By Rudolf P. Huebener
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Additional info for Conductors, Semiconductors, Superconductors: An Introduction to Solid State Physics
The points of intersection of these circles then yield the directions of maximum or minimum intensity. c Finally, for a three-dimensional point lattice we deal correspondingly with three families of cones. However, in general the resulting three series of circles on the surface of the imagined sphere no longer have common points of intersection, which mark the directions of maximum or minimum intensity. Now such common points of intersection only exist for special values of the wavelength or frequency of the X-rays extending our discussion to a three-dimensional lattice of points, we have to deal with three families of cones.
Finally, 22 2 Well Ordered Lattice Structures in Crystals Fig. 7 Generation of the Laue diagram as the interference pattern due to the diffraction of X-rays at a three-dimensional point lattice. a For a one-dimensional chain of points, the directions of maximum or minimum intensity lie on cones arranged around the one-dimensional chain. On the surface of an imagined sphere, having its center at the common tip of this family of cones, the directions of maximum or minimum intensity yield a series of circles.
7). The spherical waves originating from all points are ampliﬁed, reaching a maximum intensity, if the propagation distance starting from two neighboring points differs exactly by one wavelength or by a multiple of one wavelength. On the other hand, if the difference amounts to half a wavelength or an uneven multiple of half a wavelength, complete extinction occurs. In this way we ﬁnd that propagation directions for maximum or minimum intensity exist, and these are conically arranged around the straight line of points.