength' on the x. it shows that the minimum wavelength is produced wen intensity=0
.
X-RAY DIFFRACTION METHOD
At Proto we use the x-ray diffraction method to measure residual stress. X-ray diffraction is presently the only portable non-destructive method that can quantitatively measure residual stress in crystalline and semi-crystalline materials. Our high speed x-ray detector technology enables measurements to be performed easily on metals and ceramics; including traditionally difficult materials such as shot peened titanium. XRD uses the coherent domains of the material (the grain structure) like a strain gage which reacts to the stress state existing in the material. Residual stress and / or applied stress expands or contracts the atomic lattice spacing .
PRINCIPLES OF X- RAY DIFFRACTION
Diffraction effects are observed when electromagnetic radiation impinges on periodic
structures with geometrical variations on the length scale of the wavelength of
the radiation. The interatomic distances in crystals and molecules amount to
0.15-0.4 nm which correspond in the electromagnetic spectrum with the wavelength
of x-rays having photon energies between 3 and 8 keV. Accordingly, phenomena
like constructive and destructive interference should become observable
when crystalline and molecular structures are exposed to x-rays.
In the following sections, firstly, the geometrical constraints that have to be
obeyed for x-ray interference to be observed are introduced. Secondly, the results
are exemplified by introducing the /2ïƒ¨ï€ scan, which is a major x-ray scattering
technique in thin-film analysis. Thirdly, the /2ïƒ¨ï€ diffraction pattern is used to outline
the factors that determine the intensity of x-ray ref lections. We will thereby rely
on numerous analogies to classical optics and frequently use will be made of the
fact that the scattering of radiation has to proceed coherently, i.e. the phase information
has to be sustained for an interference to be observed.
In addition, the three coordinate systems as related to the crystal {ci}, to the sample
or specimen {si} and to the laboratory {li} that have to be considered in diffraction
are introduced. Two instrumental sections (Instrumental Boxes 1 and 2) related to the/2ïƒ¨ï€ diffractometer and the generation of x-rays by x-ray tubes supplement the chapter. One-elemental metals and thin films composed of them will serve as the material systems for which the derived principles are demonstrated.
DIFFRACTION SPECTRUM
A typical diffraction spectrum consists of a plot of reflected intensities versus the detector angle 2-THETA or
THETA depending on the goniometer configuration.
The 2-THETA values for the peak depend on the wavelength of the anode material of the X-ray tube. It is therefore
customary to reduce a peak position to the interplanar spacing d that corresponds to the h, k, l planes that caused the
reflection. The value of the d-spacing depend only on the shape of the unit cell. We get the d-spacing as a function of
2-THETA from Bragg's law.
d = ?/2 sin T
DIFFRACTOMETER SLIT SYSTEM
The focal spot for a standard focus X-ray tube is about 10 mm long and 1 mm wide, with a power capability of
2,000 watt which equals to a power loading of 200 watt/mm2. Power ratings are dependent on the thermal
conductivity of the target material. The maximum power loading for an Cu X-ray tube is 463 watt/mm2. This power
is achieved by a long fine focus tube with a target size of 12 mm long and 0.4 mm wide.
In powder diffraction we normally utilize the line focus or line source of the tube. The line source emits radiation in
all directions, but in order to enhance the focusing it is necessary to limit the divergens in the direction along the line
focus. This is realized by passing the incident beam through a soller slit, which contains a set of closely spaced thin
metal plates.
In order to maintain a constant focusing distance it is necessary to keep the sample at an angle theta (Omega)
and the detector at an angle of 2-theta with respect to the incident beam.
For an Theta: Theta goniometer the tube has to be at an angle of theta (Omega) and the detector at an of theta with respect to the sample.
X-Ray Diffraction Analysis
X-Ray powder Diffraction analysis is a powerful method by which X-Rays of a known wavelength are passed through a sample to be identified in order to identify the crystal structure. The wave nature of the X-Rays means that they are diffracted by the lattice of the crystal to give a unique pattern of peaks of 'reflections' at differing angles and of different intensity, just as light can be diffracted by a grating of suitably spaced lines. The diffracted beams from atoms in successive planes cancel unless they are in phase, and the condition for this is given by the BRAGG relationship.
nl = 2 d Sin q
l is the wavelength of the X-Rays
d is the distance between different plane of atoms in the crystal lattice.
q is the angle of diffraction.
The X-Ray detector moves around the sample and measures the intensity of these peaks and the position of these peaks [diffraction angle 2q]. The highest peak is defined as the 100% * peak and the intensity of all the other peaks are measured as a percentage of the 100% peak.
APPLICATION OF X-RAY DIFFRACTION
1) At the time of the discovery of X-ray diffraction, the knowledge of the
Structure of metals was limited to what could be revealed by optical
microscopy. From the occasional
occurrence of metallic crystals with
well defined plane faces, it was recognized that the structure of metals
was essentially crystalline. Little but speculation existed as to the
actual atomic arrangement, although the geometrical theory of spacegroups
and space-lattices had been laid down long before the detailed
atomic arrangement could be determined. The general principles of
metallic phase diagrams had been established by Roozeboom and
others, and the experimental work of Heycock and Neville (1897) had
shown how the limits of the different phase fields could be established
. to a high degree of accuracy, even in very complicated systems. At the
Same time the German School under Tammann had produced a rapid
survey of a number of metallic equilibrium diagrams, but the underlying
structures remained a mystery. The application of microscopical
methods to the study of steels had resulted in the recognition of a
number of 'constituents,' but confusion often existed as to whether
these were distinct phases with definite crystal structures, or were
mixtures of phases on a scale too fine to be resolved by optical methods.
The general position was, therefore, one in which further progress
depended on the discovery of some method by which the detailed
atomic arrangement in metals could be revealed.
2) Application of X-ray diffraction technique for characterisation of pigments and control of paints quality
References and further reading may be available for this article. To view references and further reading you must purchase this article.
.The importance of X-ray powder diffraction technique for the characterisation and standardisation of crystalline pigments used in paint industry is highlighted with 22 most commonly used commercial pigments and extenders. The need for generating an in-house library of diffraction patterns of various pigment samples and using these diffractograms along with corresponding lattice spacing (d) and relative intensity (I/I0) values for rapid identification and standardisation of unknown pigment samples from various sources or from paint samples is emphasized in this work. The limitation of this technique for characterisation of mixed phase samples is also discussed and the need for using other complementary techniques like EDX along with XRD technique is illustrated with an example.
DERIVING BRAGG'S LAW
Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle. The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z. The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB + BC if the two beams are to continue travelling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (λ) for the phases of the two beams to be the same:
nλ = AB +BC (2).
Deriving Bragg's Law using the reflection geometry and applying trigonometry. The lower beam must travel the extra distance (AB + BC) to continue traveling parallel and adjacent to the top beam.
Recognizing d as the hypotenuse of the right triangle Abz, we can use trigonometry to relate d and ï± to the distance (AB + BC). The distance AB is opposite Θ so,
AB = d sinΘ(3).
Because AB = BC eq. (2) becomes,
nλ = 2AB (4)
Substituting eq. (3) in eq. (4) we have,
nλ = 2 d sinΘï€¬ï€ (1)
and Bragg's Law has been derived. The location of the surface does not change the derivation of Bragg's Law.
EXPERIMENTAL DIFFRACTION PATTERN
The following figures show experimental x-ray diffraction patterns of cubic SiC using synchrotron radiation.
CONCLUSIONS
Working on this project was highly informative. After doing the needed work for this term paper I realised that x-ray diffraction have a lot of practical life applications. As I have mentioned x- ray diffraction can be used for characterisation of pigments and control of paints quality, recognization for the structure of metals that it is crystalline or not. Not only these, the x - ray diffraction have a huge array of other applications. Further research and experimentation done in this field will not only be productive but also very advantageous.
RERERENCE:-
1) eps www.unm.edu
2) www.eserc.stonybrook
3) www.plasma-biotal.com
4) web miniral.com
5) www.iucr.org
By-W.Hume Rothery
6)www.nist.gov
7) Introduction To INSTRUMENTAL ANALYSIS By-ROBERT D. BRAUN
8) MODERN PHYSICS
By- SERWAY/ MOSES/MOYER
