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nmdl-mizo / interface_master

A python package building CSL or approximate CSL interfaces of any two lattices and computing cell of non-identical displacement (CNID).
MIT License
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𝜆 does not appear in the inequalities shown on page 7 of the arxiv paper for this package. #26

Open hongyi-zhao opened 7 months ago

hongyi-zhao commented 7 months ago

I've noticed that 𝜆 does not appear in the inequalities shown on page 7 of the arxiv paper for this package, as shown below:

image

Is this a typo or is it just the truth? If that's the case, then the corresponding inequalities don't even use the $\lambda$ symbol. As a result, it's very confusing to read.

Regards, Zhao

jinlhr542 commented 7 months ago

Sorry for making confusion here. The lambda does not appear in the inequality because the only limitation for it is just lambda >= 1. The principle is kind of difficult for understanding and I took a long time to understand it when reading the oringinal paper which actually even did not pose the equations above the inequalities. By looking at the equations the inequalities simply make the denominators larger than the nominators. The best way to understand the principle is to draw these vectors on paper which was what I usually did when learning the CSL and DSC principles.

best, Jason

hongyi-zhao commented 7 months ago

I have recently reviewed many heterostructure construction and search algorithms, and I feel that the mathematical theories involved in this package are the most profound and complex.