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How can I accurately extract and reproduce the values of $C_{11}$ for 2D hexagonal structures with two independent in-plane constants $C_{11}$ and $C_{12}$? I've used Vaspkit to extract a value of approximately 39 N/m, but when I attempt to fit the values, I obtain an underestimated result. My approach involves the strain-energy technique, where the elastic energy is given by

$$\tag{1}E_{\textrm{elastic}} = \frac{S_0}{2} \cdot C_{11} \cdot \eta^2.$$

I also calculate $C_{11}$ using the expression:

$$C_{11} = \frac{2}{S0} \cdot \left(\frac{\partial^2 E}{\partial \eta \partial \eta}\right)\tag{2}.$$

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  • $\begingroup$ Did you fit change in energy and eta to second order polynomial? $\endgroup$ Commented May 11 at 16:22
  • $\begingroup$ Yes, I do when I get the value from second order polynomial for e.g b2x^2 + b1x +c . I take only the value of b2, then I suppose that C11=(2/S0)*b2*16.02 (to change from eV/A^2 to N/m $\endgroup$
    – Hamza Bekk
    Commented May 11 at 17:00

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