Neutron scattering length determination by means of total scattering

A new method for the measurement of bound coherent neutron scattering lengths is reported. It is shown that a relative measurement of the neutron scattering length, , of an element can be made by analysis of the neutron correlation function of a suitable oxide crystal powder. For this analysis, it is essential to take into account the average density contribution to the correlation function, as well as the contributions arising from distances between atoms in the crystal. The method is demonstrated and verified by analysis of the neutron correlation function for the corundum form of Al₂O₃, yielding a value = 3.44 (1) fm for Al, in good agreement with the literature. The method is then applied to the isotopes of iridium, for which the values of the scattering lengths were unknown, and which are difficult to investigate by other methods owing to the large cross sections for the absorption of neutrons. The neutron correlation function of a sample of Sr₂IrO₄ enriched in ¹⁹³Ir is used to determine values = 9.71 (18) fm and = 12.1 (9) fm for ¹⁹³Ir and ¹⁹¹Ir, respectively, and these are consistent with the tabulated scattering length and cross sections of natural Ir. These values are of potential application for obtaining improved neutron diffraction results on iridates by the use of samples enriched in ¹⁹³Ir, so that the severe absorption problems associated with ¹⁹¹Ir are avoided. Rietveld refinement of the neutron diffraction pattern of isotopically enriched Sr₂IrO₄ is used to yield a similar result for Ir. However, in practice the Rietveld result is shown to be less reliable because of correlation between the parameters of the fit.