### Abstract

X-ray diffraction is the basis for understanding X-ray diffraction imaging (XDI). In this chapter, the theoretical background of X-ray diffraction is introduced starting from Maxwell’s equation in the system of non-relativistic classical electromagnetism. First, fundamental equations are derived to describe electromagnetic waves emitted from accelerated electrons by solving Maxwell’s equation. The theory of dipole radiation is applied to electrons bound in atoms, and then the scattering cross section for Thomson scattering is derived. By applying this theory to a system composed of two or more electrons, the interference between the diffracted waves is described as the Fourier transform of the electron density in the system. The critical importance of the phases of the diffracted waves in structural analysis is demonstrated, and then, the experimental determination of phases in protein X-ray crystallography is briefly introduced.

Original language | English |
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Title of host publication | Springer Series in Optical Sciences |

Publisher | Springer Verlag |

Pages | 23-48 |

Number of pages | 26 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

### Publication series

Name | Springer Series in Optical Sciences |
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Volume | 210 |

ISSN (Print) | 0342-4111 |

ISSN (Electronic) | 1556-1534 |

### Fingerprint

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials

### Cite this

*Springer Series in Optical Sciences*(pp. 23-48). (Springer Series in Optical Sciences; Vol. 210). Springer Verlag. https://doi.org/10.1007/978-4-431-56618-2_2

**X-ray diffraction.** / Nakasako, Masayoshi.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Springer Series in Optical Sciences.*Springer Series in Optical Sciences, vol. 210, Springer Verlag, pp. 23-48. https://doi.org/10.1007/978-4-431-56618-2_2

}

TY - CHAP

T1 - X-ray diffraction

AU - Nakasako, Masayoshi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - X-ray diffraction is the basis for understanding X-ray diffraction imaging (XDI). In this chapter, the theoretical background of X-ray diffraction is introduced starting from Maxwell’s equation in the system of non-relativistic classical electromagnetism. First, fundamental equations are derived to describe electromagnetic waves emitted from accelerated electrons by solving Maxwell’s equation. The theory of dipole radiation is applied to electrons bound in atoms, and then the scattering cross section for Thomson scattering is derived. By applying this theory to a system composed of two or more electrons, the interference between the diffracted waves is described as the Fourier transform of the electron density in the system. The critical importance of the phases of the diffracted waves in structural analysis is demonstrated, and then, the experimental determination of phases in protein X-ray crystallography is briefly introduced.

AB - X-ray diffraction is the basis for understanding X-ray diffraction imaging (XDI). In this chapter, the theoretical background of X-ray diffraction is introduced starting from Maxwell’s equation in the system of non-relativistic classical electromagnetism. First, fundamental equations are derived to describe electromagnetic waves emitted from accelerated electrons by solving Maxwell’s equation. The theory of dipole radiation is applied to electrons bound in atoms, and then the scattering cross section for Thomson scattering is derived. By applying this theory to a system composed of two or more electrons, the interference between the diffracted waves is described as the Fourier transform of the electron density in the system. The critical importance of the phases of the diffracted waves in structural analysis is demonstrated, and then, the experimental determination of phases in protein X-ray crystallography is briefly introduced.

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U2 - 10.1007/978-4-431-56618-2_2

DO - 10.1007/978-4-431-56618-2_2

M3 - Chapter

T3 - Springer Series in Optical Sciences

SP - 23

EP - 48

BT - Springer Series in Optical Sciences

PB - Springer Verlag

ER -