Influence of mechanical manufacturing errors in diffraction instruments on the fit confidence limit
[Objective]The X-ray polycrystalline diffraction(XRPD)analysis method is pivotal in multiple disciplines,including physics,chemistry,and materials science.This technique is frequently used to study material structure.More specifically,the full spectrum structure fitting method,known as Rietveld,is often used to obtain the fine structure of materials and substances on the atomic scale.This method combines the study of material properties to uncover and improve the relationship between structure and properties to develop and obtain better materials.A key factor in these analyses is the accuracy and credibility of structural and lattice parameter analyses.Several factors can affect the accuracy of angle measurement.One of the most significant is the inherent error of the angle measuring instrument,which is primarily affected by mechanical manufacturing errors.These errors,often caused by issues with the worm gear system,cannot be overlooked.A typical X-ray diffractometer uses a worm gear system to rotate the X-ray tube,sample stage,and detector.The systematic error of the worm gear used in the diffractometer is random,and the error at every angle of each diffractometer differs.Unfortunately,these errors cannot be corrected using software and standards owing to their randomness.[Methods]In our study,we calculated and analyzed the reliability of the XRPD full spectrum fitting results.We focused on the impact of manufacturing errors in the worm gear system,using simulation calculation methods to determine their effect.Simply put,let us take Si as an example.We design a set of profile functions that vary with angle according to the actual conditions.We then calculate the theoretical spectrum without mechanical error(20°-120°)with a step distance of 0.01°.As per the requirements of the peak function,the integration intensity ratio of each peak matches the relative intensity number on the PDF 27-1402 card.Then,we set the precision of mechanical error to 0.002,0.004,0.006,and so on until 0.020°.For each given precision,we calculate the theoretical calculation spectrum of the angle error of each peak using the same profile function.Finally,we fit multiple spectra with random errors to the error-free theoretical spectra and obtain the fitting error factor.[Results]We find the maximum,minimum,and average values of the fitting error factors corresponding to the given accuracy calculated multiple times.A detailed analysis of the data reveals that for a theta-theta diffractometer,the angle accuracy of mechanical manufacturing must reach at least±0.003° for the fitting results to be deemed reliable.If it is a theta-2 theta diffractometer,the required accuracy needs to be halved.In theory,no program,including all algorithms for fitting full spectrum structures,can reduce the limitation of this error.[Conclusions]Therefore,only a diffractometer with a high-accuracy circular grating installed directly on the diffractometer axis can meet the requirements of current material structure analysis.Given the inevitable presence of other errors,the accuracy index of the circular grating installed on the diffractometer used should surpass the angle accuracy required for the analysis.
万方数据
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