*Dennis Sherwood and Jon Cooper*

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.003.0009
- Subject:
- Physics, Crystallography: Physics

This chapter discusses the underlying principles X-ray scattering by a distribution of electrons. The theory is then extended to the diffraction of X-rays by an infinite lattice of molecular motifs ...
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This chapter discusses the underlying principles X-ray scattering by a distribution of electrons. The theory is then extended to the diffraction of X-rays by an infinite lattice of molecular motifs and the concept of the structure factor, which describes the diffraction pattern, is introduced. The theory of calculating the electron density distribution within the unit cell by Fourier inversion of the structure factors is then covered. The fact that only the amplitudes and not the phases of the structure factors can be measured experimentally represents the major practical problem of diffraction analysis that is known as the phase problem. The process of calculating structure factors from a known structure can be simplified by treating each atom as a scattering centre that is assigned a scattering factor related to its atomic number. In the second half of the chapter, the rules relating the symmetry of the diffraction pattern to that of the crystal are derived, and the basis for the inherent inversion symmetry of the diffraction pattern, known as Friedel's law, is described. Situations where this important law breaks down are touched upon due to their importance in solving the phase problem. The phenomenon of systematic absences, essentially missing diffraction spots, and how they can yield key information on the symmetry of the crystal is explained.Less

This chapter discusses the underlying principles X-ray scattering by a distribution of electrons. The theory is then extended to the diffraction of X-rays by an infinite lattice of molecular motifs and the concept of the structure factor, which describes the diffraction pattern, is introduced. The theory of calculating the electron density distribution within the unit cell by Fourier inversion of the structure factors is then covered. The fact that only the amplitudes and not the phases of the structure factors can be measured experimentally represents *the* major practical problem of diffraction analysis that is known as the phase problem. The process of calculating structure factors from a known structure can be simplified by treating each atom as a scattering centre that is assigned a scattering factor related to its atomic number. In the second half of the chapter, the rules relating the symmetry of the diffraction pattern to that of the crystal are derived, and the basis for the inherent inversion symmetry of the diffraction pattern, known as Friedel's law, is described. Situations where this important law breaks down are touched upon due to their importance in solving the phase problem. The phenomenon of systematic absences, essentially missing diffraction spots, and how they can yield key information on the symmetry of the crystal is explained.

*André Authier*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199659845
- eISBN:
- 9780191748219
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199659845.003.0007
- Subject:
- Physics, Crystallography: Physics

This chapter relates the first steps of X-ray crystallography in 1913. It starts with a brief account of the flock of experiments in England and Germany, prompted by Bragg’s experiment with mica. It ...
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This chapter relates the first steps of X-ray crystallography in 1913. It starts with a brief account of the flock of experiments in England and Germany, prompted by Bragg’s experiment with mica. It then tells how Wulff, Laue himself, Ewald, and Friedel interpreted Laue’s relations in terms of the reflection by a set of lattice planes. Laue admitted his early misconceptions and gave a correct interpretation of Friedrich and Knipping’s experiment. The chapter proceeds on with Terada’s and Nishikawa’s early experiments in Japan, and de Broglie’s experiments in France. In England, W. H. Bragg developed the ionization spectrometer, and W. L. Bragg made the first crystal structure determinations. Moseley determined the high-frequency spectra of the elements and established its relations with the atomic numbers. In Zürich, Debye derived the influence of thermal agitation on the intensity of diffracted intensities. In France, de Broglie introduced the rotating crystal method, and Friedel related X-ray diffraction and crystal symmetry. In the United States, the first X-ray spectrometer was built in 1914.Less

This chapter relates the first steps of X-ray crystallography in 1913. It starts with a brief account of the flock of experiments in England and Germany, prompted by Bragg’s experiment with mica. It then tells how Wulff, Laue himself, Ewald, and Friedel interpreted Laue’s relations in terms of the reflection by a set of lattice planes. Laue admitted his early misconceptions and gave a correct interpretation of Friedrich and Knipping’s experiment. The chapter proceeds on with Terada’s and Nishikawa’s early experiments in Japan, and de Broglie’s experiments in France. In England, W. H. Bragg developed the ionization spectrometer, and W. L. Bragg made the first crystal structure determinations. Moseley determined the high-frequency spectra of the elements and established its relations with the atomic numbers. In Zürich, Debye derived the influence of thermal agitation on the intensity of diffracted intensities. In France, de Broglie introduced the rotating crystal method, and Friedel related X-ray diffraction and crystal symmetry. In the United States, the first X-ray spectrometer was built in 1914.