Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices
A review of the Miller, Laue and direction indices characterization was made. Excluding or allowing non-coprime indices, depending on whether the lattice is primitive or centred, were compared. The solution of the “spacing counting problem for centred lattices was proposed. It was shown that for cen...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2022-10-01
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| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
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| Online Access: | https://journals.pan.pl/Content/124866/PDF/3231_BPASTS_2022_70_5.pdf |
| _version_ | 1811324879005286400 |
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| author | Edward Michalski |
| author_facet | Edward Michalski |
| author_sort | Edward Michalski |
| collection | DOAJ |
| description | A review of the Miller, Laue and direction indices characterization was made. Excluding or allowing non-coprime indices, depending on whether the lattice is primitive or centred, were compared. The solution of the “spacing counting problem for centred lattices was proposed. It was shown that for centred lattices: (1) Laue indices nh nk nl can represent not only n-th order diffraction on (hkl) planes, but also the first order diffraction from a family of planes (nh nk nl); (2) “integral reflection conditions” are necessary, but not sufficient for the existence of given Miller indices. “Integral reflection conditions” for Laue indices hkl and other “conditions for Miller indices” (hkl) were distinguished. It was shown that in the case of centred lattices, the inference based on the value of n obtained from the equation of lattice planes, may not be correct. The homogeneity of the centred reciprocal lattices has been clarified. “Simple cubic cell with a base” as a choice of unit cell proposed by “general rule” was contrasted with: “unit cell, if not centred, must be the smallest one”. “Integral reflection conditions” for Laue indices and other, new “conditions for Miller indices”, resulting from transformation of centred lattices to unconventional primitive ones have been proposed. Examples of the not correct use of indices in the morphology and diffraction pattern descriptions were shown. |
| first_indexed | 2024-04-13T14:23:22Z |
| format | Article |
| id | doaj.art-ada489aac24e44a499182c2d1f8c08b4 |
| institution | Directory Open Access Journal |
| issn | 2300-1917 |
| language | English |
| last_indexed | 2024-04-13T14:23:22Z |
| publishDate | 2022-10-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| spelling | doaj.art-ada489aac24e44a499182c2d1f8c08b42022-12-22T02:43:24ZengPolish Academy of SciencesBulletin of the Polish Academy of Sciences: Technical Sciences2300-19172022-10-01705https://doi.org/10.24425/bpasts.2022.143109Some new aspects of the characterization of Miller, Laue and directions indices for centred latticesEdward Michalski0https://orcid.org/0000-0002-5292-7030Institute of Optoelectronics, Military University of Technology, Gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, PolandA review of the Miller, Laue and direction indices characterization was made. Excluding or allowing non-coprime indices, depending on whether the lattice is primitive or centred, were compared. The solution of the “spacing counting problem for centred lattices was proposed. It was shown that for centred lattices: (1) Laue indices nh nk nl can represent not only n-th order diffraction on (hkl) planes, but also the first order diffraction from a family of planes (nh nk nl); (2) “integral reflection conditions” are necessary, but not sufficient for the existence of given Miller indices. “Integral reflection conditions” for Laue indices hkl and other “conditions for Miller indices” (hkl) were distinguished. It was shown that in the case of centred lattices, the inference based on the value of n obtained from the equation of lattice planes, may not be correct. The homogeneity of the centred reciprocal lattices has been clarified. “Simple cubic cell with a base” as a choice of unit cell proposed by “general rule” was contrasted with: “unit cell, if not centred, must be the smallest one”. “Integral reflection conditions” for Laue indices and other, new “conditions for Miller indices”, resulting from transformation of centred lattices to unconventional primitive ones have been proposed. Examples of the not correct use of indices in the morphology and diffraction pattern descriptions were shown.https://journals.pan.pl/Content/124866/PDF/3231_BPASTS_2022_70_5.pdfmiller indiceslaue indicesdirection indicescentred lattices |
| spellingShingle | Edward Michalski Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices Bulletin of the Polish Academy of Sciences: Technical Sciences miller indices laue indices direction indices centred lattices |
| title | Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices |
| title_full | Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices |
| title_fullStr | Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices |
| title_full_unstemmed | Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices |
| title_short | Some new aspects of the characterization of Miller, Laue and directions indices for centred lattices |
| title_sort | some new aspects of the characterization of miller laue and directions indices for centred lattices |
| topic | miller indices laue indices direction indices centred lattices |
| url | https://journals.pan.pl/Content/124866/PDF/3231_BPASTS_2022_70_5.pdf |
| work_keys_str_mv | AT edwardmichalski somenewaspectsofthecharacterizationofmillerlaueanddirectionsindicesforcentredlattices |