Microabsorption Correction of X-Ray Intensities Diffracted by Multiphase Powder Specimens

Hermann, H.; Ermrich, M.

doi:10.1017/s0885715600013701

Cited by 15 publications

(12 citation statements)

References 11 publications

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“…Narrow divergence slits with a shorter beam and parallel beam optics reduce this error. Counting statistics: Statistical characterization of powders is best when the particle size is less than 10 μ m. Diffractograms of large crystallite sizes and non‐random orientations lead to peak intensity variations that are incongruent with an ideal powder (measured for many crystallites randomly oriented) and thus are poorly identifiable with reference patterns in the Powder Diffraction File (PDF) database. Axial/vertical divergence error: Soller slits, capillary lenses, and decreasing the vertical opening of the counter slit maximize the diffracted intensity and reduce peak assymetric broadening due the divergence of the x‐ray beam in the plane with the sample Microabsorption: This error stems from differences in the interactions of each material with the x‐ray beam, volume fractions of the components (large particles not crystallites), and on die geometrical peculiarities of their distribution . Complex composites such as cements/concretes, coal combustion by‐products (CCBs), and geologic materials are among the materials that are susceptible to microabsorption errors.…”

Section: Uncertaintymentioning

confidence: 99%

Experimental methods in chemical engineering: X‐ray diffraction spectroscopy—XRD

et al. 2020

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X-ray diffraction (XRD) analysis identifies the long-range order (ie, the structure) of crystalline materials and the short-range order of non-crystalline materials. From this information we deduce lattice constants and phases, average grain size, degree of crystallinity, and crystal defects. Advanced XRD provides information about strain, texture, crystalline symmetry, and electron density. When radiation impinges upon a solid, coherent scattering of the radiation by periodically spaced atoms results in scattered beams that produce spot patterns from single crystalline samples and ring patterns from polycrystalline samples. The pattern, intensities of the diffraction maxima (peaks or lines), and their position (Bragg angle θ or interplanar spacing d hkl ), correlate to a specific crystal structure. In 2016 and 2017 close to 100 000 articles mention XRD-more than any other analytical technique, and it was the top analytical technique of researchers that published in Can. J. Chem. Eng. A bibliographic analysis based on the Web of Science groups articles referring to XRD into five clusters: the largest cluster includes research on nanoparticles, thin films, and optical properties; composites, electro-chemistry, and synthesis are topics of the second largest cluster; crystal morphology and catalysis are next; photocatalysis and solar cells comprise the fourth largest cluster; and, waste water is among the topics of the cluster with the least number of occurrences. Researchers publishing in Can. J. Chem. Eng. focus most of the XRD analyses to characterize polymers, nanocomposite materials, and catalysts. K E Y W O R D Scrystallinity, Debye-Scherrer method, limit of quantification, nanoparticle, XRD

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Section: Uncertaintymentioning

confidence: 99%

Experimental methods in chemical engineering: X‐ray diffraction spectroscopy—XRD

et al. 2020

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“…First of all, the effects of internal standard should be well considered. A significant error may occur when the selected standard is not homogeneously mixed into the sample or when an obvious absorption contrast exists between sample and standard [20]. Furthermore, use of an appropriate amount of internal standard is also a key point to guarantee the accuracy.…”

Section: Introductionmentioning

confidence: 99%

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

Zhao

Liu

et al. 2018

Crystals

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The Rietveld-internal standard method for Bragg-Brentano reflection geometry (θ/2θ) X-ray diffraction (XRD) patterns is implemented to determine the amorphous phase content. The effect of some minor phases on quantitative accuracy is assessed. The numerical simulation analysis of errors and the related corrections are discussed. The results reveal that high purity of crystalline phases in the standard must be strictly ensured. The minor amorphous or non-quantified crystalline phases exert significant effect on the quantitative accuracy, even with less than 2 wt% if ignored. The error levels are evaluated by numerical simulation analysis and the corresponding error-accepted zone is suggested. To eliminate such error, a corrected equation is proposed. When the adding standard happens to be present in sample, it should be also carefully dealt with even in low amounts. Based on that ignorance, the absolute and relative error equations (∆ AE , ∆ RE) are derived, as proposed. The conditions for high quantitative accuracy of original equation is strictly satisfied with a lower amount of standard phase present in sample, less than 2 wt%, and a higher dosage of internal standard, larger than 20 wt%. The corrected equation to eliminate such quantitative error is suggested.

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“…There are no dramatic effects if ao and () are not too small. In the case of multiphase powders, Hermann and Ermrich [24] demonstrated that the Brindley [21] formalism, suggesting that the microabsorption effect is essentially governed by the size of the particle and the absorption contrast (/-Li-P) between the linear absorption coefficient /-Li of the i-type phase and the mean linear absorption coefficient (p) of the solid material forming the powder, is not in all cases a correct measure for the absorption…”

Section: Introductionmentioning

confidence: 99%

The Quantitative Determination of the Crystalline and the Amorphous Content by the Rietveld Method: Application to Glass Ceramics with Different Absorption Coefficients

Gualtieri¹,

Guagliardi²,

Iseppi³

2004

Diffraction Analysis of the Microstructure of Materials

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The Rietveld method provides an accurate determination of the crystalline and the amorphous fractions in polyphase mixtures. To determine the content of the amorphous phase, the sample is diluted with an internal standard which is considered as a component itself and refined with the other phases. Although the method is accurate for systems containing crystalline and amorphous phases with an absorption coefficient comparable to that of the standard, it was not thoroughly tested for systems containing a weakly or highly absorbing amorphous phase. Commonly, this is the case for glass ceramics which may contain elements with fairly different atomic number.X-ray powder diffraction data refined with the Rietveld method were utilized for the determination of the amorphous content in a number of systems containing glasses with different absorption coefficients (Li-, B-, Al-, P-, Zn-, Zr-, Ba-, Pb-glass) to check the accuracy of the method. The mixtures were prepared diluting the glass phase with corundum NIST 676 and hydroxyapatite NIST 2910 in fixed proportions. The refinements were carried out with GSAS and the new code QUANTO, especially developed for automatic quantitative phase analysis (QPA) of polycrystalline mixtures eventually including an amorphous component.The glass weights estimated by the two programs are both in good agreement with the nominal value (45 wt%) although a minor dependency of the calculated amorphous fraction on the linear absorption coefficient of the glass was observed and attributed to microabsorption effects. The Brindley (1945) correction applied here according to the formulation of Taylor and Matulis (1991) revealed not to be fully satisfactory for mixt ure containing an amorphous component with a very different absorption coefficient, especially when highly accurate determinations are required. This is in concert with the general concern that the existing models for the correction of microabsorption effects should be revised as they are not adequate even for systems containing only crystalline phases (Madsen et al., 2001).The method was successfully applied to a commercial glass ceramic indicating that it can be applied with a good accuracy also to glass ceramics with fairly different absorption coefficients. E. J. Mittemeijer et al. (eds.), Diffraction Analysis of the Microstructure of Materials

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Microabsorption Correction of X-Ray Intensities Diffracted by Multiphase Powder Specimens

Cited by 15 publications

References 11 publications

Experimental methods in chemical engineering: X‐ray diffraction spectroscopy—XRD

Experimental methods in chemical engineering: X‐ray diffraction spectroscopy—XRD

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

The Quantitative Determination of the Crystalline and the Amorphous Content by the Rietveld Method: Application to Glass Ceramics with Different Absorption Coefficients

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