An experimental assessment of X-ray diffraction theory in high purity aluminium crystals

Abstract

An experimental test of Zachariasen's X-ray diffraction formula was carried out for high purity aluminium crystals with a wide range of mosaic block sizes and mosaic block misorientations. These crystals were produced by cold rolling to different strains three samples (crystals 1, 2 and 3) cut from a large single crystal grown by the Bridgman method. The (100), (200) and (220) X-ray integrated intensities were measured for each crystal, and the block sizes and block misorientations were obtained using transmission electron microscopy techniques (the mean linear intercept method for the block size and Kikuchi line techniques for the block misorientation). With the exception of crystal 2 in the undeformed condition, for a given state the three crystals showed a common diffraction efficiency, the value of which increased with increasing deformation. The different diffraction efficiency of crystal 2 with respect to crystals 1 and 3 in the undeformed condition is rationalized in terms of a segragation of impurities at the bottom of the large single crystal. Comparison between the integrated intensities determined experimentally and the intensities calculated by substituting the measured block size and block misorientation parameters into Zachariasen's formula showed good agreement between the two sets of values. In view of this, it was concluded that Zachariasen's formula is closely consistent with the diffraction efficiency of the crystals under study; the behaviour of the crystals is characteristic of Zachariasen's type II crystals, i.e. the extinction is primarily controlled by the mosaic block size rather than by the mosaic block misorientation.