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Reciprocal Lattice 2D

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This Demonstration indexes the 2D lattice in the left graphic according to the pair of basis vectors and defined by the figure. This gives insight into the indexing of 2D electron diffraction patterns, as well as into the reciprocal-lattice indexing of 3D crystals.

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On the right, note that the reciprocal-lattice basis vectors and have lengths inversely proportional to the corresponding inter-row spacing in direct space. Also, the choice of a nonprimitive (centered) unit cell adds lattice points in direct space on the left but subtracts them in frequency space on the right.

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Contributed by: P. Fraundorf (September 2011)
Open content licensed under CC BY-NC-SA

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For more on this and related topics, see the video tutorial http://www.umsl.edu/~fraundorfp/reciprocal2D/reciprocal2D.html and [1].

Reference

[1] P. Fraundorf, W. Qin, P. Moeck, and E. Mandell, "Making Sense of Nanocrystal Lattice Fringes," Journal of Applied Physics, 98, 2005, 114308. http://www.umsl.edu/~fraundorfp/help/j_appl_phys _ 98_ 2005_ 114308.pdf.

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