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The Scherrer Formula for X-Ray Particle Size Determination
Abstract
An exact derivation of the Scherrer equation is given for particles of spherical shape, values of the constant for half-value breadth and for integral breadth being obtained. Various approximation methods which have been used are compared with the exact calculation. The tangent plane approximation of v. Laue is shown to be quite satisfactory, but some doubt is cast on the use of approximation functions. It is suggested that the calculation for the ellipsoidal particle based on the tangent plane approximation will provide a satisfactory basis for future work.
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Cited by
De Luna, P., Quintero-Bermudez, R., Dinh, C.-T., Ross, M. B., Bushuyev, O. S., Todorović, P., Regier, T., Kelley, S. O., Yang, P., & Sargent, E. H. (2018) · Nature Catalysis · doi:10.1038/s41929-017-0018-9 · Cited by 1,046
Enhanced photocatalytic removal of phenol from aqueous solutions using ZnO modified with Ag
Vaiano, V., Matarangolo, M., Murcia, J. J., Rojas, H., Navío, J. A., & Hidalgo, M. C. (2018) · Applied Catalysis B: Environmental · doi:10.1016/j.apcatb.2017.11.075 · Cited by 512
Photocatalytic reforming of biomass: A systematic study of hydrogen evolution from glucose solution
FU, X., LONG, J., WANG, X., LEUNG, D., DING, Z., WU, L., ZHANG, Z., LI, Z., & FU, X. (2008) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2008.07.068 · Cited by 342
Hassan, N., Shahat, A., El-Didamony, A., El-Desouky, M. G., & El-Bindary, A. A. (2020) · Journal of Molecular Structure · doi:10.1016/j.molstruc.2020.128029 · Cited by 133
Zhang, Y., Guo, X., Wu, F., Yao, Y., Yuan, Y., Bi, X., Luo, X., Shahbazian-Yassar, R., Zhang, C., & Amine, K. (2016) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.6b05458 · Cited by 119
Metadata
- Authors
- Patterson, A. L.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1939-11-15
- Volume
- 56
- Issue
- 10
- Pages
- 978-982
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2060429741
- Cited by
- 9,152
- References
- 0
- FWCI
- 4.88
- Type
- journal article
- Language
- en
- Open access
- closed
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- Patterson, A. L. (1939). The Scherrer Formula for X-Ray Particle Size Determination. Physical Review. https://doi.org/10.1103/physrev.56.978
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
