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Method of calculating the coherent scattering power of crystals with unknown atomic arrangements and its application in the quantitative phase analysis

Published online by Cambridge University Press:  04 January 2022

Hui Li ,
Meng He Open the ORCID record for Meng He [Opens in a new window]  and
Ze Zhang
Hui Li*
Affiliation:
Institute of Microstructure and Properties of Advanced Materials, Beijing University of Technology, 100 Ping Le Yuan, Chaoyang District, Beijing 100124, People's Republic of China
Meng He*
Affiliation:
CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, Beijing 100190, People's Republic of China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China Tianmu Lake Institute of Advanced Energy Storage Technologies, Liyang, Jiangsu Province 213300, People's Republic of China
Ze Zhang
Affiliation:
Zhejiang University, Hangzhou, Zhejiang Province 310014, People's Republic of China
*
a)Authors to whom correspondence should be addressed. Electronic mail: huilicn@yahoo.com (H. L.); mhe@nanoctr.cn (M. H.)
a)Authors to whom correspondence should be addressed. Electronic mail: huilicn@yahoo.com (H. L.); mhe@nanoctr.cn (M. H.)
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Abstract

Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its abundance. Nevertheless, the diffraction intensities of the component phases cannot be compared with each other directly since the coherent scattering power per unit cell (or chemical formula) of each component phase is usually different. The coherent scattering power per unit cell of a crystal is well represented by the sum of the squared structure factors, which cannot be calculated directly when the crystal structure data is unavailable. Presented here is a way to approximate the coherent scattering power per unit cell based solely on the unit cell parameters and the chemical contents. This approximation is useful when the atomic coordinates for one or more of the phases in a sample are unavailable. An assessment of the accuracy of the approximation is presented. This assessment indicates that the approximation will likely be within 10% when X-ray powder diffraction data is collected over a sufficient portion of the measurable pattern.

Keywords

X-ray powder diffractionquantitative phase analysiscoherent scattering powerParseval theorem

Information

Type
Technical Article
Information
Powder Diffraction , Volume 37 , Issue 1 , March 2022 , pp. 34 - 39
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of International Centre for Diffraction Data

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References

Alexander, L. E. and Klug, H. P. (1948). “Basic aspects of X-ray absorption in quantitative diffraction analysis of powder mixtures,” Anal. Chem. 20, 886–889.10.1021/ac60022a002CrossRefGoogle Scholar
Berry, C. (1970). Inorganic Index to the Powder Diffraction File, p. 1189. Joint Committee on Powder Diffraction Standards, Pennsylvania.Google Scholar
Chung, F. H. (1974a). “Quantitative interpretation of X-ray diffraction patterns of mixtures. I. Matrix-flushing method for quantitative multicomponent analysis,” J. Appl. Cryst. 7, 519–525.10.1107/S0021889874010375CrossRefGoogle Scholar
Chung, F. H. (1974b). “Quantitative interpretation of X-ray diffraction patterns of mixtures. II. Adiabatic principle of X-ray diffraction analysis of mixtures,” J. Appl. Cryst. 7, 526–531.10.1107/S0021889874010387CrossRefGoogle Scholar
Clark, G. L. and Reynolds, D. H. (1936). “Quantitative analysis of mine dusts an X-ray diffraction method,” Ind. Eng. Chem. Anal. Ed. 8, 36–40.10.1021/ac50099a015CrossRefGoogle Scholar
Copeland, L. E. and Bragg, R. H. (1958). “Quantitative X-ray diffraction analysis,” Anal. Chem. 30, 196–201.10.1021/ac60134a011CrossRefGoogle Scholar
Effenberger, H. and Zemann, J. (1979). “Refining the crystal structure of lithium carbonates, Li2CO3,” Z. Kristallogr. 150, 133–138.10.1524/zkri.1979.150.1-4.133CrossRefGoogle Scholar
Gates-Rector, S. and Blanton, T. (2019). “The powder diffraction file: a quality materials characterization database,” Powd. Diffr. 34, 352–360.10.1017/S0885715619000812CrossRefGoogle Scholar
Hill, R. J. and Howard, C. J. (1987). “Quantitative phase analysis from neutron powder diffraction data using the rietveid method,” J. Appl. Cryst. 20, 467–474.10.1107/S0021889887086199CrossRefGoogle Scholar
Hughes, H. K. (1965). “The physical meaning of parseval's theorem,” Am. J. Phys. 33, 99–101.10.1119/1.1971337CrossRefGoogle Scholar
Le Bail, A., Duroy, H., and Fourquet, J. L. (1988). “Ab-initio structure determination of LiSbWO6 by X-ray powder diffraction,” Mater. Res. Bull. 23, 447–452.CrossRefGoogle Scholar
Parrish, W. (1960). “Results of the I.U.Cr. precision lattice-parameter project,” Acta Cryst. 13, 838–850.CrossRefGoogle Scholar
Pillet, S., Souhassou, M., Lecomte, C., Schwarz, K., Blaha, P., Rérat, M., Lichanot, A., and Roversi, P. (2001). “Recovering experimental and theoretical electron densities in corundum using the multipolar model: IUCr multipole refinement project,” Acta Cryst. A 57, 290–303.CrossRefGoogle ScholarPubMed
Pollard, S. (1926). “On parseval's theorem,” Proc. London Math. Soc. 25, 237–246.10.1112/plms/s2-25.1.237CrossRefGoogle Scholar
Rietveld, H. M. (1969). “A profile refinement method for nuclear and magnetic structures,” J. Appl. Crystallogr. 2, 65–71.10.1107/S0021889869006558CrossRefGoogle Scholar
Rodríguez-Carvajal, J. (1993). “Recent advances in magnetic structure determination by neutron powder diffraction,” Phys. B 192, 55–69.10.1016/0921-4526(93)90108-ICrossRefGoogle Scholar
Scarlett, N. V. Y. and Madsen, I. C. (2006). “Quantification of phases with partial or no known crystal structures,” Powd. Diffr. 21, 278–284.CrossRefGoogle Scholar
Swanson, H. E. and Fuyat, R. K. (1953). “Standard X-ray diffraction patterns. Sodium chloride, NaCl (cubic),” Natl. Bur. Stand. US Circular 539, 41–43.Google Scholar
Toraya, H. (2016). “A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases,” J. Appl. Cryst. 49, 1508–1516.10.1107/S1600576716010451CrossRefGoogle Scholar
Toraya, H. (2017). “Quantitative phase analysis using observed integrated intensities and chemical composition data of individual crystalline phases: quantification of materials with indefinite chemical compositions,” J. Appl. Cryst. 50, 820–829.10.1107/S1600576717005052CrossRefGoogle Scholar
Toraya, H. (2018). “Direct derivation (DD) of weight fractions of individual crystalline phases from observed intensities and chemical composition data: incorporation of the DD method into the whole-powder-pattern fitting procedure,” J. Appl. Cryst. 51, 446–455.10.1107/S1600576718001474CrossRefGoogle Scholar
Toraya, H. (2019). “A practical approach to the direct-derivation method for QPA: use of observed powder patterns of individual components without background subtraction in whole-powder-pattern fitting,” J. Appl. Cryst. 52, 520–531.10.1107/S1600576719003406CrossRefGoogle Scholar
Van Der Lee, A. and De Boer, J. L. (1993). “Redetermination of the structure of hessite, Ag2Te-III,” Acta Cryst. C 49, 1444–1446.CrossRefGoogle Scholar
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