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 Fig. The second beam continues to the next layer where it is scattered by atom B. This extra distance must be an integral n multiple of the wavelength for the phases of the two beams to be the same:. The distance AB is opposite so,.
The location of the surface does not change the derivation of Bragg's Law. The following figures show experimental x-ray diffraction patterns of cubic SiC using synchrotron radiation. Friedrich and Knipping first observed Roentgenstrahlinterferenzen in after a hint from their research advisor, Max von Laue, at the University of Munich. Bragg's Law greatly simplified von Laue's description of X-ray interference. The Braggs used crystals in the reflection geometry to analyze the intensity and wavelengths of X-rays spectra generated by different materials.
Their apparatus for characterizing X-ray spectra was the Bragg spectrometer. After learning that Paul Ewald's optical theories had approximated the distance between atoms in a crystal by the same length, Laue postulated that X-rays would diffract, by analogy to the diffraction of light from small periodic scratches drawn on a solid surface an optical diffraction grating.
In Ewald constructed a theory, in a form similar to his optical theory, quantitatively explaining the fundamental physical interactions associated with XRD. From the Law of Sines we can express this distance YX in terms of the lattice distance and the X-ray incident angle:. If the path difference is equal to an integer multiple of the wavelength, then X-rays A and B and by extension C will arrive at atom X in the same phase.
In other words, given the fol lowing conditions:. If, however, this condition is not satisfied, then destructive interference will occur. From the Law of Sines we can express this distance YX in terms of the lattice distance and the X-ray incident angle: If the path difference is equal to an integer multiple of the wavelength, then X-rays A and B and by extension C will arrive at atom X in the same phase.
There are two types of interference depending on how the waves overlap one another. Constructive interference occurs when the waves are moving in phase with each other. Destructive interference occurs when the waves are out of phase.
The relationship describing the angle at which a beam of X-rays of a particular wavelength diffracts from a crystalline surface was discovered by Sir William H. Bragg and Sir W. Guide to how to use Applet: There are 2 rays incident on two atomic layers of a crystal d. At the beginning the scattered rays are in phase and interfering constructively.
If you click on the details button you can see the detector, which measures how well the phases of the two rays match.
0コメント