The limiting sphere in crystallography

[Imperatore]

Hello there !

I am writing here, because I could not find any good explanation in the literature and on the web Going straightaway to the point, my question is connected to Ewald's sphere and so called the limiting sphere. I red that limiting sphere is such a construction that appoints the detectable reflects by rotating the single crystal (Ewald's sphere) about rotating axis, it means rotation about tangent to the Ewald's sphere. As a result of this rotation we should obtain toroid, but for more( it is said- "some") rotations about several tangent we get limiting sphere with diameter two times greater than Ewald's one. I don't see it. What does " some" mean and what does it depend on how many rotations we have to do to obtain a limiting sphere ?

 

[DrDu]

You can rotate a crystal around an arbitrary axis. If you consider all possible rotations around all possible orientations of the axis, the Ewald sphere will trace out the limiting sphere.

 

[Imperatore]

I don't understand what do you mean by "all possible rotations around all possible orientations of the axis" ? Could you describe it in more details, please ?

 

[DrDu]

You are assuming that the crystal is rotated around only one axis. But in the construction of the limiting sphere, one considers all possible orientations of the crystal, not only the ones which arise by rotating around one fixed axis.
Consider diffraction from a powder consisting of numerous crystals with random orientation. The possible reflexes observed will be given by the ones inside the limiting sphere.

 

[Imperatore]

So a rotation about 1 axis trace out the limiting sphere ? I am asking because in one book it is written that by one rotation about the tangent to the Ewald Sphere we get toroid. I am confused now.

 

[DrDu]

Rotation around only one axis gives you in deed only a toroid. You have to rotate around multiple axes to get the sphere.

 

[Imperatore]

here is the point,the number of possible reflection is limited to the volume of toroid after 1 rotation ?
and second question, 2 rotations about 2 perpendicular axes is enough to trace out the limiting sphere ?