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ElATools: A tool for analyzing anisotropic elastic properties of the 2D and 3D materials
TL;DR: ElATools as discussed by the authors is a tool for the analysis of second-order elastic stiffness tensors of two-dimensional and three-dimensional (3D) crystal systems using three averaging schemes of Voigt, Reuss, and Hill.
Abstract: We introduce a computational method and a user-friendly code, named ElATools, developed for the analysis of anisotropic elastic properties. ElATools enables facile analysis of the second-order elastic stiffness tensor of two-dimensional (2D) and three-dimensional (3D) crystal systems. It computes and displays the main mechanical properties including the bulk modulus, Young's modulus, shear modulus, p-wave modulus, universal anisotropy index, Chung-Buessem anisotropy index, log-Euclidean anisotropy parameter, Cauchy pressure, Poisson's ratio, and Pugh's ratio, using three averaging schemes of Voigt, Reuss, and Hill. ElATools has a database with more than 13000 elastic stiffness constants for 3D materials available to the user. The program supports output files of the well-known computational codes IRelat, ElaStic, and AELAS. Three types of plotting and visualization tools are integrated to conveniently interface with GNUPLOT, XMGRACE, and view3dscene, offering immediate post-processing of the results. ElATools provides reliable means to investigate the mechanical stability based on the calculation of six (three) eigenvalues of the elastic tensor in 3D (2D) materials. It can efficiently identify anomalous mechanical properties, such as negative linear compressibility, negative Poisson's ratio, and highly-anisotropic elastic modulus in 2D and 3D materials, which are central properties to design and develop high-performance nanoscale electromechanical devices. Four case studies on selected material systems, ZnAu$_2$(CN)$_4$, CrB$_2$, and $\delta$-phosphorene, and a hypothetical set of systems with cubic symmetry are presented to demonstrate the descriptive and predictive capabilities of ElATools.
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01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,520 citations
TL;DR: In this paper, the authors proposed a method known as optical sectioning SIM (OSSIM) to remove the out-of-focus blur caused by the Moire effect in a wide-field fluorescence microscope.
Abstract: The resolution of an optical microscope is fundamentally limited by diffraction. In a conventional wide-field fluorescence microscope, the resolution limit is at best 200 nm. However, modern superresolution methods can bypass this limit. Pointillistic imaging techniques like PALM (photoactivated localization microscopy) and STORM (stochastic optical reconstruction microscopy) do so by precisely localizing each individual molecule in a sample. In contrast, STED uses the stimulated emission process driven to saturation to dramatically reduce the size of the region in the sample that is capable of spontaneously emitting fluorescence. Structured illumination microscopy (SIM) illuminates the sample with a pattern, typically the image of a grating. This computationally removes the out-of-focus blur, a method known as optical sectioning SIM. Furthermore, frequency mixing of the illumination pattern with the sample caused by the moire effect results in a downmodulation of fine sample detail into the frequency-sup...
387 citations