Talk:Laue equations

Derivation incomprehensible

Derivation of the relation to bragg law from \vec k_0-\vec k_i=\vec G is incomprehensible.

Relation of Figure to Text

The figure (Laue_diffraction.svg)uses symbols that bear no relation to those in the text. I think the figure could be very useful in understanding the text if this were to be fixed. ...or perhaps a better fix would be just a legend for the figure, inasmuch as the elements of the figure don't correspond directly to those of the text (ie: the figure is not really a direct illustration of the text) --PMH232 (talk) 21:51, 24 November 2012 (UTC)

I agree to both comments. There is a need for at least another comment on the derivation of the bragg's law, to make it understandable. Also the figure doesn't relate at all to the text which is unsatisfying. — Preceding unsigned comment added by 130.238.195.73 (talk) 12:51, 11 November 2013 (UTC)

Generality of Bragg's law

For lattices with interaxial angles other than 90 degrees the lattice parameters do not necessarily correspond to any interplanar spacing d. If one assumes that G is parallel to a real lattice vector x, there is actually loss of generality, contrary to what the article states. (For example, A is parallel to b x c which may or may not be parallel to a).

Observability in reciprocal space

"However, the beams corresponding to high Miller indices are very weak and can't be observed."

While it is true that backscattering, which will result from high Miller indices, is weaker than forward scattering there is also a fundamental limit to how far observations can be made in the reciprocal space. It depends on the wavelength, but possibly also on the geometry of the diffraction equipment. The radius of observation is inversely proportional to the (x-ray) wavelength (but I don't recall the proportionality constant). The radius can thus be extended by using a shorter wavelength, but the scattering is likely to get weaker, the photons may more easily escape detection, and the crystal may be more easily radiation damaged.

Using the equation for Bragg diffraction written as sin(theta)=n*lambda/2d it is clear that if d is small enough, as it will be for high Miller indices, the expression will be larger than 1 meaning that there is no real angle corresponding to theta and and this part of recirocal space thus cannot be observed giving the condition 1>=lambda/2d <=> d >= lambda/2 or in reciprocal space D <= 2/lambda (if reciprocal space defined with simple inverted values). For a compound with a cubic structure d(hkl)=a/sqrt(h^2+k^2+l^2) while for a tetragonal structure 1/d(hkl)=sqrt((h^2+k^2)/a^2+l^2/c^2) and for other crystal systems there are similar but more complex expressions.

Some crystal planes (certain Miller indices) may give weak reflections even for low angles and there are also selection rules canceling certain Miller indices. This typically applies to centred lattices (i.e. when using a larger unit cell than the primitive, i.e. if the net number of lattice points exceeds 1), but may also be be due to glide planes or screw axes. 150.227.15.253 (talk) 16:21, 6 May 2022 (UTC)