ON THE MODELING OF NEUTRON-DIFFRACTION REFLECTIONS FROM SMALL SINGLE-CRYSTALS

For the case where the rotation axis of the monochromator crystal and that of the small specimen crystal are parallel, i.e.(+, -) or (-, +) configuration, the apparatus function in two-dimensional DELTAomega, D ELTA2theta space is associated with the source, S, the monochromator c rystal, M, and an idealized specimen crystal, c, which is vanishingly small and has zero mosaic spread. For any value of t (= tan theta(c)/t an theta(M)), the apparatus function is a product of the distributions (with their respective loci of translation) of: (i) the emissivity of S; (ii) the reflectivity over the length of M; (iii) the mosaic sprea d of M; and (iv) the wavelength band arising from the vector addition in DELTAomega), DELTA2theta space of the wavelength dispersion of M an d of c. To combine the apparatus function with other components such a s the mosaic spread of a real specimen crystal, its physical dimension , the size of the aperture in front of a quantum detector or the point -spread function of a position-sensitive detector, the appropriate mat hematical operation in DELTAomega, DELTA2theta space is sequential con volution. Examples are given, for t = 0 (0.25) 1.0 (0.5) 2.0, of synth etic apparatus functions based on typical dimensions appropriate to ne utron diffraction experimental arrangements. These are presented in DE LTAomega, DELTA2theta(0)) space, which corresponds to omega-scan data collection. The advantage of modifying) these by affine transformation to DELTAomega, DELTA2theta(2) space or, equivalently, to correspond t o omega-2theta-scan data collection, is demonstrated.