When we have absolutely single atomic layer graphene, if we pass electron beam (in TEM for SAED pattern) normally to the sheet how diffraction could occur ? For any diffraction condition to be satisfied there should be the rule d sin (theta)=n (lambda), but in the normal direction how could we take "d" an inter planar spacing since, it has only one layer? How does the hexagonal electron diffraction pattern arises for a single sheet of graphene?
Dear Sir,
please note that in case of a 2-dimensional crystal the reciprocal lattice is formed by rods instead of discrete points as in case of a 3-dimensional crystal. The condition that the scattering wave vector q = ks - k0 (all vectors) has to coincidice with the reciprocal lattice therefore holds only for the components parallel to the lattice (i.e. in the graphene plane in your case). For further details, please refer to the formulas given for Low Energy Electron Diffraction (LEED) since this technique is known for probing 2-dim. systems, namely sufaces !!!
Sincerely, FM
Dear Sir,
please note that in case of a 2-dimensional crystal the reciprocal lattice is formed by rods instead of discrete points as in case of a 3-dimensional crystal. The condition that the scattering wave vector q = ks - k0 (all vectors) has to coincidice with the reciprocal lattice therefore holds only for the components parallel to the lattice (i.e. in the graphene plane in your case). For further details, please refer to the formulas given for Low Energy Electron Diffraction (LEED) since this technique is known for probing 2-dim. systems, namely sufaces !!!
Sincerely, FM
Dear FM
Thank you for the information. could you please give some links for the source of information .
Regards
SP
Hi. You should find any old textbook on diffraction. Normally diffraction is explained in a following way: scattering from a single atom, scattering from a raw of atoms, scattering from a plane and then 3d networks goes.
Dear Sir,
the Wikipedia entry for LEED provides a good survey on this topic, including the Ewald construction for the 2-dim. rod lattice.
Regards, FM
Dear Sir,
It is an interesting question. I think the core concept is consider electron beam as a propergating wave instead of traveling particles. Unlike the X-ray diffraction technique which is basically utilising reflected x-ray to probe the latice space of cirtain material, the SAED technique use the transmited electron beam to probe the relative location of atoms. Therefore the diffraction pattern you get is from atoms at lateral direction, so thinner and well ordered the material is, the clearer diffraction pattern you will get.
In the case of ideal perfect single layer graphene , due to it is highly oriented hexagonal structure in the lateral space, you can get a clear 6-fold diffraction pattern, which is actually is its reciprocal lattice (fourier transform from real space). For double layer or few layer graphene, diffraction from (0-110) and (1-210) plane would be leveled. For polycristalline or defective gaphene, a series of diffraction ring wiill occured.
https://www.researchgate.net/publication/305057053_Graphine_Synthesis_via_electrochemical_exfoliation_of_graphite_nanoplatelets_in_aqueous_sulphuric_acid
sorry I'm not sure if I have answered the question, just share my experience on it.
Lin
Conference Paper Graphine Synthesis via electrochemical exfoliation of graphi...
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