{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T13:40:10Z","timestamp":1789220410677,"version":"build-2803163510"},"reference-count":58,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,9]],"date-time":"2021-08-09T00:00:00Z","timestamp":1628467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11825203, 11832010, 11921002, 52090032"],"award-info":[{"award-number":["11825203, 11832010, 11921002, 52090032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Two-dimensional (2D) crystals provides a material platform to explore the physics and chemistry at the single-atom scale, where surface characterization techniques can be applied straightforwardly. Recently there have been emerging interests in engineering materials through structural deformation or transformation. The strain field offers crucial information of lattice distortion and phase transformation in the native state or under external perturbation. Example problems with significance in science and engineering include the role of defects and dislocations in modulating material behaviors, and the process of fracture, where remarkable strain is built up in a local region, leading to the breakdown of materials. Strain is well defined in the continuum limit to measure the deformation, which can be alternatively calculated from the arrangement of atoms in discrete lattices through methods such as geometrical phase analysis from transmission electron imaging, bond distortion or virial stress from atomic structures obtained from molecular simulations. In this paper, we assess the accuracy of these methods in quantifying the strain field in 2D crystals through a number of examples, with a focus on their localized features at material imperfections. The sources of errors are discussed, providing a reference for reliable strain mapping.<\/jats:p>","DOI":"10.3390\/ma14164460","type":"journal-article","created":{"date-parts":[[2021,8,9]],"date-time":"2021-08-09T09:03:53Z","timestamp":1628499833000},"page":"4460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Strain Characterization in Two-Dimensional Crystals"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9766-4679","authenticated-orcid":false,"given":"Shizhe","family":"Feng","sequence":"first","affiliation":[{"name":"Applied Mechanics Laboratory, Center for Nano and Micro Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2833-1966","authenticated-orcid":false,"given":"Zhiping","family":"Xu","sequence":"additional","affiliation":[{"name":"Applied Mechanics Laboratory, Center for Nano and Micro Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4495","DOI":"10.1021\/nn401113r","article-title":"Structural reconstruction of the graphene monovacancy","volume":"7","author":"Robertson","year":"2013","journal-title":"ACS Nano"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1126\/science.1217529","article-title":"Dislocation-driven deformations in graphene","volume":"337","author":"Warner","year":"2012","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"091004","DOI":"10.1115\/1.4027819","article-title":"Topological defects in two-dimensional crystals: The stress buildup and accumulation","volume":"81","author":"Song","year":"2014","journal-title":"J. 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