Use the Ewald sphere to calculate h,k,l?

[Lars Ph]

TL;DR

Is there a way to use the ewald sphere to calculate h,k,l?

I am unsure wether or not all I can use the Ewald sphere for is to calculate d_hkl for the diffracted wave vector. For cubic lattices for example d= a/sqrt(h^2+k^2+l^2). To determine the lattice constant "a" you would then need to know exactly what your h,k and l are or you use lattice-dependent requirements like "h+k+l are an even or odd number" in conjunction with the determined d_hkl to find your a (I think). My question is, is there a different way to find the lattice constant solely by using the Ewald sphere?

 

[hutchphd]

You mean without knowing d ? No. You need to know either a to find d or vice versa. This is the same as needing to know the grating spacing to determine the wavelength for light You also need to know the defracted order. In 3D, it is a bit more complicated but the physics is the same.

 

[Philip Koeck]

TL;DR Summary: Is there a way to use the ewald sphere to calculate h,k,l?

I am unsure wether or not all I can use the Ewald sphere for is to calculate d_hkl for the diffracted wave vector. For cubic lattices for example d= a/sqrt(h^2+k^2+l^2). To determine the lattice constant "a" you would then need to know exactly what your h,k and l are or you use lattice-dependent requirements like "h+k+l are an even or odd number" in conjunction with the determined d_hkl to find your a (I think). My question is, is there a different way to find the lattice constant solely by using the Ewald sphere?

The Ewald sphere depends only on the wavelength of the incident radiation so it has nothing to do with the lattice. If you look at different crystals with the same radiation the Ewald sphere is always the same. That means that it must be impossible to deduce anything about the crystal from the Ewald sphere alone.

 

[hutchphd]

Yes. The Ewald sphere is simply a statement about energy conservation in the scattering process where the periodicity of the (~infinitely massive) crystal lattice has allowed momentum to not be strictly conserved (it can change by any reciprocal lattice vector) .