Gamma-Ray Spectroscopy by Direct Crystal Diffraction

With the exception of certain early work with flat crystals by Rutherford & Andrade (1) and by Frilley (2), to date, crystal diffraction γ-ray spectroscopy has been accomplished almost entirely by means of transmission-type spectrometers using bent quartz crystal focusing. In this type of instrument, whose first conception was published in 1930 by DuMond & Kirkpatrlck (3), a thin cylindrical lamina of quartz of uniform thickness is bent so that its neutral plane, initially a right circular cylinder of radius 2R, assumes the form of a right circular cylinder of radius R. (By the "neutral plane" is meant that plane through the center of the thickness of the crystalline lamina which undergoes neither compression nor elongation when bending occurs.) The lamina is cut from the original unstressed crystal lattice so that the planes to be used in the selective reflection are made to converge after bending in such fashion that, if prolonged, they would all intersect in a common line distant 2R from the center of the lamina. Figure 1 illustrates the lamina, seen on edge, before and after bending, with lines indicating the direction of the atomic planes. These planes, after bending, converge in a line represented in projection by the point β. Confining ourselves to two dimensions, the normal projection of the neutral plane and the point β define the "focal circle," which is the locus of focal points R_ λ for radiations of different wavelength selectively reflected by the planes of the crystal in accord with Bragg’s law, nλ = 2d sin θ. In Figure 1 the thickness and the aperture angle, α, are greatly exaggerated. Cauchois has pointed out that the compression and dilation of the lattice constant, incident to bending, result in front-to-back focusing as well as side-to-side focusing, within the confines of Hooke’s law, so that the crystal behaves as though all selective reflection occurred on the neutral plane. It can also be easily shown that for selective reflection in transmission by planes normal to the lamina, the correction to Bragg’s law for crystalline refractive index diltering from unity vanishes exactly. This is explained in more detail in Reference 6, p. 241