It does not say "how long" the a* and b* vectors are in reciprocal space. If I use the definition to calculate them, it is much different from the simulation.
You can calculate the magnitude of the vectors if you consider what the 2D extension of the general 3D volume is. Instead of using the volume of the Bravais lattice in 3D, consider the area. Also the site mentions you want the final bi to be perpendicular to the associated ai vector. Looking at the original 3D formula, there is a cross-product term, which can be manipulated in the 2D case to help you find the vector direction.
It does not say "how long" the a* and b* vectors are in reciprocal space. If I use the definition to calculate them, it is much different from the simulation.
ReplyDeleteThe important relations between a1 and a2 with b1 and b2 which are reciprocal lattice vectors are:
ReplyDeleteb1.a2 = 0, b2.a1 = 0 and b1.a1 = b2.a2 = 1
Lan: The magnitude is the length.
ReplyDeleteNegar: Hmm. it seems I missed that.
b1.a1 and b2.a2 should equal 2*pi.
You can calculate the magnitude of the vectors if you consider what the 2D extension of the general 3D volume is. Instead of using the volume of the Bravais lattice in 3D, consider the area. Also the site mentions you want the final bi to be perpendicular to the associated ai vector. Looking at the original 3D formula, there is a cross-product term, which can be manipulated in the 2D case to help you find the vector direction.
ReplyDeleteI read that in the PDF that I mentioned in the blog. Although I think you are right. Because we have exp(ik.R) = 1.
ReplyDelete