{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:47:54Z","timestamp":1760028474683,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T00:00:00Z","timestamp":1738800000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Collaborative Research Centre Transregio 188: Damage Controlled Forming Processes","award":["278868966","409476157"],"award-info":[{"award-number":["278868966","409476157"]}]},{"name":"SFB 1394: Structural and Chemical Atomic Complexity: From Defect Phase Diagrams to Material Properties","award":["278868966","409476157"],"award-info":[{"award-number":["278868966","409476157"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a new efficient method for determining the 2D unit cell size from HAADF STEM images using angle-resolved lattice population density (ALPD) plots. The approach uses the maxima in these plots, which represent the lines with the highest atom peak density, to determine the cell angle of the primitive 2D unit cell. Lattice types and 2D unit cell sizes that comply with crystallographic standards can easily be obtained by introducing angle constraints for the selection of the ALPD maxima. The method is very flexible and can be applied to images with fewer than 20 atom peaks, making it valuable for the automated analysis of periodic lattices in both large and small crystalline regions. The method has been evaluated for ideal and disordered lattices and is compared in terms of processing speed and the quality of results with the recently proposed real-space motif extraction method and with the well-established Fourier-based crystallographic image processing method commonly used for this task.<\/jats:p>","DOI":"10.3390\/sym17020239","type":"journal-article","created":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T06:30:29Z","timestamp":1738823429000},"page":"239","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Angle-Resolved Lattice Population Density Plots: A Novel Approach for Fast 2D Unit Cell Determination from HAADF STEM Images"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5539-0534","authenticated-orcid":false,"given":"Thomas E.","family":"Weirich","sequence":"first","affiliation":[{"name":"Central Facility for Electron Microscopy, RWTH Aachen University, Ahornstr. 55, 52074 Aachen, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kirkland, E.J. (2020). Calculation of Images of Thin Specimens. Advanced Computing in Electron Microscopy, Springer International Publishing.","DOI":"10.1007\/978-3-030-33260-0_5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1017\/S1431927614001330","article-title":"Periodic Cation Segregation in Cs0.44[Nb2.54W2.46O14] Quantified by High-Resolution Scanning Transmission Electron Microscopy","volume":"20","author":"Heidelmann","year":"2014","journal-title":"Microsc. Microanal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1017\/S1431927619000497","article-title":"Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond","volume":"25","author":"Ophus","year":"2019","journal-title":"Microsc. Microanal."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Aroyo, M.I. (2016). International Tables for Crystallography: Space-Group Symmetry: Vol. A, International Union of Crystallography. [2nd ed.]. Section 2.1.3.4.","DOI":"10.1107\/97809553602060000114"},{"key":"ref_5","unstructured":"Hammond, C. (2001). The Basics of Crystallography and Diffraction, Oxford University Press. [2nd ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0739-6260(92)90128-Z","article-title":"Crystallographic image processing","volume":"23","year":"1992","journal-title":"Micron Microsc. Acta"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/1-4020-3920-4_18","article-title":"Structure Determination from HREM by Crystallographic Image Processing","volume":"Volume 211","author":"Weirich","year":"2006","journal-title":"Electron Crystallography"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.jsb.2006.07.020","article-title":"2dx\u2014User-friendly image processing for 2D crystals","volume":"157","author":"Gipson","year":"2007","journal-title":"J. Struct. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0304-3991(92)90102-P","article-title":"CRISP: Crystallographic image processing on a personal computer","volume":"41","year":"1992","journal-title":"Ultramicroscopy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113827","DOI":"10.1016\/j.ultramic.2023.113827","article-title":"Direct motif extraction from high resolution crystalline STEM images","volume":"254","author":"Alhassan","year":"2023","journal-title":"Ultramicroscopy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1107\/S0021889811038970","article-title":"VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data","volume":"44","author":"Momma","year":"2011","journal-title":"J. Appl. Crystallogr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1038\/nmeth.2019","article-title":"Fiji: An open-source platform for biological-image analysis","volume":"9","author":"Schindelin","year":"2012","journal-title":"Nat. Methods"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Swanson, H. (1953). Circular of the Bureau of Standards No. 539 Volume 1: Standard X-Ray Diffraction Powder Patterns, National Institute of Standards and Technology.","DOI":"10.6028\/NBS.CIRC.539v1"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Swanson, H., and Ugrinic, G. (1954). Circular of the Bureau of Standards No. 539 Volume 1: Standard X-Ray Diffraction Powder Patterns, National Institute of Standards and Technology.","DOI":"10.6028\/NBS.CIRC.539v1"},{"key":"ref_15","unstructured":"Galasso, F.S. (1970). Structure and Properties of Inorganic Solids, Pergamon Press. [1st ed.]. Chapter 7.4."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3764","DOI":"10.1016\/j.actamat.2010.03.016","article-title":"Structure of Cs0.5[Nb2.5W2.5O14] analysed by focal-series reconstruction and crystallographic image processing","volume":"58","author":"Barthel","year":"2010","journal-title":"Acta Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1038\/311238a0","article-title":"Accurate atom positions from electron microscopy","volume":"311","author":"Farrants","year":"1984","journal-title":"Nature"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1038\/382144a0","article-title":"A crystal structure determined with 0.02 \u00c5 accuracy by electron microscopy","volume":"382","author":"Weirich","year":"1996","journal-title":"Nature"},{"key":"ref_19","first-page":"701","article-title":"Alloy chemistry of \u03c3 (\u03b2-U)-related phases\u2014I. Extension of \u03bc-and occurance of \u03bc\u2019-phases in the ternary systems Nb (Ta)-X-Al (X = Fe, Co, Ni, Cu, Cr, Mo)","volume":"59","author":"Hunt","year":"1968","journal-title":"Z. F\u00fcr Met."},{"key":"ref_20","first-page":"151","article-title":"Variable-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type barium titanate phases","volume":"B72","author":"Nakatani","year":"2016","journal-title":"Acta Cryst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/239\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:27:57Z","timestamp":1760027277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,6]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020239"],"URL":"https:\/\/doi.org\/10.3390\/sym17020239","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,6]]}}}