I am working with h-BN and need to find out the strain due to in-plane lattice constant. The famous Williamson-Hall method may not be applicable here as it analyzes XRD for calculation of strain due to out-of plane which is not applicable for 2D.
The strain due to out of plane (i.e. c-axis) can be calculated by using the equation 6 of the attached file. Looking for same but due to in-plane lattice constant (a axis)
Article Strain Engineering of 2D Materials: Issues and Opportunities...
https://iopscience.iop.org/article/10.1088/2053-1583/aacfc1/pdf
Article Strain Engineering of 2D Materials: Issues and Opportunities...
https://iopscience.iop.org/article/10.1088/2053-1583/aacfc1/pdf
Dai, Zhaohe, Luqi Liu, and Zhong Zhang. "Strain engineering of 2D materials: issues and opportunities at the interface." Advanced Materials 31, no. 45 (2019): 1805417.
Shantanu Saha
There is a simple way to evaluate the strain in an 2D epilayer.
You need to know the lattice constant of the substrate a0 and the variation of in-plane aip and out-of plane aop lattices constants of the 2D epilayer (e.g. from XRD).
Then the built-in strain in the 2D epilayer is proportional to (aip - a0)/ao for in-plane strain and to (aop - a0)/a0 for out-of plane strain.
Note that:
1. if aip decreases with respect to a0, then the built-in in-plane strain in 2D epilayer is a compressive strain (negative sign because aipa0), and in this case the out-of plane strain is a compressive strain because (aop-a0)/a0 will be negative because aop will decrease in order to fulfil unit cell volume conservation condition.
see for instance the following reference:
Strain-stress study of AlxGa1−xN/ AlN heterostructures on c-plane sapphire and related optical properties
Yining Feng 1,2, Vishal Saravade3, Ting-FungChung 1, Yongqi Dong4,5, Hua Zhou5, Bahadir Kucukgok1,2, IanT. Ferguson3,6 & Na Lu1,7
Scientific reports, www.nature.com/scientificreports, july 2019
(2019) 9:10172 | https://doi.org/10.1038/s41598-019-46628-4
Best regards,
Prof. A. Kadri
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