Wavevectors

Authier, A.

doi:10.1107/97809553602060000569

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

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International Tables for Crystallography (2006). Vol. B. ch. 5.1, pp. 542-543 | 1 | 2 |

Section 5.1.6.3.1. Wavevectors

A. Authier^a ^*

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

5.1.6.3.1. Wavevectors

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When a wavefield reaches the exit surface, it breaks up into its two constituent waves. Their wavevectors are obtained by applying again the condition of the continuity of their tangential components along the crystal surface. The extremities, $[M_{j}]$ and $[N_{j}]$ , of these wavevectors $[{\bf OM}_{j} = {\bf K}_{{\bf o}j}^{(d)}\qquad {\bf HN}_{j} = {\bf K}_{{\bf h}j}^{(d)}]$ lie at the intersections of the spheres of radius k centred at O and H, respectively, with the normal n′ to the crystal exit surface drawn from $[P_{j}]$ (j = 1 and 2) (Fig. 5.1.6.3).

Figure 5.1.6.3| top | pdf |

Boundary condition for the wavevectors at the exit surface. (a) Reciprocal space. The wavevectors of the emerging waves are determined by the intersections $[M_{1}]$ , $[M_{2}]$ , $[N_{1}]$ and $[N_{2}]$ of the normals n′ to the exit surface, drawn from the tie points $[P_{1}]$ and $[P_{2}]$ of the wavefields, with the tangents $[T'_{o}]$ and $[T'_{h}]$ to the spheres centred at O and H and of radius k, respectively. (b) Direct space.

If the crystal is wedge-shaped and the normals n and n′ to the entrance and exit surfaces are not parallel, the wavevectors of the waves generated by the two wavefields are not parallel. This effect is due to the refraction properties associated with the dispersion surface.

References

International Tables for Crystallography (2006). Vol. B. ch. 5.1, pp. 542-543