International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.1, pp. 538-539   | 1 | 2 |

Section 5.1.3.2. Transmission and reflection geometries

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: authier@lmcp.jussieu.fr

5.1.3.2. Transmission and reflection geometries

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The boundary condition for the continuity of the tangential component of the wavevectors is applied by drawing from M a line, Mz, parallel to the normal n to the crystal surface. The tie points of the wavefields excited in the crystal by the incident wave are at the intersections of this line with the dispersion surface. Two different situations may occur:

  • (a) Transmission, or Laue case (Fig. 5.1.3.2)[link]. The normal to the crystal surface drawn from M intersects both branches of the dispersion surface (Fig. 5.1.3.2a[link]). The reflected wave is then directed towards the inside of the crystal (Fig. 5.1.3.2b[link]). Let [\gamma_{o}] and [\gamma_{h}] be the cosines of the angles between the normal to the crystal surface, n, and the incident and reflected directions, respectively: [\gamma_{o} = \cos ({\bf n},{\bf s}_{{\bf o}})\hbox{;} \quad \gamma_{h} = \cos ({\bf n},{\bf s}_{{\bf h}}). \eqno(5.1.3.2)] It will be noted that they are both positive, as is their ratio, [\gamma = \gamma_{h}/\gamma_{o}. \eqno(5.1.3.3)] This is the asymmetry ratio, which is very important since the width of the rocking curve is proportional to its square root [equation (5.1.3.6)[link]].

    [Figure 5.1.3.2]

    Figure 5.1.3.2 | top | pdf |

    Transmission, or Laue, geometry. (a) Reciprocal space; (b) direct space.

  • (b) Reflection, or Bragg case (Fig. 5.1.3.3[link]). In this case there are three possible situations: the normal to the crystal surface drawn from M intersects either branch 1 or branch 2 of the dispersion surface, or the intersection points are imaginary (Fig. 5.1.3.3a[link]). The reflected wave is directed towards the outside of the crystal (Fig. 5.1.3.3b[link]). The cosines defined by (5.1.3.2)[link] are now positive for [\gamma_{o}] and negative for [\gamma_{h}]. The asymmetry factor is therefore also negative.

    [Figure 5.1.3.3]

    Figure 5.1.3.3 | top | pdf |

    Reflection, or Bragg, geometry. (a) Reciprocal space; (b) direct space.








































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