Abstract
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 Rwp, 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.
Highlights
Structural study for powder materials relies on the Rietveld method, which is capable of refining the structural and magnetic parameters from diffraction data[1,2,3]
The accuracy of the lattice parameters is of an order of 0.01 Å (=10 × 10−3 Å), which is incomparably large considering that the linear thermal expansion coefficient is of an order of 10−5 K−1 to 10−6 K−1 for general solid materials[9]
This paper proposes an additional criterion, focusing on a fitting accuracy along the horizontal-axis of powder diffraction data, to determine the lattice parameters accurately
Summary
Structural study for powder materials relies on the Rietveld method, which is capable of refining the structural and magnetic parameters from diffraction data[1,2,3]. The weighted mean parameters for a-, b- and c-axes are 8.4804(4) Å, 5.3989(3) Å and 6.9605(2) Å, respectively They are in good agreement with those determined from single-crystal X-ray diffraction data[7,10] which is generally accepted to be high-accuracy. These facts mean that either smaller or larger lattice parameter compared to the true one is possibly obtained depending on a researcher by the Rietveld method. This paper proposes an additional criterion, focusing on a fitting accuracy along the horizontal-axis of powder diffraction data, to determine the lattice parameters accurately.
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