*ANDRÉ AUTHIER*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter presents the basic properties of dynamical diffraction in an elementary way. The relationship with the band theory of solids is explained. The fundamental equations of dynamical theory ...
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This chapter presents the basic properties of dynamical diffraction in an elementary way. The relationship with the band theory of solids is explained. The fundamental equations of dynamical theory are given for scalar waves as a simplification; the solutions of the propagation equation are then derived for an incident plane wave in the 2-beam case; and the amplitude ratio between reflected and refracted waves deduced. The notions of wavefields, dispersion surface, and tie points are introduced. Two experimental set-ups are considered: transmission and reflection geometries. The boundary conditions at the entrance surface of the crystal are expressed in each case and the intensities of the refracted and reflected waves calculated as well as the anomalous absorption coefficient, due to the Borrmann effect, the Pendellösung interference fringe pattern and the integrated intensity. It is shown that the geometrical diffraction constitutes a limit of dynamical diffraction by small crystals. At the end of the chapter dynamic diffraction by quasicrystals is considered.Less

This chapter presents the basic properties of dynamical diffraction in an elementary way. The relationship with the band theory of solids is explained. The fundamental equations of dynamical theory are given for scalar waves as a simplification; the solutions of the propagation equation are then derived for an incident plane wave in the 2-beam case; and the amplitude ratio between reflected and refracted waves deduced. The notions of wavefields, dispersion surface, and tie points are introduced. Two experimental set-ups are considered: transmission and reflection geometries. The boundary conditions at the entrance surface of the crystal are expressed in each case and the intensities of the refracted and reflected waves calculated as well as the anomalous absorption coefficient, due to the Borrmann effect, the *Pendellösung* interference fringe pattern and the integrated intensity. It is shown that the geometrical diffraction constitutes a limit of dynamical diffraction by small crystals. At the end of the chapter dynamic diffraction by quasicrystals is considered.

*ANDRÉ AUTHIER*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter is the first of the next few chapters devoted to plane-wave advanced dynamical theory. The fundamental equations of dynamical diffraction are derived for vector waves and the expression ...
More

This chapter is the first of the next few chapters devoted to plane-wave advanced dynamical theory. The fundamental equations of dynamical diffraction are derived for vector waves and the expression of the dispersion equation is given in the two-beam case and for absorbing crystals, the following discussion being limited to geometrical situations where neither the incidence nor the emergence angle is grazing. The notion of wavefields and the dispersion surface are introduced, and it is shown that the Poynting vector, which gives the direction of propagation of the energy, is normal to it. The boundary conditions at the entrance surface are then introduced. Transmission and reflection geometries are treated separately. For each case, the deviation parameter is introduced geometrically and the coordinates of the tiepoints determined, the Pendellösung distance (extinction distance in the reflection geometry), Darwin width, the anomalous absorption coefficient, index of refraction, the phase and amplitude ratios of the reflected and refracted waves are calculated. Borrmann's standing wave interpretation of the anomalous absorption effect is given. The last section is to the case where Bragg's angle is close to π/2.Less

This chapter is the first of the next few chapters devoted to plane-wave advanced dynamical theory. The fundamental equations of dynamical diffraction are derived for vector waves and the expression of the dispersion equation is given in the two-beam case and for absorbing crystals, the following discussion being limited to geometrical situations where neither the incidence nor the emergence angle is grazing. The notion of wavefields and the dispersion surface are introduced, and it is shown that the Poynting vector, which gives the direction of propagation of the energy, is normal to it. The boundary conditions at the entrance surface are then introduced. Transmission and reflection geometries are treated separately. For each case, the deviation parameter is introduced geometrically and the coordinates of the tiepoints determined, the *Pendellösung* distance (extinction distance in the reflection geometry), Darwin width, the anomalous absorption coefficient, index of refraction, the phase and amplitude ratios of the reflected and refracted waves are calculated. Borrmann's standing wave interpretation of the anomalous absorption effect is given. The last section is to the case where Bragg's angle is close to π/2.

*ANDRÉ AUTHIER*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter calculates the reflected intensity for the reflection, or Bragg, geometry and an incident plane wave. Both the cases of very thick and thin crystals are considered. In each case the ...
More

This chapter calculates the reflected intensity for the reflection, or Bragg, geometry and an incident plane wave. Both the cases of very thick and thin crystals are considered. In each case the boundary conditions are given, the reflectivity and the integrated intensity are determined for absorbing crystals. The shape of the rocking curves is discussed as a function of the absorption coefficient and the ratio between the real and imaginary parts of the index of refraction. The standing wave pattern formed at the surface of the crystal due to the interference of the incident and reflected waves is calculated.Less

This chapter calculates the reflected intensity for the reflection, or Bragg, geometry and an incident plane wave. Both the cases of very thick and thin crystals are considered. In each case the boundary conditions are given, the reflectivity and the integrated intensity are determined for absorbing crystals. The shape of the rocking curves is discussed as a function of the absorption coefficient and the ratio between the real and imaginary parts of the index of refraction. The standing wave pattern formed at the surface of the crystal due to the interference of the incident and reflected waves is calculated.