Rietveld Refinement

Rietveld finishing is the analysis of lithium iron phosphate battery. It is a method to determine the crystal structure by comparing the diffraction patterns of powder samples with the calculated patterns and minimizing their differences.Because the solid sample has the symmetry of the crystal space group, the diffraction peak has a certain θ Location.The crystal structure of solid samples can be determined by peak intensity, peak shape, width and peak position. In the past, the analysis of crystal structure was limited to single crystal samples, but after Rietveld refinement, we can now conduct a detailed study of the local structure of powder samples. Although the precision of Rietveld finishing is slightly lower than that of single crystal X-ray diffraction, it is especially useful for non single crystal or non single-phase materials [3].

Rietveld refined uses the least square method to calculate the Bragg angle of 2 in the powder diffraction pattern θ The peak detection intensity Iobs and the calculated intensity Ical were compared. The calculation is based on different factors, including the lattice constant of the cell, atomic position (x, y, z) and occupation, thermal parameters, baseline and peak shape (see Table 4.3). It can be seen from Figure 4.50 that the detected diffraction pattern overlaps the calculated diffraction pattern, and the difference between them is represented by the lowest curve [4]. The vertical line at the lower end of the diffraction pattern corresponds to the peak position of the Miller index hkl. Refined parameters of diffraction data include scale factor, zero point, background, lattice constant of unit cell (a, b, c), atomic position (x, y, z), thermal parameter (B) peak type, half peak width and occupancy. Here, the occupancy is the possibility of each atom occupying the corresponding position, and 1 is equal to 100%. When the atomic position is filled with the second atom, the occupancy will change and the crystal structure will be distorted.



The peak shape can be represented by different functions, such as Gaussian, Lorentzian, Pearson and Pseudo Voigt functions, among which Pseudo Voigt function is the most widely used. Refinement is carried out by minimizing Rwp (weighted residual difference square factor R), which is the difference between the detection map and the calculation map, and is defined as follows:


Where, Yi is the intensity of the scanning spectrum at step i; C is the scale factor; Wi is the weighting factor.

When the Rwp value obtained by using the least square method is less than 10, it can be considered that the Rietveld refined result is reliable.

As shown in Table 4.3, Rietveld finishing shows important information about crystal structure. The position of each atom in the crystal is determined by x, y, z coordinates, and the occupancy g can also be obtained. The thermal parameter B increases with the thermal activity of atoms, and the smaller the number of atoms, the greater the value of B. The R value below the table is the minimum value after finishing. The smaller the R value, the smaller the difference between the detected and calculated diffraction patterns.

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