Aberrations in high resolution diffractometry

As with most instruments, erroneous results may be obtained if the high resolution diffractometer is not correctly set up. In modem instmments this is greatly assisted by the manufacturers, by prealigned components, permanent alignment on installation and by automated algorithms for specimen alignment. The primary errors to be considered are 

Tilt of the Bragg plane of the specimen, so that its dispersion plane is not parallel 

Wavelength dispersion arising from the bandpass of the beam conditioner 

The theory of this aberration was worked out in the 1920s by Schwarzchild. For simphcity we shall discuss the case of a beam conditioner comprising a single crystal and an aperture as in the classic double-crystal arrangement. If the Bragg planes are tilted about an axis contained in the incidence plane and the 

Tilting about axis in incidence plane and Bragg plane 

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