Lawrence Bragg explained this result by modeling the crystal as a set of discrete parallel planes separated by a constant parameter d. According to the 2 θ deviation, the phase shift causes constructive (left figure) or destructive (right figure) interferences. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This condition is captured by the Bragg equation, Constructive interference results when this distance is an integer multiple of the wavelength. From the geometry, the difference in path lengths is 2 d sin θ 2 d sin θ. In ways reminiscent of thin-film interference, we consider two plane waves at X-ray wavelengths, each one reflecting off a different plane of atoms within a crystal’s lattice, as shown in Figure 4.25. In 1915, the unique father-and-son team of Sir William Henry Bragg and his son Sir William Lawrence Bragg were awarded a joint Nobel Prize for inventing the X-ray spectrometer and the then-new science of X-ray analysis. (The spacing of atoms in various crystals was reasonably well known at the time, based on good values for Avogadro’s number.) The experiments were convincing, and the 1914 Nobel Prize in Physics was given to von Laue for his suggestion leading to the proof that X-rays are EM waves. If a diffraction pattern is obtained, he reasoned, then the X-rays must be waves, and their wavelength could be determined. This was suspected from the time of the discovery of X-rays in 1895, but it was not until 1912 that the German Max von Laue (1879–1960) convinced two of his colleagues to scatter X-rays from crystals. Historically, the scattering of X-rays from crystals was used to prove that X-rays are energetic electromagnetic (EM) waves. Analysis of the pattern yields information about the structure of the protein. These can be studied using X-ray crystallography.įigure 4.24 X-ray diffraction from the crystal of a protein (hen egg lysozyme) produced this interference pattern. For example, more recent research in high-temperature superconductors involves complex materials whose lattice arrangements are crucial to obtaining a superconducting material. Not only do X-rays confirm the size and shape of atoms, they give information about the atomic arrangements in materials. This process is known as X-ray crystallography because of the information it can yield about crystal structure, and it was the type of data Rosalind Franklin supplied to Watson and Crick for DNA. (There is some debate and controversy over the issue that Rosalind Franklin was not included in the prize, although she died in 1958, before the prize was awarded.)įigure 4.24 shows a diffraction pattern produced by the scattering of X-rays from a crystal. For this work, Watson, Crick, and Wilkins were awarded the 1962 Nobel Prize in Physiology or Medicine. Using X-ray diffraction data produced by Rosalind Franklin, they were the first to model the double-helix structure of DNA that is so crucial to life. Perhaps the most famous example of X-ray diffraction is the discovery of the double-helical structure of DNA in 1953 by an international team of scientists working at England’s Cavendish Laboratory-American James Watson, Englishman Francis Crick, and New Zealand-born Maurice Wilkins. The process is called X-ray diffraction, and it involves the interference of X-rays to produce patterns that can be analyzed for information about the structures that scattered the X-rays. However, since atoms are on the order of 0.1 nm in size, X-rays can be used to detect the location, shape, and size of atoms and molecules. Thus, typical X-ray photons act like rays when they encounter macroscopic objects, like teeth, and produce sharp shadows. Since X-ray photons are very energetic, they have relatively short wavelengths, on the order of 10 −8 10 −8 m to 10 −12 10 −12 m. Describe interference and diffraction effects exhibited by X-rays in interaction with atomic-scale structures.By the end of this section, you will be able to:
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