A necessary criterion for obtaining accurate lattice parameters by Rietveld method

To obtain the lattice parameters accurately by the Rietveld method, the relationship between the lattice parameters and the peak-shift, which is the deviation in diffraction angle from the theoretical Bragg position, was studied. We show that the fitting accuracy of lattice parameters is related directly to the well reproducibility of the peak-shift. This study unveils that the peak-shift consists of the experimental and the analytical ones. The analytical peak-shift erroneously lowers a reliability factor R (wp), which has, so far, been the conventional criterion of fit. The conventional Rietveld method obtains a unit-cell which is a homothetic (proportional) unit-cell of the true one. We propose an additional criterion based on the peak-shift to obtain the true lattice parameters accurately. Our criterion can achieve reproducibility reasonably well for the experimental peak-shift, leading to highly improved accuracy of the lattice parameters.