Experimental determination of the instrumental transparency function of texture goniometers

The instrumental transparency functions of five commercially available texture goniometers were measured experimentally with six monocrystalline samples cut in different orientations from a large highly perfect silicon crystal with a rocking curve of less than 0.01 degrees. Transparency functions were measured in steps of 0.02 to 0.2 degrees in the pole-figure angles alpha, beta. The window size Delta alpha depends on the Bragg angle theta in the form 1/sin theta; the window size Delta omega is constant for each goniometer. The dominant instrumental parameter determining the long axis Delta alpha of the pole-figure window is the axial width of the detector entrance slit. This parameter is smallest for area detectors (smaller by more than an order of magnitude compared with conventional scintillation detectors as well as one-dimensional position-sensitive detectors). The main features of the pole-figure window and their dependence on the instrumental parameters can be deduced fairly well from a simple geometrical model. The particular shapes of the transparency functions of the studied goniometers are markedly different. Particularly, they are not very well represented by Gauss functions. The two-dimensional transparency function can be fairly well characterized by its alpha and beta profiles. The normalized profiles are virtually independent of the goniometer angles 2 theta and alpha. The increasing size of the pole-figure window with decreasing theta puts a lower limit on the Bragg angle below which pole-figure measurement ceases to be meaningful.