*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/9780198528920.003.0013
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter is devoted to the propagation of X-ray wavefields in slightly deformed crystals where the deformation is small enough for the notions of dispersion surface and wavefields to be locally ...
More

This chapter is devoted to the propagation of X-ray wavefields in slightly deformed crystals where the deformation is small enough for the notions of dispersion surface and wavefields to be locally valid. A local reciprocal-lattice vector and local effective misorientation are defined. The trajectories of the wavefields (ray tracing) are determined using the Eikonal approximation. The case of a constant strain gradient is considered in detail and it is shown that the ray trajectories are bent, giving rise to the mirage effect; both the transmission and reflection geometries are considered. The diffracted intensities are calculated for an incident plane wave and an incident spherical wave. Shape of the Pendellösung fringes in a deformed crystal is discussed.Less

This chapter is devoted to the propagation of X-ray wavefields in slightly deformed crystals where the deformation is small enough for the notions of dispersion surface and wavefields to be locally valid. A local reciprocal-lattice vector and local effective misorientation are defined. The trajectories of the wavefields (ray tracing) are determined using the Eikonal approximation. The case of a constant strain gradient is considered in detail and it is shown that the ray trajectories are bent, giving rise to the mirage effect; both the transmission and reflection geometries are considered. The diffracted intensities are calculated for an incident plane wave and an incident spherical wave. Shape of the *Pendellösung* fringes in a deformed crystal is discussed.

*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/9780198528920.003.0014
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are ...
More

This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.Less

This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.