X-ray diffraction analysis. Ewald's Construction

[Vasil7088]

Homework Statement

Hello, maybe it can help me understand the topic of Ewald's construction in the Debye-Scherrer method.

It is necessary to make an Ewald construction for the Debye method (λ=1Å, cubic F-cell, a=5Å), it is also necessary to determine the maximum indices of the planes from which reflections will fall on the film of the camera cassette. There are more questions about the Ewald construction, of course it needs to be done in the inverse lattice, it is not particularly clear what the angle of incidence is, it is not given, but if you look at the formulas, then the maximum hkl will be at an angle of 90°, like the condition from Bragg-Wolfe:
√(h^2+k^2+l^2)≤100

Here, but maybe you can help me understand how to choose these hkls further under this condition. And how do I do the Ewald construction? I can't find any high-quality and complete information. I am particularly interested in how to draw these diffraction rings in the reverse lattice (as in the attached picture). I saw somewhere that they are calculated as 1/d, but then they get less than the grid period from my calculations and don't even cross any nodes, but maybe I misunderstood something.

And then how to understand the maximum indices by intersections with the nodes of the inverse lattice? Probably, then it will turn out something like 10 0 0? But it seems to be the same plane 1 0 0, and these are the minimum indexes. In general, please correct me in my reasoning.

Sorry if there are any mistakes, English is not my native language.
Thank you in advance

Relevant Equations

Bragg-Wolfe

 

[ergospherical]

The Ewald sphere construction works because if there exists a scattered vector $\mathbf{k}'$ such that $\mathbf{k'} - \mathbf{k} = \mathbf{G}$, where $\mathbf{G}$ is a reciprocal lattice vector (between two nodes in reciprocal space), then you satisfy Bragg's equation for diffraction.

i.e. draw a vector $\mathbf{k}$ with its tip on an arbitrary selected point $(000)$ in reciprocal space, and then around the tail of this vector $\mathbf{k}$ draw a circle of radius $|\mathbf{k}| = 1/\lambda$ (for elastic scattering, $|\mathbf{k}| = |\mathbf{k}'|$). Any other reciprocal lattice point on this circle satisfies the above condition.