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I have some experience in dealing with structural, electronic, and magnetic properties of 2D materials, but I want to go further to study the elastic properties. Could you please guide me on this? which properties should be calculated and discussed?

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Elastic constants can be derived from constitutive relationship by calculating stresses from a strained system

$$\sigma_{ij}=C_{ijkl}\epsilon_{kl}$$

Once the crystal is deformed by some finite strain and stresses can be extracted from the output of any DFT packages.

Another method is to use strain energy function, where you distort the crystal and measures change in energy with respect to reference configurations.

$$C_{ij}=\frac{\partial^{2}E}{e_{i}e_{j}}$$

For 2D system, the process of calculating elastic constants is same as bulk 3D crystal. The system is distorted by series of strains and fitted with second order polynomials. In the commercial package VASP, IBRION=6 and NFREE=4 is good place to start or otherwise calculate elastic constants using external packages such as vaspkit.

A few examples from the literature where stability criteria and methods for 2D materials are given which will be a good start:

  1. Choudhary, K.; Cheon, G.; Reed, E.; Tavazza, F. Elastic Properties of Bulk and Low-Dimensional Materials Using van Der Waals Density Functional. Physical Review B, 2018, 98. DOI
  2. Yuan, J.N.; Cheng, Y.; Zhang, X.Q.; Chen, X.R.; Cai, L.C. First-Principles Study of Electronic and Elastic Properties of Hexagonal Layered Crystal MoS2 Under Pressure. Zeitschrift für Naturforschung A, 2015, 70, 529–537. DOI
  3. Maździarz, M. Comment on ‘The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals.’ 2D Materials, 2019, 6, 048001. DOI
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