Abstract
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.
Highlights
To understand mechanical processes such as structural distortion, phase transformation, fracture in two-dimensional (2D) crystals, and explore their strain-engineering applications, characterization of inhomogeneous strain distribution is crucial
We first validate the methods of strain characterization for samples with uniform strain or a uniform strain gradient, by applying uni-axial stretch to rectangular and trapezoidal graphene monolayers that can be shaped by focused ion beams (FIB) in experiments [41]
By comparing the strain values characterized at different loading amplitudes (Figure 2c), we find that geometrical phase analysis (GPA) and bond methods yield accurate measure
Summary
To understand mechanical processes such as structural distortion, phase transformation, fracture in two-dimensional (2D) crystals, and explore their strain-engineering applications, characterization of inhomogeneous strain distribution is crucial. Lattice distortion around imperfections such as point defects and dislocations in graphene were measured, which can be used to validate the continuum theory of elasticity [1,2,3]. In the continuum field theory, strain at a material point can be defined and calculated from the dimensional change of volume elements. This approach applies to the lattice representation of crystals as the Cauchy–Born approximation is valid [11]. Quantifying inhomogeneous strain at imperfections are challenging due to the loss of lattice symmetry, as well as its localized and irregular nature
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