The accuracy of Quantitative Rietveid Analysis (QRA) was examined in terms of the plausibility of the set of refined parameters as well as the realization of the expected quantitative result. This route was pursued due to the two mutually exclusive characteristics that a powder exhibiting the calculated (ideal) diffraction intensity would possess; it would have infinitesimal domains to alleviate the effects of extinction but at the same time infinitesimal surface area to eliminate the volume of the disordered surface or amorphous phase. The specimens were mixtures of NIST Standard Reference Material (SRM) 640b, a silicon powder with a mean particle size of 7 pin (certified with respect to lattice parameters), and SRM 676, an alumina powder with a submicrometer crystallite size (certified for quantitative analysis). Good agreement between the particle size of SRM 640b, determined by laser scattering measurements, and its domain size, determined by using the Sabine model for extinction, were obtained with the use of improved background functions in refinements of neutron time-of-flight (TOF) powder diffraction data. These data, in conjunction with the plausibility of other refined parameters such as temperature factors, led to a credible measurement of the amorphous content of SRM 676 and a verification that TOF data can yield unbiased quantitative results. A new SRM for quantitative analysis of silicon nitride was certified with respect to the a, p and amorphous (impurity) phase content with the use of TOF diffraction and SRM 676 as the reference phase. Results from XRD data were found to be less sensitive to background function, though improvements in the Rietveid analysis of XRD data were achieved.