On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction
The present work briefly reviews the convolution of crystallite shape functions and discusses its experimental limitations. The diffraction from a theoretical spherical shape powder is used to exemplify the limits of the convolution procedure. Mean lattice distortions were not considered since the d...
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| Format: | Article |
| Language: | English |
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Associação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol)
2018-03-01
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| Series: | Materials Research |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392018000300018&tlng=en |
| _version_ | 1818973525673771008 |
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| author | Roberto Ribeiro de Avillez Fernanda Gonçalves Abrantes Sonia Letichevsky |
| author_facet | Roberto Ribeiro de Avillez Fernanda Gonçalves Abrantes Sonia Letichevsky |
| author_sort | Roberto Ribeiro de Avillez |
| collection | DOAJ |
| description | The present work briefly reviews the convolution of crystallite shape functions and discusses its experimental limitations. The diffraction from a theoretical spherical shape powder is used to exemplify the limits of the convolution procedure. Mean lattice distortions were not considered since the discussed limitations are inherent to the convolution method using Fourier transforms. The diffraction pattern and the convolution were calculated using appropriate macros for the Topas program. It is shown that very small crystallites require a large 2θ convolution span and the smallest subdivision for the distribution will depend on this convolution span. To show the importance of the convolution limits and its application, the nanocrystalline CeO2 round-robin diffraction pattern was evaluated. The chord frequency distribution by XRD showed conformity with the chord distribution calculated from a grain size histogram obtained by transmission electron microscopy for this sample. |
| first_indexed | 2024-12-20T15:25:33Z |
| format | Article |
| id | doaj.art-eea6f79d90954452921ef18d8ba56550 |
| institution | Directory Open Access Journal |
| issn | 1516-1439 |
| language | English |
| last_indexed | 2024-12-20T15:25:33Z |
| publishDate | 2018-03-01 |
| publisher | Associação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol) |
| record_format | Article |
| series | Materials Research |
| spelling | doaj.art-eea6f79d90954452921ef18d8ba565502022-12-21T19:35:52ZengAssociação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol)Materials Research1516-14392018-03-0121310.1590/1980-5373-mr-2017-0980On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders DiffractionRoberto Ribeiro de Avillezhttps://orcid.org/0000-0002-2192-1082Fernanda Gonçalves AbrantesSonia LetichevskyThe present work briefly reviews the convolution of crystallite shape functions and discusses its experimental limitations. The diffraction from a theoretical spherical shape powder is used to exemplify the limits of the convolution procedure. Mean lattice distortions were not considered since the discussed limitations are inherent to the convolution method using Fourier transforms. The diffraction pattern and the convolution were calculated using appropriate macros for the Topas program. It is shown that very small crystallites require a large 2θ convolution span and the smallest subdivision for the distribution will depend on this convolution span. To show the importance of the convolution limits and its application, the nanocrystalline CeO2 round-robin diffraction pattern was evaluated. The chord frequency distribution by XRD showed conformity with the chord distribution calculated from a grain size histogram obtained by transmission electron microscopy for this sample.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392018000300018&tlng=enX-ray diffractionconvolution limitscrystallite size distributionNyquist Theoremnanopowder |
| spellingShingle | Roberto Ribeiro de Avillez Fernanda Gonçalves Abrantes Sonia Letichevsky On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction Materials Research X-ray diffraction convolution limits crystallite size distribution Nyquist Theorem nanopowder |
| title | On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction |
| title_full | On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction |
| title_fullStr | On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction |
| title_full_unstemmed | On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction |
| title_short | On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction |
| title_sort | on the intrinsic limits of the convolution method to obtain the crystallite size distribution from nanopowders diffraction |
| topic | X-ray diffraction convolution limits crystallite size distribution Nyquist Theorem nanopowder |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392018000300018&tlng=en |
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